1 Introduction

Upstream from Earth’s magnetosphere, many types of transient structures have been frequently observed in or near the foreshock (such as hot flow anomalies (HFAs), foreshock cavities, and foreshock bubbles (FBs)), in the magnetosheath (such as magnetosheath jets), and at the magnetopause (such as flux transfer events and surface waves). They play a significant role in the solar wind-magnetosphere coupling, e.g., by transporting mass, energy, and momentum from the solar wind into the magnetosphere, thereby impacting the whole magnetosphere-ionosphere system.

In the foreshock region, transient structures including HFAs, spontaneous hot flow anomalies (SHFAs), FBs, foreshock cavities, and foreshock cavitons exhibit a common characteristic: low density core regions. In the core regions of HFAs, SHFAs, and FBs, the plasma bulk velocity is significantly deflected. As a result, the dynamic pressure in the core regions of foreshock transients is very low compared to the surrounding solar wind. Since the bow shock location is controlled by the solar wind Mach number and dynamic pressure, when these foreshock transients encounter the bow shock, the local bow shock moves outward resulting in significant perturbations that can propagate into the magnetosheath and disturb the magnetopause (e.g., Sibeck et al. 1999; Archer et al. 2015). Magnetopause perturbations launch field-aligned currents into the magnetosphere that drive traveling convection vortices and plasma flow in the high-latitude ionosphere. Foreshock transients can also transmit compressional waves into the magnetosphere that can excite resonant ultra low frequency (ULF) waves (e.g., Eastwood et al. 2011; Hartinger et al. 2013) and cause particles to scatter into the loss cone and precipitate into the ionosphere, driving transient auroral brightenings (Sibeck et al. 1999; Fillingim et al. 2011).

Jets, localized structures with enhanced dynamic pressure, are often observed in the magnetosheath (e.g., Plaschke et al. 2018a). One explanation is that they are less compressed and thermalized solar wind that penetrates through the rippled bow shock (e.g., Hietala and Plaschke 2013). They are associated with enhanced dynamic pressures that can disturb the magnetopause, resulting in associated geoeffects (e.g., Plaschke et al. 2018a).

At the dayside magnetopause, magnetic reconnection, a fundamental process of energy conversion from electromagnetic fields to charged particles, is the primary process transferring momentum and energy from the solar wind to the magnetosphere. Flux transfer events (FTEs) and their ionospheric signatures play a key role in understanding dayside magnetopause reconnection. On the magnetopause, there are also surface waves (e.g., Hasegawa et al. 2004; Sundberg et al. 2012; Masters et al. 2012). They can be excited by the solar wind pressure variations, transient phenomena near the bow shock, or the Kelvin-Helmholtz instability (KHI) on the magnetopause.

Significant progress has been made on dayside transient phenomena and their impact on the magnetosphere and ionosphere in the past 20 years. This paper provides a comprehensive review of the present understanding of these phenomena. Dayside transient processes occurring at other planets are also discussed. In the following, we start with transient processes in the foreshock, bow shock, and magnetosheath (Sect. 2), then followed by transient dayside magnetopause processes and transport (Sect. 3) and geoeffects of dayside transients (Sect. 4). We discuss some specific outstanding questions at the end of each section. Finally, we summarize the main conclusions of the paper and list some outstanding questions (Sect. 5).

2 Transient Processes in the Foreshock, Bow Shock, and Magnetosheath

2.1 Introduction to Earth’s Ion Foreshock

The terrestrial magnetosphere plays the role of a magnetic obstacle with respect to the continuous and super-fast-magnetosonic flow of the solar wind. A permanent bow shock results, brakes/deviates the flow and allows a transition from the super-fast-magnetosonic to sub-fast-magnetosonic regime. Due to its curved shape, the features of the shock front drastically change according to the local angle (\(\Theta _{Bn}\)) between the shock normal and the average upstream Interplanetary Magnetic Field (IMF), and are classified into two categories: \(90^{\circ } > \Theta _{Bn} > 45^{\circ }\) (so called quasi perpendicular i.e. “Q” shock) and \(45^{\circ } > \Theta _{Bn} > 0^{\circ }\) (so called quasi parallel i.e. “Q\(_{\parallel }\)” shock). For “Q” shock, when \(\Theta _{Bn}\) is large enough (\(> 65^{\circ }\), typically), the region upstream from the bow shock is very quiet (solar wind), and the shock transition itself is well defined and presents a sharp and narrow transition between upstream and downstream plasma states. In contrast, the “Q\(_{\parallel }\)” shock transition is much less clearly defined, and is characterised by an extended and less quiet transition region that extends to distances far upstream from the shock front. It is important to mention that since the Earth’s bow shock is curved, both bow shock types can be found at the same time, adjacent to each other which can have an important implication for ion acceleration mechanism (Lembege et al. 2004; Otsuka et al. 2018; Kis et al. 2018). The foreshock region is often mentioned as a “turbulent area” in the literature. This label is mainly used when comparing it—by contrast—with the (“quiet”) region upstream from Q shocks (Fig. 1). However, thanks to a large number of complementary studies, an improved understanding of the whole foreshock has progressively allowed to identify some distinct wave modes and enhanced power at particular frequencies which emphasizes the point that the foreshock is much more than just a “turbulent” area. In the present context, we will rather use the label ‘nonstationary’ to refer the foreshock regions where important wave activities take place.

Fig. 1
figure 1

Sketch of the curved terrestrial shock and associated foreshocks; \(\Theta _{Bn} = (\mathbf {n}, \mathbf {B}_{0})\) where \(\mathbf {n}\) is the local normal to the front. Green dashed lines define the edges of electron and ion foreshock (EF and IF) respectively. (From Tsurutani and Rodriguez 1981)

Moreover, solar wind particles (electrons and ions) interact quite differently with the shock front and according to which Q or Q\(_{\parallel }\) shock region is concerned. Typically, for each species, a large percentage of particles succeed to be directly transmitted, but a certain percentage are reflected by the front and reinjected upstream into the incoming solar wind. More precisely, for \(\Theta _{Bn} = 90^{\circ }\), the macroscopic electric field (due to the difference in penetration depth of solar wind ions and electrons) in the front has the appropriate sign to leave electrons passing through the shock front (these are directly transmitted). By contrast, a certain percentage of ions are reflected by the front, suffer a large gyromotion under the combined effect of local macroscopic electric and magnetic fields, gain enough energy during this large gyration and succeed to pass through the front and penetrate downstream; these cannot escape far upstream. Then, the downstream region is composed of both directly transmitted ions (which do not suffer any reflection) and these energetic ions (after being once reflected). The relative percentage of reflected ions strongly depends on the Mach regime of the solar wind and has a strong impact on the microstructures of the shock front itself. Typically, the shock is called supercritical for \(M_{\mathrm{{A}}} > 2.5\)–3 (with a strong percentage of reflected ions) and is characterized by a foot (upstream of the ramp) and an overshoot (just behind the ramp), both structures being associated with the singly-reflected ions; the percentage does not exceed 20–25% for very high \(M_{\mathrm{{A}}}\). In contrast, the shock is called subcritical for \(M_{\mathrm{{A}}} < 2\)–3 (for a weak percentage of reflected ions, typically a few percents) and presents a laminar profile (i.e. without the presence of a foot or overshoot). For \(\Theta _{Bn} = 90^{\circ }\), no particles are reinjected back into the solar wind. However, the situation changes drastically as \(\Theta _{Bn}\) deviates from 90°, since the impact of the magnetic field is reduced in terms of controlling the particles’ gyromotion. For each species, an important percentage of particles still succeeds to be directly transmitted but the gyromotion of reflected particles is distorted and some succeed to escape far upstream along the magnetic field lines, depending on the angular deviation of the shock normal as detailed below. In short, the shock front appears as an efficient energy converter (via intricate wave-particles interactions), through which the bulk solar wind energy is transformed into thermal energy, but also as a source of energetic particles backstreaming far upstream. These backstreaming particles are at the origin of the so-called foreshock region, and interact with incoming solar wind to generate various types of microinstabilities which lead to an important upstream wave activity. The features of this wave activity strongly vary according to its origin i.e. in Q or Q\(_{ \parallel }\) shocks region, and to the percentage of backstreaming particles. Basically, one identifies two foreshock regions: (i) the “electron foreshock” mainly defined by backstreaming electron beams where the upstream edge is tangent to the curved shock front at \(\Theta _{Bn} = 90^{\circ }\) (see Fig. 1). A small deviation from \(90^{\circ }\) allows electrons to be easily reflected at the front and escape far upstream, while ions suffer only one or several gyrations forcing these to come back to the front. A much larger deviation from \(90^{\circ }\) is necessary for ions to be reflected and escape upstream. (ii) The “ion foreshock” is located deep inside the electron foreshock (see Fig. 1), where its upstream edge starts typically around \(\Theta _{Bn} = 62\)\(67^{\circ }\) in the examples reviewed by Kucharek et al. (2008) i.e in the Q domain, and is characterised by the presence of backstreaming ion beams (Gosling et al. 1978; Paschmann et al. 1981). In this region, both electron and ion foreshocks coexist. Moreover, experimental observations have evidenced different types of local ion distributions upstream of the front: (a) the so-called “field aligned beam” (FAB) ions (Paschmann et al. 1980, 1981; Thomsen et al. 1983, 1985; Schwartz and Burgess 1984; Oka et al. 2005; Mazelle et al. 2005), (b) the so called “Gyro-Phase Bunched” (GPB) ions (Gurgiolo et al. 1983; Thomsen et al. 1985; Fuselier et al. 1986; Meziane et al. 2001; Mazelle et al. 2003), (c) the “diffuse” ions characterised by a very broad flat energy spectra. The produced beams are considered as the most important source of free energy to generate ULF waves in the ion foreshock (Kucharek and Scholer 1991; Kis et al. 2004; Bonifazi and Moreno 1981a,b), and (d) the “intermediate” ions which are a combination of “FAB” and “diffuse” ions (Oka et al. 2005). FAB ions are characterised by gyrotropic and centered pitch angle distribution, while GPB ions are characterised by non gyrotropic and non-zero centered pitch angle distribution.

Different scenarios have been proposed to account for these various distributions and are summarized in Kucharek et al. (2008) and in Savoini et al. (2013). Kucharek et al. (2004) investigated the origin of FABs and found that they are reflected at the Q side of the bow shock surface. Different mechanisms of FABs formation have been proposed which have been reviewed by Meziane et al. (2005). Paschmann et al. (1981) argued that the initially collimated ion beam can interact with upstream waves and that this interaction leads to the scattering of the beam ions which has been confirmed later by Kis et al. (2007) using data of the Cluster mission. These scattered ions are convected deeper into the foreshock region leading to the appearance of the so-called toroidally gyrating ions, as analyzed by Paschmann et al. (1981) and Thomsen et al. (1985). Gurgiolo et al. (1983) argued that GPB and diffuse ions may be closely related (diffuse ions might directly result from a gyrophase mixing of GPB ions in the upstream region). The diffuse ions present a highly isotropic, doughnut-shaped distribution in velocity space (Paschmann et al. 1981). Trattner et al. (1994) demonstrated, based on a statistical study, that the diffuse ion partial density profile decreases exponentially in the upstream direction along the magnetic field lines. The steepness of the exponential profile depends on the diffuse ion energy. This would suggest that the shock might be the source and the diffuse ions may be indeed shock accelerated particles. The Cluster mission made possible the first direct determination of the diffuse ion spatial profile based on simultaneous multi-spacecraft measurements (Kis et al. 2004). Kronberg et al. (2009) extended this study to higher ion energies. Several numerical simulation/theoretical works have been stimulated in order to account for these different ion populations and for different mechanisms of ion diffusion, which are summarized in Sect. 2.5. Let us specify that “FAB” and “GPB” distributions can be associated with the Q shock, while “diffuse” population more closely associated with the Q\(_{\parallel }\) shock, with an intermediate population lying at the transition between Q and Q\(_{\parallel }\) shock regions.

Finally, additional boundaries have been identified. Further within the ion foreshock, a third frontier named “ULF waves boundary” (ULFWB) has been evidenced experimentally by Greenstadt and Baum (1986), where ULF waves are generated by the interaction between incoming and backstreaming ion beams (see review of foreshock ULF waves by Wilson (2016)). Throughout this frontier, FAB distributions without ULF waves gradually change to gyrating distributions with the presence of ULF waves. This boundary strongly depends on the IMF cone angle defined between the IMF and the GSE \(x\) axis (pointing towards the sun). These observations have been confirmed and analyzed in more detail in later works (Andrés et al. 2015) and supported by theoretical analysis (Skadron et al. 1988). Finally, a fourth boundary named the Foreshock Compressional Boundary (FCB) has been identified consisting of a fast magnetosonic pulse (Sibeck et al. 2008) associated with increased density and magnetic field strength. A deeper investigation of the FCB has been performed by Omidi et al. (2009). All these boundaries are discussed in more detail in Sect. 2.4.4.

2.2 Overview of Transient Phenomena in the Foreshock

This section provides a list and a very short description of foreshock transients based on observations including hot flow anomalies (HFAs), spontaneous hot flow anomalies (SHFAs), foreshock bubbles (FBs), foreshock cavities, foreshock cavitons, foreshock compressional boundaries, density holes, and Short Large-Amplitude Magnetic structures (SLAMs). Table 1 shows a comparison of their characteristics. They are described in detail in Sects. 2.3 and 2.4.

Table 1 Comparison of transient phenomena at the bow shock. Durations and scale sizes of the events depend on how they move/convect past a spacecraft in the spacecraft frame. (After Zhang and Zong 2020)

Hot Flow Anomalies (HFAs)

HFAs have been studied for over 30 years. They are characterized by a low field strength and low density core with heated plasma and substantial flow deflection with sizes of several \(R_{\mathrm{{E}}}\) (e.g., Schwartz et al. 1985; Schwartz 1995; Schwartz et al. 2018; Thomsen et al. 1986; Lucek et al. 2004b; Facskó et al. 2008; Zhang et al. 2010; Wang et al. 2013b). Figure 2 shows an example of an HFA observed by THEMIS. HFAs are typically driven by a solar wind tangential discontinuity (TD) that intersects the bow shock with solar wind convection electric field pointing inward on at least one side of the TD (e.g., Thomas et al. 1991; Schwartz et al. 2000). Such a TD can locally trap foreshock ions leading to the HFA formation while propagating along the bow shock surface. HFAs may accelerate particles efficiently through Fermi acceleration, i.e., bouncing between the converging HFA boundary and the bow shock (Turner et al. 2018). Lee et al. (2020) provided an alternative explanation for these energetic ions observed upstream from the bow shock and in the magnetosheath. They suggested that the energetic ions have escaped from the outer magnetosphere.

Fig. 2
figure 2

A mature HFA observed by THEMIS C upstream from the bow shock. From top to bottom: (a) components of the magnetic field in GSM coordinate system, (b) magnetic field magnitude, (c) plasma ion density, (d) components of plasma flow, (e) plasma ion spectrum, (f) plasma electron spectrum (from Zhang et al. 2010)

Spontaneous Hot Flow Anomalies (SHFAs)

SHFAs have the same characteristics as HFAs except that they are not associated with any solar wind discontinuities (Zhang et al. 2013). They form intrinsically in the quasi-parallel regime, likely due to the interaction between foreshock cavitons and the bow shock (Omidi et al. 2013b). Figure 3 shows an example of an SHFA observed by THEMIS.

Fig. 3
figure 3

An overview plot of THEMIS A observations of a spontaneous HFA upstream from the bow shock. From top to bottom: (a) components of the magnetic field in the GSM coordinate system, (b) magnetic field magnitude, (c) plasma ion density, (d) components of plasma flow in GSM coordinate system, (e) plasma ion spectrum, (f) plasma electron spectrum with 3 s time resolution (from Zhang et al. 2013)

Foreshock Bubbles (FBs)

When backstreaming foreshock ions interact with a solar wind rotational discontinuity (RD) that does not necessarily intersect the bow shock, FBs form upstream of the RD and convecting anti-sunward with it (Omidi et al. 2010, 2020b; Turner et al. 2013). Later observations (Liu et al. 2015, 2016b) and simulations (Wang et al. 2021) found that TDs can also drive FBs. FBs are also characterized by a heated, tenuous core with significant flow deflection (Fig. 4). Different from HFAs and SHFAs, the expansion of FBs is super-fast-magnetosonic and dominantly in the sunward direction. Because of the sunward super-fast-magnetosonic expansion, a shock forms upstream of the core, and the FB size in the expansion direction can reach 5-10 \(R_{\mathrm{{E}}}\), larger than typical HFAs and SHFAs. In addition to their significant dynamic pressure perturbations, FBs are also efficient particle accelerators due to the presence of the shock (e.g., shock drift acceleration (Liu et al. 2016a) and Fermi acceleration (Liu et al. 2017d, 2018; Omidi et al. 2021) as the shock converges towards the bow shock).

Fig. 4
figure 4

A foreshock bubble observed by THEMIS C upstream from the bow shock. From top to bottom: components of the magnetic field in GSM coordinate system, magnetic field magnitude, plasma ion and electron density, ion temperature, components and magnitude of plasma flow in the GSM coordinate system, plasma ion spectrum, plasma electron spectrum with 3 s time resolution (from Turner et al. 2013)

Foreshock Cavities

Foreshock cavities are characterized by low density, low field strength core regions with high density, high field strength compressional boundaries on two sides (e.g., Sibeck et al. 2002, 2004; Schwartz et al. 2006; Billingham et al. 2008). But different from HFAs, the flow deflection inside foreshock cavities is rather weak and plasma heating is not significant (Fig. 5). When slabs of magnetic field lines connected to the bow shock are bounded by broader regions of magnetic field lines that remain unconnected to the bow shock, only the slabs are filled with energized particles reflected from the bow shock. The presence of foreshock particles enhanced the thermal pressure, causing an expansion on two sides. Such an expansion decreases the plasma density and magnetic field strength inside the slabs and increases the density and field strength at two boundaries, i.e., a foreshock cavity forms (Schwartz et al. 2006).

Fig. 5
figure 5

A foreshock cavity observed upstream from the bow shock. From top to bottom: magnitude of the magnetic field and its components in GSE coordinates, density of the thermal ion population, flux of energetic ions (≥27 keV), bulk flow speed, ion temperature (from Billingham et al. 2008)

Foreshock Cavitons

Foreshock cavitons are also characterized by a core region with low density and field strength bounded by two boundaries with high density and field strength, without clear heating and flow deflection (Fig. 6). Their sizes are about one \(R_{\mathrm{{E}}}\). They form due to the nonlinear evolution of two types of waves: the parallel propagating sinusoidal waves and the highly oblique, linearly polarized, fast magnetosonic waves (Lin 2003; Lin and Wang 2005; Omidi and Sibeck 2007; Blanco-Cano et al. 2009, 2011). Thus, foreshock cavitons are embedded in foreshock ULF waves, whereas foreshock cavities are isolated due to their different formation mechanisms.

Fig. 6
figure 6

Cluster C1 observations of a foreshock caviton upstream from the bow shock. From top to bottom: components and magnitude of the magnetic field, plasma density, bulk flow velocity (from Blanco-Cano et al. 2009)

Foreshock Compressional Boundaries

Foreshock compressional boundaries (FCBs) (Sibeck et al. 2008; Omidi et al. 2009) have enhanced density and field strength (Fig. 7). They occur at the boundary between the foreshock and the pristine solar wind. Because of the high thermal pressure due to the presence of foreshock ions, the foreshock region expands into the ambient pristine solar wind, leading to the formation of an FCB. FCBs are sometimes associated with local density and field strength depletion on their foreshock side. FCBs can form under either steady or nonsteady IMF conditions.

Fig. 7
figure 7

FCB (grey shaded region) observed by Cluster 1 on 12 February 2002. From top to bottom: plasma density, magnitude and components of the magnetic field, magnitude and components of the bulk flow, ion temperature parallel to the magnetic field, thermal plus magnetic pressure, cone angle, Hot Ion Analyzer (HIA)-HS omnidirectional ion energy spectrum, HIA-LS omnidirectional ion energy spectrum, flux of energetic protons (from Rojas-Castillo et al. 2013)

Short Large-Amplitude Magnetic Structures (SLAMS) and Shocklets

SLAMS are magnetic pulsations with amplitudes at least two times the ambient magnetic field strength (e.g., Schwartz and Burgess 1991; Wilson 2016). Two dimensional hybrid simulations showed that SLAMS have typical spatial scales up to a thousand kms and more in the direction parallel to the shock normal and around 3000 km in the direction perpendicular (Dubouloz and Scholer 1995) which are consistent with observations showing scales larger than 1000 km and 3000 km respectively (Greenstadt et al. 1982; Lucek et al. 2004a, 2008) which covers many ion gyroradii (where the thermal ion gyroradius is typically 160 km in the solar wind) and grow rapidly with time scales of ∼seconds (e.g., Lucek et al. 2008). Observational examples of SLAMS are shown in Fig. 8. Shocklets are also magnetic structures (nonlinearly steepened magnetosonic waves), but differ from SLAMS in terms of amplitude, spatial scale, growth rate, and propagation angle (see Table 3). The relationship between SLAMS and shocklets and their relative origin are detailed in Sect. 2.4.5.

Fig. 8
figure 8

Short Large-Amplitude, Magnetic Structures (SLAMs) observed upstream from the Earth’s bow shock. From top to bottom: the magnitude, azimuth angle, and latitude of the magnetic field (from Schwartz et al. 1992)

Density holes are characterized by similarly shaped magnetic holes with enhanced density and field strength at one or both edges (Fig. 9). The definition of density holes overlaps with HFAs, SHFAs, FBs, foreshock cavities, and foreshock cavitons. A recent statistical study (Lu et al. 2022) showed that ∼66% of 411 density holes cannot be categorized by any of these foreshock transient types. Therefore, it is necessary to make density holes a separate category. A better definition of density holes is needed to definitely distinguish them from other foreshock transient types, which requires further studies. The formation could be due to the interaction between backstreaming particles and the original solar wind (Parks et al. 2006).

Fig. 9
figure 9

A density hole observed by Cluster upstream from the bow shock. From top to bottom: ion energy spectrum (in eV), ion density (in cm−3), components of the plasma flow velocity (in km/s) in GSE coordinates, ion temperature (in MK), the magnitude and components of the magnetic field in GSE coordinates (from Parks et al. 2006)

2.3 Hot Flow Anomalies (HFAs) and Spontaneous Hot Flow Anomalies (SHFAs)

2.3.1 HFAs and SHFAs: Universal Phenomena

Numerical simulations (Thomas et al. 1991; Lin 1997; Omidi and Sibeck 2007) and observations (Thomsen et al. 1993) indicate that HFAs form when tangential discontinuities with electric fields pointing towards the discontinuities on at least one side glide slowly along standing shock waves, giving the events sufficient time to form (e.g., Schwartz et al. 2000). Consequently, there is reason to expect them to occur at all of the standing shock waves that occur throughout the heliosphere (Lucek et al. 2004b), namely at each of the planets, in particular the giant planets in the outer heliosphere (Facskó et al. 2008), and at the termination shock.

To the degree that instrument capabilities suffice, there is in fact considerable evidence for this. HFAs are of course well observed and common at Earth in the high cadence plasma and magnetic field observations returned by a host of missions. Here they occur at a rate of several per day (Schwartz et al. 2000), but sometimes more frequently, and have dimensions on the order of 1-2 \(R_{\mathrm{{E}}}\) (Facskó et al. 2009). MESSENGER magnetic field and plasma observations provide some evidence for HFA-like magnetic field perturbations associated with suprathermal ions at Mercury (Uritsky et al. 2014). Similarly, Slavin et al. (2009) have presented MESSENGER magnetic field observations of features which resemble HFAs in the foreshock of Venus. Collinson et al. (2012a, 2014, 2017) have reported the results of more extensive surveys of Venus Express observations that provide evidence for the presence of the magnetic field perturbations and heated, deflected plasma expected for HFAs and spontaneous HFAs in the Venusian foreshock. HFA sizes at Venus are large compared to those of the planetary obstacle and events may have an important effect on the solar wind interaction with Venus (Fig. 11). Motional electric fields point inward on at least one side of all events reported at Venus. Omidi and Sibeck (2007) reported the successful simulation of SHFAs in a hybrid code simulation of the solar wind’s interaction with Venus.

Øieroset et al. (2001) reported Mars Global Surveyor magnetic field and electron observations of two hot, diamagnetic cavities that exhibited magnetic field strength and electron density depressions associated with electron heating, in a manner similar to HFAs in the foreshock upstream from Mars. Instrumental limitations prevented identification of flow deflections, if any. The comprehensive instrumentation on MAVEN subsequently permitted Omidi et al. (2017a) to identify all of the features that characterize an SHFA in the foreshock of Mars.

Valek et al. (2017) reported Juno observations of a very large HFA at the intersection of an interplanetary discontinuity with the Jovian bow shock. This event exhibit the density, magnetic field, and flow deflections expected for an HFA. Its dimensions were estimated to be on the order of \(2 \times 10^{6}\mbox{ km}\). Masters et al. (2008) reported Cassini electron plasma and magnetic field observations of two HFAs at Saturn. See Fig. 10 for an example. The events occurred at the intersection of IMF discontinuities with the planetary bow shock. By contrast to HFAs observed elsewhere, there were electron density enhancements within the core region of the events. Event dimensions were again large, 2 and 6 Saturnian radii. As shown in Fig. 12, the event dimension at different planets increases with increasing distance from the Sun.

Fig. 10
figure 10

An HFA analogy in the Saturn system. (a-c) Magnitude and direction of the magnetic field in spherical polar coordinates. (d) Electron and ion number densities. (e) Election and ion temperatures. (f) Components of the flow velocity. (g) Time-energy spectrogram of electron count (from Masters et al. 2009b, Fig. 4)

Fig. 11
figure 11

Comparison of HFA sizes relative to their parent magnetosphere in units of planetary radii. Each HFA is artificially moved and rotated to lie along the planet-Sun line. (a) Venus (this study); (b) Earth according to Thomsen et al. (1986) (c) Saturn according to Masters et al. (2009b). (d) Scale showing actual diameters (in kilometers) of Venus, Earth, and Saturn, and HFAs at each (from Collinson et al. 2014, Fig. 5)

Fig. 12
figure 12

Comparison of typical sizes of HFAs for various planets. Diamonds and bars indicate the typical and largest HFA sizes, respectively. The HFA sizes and planetary bow shock standoff distances are from Uritsky et al. (2014) except for Jupiter. (From Valek et al. 2017, Fig. 4)

Finally, Giacalone and Burgess (2010) presented hybrid code simulations for the interaction of the Heliospheric Current Sheet with the termination shock. They concluded that as the inclination of the current sheet increased relative to the shock normal, the chance of generating a HFA diminished. Since the heliospheric current sheet is highly inclined to the radial direction, they concluded that HFA formation was highly unlikely.

2.3.2 Size, Evolution and Propagation Characteristics of HFAs

As HFAs are driven by TDs that intersects the bow shock, HFAs convect with the driver TD along the bow shock surface. The size of an HFA can be estimated based on such motion across spacecraft. Schwartz et al. (1985) showed that the thickness of an HFA along the TD normal direction was 2-3 \(R_{\mathrm{{E}}}\). Later observations showed similar spatial scales of several \(R_{\mathrm{{E}}}\) (e.g., Thomsen et al. 1986; Sibeck et al. 1999). The HFA size in global hybrid simulations performed by Lin (2002) is 1-2 \(R_{\mathrm{{E}}}\). Facskó et al. (2009, 2010) determined sizes of HFAs using two different methods based on Cluster observations. In the first method, they assumed that the expansion speed of each boundary is the Alfvén speed and used the expansion speed and the event duration to calculate the size. In the second method, the HFA size along the bow shock surface is calculated using the HFA time interval multiplied by the transit speed of the driver TD (Eq. (1)). The determined sizes were 2-3 \(R_{\mathrm{{E}}}\) using the first method, and the second method gave up to 1 \(R_{\mathrm{{E}}}\) larger sizes. The differences might be due to the high sensitivity of the methods to the measurement accuracy (Fig. 13). Using MMS observations, Schwartz et al. (2018) calculated the size of an HFA along the bow shock surface as 2.3 \(R_{\mathrm{{E}}}\). MMS observed HFAs, SHFAs, or FBs that just started to form with spatial scales of around one foreshock ion gyroradius (1000 to 2000 km) along the solar wind direction (Liu et al. 2020a). ARTEMIS in the midtail foreshock at \(X=-40\) to −50 \(R_{\mathrm{{E}}}\) observed an HFA with a spatial scale of 1.7 \(R_{\mathrm{{E}}}\) along the bow shock surface (Liu et al. 2020e).

Fig. 13
figure 13

The size distributions of HFAs by assuming that the expansion speed is the Alfvén speed (black line, scale at the bottom) and using the TD transit speed along the bow shock surface from Cluster-1 and -3 CIS HIA measurements (red and blue lines, scale at the top). The average sizes are (1.9±1.0) \(R_{\mathrm{{E}}}\), (7.0±4.3) \(R_{\mathrm{{E}}}\), and (6.6±4.2) \(R_{\mathrm{{E}}}\), respectively. (From Facskó et al. 2009, Fig. 5)

To obtain accurate expansion speeds of HFAs, Xiao et al. (2015) used the timing method based on four Cluster observations to obtain the normal directions of two HFA boundaries and speeds along the normal directions. They found that 4 HFAs (out of 21) were contracting at a few tens km/s and 5 HFAs were expanding at a few tens to above one hundred km/s. The remaining 12 HFAs were stable without clear contraction or expansion. They explained that the difference in the sum of magnetic and thermal pressure across HFA boundaries determines whether HFAs contract, expand, or remain stable. Later, Liu et al. (2016b) also used four spacecraft timing method on five THEMIS spacecraft observations to calculate the boundary normal and speed along the normal for 6 HFAs. The HFAs were expanding at several tens to around one hundred km/s, smaller or comparable to the local fast wave speed, consistent with the fact that the HFAs did not have clear shocks as their boundaries. Sizes of the HFAs were 0.5-3 \(R_{\mathrm{{E}}}\) based on the expansion speed. For comparison, sizes of 6 FBs in their studies were 2-15 \(R_{\mathrm{{E}}}\) with super-fast-magnetosonic expansion consistent with simulation results that FBs are typically larger than HFAs and have shocks as their upstream boundaries (e.g., Omidi and Sibeck 2007; Omidi et al. 2010). In the midtail foreshock, the HFA reported by Liu et al. (2020e) was in a stable state while propagating tailward.

In addition to the spatial scale along the dimension that the spacecraft crossed or along the expansion direction, Zhang et al. (2010) estimated how far HFAs extend upstream from the bow shock. Based on the separation between two THEMIS spacecraft, the HFAs can extend to at least 9 \(R_{\mathrm{{E}}}\) away from the bow shock. Similarly, in the midtail foreshock observed by two ARTEMIS spacecraft (Liu et al. 2020e), an HFA extended at least 4.7 \(R_{\mathrm{{E}}}\) along the TD surface away from the bow shock. A statistical study by Chu et al. (2017) showed that HFAs were observed within 7 \(R_{\mathrm{{E}}}\) upstream from the bow shock. Based on the normal direction of two boundaries, Schwartz et al. (2018) calculated that the two boundaries of an HFA intersected at 1 \(R_{\mathrm{{E}}}\) upstream from the bow shock. By calculating the trajectory of ions leaked from HFAs based on dispersed ion distributions, Liu et al. (2017a) diagnosed the curved shape of HFA boundaries in three dimensions. They estimated that the HFA can extend to around 5 \(R_{\mathrm{{E}}}\) upstream from the bow shock.

Zhang et al. (2010) compared HFAs in different evolution stages. Proto-HFAs are structures that later develop into HFAs. They exhibit decreases in magnetic field strength and plasma density, moderate plasma heating, and fluctuating, not very deflected ion bulk velocity. Young and mature HFAs are structures that have already become HFAs. The difference is that young HFAs have distinct two ion populations (solar wind and foreshock ions) whereas mature HFAs have one very diffuse ion population inside them (Lucek et al. 2004b). It is likely that the two ion populations release free energy between them and merge into one population, which could explain the increase in the amplitude of magnetic pulsations inside HFAs during the evolution from proto-HFAs (\(\delta B/B <50\%\)) to young HFAs (\(\delta B/B \sim 1\)) and to mature HFAs (\(\delta B/B \sim 4\)). A statistical study by Wang et al. (2013b) demonstrated that in addition to the difference in ion distributions, electron spectra inside young HFAs can be fitted by a single drift\(-\kappa \) distribution, whereas in mature HFAs the spectra can be fitted by a combination of a heated population and a drift-Maxwellian distribution with peak energy below 10 eV. Using high resolution observations from the MMS spacecraft in a string-of-pearls formation, Liu et al. (2020a) illustrated the fast evolution of an HFA, SHFA, or FB that just started to form. During the event, two distinctive ion populations were identified, and the foreshock ions were demagnetized, resulting in a Hall current that determined the magnetic field structure. During the evolution, the mass flux of cold plasmas and magnetic flux were transported outward to the boundary. Solar wind ions became more deflected, and more foreshock ions were trapped within the structure.

HFAs have been observed at other planets too. Their size is controlled by the standoff distance of the bow shock and/or local solar wind conditions. Their size relative to the planet is similar to their terrestrial counterpart. At Mercury, the size is thousands of km comparable to 1 Mercury radius (Uritsky et al. 2014). At Venus, the size is 0.4 to 1.7 Venus radii (Collinson et al. 2014). The HFA observed at Mars is 0.66 Mars radii (Collinson et al. 2015). At Jupiter, the size is \(2 \times 10^{6}\mbox{ km}\) (Valek et al. 2017). At Saturn, the spatial scale is ∼4.6 Saturn radii (Masters et al. 2009b).

2.3.3 Flow Deflection Inside HFAs

Wang et al. (2013a) examined 87 HFAs observed by Cluster C1 in which the magnitude of the GSE \(V_{y}\) and \(V_{z}\) deflections exceeded 200 km/s from 2003 to 2009. They found that the large flow deflections in HFAs strongly depend on the location (Fig. 14), i.e., the velocity direction change is away from the local bow shock normal direction. They interpreted that the deflection is due to the presence of reflected ions (foreshock ions). By assuming that the density ratio of reflected ions to solar wind ions was \(20\%\), they estimated the velocity of reflected ions. They showed that the reflected ion velocity direction is close to the predicted near-specularly reflected direction from the bow shock (Fig. 15). They also showed that HFAs closer to the bow shock exhibit more significant \(V_{x}\) decreases.

Fig. 14
figure 14

Flow deflections in HFAs. The green (red) arrows represent the background solar wind velocity (flow velocity at the center of HFAs). The length of the arrow represents the ratio between the velocity component in this direction and the speed. The absolute value of R is the distance to the Sun-Earth line, and the sign of R is in the same sense as the sign of GSE Y. The curved dashed line represents the normalized bow shock location. (From Wang et al. 2013a, Fig. 4)

Fig. 15
figure 15

HFA event number distribution for the angle differences (\(\theta _{\mathit{diff}}\)) between the foreshock ion velocity direction (inferred from CIS data and an assumed foreshock ion density ratio) and the predicted direction of reflected ions based on specular reflection model (from Wang et al. 2013a, Fig. 9)

Case studies from THEMIS and MMS observations showed that the ion bulk velocity deflection is due to the presence of foreshock ions and the expansion or outward motion of solar wind ions (Liu et al. 2018, 2020a). Additionally, Liu et al. (2020a) found that the ion bulk velocity becomes more and more deflected during the evolution of a foreshock transient that just formed, and two reasons have been identified. One is that the solar wind ions are decelerated in the spacecraft frame or accelerated in the background solar wind rest frame likely driven by the increasing induced electric field. The other is that the density ratio of foreshock ions to solar wind ions increases, because more and more foreshock ions are trapped within the foreshock transient whereas solar wind ions are transported outward to the boundary (i.e., expansion).

2.3.4 Plasma, Magnetic Field, Waves and Turbulence Inside HFAs and SHFAs

Inside HFAs, the magnetic field is usually very turbulent with various wave activities. Inside a young HFA, Tjulin et al. (2008) identified two wave modes using \(k\)-filtering technique with multi-point Cluster observations. The two wave modes were at around 1 Hz with Poynting vector coinciding with the moving direction of solar wind ions and foreshock ions, respectively. They were interpreted as the combination of inherent fluctuations in the solar wind and foreshock. Because of the free energy between the two ion populations, the ion beam instability could enhance the wave amplitude inside the HFA until the two ion populations become one diffuse population, i.e., a young HFA evolves into a mature one.

From THEMIS observations, Zhang et al. (2010) also identified electromagnetic waves near lower hybrid frequency (e.g., 0.1-1 Hz) inside both young and mature HFAs using wavelet analysis. Lower hybrid waves were considered as one of the possible interpretations, which could contribute to electron heating inside HFAs. In addition, Zhang et al. (2010) examined lower frequency waves (0.03 Hz in the spacecraft frame). They showed that inside a proto-HFA the waves were quasi-parallel propagating (wave normal angle \(18.9^{\circ }\)) in the sunward direction, left hand polarized in the spacecraft frame, but right hand polarized in the solar wind rest frame. The fluctuations of magnetic field strength and density were correlated with relatively small amplitude (\(\delta B/B <50\%\)). Similar waves were also observed inside young HFAs but with larger amplitude (\(\delta B/B \sim 1\)). Inside mature HFAs, magnetic pulsations with very large amplitude (\(\delta B/B \sim 4\)) were observed. These waves inside proto-, young, and mature HFAs correspond to the early, middle, and late (nonlinear) stages of the right-hand resonant instabilities, which could play a role in thermalizing ions. These “30s waves” are common in Earth’s foreshock (Wilson 2016).

Right outside HFAs, gyrophase-bunched ions with energy dispersion and gyrophase evolution are sometimes observed (e.g., Tjulin et al. 2009; Liu et al. 2017a). Cluster observations (Tjulin et al. 2009) showed that outside the leading boundary of an HFA such ions were accompanied by waves at frequencies varying from 0.5 to 1 Hz propagating obliquely without clear polarization. Outside the trailing boundary without those ions, on the other hand, the waves were at nearly constant 1.5 Hz quasi-parallel propagating with left hand polarization in the spacecraft frame. Since the background conditions on two sides of the HFA are similar, different properties of the two wave modes are possibly caused by the gyrophase-bunched ions outside the leading boundary through the mechanism described in Wong and Goldstein (1987, 1988). The waves outside the trailing boundary, on the other hand, are consistent with “1 Hz waves” commonly observed in Earth’s foreshock (Wilson 2016).

From THEMIS observations, Shi et al. (2020a) identified broadband quasi-parallel propagating whistler waves at around half electron gyrofrequency (several tens to 100 Hz) inside the compressional boundary of HFAs and FBs. The power spectral density contours of electron distributions followed the diffusion surface very well, suggesting that the electrons were efficiently scattered by the whistler waves. The calculated pitch angle diffusion coefficient was large enough compared to the time scale that electrons spent in the compressional boundary (several seconds). The excitation mechanism is that during the formation and evolution of an HFA or FB, the magnetic flux is transported outward resulting in betatron acceleration at the compressional boundary (Liu et al. 2019a, 2020a), which can increase the electron perpendicular anisotropy, leading to the generation of whistler waves.

Kovács et al. (2014) analyzed turbulence dynamics inside an HFA observed by Cluster. Figure 16 shows the power spectral density of the magnetic field inside and before the HFA. Both show a power-law character with a spectral slope close to that of Kolmogorov spectra, except the spectrum inside the HFA shows a spectral break at around 3 Hz and then steepens dramatically. Inside the HFA, the power-law approach fails to accurately fit the spectrum between about 0.4 and 1 Hz, likely caused by considerable wave activities discussed above and the plasma heating. Considering that the lower hybrid frequency was around 3.2 Hz, lower hybrid waves could play a role in electron heating (Zhang et al. 2010) before the break, whereas beyond the break another cascade process emerges involving energy remnant after the considerable plasma heating.

Fig. 16
figure 16

Power spectral density (PSD) of the magnetic field time-series recorded by the Cluster SC2 spacecraft inside and before an HFA. The bottom panels show the differences between the PSD and the fitted power-law curves. (From Kovács et al. 2014, Fig. 6)

Kovács et al. (2014) also examined the temporal increments of single-spacecraft and spatial differences of simultaneous multi-spacecraft magnetic field records of the HFA. They employed sliding-window analysis in which moving overlapped sequences of the non-stationary signal were analyzed separately. Due to the presence of the low-frequency and large-amplitude waves, they applied high-pass filtering to minimize the contribution from the waves. They concluded that the filtering considerably enhanced the non-Gaussian character of the HFA magnetic time-series and confirmed the prevailing nature of intermittent multi-scale processes in the HFA. The strongest intermittency appeared at the compressional boundary of the HFA. The high-frequency components of the HFA magnetic fluctuations exhibited spatial coherency among the Cluster spacecraft.

2.3.5 Reconnection Inside HFAs

Direct and indirect evidence has shown that magnetic reconnection can occur inside HFAs. A magnetic flux rope was identified inside a magnetosheath HFA observed by Cluster (Hasegawa et al. 2012). Properties of the identified flux rope, including its low velocity with a sunward component, the absence of magnetospheric electrons, and magnetic field variations, indicate that it was created by magnetic reconnection inside the magnetosheath HFA. A flux rope was also identified inside the compressional boundary of an HFA observed by MMS in the foreshock (Bai et al. 2020). Observations by Cluster, THEMIS, and MMS have revealed various types of reconnection induced in the magnetosheath and at the bow shock: reconnection due to compression of a non-reconnecting solar wind current sheet at the bow shock (Phan et al. 2007), reconnection spontaneously generated in the transition region of the bow shock (Wang et al. 2019a; Gingell et al. 2019), reconnection close to the magnetopause due to compression of a magnetosheath current sheet against the dayside magnetopause (Phan et al. 2011), and reconnection in current sheets of the turbulent magnetosheath downstream of the quasi-parallel bow shock (Retinò et al. 2007; Phan et al. 2018). Upstream from the bow shock, reconnection was also identified inside HFAs and FBs from recent MMS observations (Liu et al. 2020d). The reconnection occurred in micro-scale current sheets of thickness comparable to or less than one ion inertial length with a super-ion-Alfvénic electron outflow, positive \(\mathbf {j} \cdot \mathbf {E'}\), and the electron temperature increases without clear ion coupling. The possible generation mechanism could be compressed solar wind currents or turbulence in HFAs and FBs, which requires further investigation. Additionally, reconnecting current sheets inside SLAMS have been identified from recent MMS observations (Wang et al. 2020a).

2.3.6 Ion and Electron Heating and Acceleration Inside HFAs

By definition, plasma is heated/thermalized inside HFAs (and FBs). As for ions, a statistical study based on Cluster measurements showed a strong correlation between the increase in thermal energy and decrease in kinetic energy, indicating that the thermal energy of HFAs is mainly converted from the kinetic energy of the coupled solar wind and foreshock ions (Wang et al. 2013b). This is consistent with what Thomsen et al. (1988) suggested. A recent PIC simulations by An et al. (2020) examined how foreshock ions couple with solar wind ions, electrons, and the magnetic field through the electric field during the formation process of HFAs/FBs. As foreshock ions gyrate out from a discontinuity, a static electric field arises due to the gyroradius difference between foreshock ions and electrons. Such a static electric field decreases ion energy and increases electron energy. Meanwhile, the evolution of the magnetic structure induces an electric field. The Hall current due to demagnetized foreshock ion motion and magnetized electron motion is against the induced electric field, transferring energy to the magnetic field. The induced electric field also drives the frozen-in plasma to move outward from the HFA/FB core, i.e. expansion, which is one reason for observed plasma deflection. Overall, in the solar wind rest frame, the foreshock ions provide energy to heat and accelerate the solar wind ions and electrons and build up magnetic field structures. Such a process is supported by MMS observations recently reported by Liu et al. (2020a). The statistical study by Liu et al. (2017b) showed that ion energies are generally lower inside than outside HFAs and FBs, also suggesting that the foreshock ions are the energy source. In addition, because of the free energy available between the counterstreaming solar wind ions and foreshock ion populations, Zhang et al. (2010) suggested that right-hand resonant instabilities could occur and thermalize ions, causing two distinct ion populations (young HFAs) to merge into one very diffuse population (mature HFAs). MMS observations by Schwartz et al. (2018) found that the solar wind helium ions also contribute to the ion heating. As for electrons, PIC simulations by An et al. (2020) showed that the electron heating is intrinsic during the formation process caused by the electrostatic field. Based on observed wave activities, Zhang et al. (2010) suggested that lower hybrid instabilities could contribute to the electron heating. Depending on the temperature anisotropy, the firehose instability (Eastwood et al. 2008) or whistler waves (Shi et al. 2020a) can isotropize electrons.

In addition to particle heating/thermalization, particle acceleration is also common for HFAs/FBs. Particle acceleration by foreshock transients was first found at SLAMS (Kis et al. 2013; Wilson et al. 2013). Later, Wilson et al. (2016) identified relativistic electrons inside HFAs/FBs, indicating their significant acceleration ability. A statistical study by Liu et al. (2017b) showed that suprathermal electron energies are greater inside than outside almost all HFAs and FBs and these energies are correlated with solar wind speeds. Some of them can reach 100s of keV. Foreshock ion energies are also greater inside than outside some events, suggesting additional ion acceleration, and the energy is also proportional to the solar wind speed. Multiple acceleration mechanisms have been identified. One mechanism is Fermi acceleration. As the upstream compressional boundary of an HFA/FB convects earthward towards the bow shock, i.e., they are converging, particles can bounce between the bow shock and the inner edge of the compressional boundary to gain energy. Note that if the bouncing is between the boundaries of an HFA/FB, as the boundaries move away from each other, particles lose energy to support the expansion. Using THEMIS observations in comparison with test particle simulations, Liu et al. (2017d) showed the evidence of electron Fermi acceleration. Because of wave-induced pitch-angle scattering, the efficiency of acceleration decreases by 2/3 as the increasing parallel energy is scattered to the perpendicular direction. Using THEMIS observations and particle tracing in a 3D global hybrid simulation, Liu et al. (2018) showed that ions can at least complete one bounce between the bow shock and the upstream boundary. By comparing MMS observations with theoretical prediction, Turner et al. (2018) presented the ion Fermi acceleration process which accelerates protons and heavy ions to energies of around 200 keV and almost 1 MeV, respectively. During the acceleration process, due to their very large gyroradius, some of the accelerated ions leaked out both into the ambient solar wind and magnetosheath. Lee et al. (2020) provided an alternative explanation for these energetic ions observed upstream from the bow shock and in the magnetosheath. They suggested that the energetic ions have escaped from the outer magnetosphere. Liu et al. (2017a) examined the energetic ion leakage from HFAs using THEMIS observations and found that the observations agree well with single particle motion model. Using hyrbid simulations and test particle simulations, Omidi et al. (2021) examined ion acceleration inside FBs and identified second-order Fermi acceleration.

Liu et al. (2019a) employed hybrid simulations and THEMIS observations to show that magnetic flux is transported outward during the formation and expansion process, resulting in a low-field strength core and compressional boundaries. During the magnetic flux transport, electrons can be locally accelerated by betatron acceleration at the compressional boundary. After the acceleration, some of the electrons can move along the field lines into the core region without losing energy but with evolving pitch angles. As the field lines are continuously transported from the core to the boundary, these electrons can experience another instance of betatron acceleration. Such a process can further energize foreshock electrons from 10s of keV to 100s of keV. If considering the wave scattering effect, the acceleration efficiency decreases by 1/3, as the increasing perpendicular energy is scattered to the parallel direction. Such a process can also work for HFAs. From recent MMS observations, Liu et al. (2020a) identified a similar process for thermal electrons during the formation of foreshock transients, which enhances electron perpendicular anisotropy, leading to the excitation of whistler waves that in return decreases the anisotropy (Shi et al. 2020a). If the expansion of an HFA/FB is super-fast-magnetosonic, the compressional boundary can steepen into a shock. Such a shock has been observed to accelerate solar wind ions through shock drift acceleration and form a new foreshock (Liu et al. 2016a). Inside HFAs/FBs, magnetic reconnection has been identified using MMS observations, which energizes electrons through the parallel electric field along the guide field (Liu et al. 2020d).

Particle acceleration by HFAs/FBs could contribute to shock acceleration. One important shock acceleration mechanism is diffusive shock acceleration (Treumann 2009; Lee et al. 2012). However, there are still some open questions. For example, particles need certain initial energy to participate in the acceleration, but the energy source is unknown. In addition, the theoretical acceleration efficiency at Q\(_{\parallel }\) shocks is likely underestimated. It is possible that foreshock transients could be one of the energy sources to initiate diffusive shock acceleration. For example, the shocks of FBs and HFAs can first accelerate solar wind particles through shock drift acceleration and bring them towards the bow shock for further acceleration (Liu et al. 2016a). Foreshock transients could also increase the acceleration efficiency at Q\(_{\parallel }\) shocks. For example, FBs and HFAs can directly participate in the Fermi acceleration process at the bow shock (Liu et al. 2017d, 2018; Turner et al. 2018; Omidi et al. 2021). They can also further energize particles that are accelerated at the bow shock (Liu et al. 2019a). As foreshock transients are very likely common in the universe, the role of foreshock transients in shock acceleration should be considered.

2.3.7 Discovery of SHFAs and Their Parametric Dependencies

Omidi et al. (2013b) used global hybrid simulations to demonstrate that the convection of foreshock cavitons and their interaction with the bow shock results in the formation of SHFAs. Figure 17 shows examples of SHFAs formed in a hybrid run with solar wind Alfvén Mach number \(M_{\mathrm{{A}}}=\) 7 and radial IMF. Panel (a) shows the density normalized by that of the solar wind focused around the quasi-parallel shock and magnetosheath. Examples of SHFAs characterized by cores of low density and rims of high density are evident in the figure. Panels (b)-(d) show ion temperature, total magnetic field, and density as measured by a simulated spacecraft located at X= 1250, Y= 800 respectively. The shadowed regions correspond to the detection of two SHFAs whose time series signatures resemble that of HFAs. Subsequent studies using global hybrid simulations have demonstrated that SHFAs form at shocks with \(M_{\mathrm{{A}}} \geq \)3 regardless of the IMF cone angle and that they are an inherent part of ion dissipation processes at the quasi-parallel bow shock with significant impacts on the magnetosheath and the magnetopause such as the formation of Magnetosheath Filamentary Structures (MFS) and sheath cavities (Omidi et al. 2014a,b, 2016). Hybrid-Vlasov global simulations by Blanco-Cano et al. (2018) also showed SHFAs evolved from foreshock cavitons and affected the local bow shock and magnetosheath consistent with Omidi et al. (2013b).

Fig. 17
figure 17

Results of a global hybrid run during radial IMF. The configuration is similar to that in Fig. 2 of Omidi et al. (2020b). (a) density normalized by that of the solar wind focused around the quasi-parallel shock and magnetosheath. (b)-(d) ion temperature, magnetic field strength, and density as measured by a simulated spacecraft located at X= 1250, Y= 800. The shadowed regions correspond to the detection of two SHFAs. (Credit: Nick Omidi)

Zhang et al. (2013) reported an SHFA during different evolution stages observed by five THEMIS spacecraft. THEMIS A observed a structure near the bow shock which exhibited a core region with low field strength, low density, strong plasma heating, and significant plasma deflection bounded by two compressional boundaries (Fig. 3). The characteristics are consistent with typical HFAs, except that there is no clear magnetic field direction change across the structure. Therefore, the HFA-like structure was not driven by a discontinuity and must thus be identified as an SHFA. The multiple THEMIS spacecraft also observed the early stage of the SHFA, i.e., a proto-SHFA. Similar to proto-HFAs, the proto-SHFA did not show clear plasma heating and/or significant flow deflection and exhibited two distinctive ion populations (foreshock and solar wind ions) inside it. The proto-SHFA showed depressed magnetic field strength and plasma density, similar to cavitons in hybrid simulations performed by Omidi et al. (2013b). The observations are consistent with the hybrid simulations by Omidi et al. (2013b), confirming that HFAs can spontaneously form at the quasi-parallel bow shock. Collinson et al. (2017) reported ESA Venus Express and NASA Mars Atmosphere and Volatile EvolutioN (MAVEN) observations indicating that SHFAs also exist in the foreshocks of Venus and Mars. These SHFAs form via the same mechanisms as those in the terrestrial foreshock according to 3-D hybrid simulations reported by Omidi et al. (2017a). Statistical studies (Chu et al. 2017; Wang et al. 2013b) showed that there are no significant differences between SHFA and HFA properties and occurrence patterns.

2.3.8 When/Where do HFAs Occur—Favorable Formation Conditions

HFAs typically form at the Q\(_{\parallel }\) bow shock. For example, global hybrid simulations by Lin (2002) showed HFAs driven by a TD with a Q\(_{\parallel }\) bow shock on two sides. Global hybrid simulations by Omidi and Sibeck (2007) used a TD that changed the local bow shock from Q\(_{\parallel }\) to Q. An HFA formed on the Q\(_{\parallel }\) side. Observations show that most HFAs have Q\(_{\parallel }\) bow shock on at least one side, and a few HFAs have Q bow shock on both sides (Schwartz et al. 2000; Facskó et al. 2009; Wang et al. 2013b). One possibility is that as the bow shock is curved, HFAs may form in the Q\(_{\parallel }\) region and propagate to the spacecraft in the Q region.

Regarding the solar wind conditions, Cluster observations suggest that HFAs occur preferentially during fast solar wind (Facskó et al. 2008, 2009, 2010). Such a formation condition was later confirmed by THEMIS and ARTEMIS observations in the midtail foreshock at \(X=-30\) to −50 \(R_{\mathrm{{E}}}\). This may also be true for SHFAs and FBs, from both statistical studies (Chu et al. 2017; Liu et al. 2017b, 2021) and case studies (e.g., Turner et al. 2013; Liu et al. 2016b). A possible explanation is that faster solar wind causes higher foreshock ion speed, and the foreshock ion energy is the energy source for the formation process (e.g., An et al. 2020; Liu et al. 2020a). A statistical study using Cluster observations (Facskó et al. 2009) suggested that the dynamic pressure is not an important factor. The solar wind densities before HFAs were slightly lower than the average value of the solar wind density (Facskó et al. 2009). Statistical studies using THEMIS (Liu et al. 2017b) and ARTEMIS (Liu et al. 2021) observations also found that the solar wind density does not affect the HFA, SHFA, and FB occurrence, but that low IMF strengths favor occurrence. High fast magnetosonic Mach number (\(M_{\mathrm{{MS}}}\)) also favors the formation of HFAs. No events were found below \(M_{\mathrm{{MS}}} = 6\) (Facskó et al. 2008, 2009, 2010). Similarly, recent hybrid simulations by Omidi et al. (2020b) showed that when the Alfvén Mach number is larger than \(\sim 7\), FBs can form. The statistical study of foreshock transients in the midtail foreshock also showed that high solar wind Alfvén Mach number is a favorable condition (Liu et al. 2021). PIC simulations by An et al. (2020) suggested that high Mach numbers favor the formation and expansion of HFAs and FBs by providing larger foreshock ion energy and greater density ratios of foreshock to solar wind ions. Consistently, THEMIS and MMS observations showed that the expansion speed of FBs is proportional to the solar wind speed and Alfvén Mach number (Liu et al. 2016b; Turner et al. 2020).

HFAs are typically driven by TDs that satisfy certain conditions. Schwartz et al. (2000) showed that there is a slight tendency for HFAs to occur preferentially for ∼ 90 shear angle (the angle between the magnetic field downstream and upstream of the driver TDs). Facskó et al. (2009, 2010) showed that HFAs preferentially occur at large shear angles of \({\sim} 70^{ \circ }\). Later, Zhao et al. (2017) confirmed that large shear angles favor the formation of HFAs (Fig. 18). The statistical study of midtail foreshock transients showed the same preference (Liu et al. 2021). Moreover, Schwartz et al. (2000) showed that a large angle between the TD normal and the Earth-Sun direction is a favorable condition. This was confirmed by Facskó et al. (2008, 2009, 2010) who showed that this angle is larger than \(45^{\circ }\) in the majority of HFAs. Schwartz et al. (2000) suggested an explanation by using the following formula to calculate the transit velocity of the TD on the surface of the bow shock:

$$ \mathbf {V_{tr}}= \frac{\mathbf {V_{sw}}\cdot \mathbf {n_{cs}}}{\sin ^{2}\theta _{cs:bs}}( \mathbf {n_{cs}}-\cos \theta _{cs:bs}\mathbf {n_{bs}}) $$

where \(\mathbf {V_{tr}}\) is the transit velocity, \(\mathbf {V_{sw}}\) is the solar wind velocity, \(\mathbf {n_{cs}}\) is the normal of the TD, \(\mathbf {n_{bs}}\) is the normal of the bow shock, and \(\theta _{cs:bs}\) is the angle between \(\mathbf {n_{cs}}\) and \(\mathbf {n_{bs}}\). When \(\theta _{cs:bs}\) is large, the transit velocity is slow meaning that the driver TD has sufficient time to trap foreshock ions to form an HFA. The statistical analysis by Facskó et al. (2009, 2010) confirmed this statement. Hybrid simulations for the heliospheric termination shock by Giacalone and Burgess (2010) showed that large \(\theta _{cs:bs}\) favors the formation of HFAs. The statistical study of midtail foreshock transients by Liu et al. (2021) supports this. However, Liu et al. (2021) pointed out that as the midtail bow shock is very tilted, the preference to large \(\theta _{cs:bs}\) cannot result in slow \(\mathbf {V_{tr}}\) due to the strong tangential component of the solar wind velocity. How exactly TD parameters affect the formation process requires further investigation.

Fig. 18
figure 18

Statistical analysis of shear angle distributions. (a) Shear angle distribution of 138 HFA events. (b) Shear angle distribution of 90135 discontinuities in the solar wind. (c) Normalized shear angle distribution of HFAs by that in the solar wind (from Zhao et al. 2017, Fig. 6)

In early studies, Burgess (1989b) used test particle simulations showing convection electric fields pointing towards a TD to show that TDs can trap bow shock-reflected ions along the TD. This was later confirmed by hybrid simulations (e.g., Thomas et al. 1991; Lin 1997) and observations (e.g., Schwartz et al. 2000) that such a field configuration favors the formation of HFAs. However, a statistical study by Wang et al. (2013b) showed that the electric field pointing towards TDs is not a necessary condition for HFA formation. Later, Zhao et al. (2017) showed convection electric fields point inwards toward TD on the leading and trailing sides of 74% and 72% of HFAs, respectively. Decreases in plasma parameters and the magnetic field strength within HFAs exhibiting inward convection electric field on both sides are larger than those with convection electric field inward on only one side. The formation model presented by Liu et al. (2020a) suggested that since the solar wind velocity is always anti-sunward, the direction of the convection electric field relative to the TD normal is determined by the IMF direction relative to the TD normal, which is independent of the frame of reference. When the convection electric field points towards the TD, the corresponding IMF configuration relative to the TD allows the Hall current from demagnetized foreshock ions to increase and thus enables the growth of the magnetic field structure, i.e., the formation of a foreshock transient.

Additionally, Zhao et al. (2017) showed that the formation of HFAs requires the magnetic field on at least one side of the TDs to be connected to the bow shock. They also calculated the thickness of TDs by fitting with the Harris current sheet model. They showed that thicknesses of TDs and HFAs are strongly correlated and thinner TDs form HFAs more efficiently. They also showed that HFAs preferentially form when the calculated specularly reflected flow from the bow shock is along the TD plane.

HFAs and their magnetosheath perturbations (e.g., Eastwood et al. 2008; Hasegawa et al. 2012) have been observed not only on the dayside but also on the nightside. Facskó et al. (2015) reported HFA-like disturbances in the far tail magnetosheath using STEREO magnetic field and electron plasma measurements. Recently, multiple spacecraft observations showed that the disturbances associated with foreshock transient events can propagate to the midtail magnetosheath and affect the nightside magnetopause (Wang et al. 2018a). Using ARTEMIS observations, Liu et al. (2020e) identified HFAs and other types of foreshock transients in the midtail foreshock, which were statistically studied by Liu et al. (2021). Using 3D global hybrid simulations, Wang et al. (2020b) simulated an FB formed in the dayside foreshock and propagated to the midtail foreshock. These results suggest that HFAs and other types of foreshock transients can disturb not only the dayside but also the nightside bow shock, magnetosheath, and magnetopause.

2.3.9 Hydromagnetic HFA Formation Mechanism

One of the most remarkable properties of HFAs is the strong deflection of the solar wind bulk flow which can be large enough that inside an HFA the flow can actually show a sunward component. While there is always the presence of back streaming ions in the foreshock region of the Earth’s bow shock, the momentum and energy transport of these foreshock particles is far to small too explain HFA properties for typical conditions at the bow shock. This consideration motivated a very different approach to explain the presence of HFAs at the bow shock. It is straightforward to demonstrate that a transient region of lower density in the solar wind interacting with the fast shock can cause the disruption of the fast shock and leads to a new shock that actually travels into the upstream direction with plasma behind this new shock having a much smaller momentum density and velocity than the original solar wind.

Using two-dimensional MHD simulations Otto and Zhang (2021) modeled such a scenario by assuming the presence of a low density flux tube in the upstream solar wind region. The initial configuration used in these simulations was that of an oblique fast shock and a low density magnetic flux tube in the upstream region that is convected into the fast shock. As soon as the low density flux tube touches the fast shock, a bulge forms at the shock that expands rapidly into the upstream region. It is noted that in one dimension with a simple parallel shock this problem can be solved analytically demonstrating the newly formed fast shock moved fast into the upstream region with a speed that depends on the solar wind speed (or Mach number) and the reduction in density in the depleted flux tube, i.e., the sunward velocity of the newly formed shock is faster for faster solar wind and for stronger reduction in density. For a reduction to about 20% of the original density the speed of the newly formed shock is close to 1/2 of the solar wind speed and the material behind the newly formed shock is stagnant (in the original shock frame).

Figure 19 illustrates the resulting bulge of the interaction of the low density flux tube with a fast shock about 3 minutes into the simulation. Here the solar wind Mach number is 5, solar wind speed is 500 km/s, density is normalized to 3 cm−3, and distances are in units of 300 km. The density plot shows the low density at the outermost edge of the bulge which extends about 4 \(R_{\mathrm{{E}}}\) out of the original fast shock with \(\Theta _{Bn}=15^{\circ }\).

Fig. 19
figure 19

Left: Temperature (color), velocity (arrows), and magnetic field (lines); middle: Density (color); right: Sketch of the different characteristic regions of the HFA-like structure as a result of the interaction of a density depleted flux tube (dark green) with a fast oblique shock (vertical dashed line) for the entropy distribution in our reference case. Here, red indicates leading and trailing shocked plasma regions, yellow indicates the shocked plasma from the density depleted flux tube, and cyan is the inner region of plasma that is a mixture of original magnetosheath material and plasma from the leading edge region which is channeled back into the interior through a vortex motion. (after Otto and Zhang 2021)

The figure illustrates a number of typical properties that are consistent with observations of HFAs. The interior of the HFA-like structure is strongly heated and almost stagnant. Note that this simulation is in the de Hoffmann-Teller frame of the original shock in which the HFA is just expanding but not moving along the original shock. In the normal incidence frame the structure is actually moving downward along the shock with a velocity that depends on the solar wind speed and \(\Theta _{Bn}\) as indicated in the sketch on the right. This also implies that average interior plasma velocities of HFAs should depend on the inclination of the magnetic field with the shock and the solar wind speed.

Asterisks in the left panel of Fig. 19 show fluid elements that were originally placed along a straight line with uniform spacing. These demonstrate a strong vortical motion which is caused by the flow deflection around the bulge. It is also noted that the leading and trailing edges of the structure show significant density increases consistent with shocks at these boundaries. The pressure in the interior is higher than in the solar wind, leading to the expansion along the original shock, and it is lower than in the adjacent magnetosheath (downstream region) causing a flow of magnetosheath material into the rear part of the HFA-like structure.

The typical regions of this HFA structure are illustrated in the sketch on the right of Fig. 19. These different colored regions and their boundaries are clearly seen in the entropy and density plots in Fig. 19 where, for instance, the leading and trailing shocked regions are dark violet in the entropy and light blue in the density plot. Actual in-situ observation of these structures should show an asymmetry because the trailing edge encounter takes place at a time where the structure is older such that the trailing edge shocked region should be more developed and thicker while the leading edge shock may not have fully developed at the time of the encounter. Also, the interior region is separated from the leading and trailing shocked plasma by tangential discontinuities, and it is a region of strongly varying magnetic field and pressure generating current layers, strong enough to cause magnetic reconnection inside the HFA-like structure in the simulation.

While different solar wind conditions and values of \(\Theta _{Bn}\) have an influence on the evolution (faster and hotter for higher solar wind speed) the qualitative structure does not depend on the specific values used for the simulations. An open question for this mechanism concerns the origin of the low density flux tube. However density cavities are fairly frequent in the vicinity of the foreshock region such that it is conceivable that such cavities can interact with the bow shock preferably for fairly radial IMF conditions. The simulations also demonstrate that the HFA-like structure grows much faster for small \(\Theta _{Bn}\) consistent with statistical properties of HFA occurrence. Clearly these simulation cannot provide the observed rich kinetic structure of HFAs but they appear to be consistent with the observed bulk properties. It would also be highly desirable to conduct similar studies using kinetic simulation models.

2.3.10 Kinetic Formation Model

Hybrid simulations (e.g., Thomas et al. 1991; Lin 2002; Omidi and Sibeck 2007; Omidi et al. 2010) show that HFAs and FBs form when foreshock ions interact with a solar wind discontinuity. The discontinuity can concentrate and thermalize foreshock ions resulting in high thermal pressure, which causes an expansion that piles up plasma outward forming a low density core bounded by compressional boundaries or shocks. To explain how foreshock ions interact with a discontinuity, Archer et al. (2015) proposed that when foreshock ions cross an RD, their parallel speed has to be projected to the perpendicular direction due to the magnetic field direction change. This leads to a conversion from the kinetic energy to the perpendicular thermal energy. Additionally, because of the decrease in parallel speed and conservation of mass flux of foreshock ions across the discontinuity, the density of foreshock ions increases. Both the increases in foreshock ion density and thermal energy result in a large thermal pressure enhancement. Similarly, Liu et al. (2015) proposed that when foreshock ions gyrate across a tangential discontinuity due to their large gyroradius, the tangential discontinuity (under a certain IMF configuration) can also transfer foreshock ion kinetic energy to thermal energy.

These models, however, are still insufficient. For example, foreshock ion gyroradii can be thousands of km or even several \(R_{\mathrm{{E}}}\) in the core region with low field strength, which are larger than or comparable to the discontinuity thickness or HFA/FB spatial scale. The ion gyroperiod (10-20 s) can also be larger than or comparable to the formation/evolution time scale of HFAs/FBs. Therefore, the concept of “thermal pressure” is not suitable to describe foreshock ions and their kinetic effects should be considered. As shown in Fig. 20, greater ion than electron gyroradii cause inward pointing static electric fields to accompany discontinuities (An et al. 2020). Such an electrostatic field drives electrons to \({\mathbf{E}} \times {\mathbf{B}}\) drift, but ions cannot drift because this process happens within one ion gyroperiod. The electron motion together with the partial gyration of foreshock ions results in a Hall current, which decreases the field strength in the core region and increases the field strength at the boundary. Because of the magnetic field variation, there is an induced electric field, which drives cold plasmas to expand outward together with the magnetic field lines. This model provides a more physical description of the formation and expansion process of HFAs/FBs. The energy comes from the foreshock ions through partial gyration against the induced electric field. As a result, higher foreshock ion energy can lead to faster expansion as shown in their parameter scan. Using a more realistic setup, An et al. (2020) showed that when initially field-aligned foreshock ions cross an RD, they cannot immediately change their velocity direction and start to gyrate partially. In addition, because electrons are almost always magnetized and move along the field lines, Hall currents form which determine the basic magnetic profile of an FB.

Fig. 20
figure 20

The sketch of formation process. The orange region fills with both foreshock (hot) ions and cold plasma with thickness same as foreshock ion gyroradius (\(\rho _{h}\)). The white region only has cold plasma. (From An et al. 2020, Fig. 1)

Liu et al. (2020a) confirmed this model by analyzing MMS observations of foreshock transients that just started to form. They showed that in the background foreshock, foreshock ions move along the field lines with complete gyration and \({\mathbf{E}} \times {\mathbf{B}}\) drift. In the core region, although the magnetic field direction has changed, the foreshock ions still move roughly in the same direction as in the background. As a result, the foreshock ions’ initial parallel speed is projected to the perpendicular direction, i.e., the foreshock ions partially gyrate. Because electrons are almost always magnetized, a Hall current forms. Such a Hall current curves the magnetic field lines, inducing an electric field that drives the cold plasma to \({\mathbf{E}} \times {\mathbf{B}}\) drift outward together with the field lines. As the mass flux and magnetic flux are transported from the core to the boundary, the boundary steepens with enhanced field strength. As a result, more foreshock ions are trapped within the core region leading to a stronger Hall current, which in return further steepens the boundary. This completes a positive feedback loop resulting in a kind of “instability” that enables the structure to grow. As this is an “instability”, the magnetic field variation is nonlinear causing the induced electric field to increase, which drives the cold plasma to move outward faster and faster. This explains how the expansion speed of HFAs/FBs accelerates from 0 to a certain value.

Based on this model, Liu et al. (2020a) suggested that to form an HFA/FB, a certain magnetic field configuration across a discontinuity is needed. For example, when the Hall current can decrease the field strength at the discontinuity, foreshock ions can more easily cross the discontinuity and become more demagnetized due to locally larger gyroradii, which enhances the Hall current, i.e., an “instability” can occur, and an HFA/FB starts to develop. However, if the Hall current increases the field strength at the discontinuity, fewer foreshock ions can cross the discontinuity and become less demagnetized, and a stable solution will be reached, resulting in a static modification to the magnetic profile around the discontinuity. For tangential discontinuities, the two magnetic field configurations have a convection electric field in the bow shock rest frame pointing toward and away from the discontinuity, respectively. Thus, this model can also partially explain why the convection electric field needs to point towards the tangential discontinuity on at least one side to form HFAs (e.g., Schwartz et al. 2000).

2.4 Other Foreshock Transients

2.4.1 Foreshock Bubbles

Using the results from global hybrid simulations of solar wind interaction with the magnetosphere, Omidi et al. (2010) predicated the formation of a new non-linear structure named foreshock bubble (FB). Foreshock bubbles form when IMF discontinuities interact with backstreaming ion beams in the foreshock. In contrast to HFAs that form after the interaction of interplanetary discontinuities with the bow shock, FBs can form prior to such an interaction. FB formation is initiated when the discontinuity encounters the backstreaming ion beam resulting in its deflection due to the magnetic field direction change. The deflected beam interacts with the solar wind, resulting in the deceleration of the latter and the formation of a fast magnetosonic shock wave that expands sunward with time. Downstream of the shock wave there is a sheath (shocked solar wind) plasma followed by a core region with low magnetic field strength and containing a hot and tenuous plasma with energetic particles.

Panel (a) of Fig. 21 illustrates the structure of a foreshock bubble formed in a local 2.5-D (2-D in space, 3-D currents, fields) hybrid simulation of the interaction between a solar wind RD and a beam of ions. It shows the density (normalized to solar wind value) in a run with the solar wind moving from left to right, interacting with a finite width (in the Y direction) backstreaming ion beam injected from the right hand boundary moving to the left. A foreshock bubble forms on the sunward (upstream) side of the RD embedded in the solar wind. The original foreshock with the associated Foreshock Compressional Boundary lies downstream (to the right) of the RD. The shock wave associated with the foreshock bubble consists of quasi-perpendicular and quasi-parallel geometries and results in the formation of a new foreshock upstream of the FB. It was shown by Omidi et al. (2010) that the width of the FB scales with the width of the ion foreshock and at Earth would correspond to ∼10 \(R_{\mathrm{{E}}}\) or more. Foreshock bubbles are carried anti-sunward by the solar wind and depending on the IMF cone angle collide with different parts of the bow shock and magnetosphere.

Fig. 21
figure 21

Structure of foreshock bubbles in 2-D and 3-D hybrid simulations. (a) density (normalized to solar wind value) from a local 2.5-D hybrid simulation (b-c) magnetic field strength from a 3-D global hybrid simulation of solar wind interaction with Venus (from Omidi et al. 2010, 2020a)

The discovery of foreshock bubbles was greatly facilitated by simultaneous THEMIS mission observations from far upstream to inside the magnetosphere, making it possible to study the formation, growth and interaction of FBs with the bow shock and the magnetosphere. The use of ground-based magnetometers has allowed us to observe the global impacts of FBs on the ground. The first direct evidence for the existence of foreshock bubbles was presented by Turner et al. (2013). Initial observations of FBs confirmed the model prediction that they form as a result of the interaction between solar wind RDs and backstreaming ions. However, subsequent observations of FBs have shown that tangential discontinuities in the solar wind can also generate foreshock bubbles (Liu et al. 2015, 2016b). Liu et al. (2015) proposed that when foreshock ion gyroradii are larger than the TD thickness, they can gyrate across a TD and form an FB. Recent global hybrid simulation by Wang et al. (2021) generated a TD-driven FB and confirmed this hypothesis. Both global hybrid simulations and spacecraft observations have established foreshock bubbles as highly efficient accelerators of particles. The FB shock can reflect and accelerate solar wind particles through shock drift acceleration forming a new foreshock (Liu et al. 2016a). As the FB shock convects toward the bow shock, electrons and ions can bounce between the bow shock and the FB shock (at the magnetic gradient of the anti-sunward edge) and gain energy through Fermi acceleration (Liu et al. 2017d, 2018; Omidi et al. 2021). Because of the super-fast-magnetosonic expansion, magnetic flux is transported outward very rapidly towards the FB shock. As a result, electrons are observed to be further energized by a factor of 10 up to 100s of keV through betatron acceleration (Liu et al. 2019a).

As discussed in Omidi et al. (2010), upon encountering the bow shock, the lower pressure in the FB core results in the outward motion of the bow shock and sunward flows in the dayside magnetosheath and the outward expansion of the magnetopause and the dayside magnetosphere, which can result in magnetospheric ULF waves as shown in Hartinger et al. (2013). The interaction also results in the injection of high energy particles into the magnetosheath and magnetosphere. Subsequently, the portion of the bow shock colliding with the FB is dissipated and replaced with the FB shock. This results in the return of the anti-sunward flows in the magnetosheath and compression of the magnetopause. Archer et al. (2015) used multi-spacecraft and ground-based observations to demonstrate that FBs have a global impact on the magnetosphere-ionosphere system. Specifically, they showed that measurements in the magnetosheath, magnetopause, the inner magnetosphere and on the ground all show signatures associated with the passage of the FB. They also established that among numerous other foreshock phenomena such as HFAs, foreshock bubbles have the biggest impact on the magnetosphere. Global hybrid simulation by Wang et al. (2020b) shows that FBs can propagate from dayside to the midtail and continuously disturb the local bow shock, magnetosheath, and magnetopause. Much more remains to be understood about the impacts of FBs on the magnetosphere.

In a recent study by Omidi et al. (2020a), 3-D global hybrid simulations and data from Venus Express (VEX) spacecraft was used to investigate the formation of foreshock bubbles at the planet Venus. Panels (b and c) in Fig. 21 show the magnetic field strength from a 3-D global hybrid simulation of solar wind interaction with Venus where an FB has formed upstream of the bow shock due to the presence of an RD in the solar wind. As expected, the size of the FB is similar to the width of the foreshock at Venus which is slightly larger than the diameter of the planet. It is evident from Fig. 21 that the 2- and 3-D structures of FBs are quite similar including the formation of a new foreshock upstream of the bubble in agreement with the observations by Liu et al. (2016a). Examination of VEX data shows ample evidence for the existence of FBs at Venus. Based on the results presented in Omidi et al. (2020a), we expect FBs to have a significant impact on the Venusian ionosphere and loss of planetary ions.

2.4.2 Foreshock Cavities

Foreshock cavities are regions with enhanced suprathermal ion fluxes but depressed densities and magnetic field strengths that are bounded by regions without enhanced suprathermal ion fluxes but enhanced densities and magnetic field strengths (Sibeck et al. 2002). They have been detected at Earth, Venus, and Mars (Collinson et al. 2020). At Earth, they typically have durations ranging from one to several minutes, but some can last longer than one hour (Sibeck et al. 2001; Billingham et al. 2008). Event amplitudes decay with distance from the bow shock, and their simultaneous appearances can be very different upstream from the dawn and dusk bow shock (Sibeck et al. 2004). Foreshock cavities tend to occur during intervals of enhanced solar wind velocity (Sibeck et al. 2001; Billingham et al. 2008), which may be equivalent to a statement that they tend to occur during intervals of radial IMF, because the IMF tends to be more radial during intervals of enhanced solar wind velocity.

The cavities are well-explained by numerical simulations for wave particle interactions occurring in spatially limited regions. The heating increases ion thermal pressures and causes regions connected to the bow shock to expand outward at the expense of surrounding regions where no heating is occurring. This results in field-aligned diamagnetic cavities with depressed magnetic field strengths bounded by enhanced densities and magnetic field strengths, both in simplified (Thomas and Brecht 1988) and more realistic geometries (Lin 2003).

Two explanations have been provided for foreshock cavities. In some global hybrid code simulations, the steady-state foreshock that occurs during intervals of nearly radial IMF orientation is bounded by regions of enhanced density and magnetic field strength, namely the foreshock compressional boundaries. The strengths of these boundaries increase with increasing solar wind Mach number, or equivalently velocity (Omidi et al. 2009). These boundaries might sway back and forth across a nearby spacecraft, resulting in transient entries and exits from the foreshock bounded by these enhancements (Sibeck et al. 2008). Alternatively, as argued by Billingham et al. (2008), transient entries into foreshock cavities may simply result from the passage of antisunward-moving slabs of magnetic field lines connected to the bow shock embedded within regions that are not connected to the bow shock.

Simulations and observations indicate that the cavities are readily transmitted across the bow shock and into the magnetosheath (Sibeck et al. 2021), where they can again be recognized on the basis of correlated density and magnetic field strength enhancements bounding heated plasmas accompanied by depressed and fluctuating magnetic field strengths and densities. However, there is one big difference between the boundaries of cavities in the magnetosheath and upstream from the bow shock. The boundaries of cavities in the magnetosheath exhibit flow velocity enhancements or jets relative to the surrounding plasma, where as the boundaries of cavities upstream in the foreshock do not (Kajdič et al. 2021; Sibeck et al. 2021). Foreshock cavities can drive strong pressure variations in the sheath and along the magnetopause, resulting in strong magnetopause motion (Turner et al. 2011).

2.4.3 Foreshock Cavitons

Foreshock cavitons are transient structures with low magnetic field strength and plasma density core bounded by a rim of enhanced magnetic field strength and plasma density, which can develop self-consistently in the foreshock region (Lin 2003; Blanco-Cano et al. 2009). Lin (2003) predicted this type of crater-like foreshock structures using a 2-D hybrid simulation and called them “diamagnetic cavities”. There is no plasma heating or flow deflection inside cavitons. Cavitons are not associated with IMF discontinuities and often surrounded by a train of ULF waves (Blanco-Cano et al. 2009), which are different from isolated cavities with no ULF waves nearby (Schwartz et al. 2006). Lin (2003) suggested that the formation of foreshock cavitons is related to the interaction between the solar wind ions and the backstreaming ion beams. Hybrid simulations (Blanco-Cano et al. 2009, 2011) suggested that the nonlinear interaction of two types of ULF waves generated by backstreaming ions via ion beam instabilities, the parallel-propagating weakly compressive waves and oblique-propagating linearly polarized fast magnetosonic waves, contributes to the generation of foreshock cavitons. Foreshock cavitons can exist in the foreshock region under different IMF orientations and their major features are independent of the IMF orientation. Foreshock cavitons develop into elongated structures along the magnetic field lines under radial IMF conditions, while they are field-aligned filaments or crater-like structures under oblique IMF conditions (Lin 2003). Figure 22 indicates the existence of foreshock cavitons for different IMF geometries in hybrid simulations. Figure 6 shows an example of a foreshock caviton observed by Cluster on 27 January 2003 (Blanco-Cano et al. 2011). Kajdič et al. (2017) found that foreshock cavitons might exist inside the traveling foreshocks bounded by two RDs. Their statistical results showed that the changes in magnetic field magnitude and plasma density are mostly correlated in foreshock cavitons.

Fig. 22
figure 22

Hybrid simulation results of the ion foreshock and the region filled with waves and cavitons under (a) radial and (b) oblique IMF orientations. Cavitons appear as red spots in panel (a) and pink and white spots in panel (b). (Blanco-Cano et al. 2011)

The first statistical study based on Cluster observations (Kajdič et al. 2013) showed that distinct cavitons appear under a wide range of solar wind and IMF conditions. The average duration of cavitons is 65 s and their average size is 4.6 \(R_{\mathrm{{E}}}\). The depletions in the magnetic field strength and density are greater near the bow shock (Tarvus et al. 2021). Kajdič et al. (2011) analyzed two foreshock cavitons observed by Cluster and found that these two cavitons are highly structured. They also found that these two cavitons were propagating sunward at a speed of 188 km/s and 120 km/s in the solar wind frame. Wang et al. (2019b) studied the propagation properties of twelve foreshock cavitons observed by four Cluster satellites using multi-spacecraft analysis methods, including the timing method, MDD method (Shi et al. 2005) and STD method (Shi et al. 2006, 2019). Their results showed that all cavitons propagate towards the Earth in the spacecraft frame and eleven structures move towards the sun in the solar wind frame. They also found that cavitons with larger sizes move faster in the solar wind frame. The propagation speed of cavitons in the solar wind frame is less than that of SHFAs (Tarvus et al. 2021).

Omidi et al. (2013a) studied the result of foreshock cavitons interacting with terrestrial bow shock using 2.5-D electromagnetic hybrid simulations. Their simulations showed that a new type of transient structures can be generated from this interaction process, i.e., SHFAs, which were observed by THEMIS (Zhang et al. 2013). Ion trapping by foreshock cavitons and Fermi acceleration from the back and forth motion of ions between the cavitons and the bow shock may play an important role in the particle acceleration (Omidi et al. 2013a). Tarvus et al. (2021) used the global hybrid-Vlasov simulation model Vlasiator to investigate caviton-to-SHFA evolution and their properties. They found that a third of the cavitons evolve into SHFAs and SHFAs can form independently near the bow shock.

2.4.4 Foreshock Compressional Boundaries

The ion foreshock boundary separates the pristine solar wind from a region, upstream of the quasi-parallel bow shock, containing beams of backstreaming ions reflected or leaked from the shock. Additional boundaries have been defined to mark the region containing ion beams and ULF waves (ULF wave boundary) and the region containing compressional ULF waves named the “compressional ULF foreshock boundary” (e.g., Greenstadt and Baum 1986). More recently, Sibeck et al. (2008) identified a new foreshock boundary consisting of a fast magnetosonic pulse in global hybrid simulations of solar wind interaction with the magnetosphere. This was followed by a more detailed investigation of this boundary named the Foreshock Compressional Boundary (FCB) where the effects of solar wind Mach number and the IMF cone angle were examined and an example of this boundary observed by spacecraft was provided (Omidi et al. 2009). Figure 23 shows an example of the FCB formed in a global hybrid simulation with solar wind Alfvén Mach number of \(M_{\mathrm{{A}}} =\) 15 and cone angle of 0 (radial IMF). Panels (a) to (d) in this figure show the density, total magnetic field strength, the \(Y\) component of magnetic field, and ion temperature, respectively. The FCB is associated with increased density and magnetic field strength as expected for a fast magnetosonic pulse. Based on the radial nature of the IMF and symmetry around it, the FCB is a cylindrical boundary in 3-D (see 3-D example in Omidi et al. 2017b).

Fig. 23
figure 23

Results of a global hybrid run during radial IMF. The configuration is similar to that in Fig. 2 of Omidi et al. (2020b). (a) density (b) magnetic field strength (c) \(Y\) component of the magnetic field (d) ion temperature (Credit: Nick Omidi)

Formation of the FCB is directly tied to the generation of foreshock cavitons and the associated plasma and field excavation that results in the lateral expansion of the foreshock plasma and the drop in average density and magnetic field levels. The interaction between this laterally expanding plasma and the solar wind results in plasma and field pile up forming the FCB. The formation and the presence of cavitons in Fig. 23 can be noted by the associated drops in density and magnetic field in their cores. Given the connection between the FCB and cavitons, the former can be viewed as the boundary between the region in the foreshock where cavitons are formed and the region where they are not. Panel (d) in Fig. 23 demonstrates this point in a clear fashion where the white dashed lines show the locations of the ion foreshock boundary and the FCB. The fact that the two boundaries do not coincide indicates that typically the foreshock can extend beyond the FCB. Examination of panel (c) in Fig. 23 shows that the waves generated between the FCB and the ion foreshock boundary have smaller wavelength (∼10 \(c/\omega _{\mathrm{p}}\)) as compared to the ones generated in the region where cavitons are formed (∼200 \(c/\omega _{\mathrm{p}}\)). However, it is also possible that at times the FCB and the ion foreshock boundary may coincide such that it separates the foreshock plasma from pristine solar wind. This result is consistent with the study by Rojas-Castillo et al. (2013) who used spacecraft data to investigate the properties of FCBs. They found that at times the FCB is between the pristine solar wind and foreshock plasma while at other times it falls inside the ion foreshock boundary.

Omidi et al. (2009) examined the impacts of solar wind Mach number on the FCB and showed that the amplitude of the magnetosonic pulse associated with the FCB increases as solar wind Mach number becomes larger. This is tied to the fact that as the solar wind Mach number increases, so do the size and strength of the foreshock cavitons (Omidi et al. 2013a), which enhances the expansion of the foreshock and the strength of the FCB. For sufficiently high Mach numbers, the steepening of the magnetosonic pulse results in FCB being associated with a shock wave. Spacecraft observations confirm this dependence of the FCB strength on solar wind Mach number (Rojas-Castillo et al. 2013). It was also demonstrated by Omidi et al. (2009) that as the cone angle increases to \({\geq} 20^{ \circ }\), the FCB does not form symmetrically around the foreshock and appears on the side that falls deep within the foreshock where cavitons are formed.

As was demonstrated by Omidi et al. (2013a), the FCB is a highly dynamic boundary in that as the lateral expansion of the foreshock due to caviton formation continues the FCB can proceed to move out laterally. In addition, the FCB is continually carried by the solar wind towards the bow shock and into the magnetosheath resulting in FCB footprint in this plasma. For example, note the regions of enhanced density and magnetic field in the sheath that connect to the FCB demonstrating the amplification of the FCB pulse as it enters the magnetosheath. By introducing solar wind discontinuities in the simulations, it was shown by Omidi et al. (2013a) that FCBs are also observed in connection with foreshock cavities. For example, connection of a bundle of IMF lines to the bow shock can result in the formation of traveling foreshocks with FCBs at their edges. Kajdič et al. (2017) used spacecraft data to confirm the formation of traveling foreshocks with FCBs at the edge.

2.4.5 ULF Wave Growth/Shocklets/SLAMS in the Dayside and Tail Foreshock

As mentioned in Sect. 2.1, the foreshock region is characterized by the presence of backstreaming particles. The features of the ion interactions with the bow shock strongly vary between Q and Q\(_{ \parallel }\) shock regions. For perpendicular shock, the maximum upstream excursion of reflected ions is restricted to the gyromotion that they suffer at the shock front under the effect of the magnetic field; they cannot escape upstream. As the angle between the shock normal and the IMF departs from 90, this gyromotion is distorted and some reflected ions move upstream and succeed to cover a larger upstream excursion. For Q\(_{ \parallel }\) shock, the impact of the magnetic field is strongly reduced in the sense that most reflected ions succeed to escape very far upstream along the magnetic field and are reinjected into the solar wind. As a consequence, a large ion density gradient takes place upstream of the front. An extended ion foreshock forms ahead of the shock front and is connected magnetically to it.

Moreover, earliest works on the upstream region of quasiparallel bow shock have noted that the magnetic field profile often consists of large amplitude “magnetic fluctuations” also named “magnetic pulsations” (Greenstadt et al. 1968a,b, 1977) and what appeared to be nonlinearly steepened ULF waves (e.g., Fairfield 1969; Russell et al. 1971). Further works have identified these nonlinearly steepened ULF waves as magnetosonic whistler modes which have been named “shocklets” since these look like small-shock structures (Hoppe et al. 1981). These shocklets are magnetosonic and some have whistler waves packet attached. Then, the ion foreshock region appears to be also characterized by a large variety of ULF waves (with frequencies much less than the ion gyrofrequency) in addition to various suprathermal ion distributions. These ULF waves also include so called “30 second waves”, “10 seconds waves”, “3 second waves” and “1 Hertz waves” (Burgess 1997; Eastwood et al. 2005). The features of the different magnetic structures and associated ion populations may be found in previous reviews (Greenstadt et al. 1995; Burgess et al. 2005; Wilson 2016).

Later on, magnetic structures with features “apparently” different from “shocklets” have been identified and named SLAMS (Short Large Amplitude Magnetic Structures) (Schwartz et al. 1992). Both structures are illustrated in Fig. 24. However, the over-use of these different labels (sometimes inappropriate) in the literature has led to a certain confusion and raised the following questions: are “shocklets” and “SLAMS” similar or quite different entities? are these issued from similar or different mechanisms? Answering these questions have been clarified with the help of simulations and comparison between experimental and simulations results, and are addressed below.

Fig. 24
figure 24

(A) Example of “shocklets” observed by Cluster 1 on February 18 2003; (B) Example of a “SLAMS” on February 2 2001. In both examples, panels (from top to bottom) show the amplitude of the magnetic field, its components, the plasma density, the bulk velocity (amplitude and its components), the total temperature T (including solar wind and suprathermals), and the proton energy spectrum. (From Plaschke et al. 2018a, Fig. 19)

Let us remind that backstreaming ions can propagate far within the upstream foreshock region and do have quite enough time to interact with the incoming solar wind ions and excite some instabilities (ULF waves). Far from the front (where the ion density gradient is still relatively weak), these ULF waves propagate almost parallel to the magnetic field. One accepted scenario is that these ULF waves suffer progressively a refraction when approaching the shock front where the density gradient becomes very large and their direction changes into parallel to the density gradient i.e. along the averaged shock normal direction (Scholer 1993). During the linear/nonlinear stage, these ULF waves suffer a progressive steepening as these are convected back to the shock front by the solar wind through the ion density gradient, and form the so-called SLAMS (Giacalone et al. 1993, 1994b). Many works based on hybrid simulations (Scholer et al. 1993; Scholer 1993; Dubouloz and Scholer 1993, 1995) and PIC simulations (Scholer et al. 2003; Tsubouchi and Lembège 2004) have confirmed such a scenario. More recently, this scenario has also been confirmed based on both measurement of the MMS mission and PIC simulations by Chen et al. (2021) who brought more precise information on the nonlinear ULF waves development into SLAMS. Three effects contribute: (i) gyro resonance between solar wind ions and right-hand circularly polarized electromagnetic waves results in magnetic field amplifications, (ii) gyro-trapping by the growing magnetic field builds up the plasma density that enhances the current and magnetic field, and (iii) the magnetic field is amplified at discrete isolated locations at the |B| maximal of the wave envelope where the initial density enhancement and longitudinal electric field develop. Typical spatial/time scales of ULF waves/SLAMS/whistler precursor measured during this scenario may be found in Table 2.

Table 2 Spatial and time scales of ULF waves, SLAMS and whistler precursor measured in 1D PIC simulation (issued from Tsubouchi and Lembège 2004, Table 2)

In order to distinguish more clearly shocklet and SLAMS, we need to emphasize these respective features. In short, SLAMS are identified by the following magnetic field signatures: (i) the magnetic field magnitude is enhanced over the undisturbed B field by at least \(\delta \)B/B\(>2-2.5\), with a duration of the order of 10 s in the spacecraft frame; (ii) they have a well defined smooth “near monolithic” profile; (iii) their spatial scales decrease with increasing amplitude (Schwartz et al. 1992; Mann et al. 1994), (iv) these show decreasing convection velocity (in the spacecraft frame) with decreasing distance to the bow shock (Mann et al. 1994); (v) scales sizes parallel to the shock normal and tangential to the shock surface are respectively larger than 1000 km and around 1300 km as observed experimentally by Lucek et al. (2004a, 2008) and retrieved in 2D simulations (respectively >1000 km and 3000 km) by Dubouloz and Scholer (1995); (vi) their gradient scale lengths are around 100 km (Lucek et al. 2004a, 2008). They occur in regions of ULF wave activity (isolated SLAMS) and within regions of stronger magnetic field pulsations associated with decelerated and heated plasma (embedded SLAMS), as well observed in experimental data (Schwartz et al. 1992; Mann et al. 1994; Lucek et al. 2002, 2004a); embedded SLAMS have larger amplitude than isolated SLAMS (Schwartz et al. 1992). They are found to propagate sunward in the plasma frame but are convected anti-sunward by the solar wind. They exhibit mixed polarization, biased towards right-hand polarized signatures (in the spacecraft frame) but often with a remnant of a left-handed (in the plasma rest frame), high frequency whistler wave on the leading edge similar to those at the lower amplitude (Schwartz et al. 1992). One striking feature is that local measurements show that the upstream (steepened) edge of the SLAMS is behaving as a local Q shock (Mann et al. 1994), which has been confirmed by 1D PIC simulation (Tsubouchi and Lembège 2004). Later on, data issued from Cluster multi-spacecraft mission have confirmed the observations of SLAMS in particular at different stages of their formation (Lucek et al. 2002, 2004a; Behlke et al. 2003; Burgess et al. 2005). Note that for large amplitude SLAMS, the amount of reflected solar wind ions reaches values around 30%. Thus, SLAMS represent effective ion reflectors of both solar wind ions and shock-reflected ions and are expected to play an important role in dissipation upstream of and at the Q\(_{ \parallel }\) bow shock (Behlke et al. 2003).

Shocklets features differ from SLAMS in several aspects: (i) in terms of their magnetic compression ratio \(\delta \)B/B \(<2\) (e.g., Schwartz et al. 1992), whereas ULF waves typically have \(\delta \)B/B=1; (ii) scale sizes of shocklets are similar to those of “30 second waves” i.e. up to a few \(R_{\mathrm{{E}}}\) (Hoppe et al. 1981; Le and Russell 1994; Lucek et al. 2002); (iii) discrete wave packets associated with shocklets are characterized by wavelengths of 30 km to 2100 km and their propagation angles versus the magnetic field are around \(20^{\circ }-30^{\circ }\) (Russell et al. 1971; Hoppe et al. 1981).

For a further comparison, more recent works have focussed on the features of shocklets, SLAMS, associated wave packets and dispersive precursor observed experimentally which are summarized in Table 3. But, the fact that shocklets and SLAMS do not have the same scales/amplitude/time duration does not mean that these are necessarily issued from different origins, in contrast with Wilson et al. (2013) and Wilson (2016) statements. Indeed, despite of their differences illustrated in Table 3 (and which may be found also in references of Wilson (2016)), these present strong similarities in their nature: (i) both are magnetosonic with the density inside them in phase with the magnetic field magnitude; (ii) both propagate sunward in the plasma frame of reference but are carried earthward by the solar wind, as their phase speed is much lower than the solar wind speed; (iii) both can exhibit left-hand polarizations (in the plasma rest frame); (iv) both can dispersively radiate an upstream whistler precursor (directed sunward in the plasma rest frame); (v) both modes contain a low frequency, large-scale compressional pulse (i.e. shocklet and SLAMS) and a higher frequency, smaller wave packet labelled “discrete wave packets” (Russell et al. 1971) which are identified now as a whistler precursor; it is important to remind that not all SLAMS or shocklets have an associated whistler precursor (Hoppe et al. 1981; Schwartz et al. 1992). All these similar features strongly suggest that both magnetic structures may be issued from a same origin as proposed in many previous works.

Table 3 Summary of the characteristics of the main different magnetic structures measured experimentally in the ion foreshock region (extracted from Wilson 2016, Table 1)

In order to support this idea, a more precise approach of the scenario looks necessary as summarized as follows. Let us remind that SLAMS have smaller scale sizes than shocklets and ULF waves (Lucek et al. 2002), and the amplitude of SLAMS is higher than those of shocklets and ULF waves. When an original upstream ULF wave is convected back to a region of increasing diffuse ion density upstream of the shock, the wave steepens, becoming a pulsation-like wave packet (as for so called “shocklets”). Then, a shrinking takes place so that their spatial scale decreases while their amplitude increases. But, one additional condition is necessary for the wave to grow and reach the “ultimate” stage of a pulsation-like structure (as for so called “SLAMS”): the characteristic scale length of the ion density gradient has to be of the same order as the wavelength of the original ULF wave as mentioned originally in hybrid simulations (Scholer 1993) and later on confirmed in PIC simulations (Tsubouchi and Lembège 2004). Let us complete with one additional point: this wave shrinking and steepening (at the leading edge) may continue until nonlinear effects reach a limit. This limit takes place as nonlinear effects are balanced by dispersive effects (emission of a whistler precursor) and/or dissipation effects (local ion reflection as in Tsubouchi and Lembège (2004)), and/or ion trapping within the emitted whistler wave train (as in Scholer et al. 2003); a SLAMS forms at this “ultimate” stage. This is coherent with the fact that the structure/dynamics of the leading edge of the SLAMS behaves as a Q shock front (Mann et al. 1994; Tsubouchi and Lembège 2004). Scholer et al. (2003) have shown that at some time of the simulation, the SLAMS consists of two regions with different distributions: in the upstream part, the distribution is decelerated and adiabatically heated, and in the whistler wave train the distribution has a high energy tail. In the extreme case where dispersive effects are very important (emission of a strong whistler precursor), these can refrain or even stop the local steepening, and the “ultimate” stage of SLAMS formation could be hardly or could not be reached. The impact of this competition between these different effects may require a deeper investigation.

In addition to the conditions mentioned above, this scenario can be refined with the following reminder: the upstream region of a Q\(_{\parallel }\) shock is strongly nonstationary (in time) and inhomogeneous (in space), which will impact the local plasma conditions of the wave refraction/shrinking. The relative occurrence of shocklet and SLAMS in time and space may also result from an “interplay” between the local strength of the convection velocity and the amplitude of the local ion density gradient through which the plasma is convected to the shock front. If the local ion density gradient is finite but relatively weak, the growth of shocklets from the ULF can take place but its steepening may not be strong enough during the convection to reach the ultimate stage and to be categorized into a SLAMS: then, signature of shocklets may be dominant. In contrast, if the ion density gradient is high, the steepening of the growing shocklet may be strong enough to reach the ultimate stage of a SLAMS which will be the final dominant signature. Moreover, let us precise that how quick shocklets or SLAMS are formed may depend on the convection velocity of the plasma within the ion density gradient. If the local convection is high, the signature of an “intermediate” shocklet may not be clearly evidenced during the rapid growth/steepening of the SLAMS. The dependence of this scenario versus local varying plasma conditions may account for a certain range of spatial scales/amplitude/duration of the magnetic structures as illustrated in Table 3 for shocklets and SLAMS. In summary, each magnetic structure results from an “interplay” between different effects: wave refraction/shrinking conditions, local steepening versus dispersion/dissipation effects, and impact of local varying plasma conditions (nonstationary upstream region). This interplay will give birth—both in time and space—to the possible emergence of shocklets or SLAMS, keeping in mind that large amplitude SLAMS correspond to the “ultimate” stage of the scenario. A combination of global and local 2D/3D simulations could be helpful for refining these different stages which contribute to the “patchwork” of magnetic signatures initially proposed by Schwartz and Burgess (1991).

This scenario supports well old and recent experimental and simulation results but may not be unique. Let us remind a “variante” to this scenario proposed by Scholer and Burgess (1992). The main difference is that SLAMS can be formed not from the steepening of nonlinear ULF waves originally issued from the interaction of incoming solar wind and reflected gyrating ion beam. Instead, by using 1D hybrid simulations, Scholer and Burgess (1992) let a magnetic field perturbation (convected with the solar wind) interact with a finite length beam (without a shock). The beam ions are deflected by the magnetic field perturbation. Depending on the angle \(\Theta _{bi}\) between the magnetic field (in the perturbation) and the direction of the reflected ion beam, the local beam density increases, which in turn increases locally the magnetic field. This then may also lead to large-amplitude magnetic field structures. The idea is that during small \(\Theta _{bi}\) the beam of more or less specularly reflected ions can travel far upstream where it encounters a magnetic field perturbation with a locally large \(\Theta _{bi}\). There, the feedback loop occurs and the SLAMS rises up. But, at that time, the authors did not focus on possible raise/identification of “shocklet” before the “SLAMS” stage is finally reached. This point needs to be clarified. In summary, the main difference is that SLAMS can build up from (i) either the steepening of ULF waves originally self-generated by the shock front itself (common scenario), (ii) either the steepening of an external magnetic perturbation carried by the solar wind. This last variante could be analyzed in more detail when applied to some transient structures reviewed in the present document (see Sect. 2.3.10).

ULF Waves/Shocklet/SLAMS Versus Self-Reformation/Nonstationarity of the Shock Front:

Another confusion may also appear due to the over-use of the “self-reformation” label in the literature. As well known, nonlinear structures/shocklets/SLAMS have a strong impact on the shock front itself. While convected back to the shock front, these interact/merge with it and are responsible for the strong inhomogeneity (front ripples) and nonstationarity of the front. For clarifying, we need to distinguish “nonstationary” effects and “self-reformation” processes. Let us remind that both 1D hybrid simulations (Burgess 1989a; Scholer and Burgess 1992) and 1D PIC simulations (Scholer et al. 2003; Tsubouchi and Lembège 2004) have shown that this nonstationarity leads to a self-reformation of the shock front (characterized by a cyclic time period). But, the situation strongly differs as shown in more recent 2D hybrid simulations (Hao et al. 2016, 2017). Indeed, because of the presence of large amplitude ripples at the shock front, the self-reformation cannot be synchronous along the whole front; only “local” self-reformation (i.e. over a small part of a ripple) can take place. Moreover, this “local” self reformation is only “intermittent” since the features/locations of the ripples vary in time as upstream nonlinear ULF waves/SLAMS are continuously convected back by the solar wind and hit the shock front at different locations (Hao et al. 2016). This is illustrated by red arrows in Fig. 25, which shows that the self-reformation strongly depends on the y-locations. The shock front is nonstationary in plots (i) and (ii) but no cyclic self-reformation can be clearly identified. However, the self-reformation can be identified at some other y-locations but is intermittent (i.e. not continuous in time) as in plots (iii) and (iv). In other words, a crossing of a multi-satellites set moving along a local shock normal can identify a local self-reformation during a certain time range. In contrast, a similar satellites crossing performed at different y-locations (if local \(y\)-axis is assumed along the shock front) may confirm that the shock front is nonstationary but no local self-reformation can be identified.

Fig. 25
figure 25

(a) Isocolors of the total magnetic field B(x,y) amplitude measured at late time of the 2D hybrid simulation; (b) Time variation of the total B field when measured at the four fixed locations y= (i) 120, (ii) 150, (iii) 196, et (iv) 225 c\(/\omega _{pi}\) indicated by horizontal dashed lines in plot (a); red arrows indicate the cyclic self-reformation of the shock front when possible to identify it. (Issued from Hao et al. 2016)

2.4.6 Transient, Local Ion Foreshocks

Omidi et al. (2013a) used several global hybrid simulation runs for steady and time-varying IMF conditions to study the dynamics of the FCB and examine the relationship between the FCB and foreshock cavities generated. In one of their runs, two discontinuities were launched convecting along the bow shock surface. The IMF was quasi-parallel and perpendicular to the bow shock normal between and outside two discontinuities, respectively. As a result, a local foreshock formed between two discontinuities bounded by two FCBs. Such a local foreshock was called the traveling foreshock as it traveled with the IMF between two discontinuities. As for the regular foreshock, its boundary is due to the curved bow shock surface that varies \(\Theta _{Bn}\) to be quasi-perpendicular. In their another run, when the IMF was time varying, the boundary of the foreshock oscillated back and forth. If there is spacecraft close to the boundary, it will temporarily enter the foreshock from the solar wind and exit resulting in an observation signature that is consistent with foreshock cavities.

Kajdič et al. (2017) used observations from five THEMIS spacecraft that were in a string-of-pearls formation to distinguish the two scenarios described in Omidi et al. (2013a). They found a foreshock bounded by two FCBs. Based on the time sequence of multiple spacecraft observations, they determined that the foreshock was traveling with two discontinuities rather than oscillating back and forth. This foreshock was thus identified as a traveling foreshock. Kajdič et al. (2017) suggested that isolated foreshock cavities could be a subset of traveling foreshocks.

Pfau-Kempf et al. (2016) presented a scenario resulting in time-dependent behavior of the bow shock and transient, local ion reflection under steady solar wind conditions. Dayside magnetopause reconnection creates FTEs which drive fast-mode wavefronts in the magnetosheath. These fronts create a bulge on the bow shock surface because of their large downstream pressure. The resulting bow shock deformation leads to a configuration favorable to localized ion reflection. This process has been identified in 2D global Vlasiator simulations (Fig. 26). Pfau-Kempf et al. (2016) also presented observational data showing the occurrence of dayside reconnection and FTEs at the same time as Geotail observed transient foreshock-like field-aligned ion beams.

Fig. 26
figure 26

(a) A local foreshock in the simulation with color indicating the parallel temperature that is sensitive to the presence of an ion beam. The solid white curve shows the bow shock location based on the density contour. The dashed white curve illustrates the approximate bow shock location without perturbations in the magnetosheath. The solid and dashed segments indicate the direction normal to each curve (\(\Theta _{Bn}\): 41 and 54). (b) 2-D projected contour and (c) 3-D contour plots of the ion velocity distribution (PSD in s3 m−6; 3-D contour at \(1\times 10^{-15}~\mbox{s}^{3}\,\mbox{m}^{-6}\)) at the white cross in panel (a). Both distributions show the field-aligned beam that is directly comparable to Figs. 2 and 6 in Kempf et al. (2015). (From Pfau-Kempf et al. 2016, Fig. 5)

2.5 Understanding Foreshock Effects in Simulations

As noted in Sect. 2.1, the foreshock is the region with magnetic field lines connected to the bow shock and filled with particles backstreaming from the bow shock. Among the different types of backstreaming ions, the formation mechanisms for field aligned beams (FABs) and gyro-phase bunched (GPB) backstreaming ions are still under active investigation. Different “scenarios” have been proposed (Möbius et al. 2001; Kucharek et al. 2004), each of which has some drawbacks. Some scenarios are based on the guiding center approximation and rough conservation of the magnetic moment, i.e. adiabatic reflection (Sonnerup 1969; Paschmann et al. 1980; Schwartz et al. 1983; Schwartz and Burgess 1984). Others invoke simple geometrical considerations consistent with specular reflection (Gosling et al. 1982; Paschmann et al. 1982; Meziane et al. 2001; Yamauchi et al. 2011). Yet others invoke leakage of some magnetosheath ions to produce low energy FABs (Edmiston et al. 1982; Tanaka et al. 1983; Thomsen et al. 1983). Particle diffusion processes have also been invoked to explain the diffusion of reflected “gyrating ions” by upstream magnetic fluctuations (Giacalone et al. 1994a) and the ion diffusion that takes place within the shock ramp due to pitch angle scattering during the reflection process (Möbius et al. 2001; Kucharek et al. 2004; Bale et al. 2005). Understanding the origin of the GPB population poses an even greater problem. These ions are observed near the quasi-parallel shock front (Gosling et al. 1982; Meziane et al. 2004) after undergoing specular reflection. However, they can also be observed at some distance from the shock front (Thomsen et al. 1985; Fuselier et al. 1986). These synchronized nongyrotropic distributions can be explained by different processes: (i) trapping by low-frequency monochromatic waves (Mazelle et al. 2003, 2005, 2007; Hamza et al. 2006), or (ii) beam-plasma instabilities (Hoshino and Terasawa 1985) which trap ions and can create the GPBs, or (iii) short time interaction with the macroscopic electric and magnetic fields at the front (Savoini and Lembège 2015). However, it is difficult to distinguish between these different possibilities which may or may not be present simultaneously.

The different ion populations within the ion foreshock exhibit spatial distributions whose characteristics depend upon distance from the bow shock, the length of time period when the field lines have been connected to the bow shock, and bow shock curvature (Eastwood et al. 2005). This point has stimulated several global foreshock simulations, still few in number in contrast to experimental studies. Three different global approaches are under use: (i) 2D/3D Hybrid-PIC, (ii) 2D Hybrid-Vlasov, and (iii) 2D Full PIC simulations.

a) Two dimensional Hybrid-PIC simulations (kinetic ions and fluid electrons) have been performed by different authors for the full range of Q and Q\(_{\parallel }\) foreshock regions, i.e. for the full range of angles between the IMF and the normal to the bow shock (Karimabadi et al. 2014; Blanco-Cano et al. 2006). In particular, Blanco-Cano et al. (2006) have analyzed coupling between the solar wind and the terrestrial magnetosphere for magnetic dipoles with different strength and consequences of these choices on the foreshock morphology and associated wave activity. Basically, they find two types of ULF waves excited by kinetic instabilities generated by two different ion populations (Fig. 27): (i) sinusoidal almost parallel propagating waves generated by FABs of backstreaming ions via the right-hand (RH) resonant instability, and (ii) highly compressive obliquely propagating fluctuations near the shock generated by gyrating ion beams closer to the front. A comparison of these results with observations show that the features of the sinusoidal waves (i) resemble the properties of 30-sec sinusoidal quasi-monochromatic waves in the foreshock. By contrast, the compressive waves exhibit properties similar to the observed right-handed steepened fluctuations. Results have also been compared with previous experimental work obtained from the Cluster mission (Mazelle et al. 2003, 2005; Meziane et al. 2004).

Fig. 27
figure 27

(Top) Temperature and \(B_{z}\) magnetic field component within the simulation box. The ion foreshock boundary, the ULF waves boundary (so called ULFWB in Sect. 2.1), and the direction of the IMF are indicated. (Bottom) Waves profiles along three trajectories within the foreshock. Cut A shows sinusoidal waves, while cuts B and C illustrate compressive wave profiles. The number below cuts A-C corresponds to the extension of each trajectory expressed in ion inertial length c/\(\omega _{pi}\). (From Blanco-Cano et al. 2006)

The challenge in the three dimensional (3D) hybrid-PIC simulation of the Earth’s foreshock is their high computational costs because of the large spatial scale compared with ion’s kinetic plasma scales (ion gyroradius, ion skin depth). However, computational cost can be reduced by investigating Mercury-solar wind interaction where the size of the bow shock and the magnetosphere is smaller than at Earth because of Hermean small intrinsic magnetic field compared to Earth. Recent 3D hybrid-PIC Mercury simulations suggest the planet has a dynamic and well-developed ion foreshock and a suprathermal, and partly backstreaming, foreshock ion population, which is associated with coherent, large-scale ULF waves at ∼5 s period (Jarvinen et al. 2019). This recent work shows that local ion distribution within the foreshock has a crescent shape resembling the intermediate distribution in the terrestrial ion foreshock, away from the bulk solar wind population (Figs. 28d and 28e).

Fig. 28
figure 28

Examples of parameters from a global 3D hybrid-PIC simulation of the Mercury-solar wind interaction and the ion foreshock. (a) The magnetic field lines near Mercury. The solar wind is flowing along the -x direction. The temperature of the solar wind protons is shown in equatorial (\(x-y\)) and meridian (\(x-z\)) planes. (b) The density of the solar wind protons in the equatorial plane at \(z = 0\). The black arrows show the solar wind bulk velocity. (c) The \(B_{y}\) component of the magnetic field in the equatorial plane at \(z = 0\); (d, e) The velocity distribution function of H+ ions measured on the point P1 shown in panel (b). In (d) the 3D velocity distribution function is projected on the \(V_{x}\)-\(V_{y}\) plane and in (e) on the \(V_{x}\)-\(V_{z}\) plane. The white arrow shows the direction of the average magnetic field vector. (Jarvinen et al. 2019)

However, some phenomena seen at the Earth’s foreshock may not correspond to Mercury’s foreshock for several reasons. First, Mercury does not have an ionosphere through which magnetospheric currents can close. The electric current can, however, close through planetary interior provided that the conductivity of the planet is large enough (Janhunen and Kallio 2004). Second, Mercury’s intrinsic magnetic field is weak, only about 190 nT at the magnetic equator (Anderson et al. 2011; Hauck et al. 2013), compared with the IMF so that part of the planetary surface is continuously magnetically connected to the solar wind (Kallio and Janhunen 2003). Therefore, the Hermean magnetosphere is a “pocket size magnetosphere” and consequently, also the time scales of plasma physical processes are smaller than in the Earth’s magnetosphere. Third, the plasma parameters at Mercury’s orbit at 0.31-0.47 AU differs considerably from plasma parameters at the Earth distance. Especially, the average Parker spiral angle is much smaller at Mercury than at Earth resulting in different parallel-perpendicular bow shock conditions at Mercury compared with the Earth’s bow shock.

b) Two-dimensional “global” Hybrid-Vlasov simulations (Vlasov ions and fluid electrons) performed by Kempf et al. (2015) reproduce the well known foreshock ion distributions very well and have been compared with observations from the THEMIS mission. The simulations reproduce two important features: (a) the decrease of the backstreaming beam speed with increasing radial distance from the edge of the foreshock, and (b) beam speed increases and density decreases with increasing radial distance from the bow shock. More precisely, FAB and ring beam are seen at the upstream edge of the foreshock; in contrast, deeper within the foreshock (further from the edge of the foreshock) intermediate distributions dominate which eventually get disrupted by ULF waves to become gyrophase-bunched distributions. This supports the scenario proposed by Meziane et al. (2001), in which the foreshock waves are the consequences of the ion beam activity generated by backstreaming ion populations and the GPB ion distributions associated with strong ULF waves result from beam disruption by the waves. Figure 29 summarizes the locations of the different ion distributions in the ion foreshock in results from the 2D Hybrid-Vlasov simulations (Kempf et al. 2015).

Fig. 29
figure 29

Central plot represents the ion number density in the ion foreshock and magnetosheath regions of the global 2D Hybrid Vlasov simulations; Color code (not shown here) extends from low (blue: 6.50 e+04) to high (red: 5.50 e+06) values of the ion number density. Black line represents the ion foreshock edge upstream of which there is only Maxwellian distribution of solar wind ions; this edge starts in the Q shock region at angle lower than 90 from the front (not to be confused with the location of the electron foreshock edge excluded in this simulation). White plus signs and letters A-I represent the location of the ion distribution functions which are shown outside the central plot following: A for FAB; B for ring beam; C for diffuse distribution; D for intermediate; E for partial ring beam; F for multicap distribution; G for lightly disturbed cap; H for strongly disturbed cap; I for spiral distribution respectively. Coordinates XGSE-YGSE plane are scaled in Earth radii (\(R_{\mathrm{{E}}}\)). (Inspired from results of Kempf et al. (2015))

c) Two-dimensional “global” PIC simulations (fully kinetic ions and electrons) of the curved shock and associated ion foreshock region have been performed by Savoini et al. (2013) and Savoini and Lembège (2015). Because of computational constraints, the analyses were restricted to the Q region (\(90^{ \circ } > \Theta _{Bn} > 45^{\circ }\)). These studies concentrated on GPB and FAB ion distributions observed near the front as ULF waves did not have time to reach substantial amplitudes. Both populations have been identified as occurring self-consistently and spatial mapping of local FAB and GPB distribution functions show that these can be observed simultaneously. One striking feature is that these distributions result only from their interaction with the macroscopic fields at the front; no waves or instabilities are necessary. Both statistical study and time trajectory analysis have shown that these populations can be differentiated from each other solely by the time spent within the shock front, from a short time (involving Fermi type acceleration) to a long time (with a mechanism still under investigation). The access to these different time ranges depends primarily on the so-called “injection angle” defined between the ion gyrating velocity vector and the local shock normal at the time the ion hits the front; no specific initial conditions need to be satisfied for the incoming solar wind ions in terms of energy, velocity distributions or pitch angle. In addition, these studies show that the nonstationarity of the shock front may have a strong impact on the backstreaming particles, since incoming particles will see different shock profiles when they strike the front and during their interaction time (short or long) with the front (Fig. 30).

Fig. 30
figure 30

Schematic diagram of the scenario of processes involved in the formation of the quasi-perpendicular ion foreshock (from Savoini and Lembège 2015)

Recently, Savoini and Lembège (2020) have analyzed more deeply the formation processes of backstreaming ions into the upstream ion foreshock after interacting with a quasi-perpendicular curved front by using two different approaches of test particle simulations: (i) a fully consistent expansion (FCE) of the front which includes all self-consistent shock profiles at different times (time dependence included), and (ii) an homothetic expansion (HE) model where shock profiles are chosen at certain fixed times and are artificially expanded in space (time dependence excluded); in both cases, the shock profiles are issued from a previous full 2D-PIC simulation. For each case, particles have been released from different boxes initially located along the curved front within the shock angular range (\(90^{\circ } > \Theta _{Bn} > 45^{\circ }\)) in order to determine the impact of the front curvature. These combined approaches have allowed to analyze the origin and formation of backstreaming ions under angular and/or temporal dependences separately. Main results show that the formation of ion foreshock is not a continuous process but is time dependent which leads to bursty emissions of backstreaming ions. Moreover, four different processes contribute to the formation of backstreaming ions: (i) the electrostatic \(E_{l}\) field component which has a strong impact particularly for high \(\Theta _{Bn}\) angles (i.e. when approaching the edge of the ion foreshock), (ii) the magnetic field B (via the magnetic mirror reflection) whose impact is particularly relevant for lower \(\Theta _{Bn}\), (iii) the \(E_{t} \times B\) drift in the velocity space mainly supported by the convective \(E_{t}\) electric field which is necessary to generate both FAB and GPB populations (Savoini and Lembège 2015), and (iv) a comparison of results obtained between the simulations indicates that fields’ time variations (FCE case) are much more efficient at diffusing particles than the fields’ spatial variations (HE case). A deep impact of shock front non-stationarity is more difficult to analyze for two reasons: a) the time-of-flight effects mix reflected ions issued from different shock profiles (met at different times and at different locations of the curved front); (b) some shock profiles have been shown to be more efficient than others (in time) for reflecting ions, but the differences of their respective impacts rapidly disappear since they are being blurred out by the impact of less efficient profiles on particles as time evolves.

At last, by using 2D large scale PIC simulations, the electron foreshock has been analyzed self consistently by Savoini and Lembège (2001) who recovered local electron distribution functions and velocity space in good agreement with local experimental observations (Feldman et al. 1983; Fitzenreiter et al. 1990). Basically, three different types of electron distributions have been identified according to their penetration depth within the front (Savoini and Lembege 2010): (i) the “magnetic mirrored” ones which only suffer one specular reflection at the front; (ii) the “trapped” ones which suffer a local trapping within the parallel electrostatic potential at the overshoot, and (iii) the “leaked” electrons which penetrate even more deeply into the downstream region before being reinjected back upstream. The low energy part electrons (i) are characterized by a loss cone distribution (and a ring in the perpendicular velocity space), while the high energy part electrons ((ii) and (iii)) contribute to the bump-in-tail part of the electron distribution (Fig. 31).

Fig. 31
figure 31

Local electron perpendicular momenta space of backstreaming electrons selected with low parallel kinetic energy only, represented respectively within each sampling box labelled from 0 to 24. For reference, the left-hand top panel illustrates locations of the curved shock front, of the backstreaming electrons, and of the sampling boxes within the simulation plane; the foreshock edge is indicated by the projected magnetic field line tangent to the curved front (dashed line). (From Savoini and Lembège 2001, Fig. 9b)

In summary, “global” hybrid simulations allow us (i) to cover the full range of ion foreshock shock normal angles and up to large distances from the shock front, but exclude consideration of the electron foreshock and (ii) to analyze any ion wave activity, but (iii) are often restricted by the limited spatial resolution which impacts shock front and upstream wave steepening (and in return local ion interactions). By contrast, current “global” 2D PIC simulations are restricted to short distances from the shock front (a few Earth radii only) and to Q shocks at present time. As a consequence, they predicted no ion wave activity and as yet unstudied electron wave activity, but did (i) reproduce the spatial ranges and kinetic features of both the ion and electron foreshocks (for both statistical and time trajectory analysis), (ii) provide access to shock front scale sizes smaller than those associated with ions (in particular the shock ramp and/or steepened precursor) which can affect particle acceleration processes at the front, and (iii) include some nonstationary processes of the front self-consistently (see review by Lembege et al. (2004)) on spatial scales smaller than those associated with ions which can also impact local acceleration processes. Consequently, hybrid and PIC simulations play complementary roles. As a final reminder, one must keep in mind that backstreaming particles represent only a small percentage of incoming solar wind particles, and a significant number of particles are needed to obtain satisfactory results for backstreaming populations within the foreshock.

2.6 Magnetosheath Transients

The bow shock may be considered as both an energy converter (transforming the bulk motion of the upstream solar wind plasma into heated plasma in the downstream region) and a source of energetic particle acceleration in upstream region. But, signatures of energy conversion are very different between Q and Q\(_{\parallel }\) regions. For Q region, a large part of incoming plasma is directly transferred to downstream region while a certain percentage is reflected by the shock front. Depending on the angle between the shock normal and the upstream IMF, reflected ions suffer one large gyromotion under the magnetic field before penetrating the downstream region (for a \({\Theta _{Bn}}=90^{\circ }\) shock) or suffer a distorted gyromotion and a part of reflected ions flows back upstream along the magnetic field (as \(\Theta _{Bn}\) departs from 90). Then, different instabilities can take place in downstream region which have been analyzed by different authors: (i) relaxation of the ion ring formed by the gyrating ions, (ii) strong temperature anisotropy driven instabilities (so called the mirror-type instability and the Alfvén ion cyclotron instability) since ions suffer an important perpendicular heating at the front and downstream, which results in a noticeable temperature anisotropy (Winske and Quest 1988; Shoji et al. 2009).

The situation strongly differs for Q\(_{\parallel }\) shocks which are much less quiet than Q shocks. Surprisingly, some filamentary structures have been identified (under different labels within the last two decades) in experimental results. It was effectively a surprise, since these structures are mainly observed in the downstream of Q\(_{\parallel }\) shock, have an apparent well coherent structure and have been shown to persist far downstream in the magnetosheath. These structures have been well retrieved in simulations and have stimulated many efforts (still in course) in a detailed comparison between experimental/numerical simulation analyses.

In addition to these transients inherent to the dynamics of the shock front itself, some structures/transients are directly carried by the solar wind itself, interact with the shock front, and succeed to penetrate the magnetosheath. The sections below illustrate the diversity of these transients. The present main goal is to reach a synthetic view and to evidence that many of these are related to each other.

2.6.1 Magnetosheath Jets/Magnetosheath Filamentary Structures

Two decades ago, observations from Interball-1 and Magion-4 satellites (Němeček et al. 1998) have evidenced the presence of “enhanced structures” more precisely of “transient flux enhancements” in dynamic pressure within the downstream region of Q\(_{\parallel }\) shocks; these structures are typically caused by increases in plasma velocity. Similar structures have also been identified by Savin et al. (2008) with Interball-1 and Cluster satellites, which have been named “high kinetic energy jets” and later “high speed jets”, “HSJs”, or “magnetosheath jets”. Later on, statistical studies have identified more clearly the main features of magnetosheath jets: (a) magnetosheath jets are defined as intervals when the plasma dynamic pressure along the anti-sunward direction in the subsolar magnetosheath is greater than half of the upstream solar wind value; (b) relative to the ambient magnetosheath, magnetosheath jets exhibit some enhancements of both density and magnetic field intensity but lower and more isotropic temperatures; (c) magnetosheath jets occur predominantly downstream of Q\(_{ \parallel }\) shocks (i.e. when IMF cone angles are low), but jet occurrence is only very weakly dependent on other upstream plasma conditions or solar wind variability; (d) typical duration and recurrence times are from a few seconds to several minutes or have a spatial scale less (or sometimes higher) than one \(R_{\mathrm{{E}}}\) (Archer et al. 2012; Hietala et al. 2012; Plaschke et al. 2013); and (e) magnetosheath jets are almost always super-Alfvénic and often even super magnetosonic. Consequently, magnetosheath jets are likely to have important effects on the magnetosphere and ionosphere if these impinge on the magnetopause. Based on Cluster observations, Hietala et al. (2012) have shown that magnetosheath jets with very high dynamic pressure can perturb the local magnetopause; during the interval of jet observations, irregular pulsations were observed at the geostationary orbit and localized flow enhancements were detected in the ionosphere, suggesting that magnetosheath jets can cause inner magnetospheric phenomena (see Sect. 3.3).

Different scenarios have been proposed in order to identify the source mechanisms of these magnetosheath jets: (i) early works of Němeček et al. (1998) and later Savin et al. (2008) did not identify a clear source mechanism for the magnetosheath jets but only invoke a local reconnection process; (ii) Lin et al. (1996a,b) have analyzed the interaction of the bow shock with an RD moving in the IMF by using hybrid and magnetohydrodynamic models; (iii) Savin et al. (2004, 2008, 2012) have proposed that HFAs may locally trigger magnetosheath jets by keeping the local flux balance due to the bow shock deformation by HFAs; (iv) based on Cluster experimental observations, Hietala et al. (2009, 2012) have proposed a scenario in which magnetosheath jets are due to local ripples inherent to a quasi-parallel shock (which cause the local curvature variations in the shock front) combined with the nonstationarity of the shock front. This scenario invokes the presence of a secondary shock as a super-fast-magnetosonic jet encounters the magnetopause; then, the jet is not decelerated (or very weakly) but only deviated by this secondary shock provided that the local angle between the upstream bulk velocity and local shock normal is large (due to the local large scale front rippling). Through a quantitative comparison study between magnetosheath jets and quasi-parallel bow shock ripples, Hietala and Plaschke (2013) concluded that 97% of the observed jets can be generated by local ripples.

A very detailed analysis of the internal structure of a special leading “jet” has been recently performed by Plaschke et al. (2017) based on observations made by the MMS mission, which reveal large amplitude density, temperature and magnetic field variations inside the jet, over small scale/short periods of time. These structures mainly convect with the jet plasma; the leading jet is the strongest and exhibits the largest dynamic pressure. Then, during an interval when repeated jets were observed, the plasma velocity varies significantly including sunward plasma flows in the subsolar magnetosheath: in other words, within the jet, structures propagate forward in the jet’s core region and backward outside of that region. Unfortunately, due to the short interdistance between the MMS spacecraft, it was not possible to confirm that the sunward flows were caused by the nearby passage of magnetosheath jets. Recent statistical work of Plaschke and Hietala (2018) based on 662 events observed by two THEMIS satellites (one observing the jet, the other one providing observations of nearby plasma to uncover the flow patterns in and around the magnetosheath jet), has clarified this point: (a) along the jet’s path, slower plasma is accelerated and pushed aside ahead of the fastest core jet plasma; (b) behind the jet core, plasma flows into the path to fill in the wake. This plasma motion affects the ambient magnetosheath close to the jet’s path. Diverging and converging plasma flows ahead and behind the jet are complemented by plasma flows opposite to the jet’s propagation direction in the vicinity of the jet. In the frame of reference of the background magnetosheath flow, the plasma clearly performs a vortical motion. This vortical motion leads to a deceleration of the ambient plasma when a jet passes by.

All these observations have strongly stimulated numerical works in terms of global and local simulations. Global 2D hybrid simulations of Karimabadi et al. (2014) have observed downstream structures similar to magnetosheath jets and indicated that it is possible to form a bow wave/shock ahead of a super-fast-magnetosonic magnetosheath jet during its propagation deeper into the magnetosheath with a typical Mach number \(M_{\mathrm{{A}}}=\) 8, to be compared with the experimental conditions (\(M_{\mathrm{{A}}}=\) 12) of Hietala et al. (2009, 2012). Other global 2D hybrid simulations (Omidi et al. 2014a) have focussed on the main features of downstream filamentary structures and shown that these form over a wide range of solar wind \(M_{\mathrm{{A}}}\) and IMF cone angles. The formation of these structures is connected to the existence of localized regions with increased ion temperature at and upstream of the Q\(_{ \parallel }\) shock. Upon injection of these energetic ions into the downstream region, they follow the field line and the enhanced pressure in flux tubes containing the shock accelerated ions depletes the thermal plasma in these flux tubes and enhances density in the surrounding flux tubes without energetic ions. As a consequence, an anticorrelation is observed between plasma density and ion temperature within the filamentary structures.

Recent THEMIS observations identify that when a magnetosheath jet is super-fast-magnetosonic relative to the ambient magnetosheath flow, a bow wave forms ahead of it (Liu et al. 2019b) consistent with simulations by Karimabadi et al. (2014). Case studies show that ions/electrons are accelerated at magnetosheath jet-driven bow waves likely through grad-B drift along/against the convection electric field (Liu et al. 2019b, 2020c). A statistical study by Liu et al. (2020b) shows that it is common for the bow waves to accelerate particles and large solar wind dynamic pressure, large Mach number, and large solar wind plasma beta favor the occurrence of the bow waves. These results suggest that under favorable upstream conditions, magnetosheath jets can contribute to particle acceleration, especially at high Mach number shocks. In Sect. 2.3.6, foreshock transients are shown to accelerate particles, which implies that nonlinear structures both upstream and downstream of shocks should be included in shock acceleration models (Fig. 32).

Fig. 32
figure 32

A sketch illustrating the presence of nonlinear transient structures, such as foreshock transients and magnetosheath jets, both upstream and downstream of the primary shock. They can form a secondary bow wave/shock which can accelerate particles and contribute to particle acceleration at the primary shock. HSJ holds for high speed jet. (From Liu et al. 2020b)

More recently, using 2D local hybrid simulations of a typical quasi-parallel shock where the angle between the normal to shock front and the IMF is \(\Theta _{Bn}=30^{\circ }\), Hao et al. (2016) have analyzed the link between the time dynamics of the shock front and the formation of the associated magnetosheath jets. As well known, the Q\(_{\parallel }\) shock front is strongly nonstationary. Some upstream nonlinear ULF waves structures/SLAMS form after the interaction of backstreaming ions and incoming ions and are convected back by the solar wind to the shock front; when interacting with the front, these structures contribute to both its strong spatial inhomogeneity (front rippling which generates strong local curvatures) and to its time nonstationarity (see Sect. 2.4.5). Simulations of Hao et al. (2016) clearly confirm the scenario of Hietala et al. (2009, 2012) and typical features/scales of magnetosheath jets observed experimentally (Fig. 33). However, some differences appear in the formation of the secondary shock. In Hao et al. (2016), since the upstream flow is lower at \(M_{\mathrm{{A}}}=\)5.5, a secondary shock forms shortly due to the pile-up of nonlinear upstream structures at the front; it is located just downstream of the main shock front and does not propagate deeply within the magnetosheath.

Fig. 33
figure 33

Comparison of the main signatures of one magnetosheath jet measured (1) in experimental observations of THEMIS (Plaschke et al. 2013) and (2) in 2D local hybrid simulations (Hao et al. 2016). From the top to bottom of Panel (1), (plots a to e): magnetic field and ion velocity measurements in GSE, ion density, ion energy flux density and dynamic pressure. (c) shows magnetosheath (MSH) measurements in black and the corresponding solar wind (SW) ion densities (nSW and 2⋅nSW) are shown in red and blue respectively. (e) shows the GSE \(x\) component dynamic pressure (P\(_{\mathrm{{d,msh,x}}}\)) in black; corresponding SW data (P\(_{ \mathrm{{d,sw}}}\), P\(_{\mathrm{{d,sw}}}/2\) and P\(_{\mathrm{{d,sw}}}/4\)) are shown in red, blue and green. From the top to bottom of Panel 2 (plots i to vi): spatial profiles of magnetic field and ion velocity measurements, kinetic energy, ion temperatures, ion density, and \(x\) component (solar wind direction) of the dynamic pressure. Caution: the \(x\) axis is respectively the UT in Panel (1), and the distance X normalized with respect to the ion inertial length (\(c/\omega _{pi}\)) in Panel (2)

All scenarios (i) to (iii) of magnetosheath jets formation summarized above require the presence of an external structure carried by the solar wind and interacting with the bow shock to generate magnetosheath jets. In contrast, one striking feature of the last scenario (iv) (Hietala et al. 2009, 2012), confirmed by hybrid simulations of Karimabadi et al. (2014) and Hao et al. (2016), is that the front of quasi-parallel shock which is strongly inhomogeneous and nonstationary, succeeds to generate self-consistently well coherent and structured flows persisting downstream even if their occurrence can take place anywhere within the Q\(_{\parallel }\) shock domain. The generation of these magnetosheath jets does not need any “external” upstream pressure fluctuations/discontinuities in the solar wind.

2.6.2 Mirror Mode/Magnetic Holes/Peaks in the Magnetosheath

Magnetic holes, also termed magnetic cavities, magnetic dips, or depression structures, have an observable magnetic field decrease in a short time span and have been widely observed in the solar wind plasmas (e.g., Turner et al. 1977; Winterhalter et al. 1994; Zhang et al. 2008; Xiao et al. 2010, 2011, 2014), comet magnetospheres (Russell et al. 1987; Plaschke et al. 2018b), terrestrial/planetary magnetosheaths (e.g., Tsurutani et al. 1982; Bavassano Cattaneo et al. 1998; Joy et al. 2006; Lucek et al. 1999; Balikhin et al. 2003, 2009; Walker et al. 2002, 2004; Soucek et al. 2008), magnetospheric cusps (Shi et al. 2009), and the magnetotail (Ge et al. 2011; Sun et al. 2012) since 1970s. Here we mainly focus on linear magnetic holes across which the magnetic field direction does not change significantly. Magnetic peaks, which are sudden enhancements of magnetic strength, are often observed in the magnetosheath of Earth and other planets. Magnetic peaks observed in the magnetosheath are often flux ropes (see Sect. 3.2) or magnetic mirror mode structures.

Magnetic mirror mode structures or mirror waves include both magnetic holes and magnetic peaks. In the downstream of the Q bow shock, ions are mainly heated in the perpendicular direction, creating an anisotropy in the ion temperature with \(T_{\perp }>T_{\parallel }\). In this region, the mirror instability can be easily excited, generating mirror mode structures. The threshold of mirror instability in a proton-electron plasma with cold electrons (Hasegawa 1969; Southwood and Kivelson 1993) can be written as

$$ R>\frac{T_{\perp }/T_{\parallel }}{1+1/\beta _{\perp }} $$

where \(\beta \), \(T_{\perp }\) and \(T_{\parallel }\) denote the plasma beta, perpendicular and parallel ion temperature, respectively. If this condition is satisfied, non-propagating (in the plasma frame) quasi-sinusoidal compressional waves grow in the linear stage of the mirror instability. This is consistent with some of the structures observed in the magnetosheath, which are usually characterized by a series of magnetic holes (dips and troughs) and peaks (humps). Embedded in the ambient plasma flow, these structures exhibit anti-correlated magnetic field strength and plasma density (e.g., Horbury et al. 2004; Soucek et al. 2008; Yao et al. 2019b), i.e., they are non-propagating and pressure balanced. Generation of magnetic holes by the mirror instability in high \(\beta \) anisotropic magnetosheath plasmas was first proposed by Kaufmann et al. (1970). This explanation was later applied to magnetic holes in the solar wind (Tsurutani et al. 1982; Winterhalter et al. 1994; Stevens and Kasper 2007).

However, isolated structures observed by satellites in space plasmas often appear as large amplitude magnetic dips or peaks in the magnetosheath where the mirror instability condition described by linear instability theory (Bavassano Cattaneo et al. 1998; Soucek et al. 2008; Génot et al. 2009) is far from satisfied. The mirror instability in the nonlinear stage is likely the source of these structures. These nonlinear effects during this later stage were described theoretically using kinetic approaches (Kivelson and Southwood 1996; Kuznetsov et al. 2007; Pokhotelov et al. 2005, 2008). Numerical simulations suggested that the large-amplitude structures can be stable enough to survive for an extended period of time under mirror stable conditions (Baumgärtel et al. 2003; Califano et al. 2008). Detailed analysis by Balikhin et al. (2009) using THEMIS data showed that the plasma inside magnetic mirror holes is unstable to the linear mirror instability although the ambient plasma is mirror-stable. This observation has been predicted by Pokhotelov et al. (2008) using the nonlinear theory, in which the mirror structures can be stabilized by ions trapped inside them. After tracing the evolution of mirror modes in Saturn’s magnetosheath, Bavassano Cattaneo et al. (1998) found that mirror structures evolve from quasi-sinusoidal waves to non-periodic structures in the form of magnetic peaks and dips, as they propagate from the Q shock to the magnetopause, and finally become dips when close to the magnetopause (Fig. 34). Similar trends were found in the magnetosheath of Jupiter (Joy et al. 2006) and Earth (Soucek et al. 2008; Génot et al. 2009). The nonlinear magnetic peaks and dips and their relationship with the nonlinear stage of the mirror instability are still areas of active research.

Fig. 34
figure 34

Cluster observation of magnetic peaks (upper panel) and holes (lower panel) in the magnetosheath which were interpreted as mirror mode structures by Soucek et al. (2008)

Magnetic peaks and holes have also been interpreted as solitary waves, with bright solitons corresponding to magnetic peaks and dark solitons corresponding to magnetic holes. A soliton model based on the Hall-MHD theory was proposed and tested using hybrid simulations (Baumgärtel 1999; Baumgärtel et al. 2003). This model was used to explain some structures observed in the magnetosheath (Stasiewicz 2004a,b). One of the main differences between the mirror mode mechanism and the soliton approximation in observation is that the mirror mode-produced magnetic holes are frozen in the background plasma, while the solitons can propagate in the plasma. Examinations of more magnetic structures detected by four MMS spacecraft are needed to determine their generation mechanisms.

Particle behaviors in the nonlinear stage of the mirror mode were investigated by Kivelson and Southwood (1996). They pointed out that, during the formation of the mirror mode structure, the trapped ions lose or gain energy by Fermi deceleration or acceleration, respectively. The deeply trapped particles are further decelerated by the betatron mechanism when the magnetic troughs get deeper (e.g., Konjukov and Terietskij 1958; Liu et al. 2017c; Northrop 1963). As a result, particles are decelerated at close to \(90^{\circ }\) pitch angles and accelerated at intermediate pitch angles. Chisham et al. (1998) studied the behaviors of the mirror-mode electron distribution in the terrestrial magnetosheath and showed that the deeply trapped electrons are cooled and the shallowly trapped electrons are heated with respect to the rest of the electron velocity distributions. Using high-resolution data from the MMS mission, Yao et al. (2018b) found that most electrons are trapped inside the mirror-mode troughs and exhibit donut-shaped pitch angle distributions (Fig. 35). They demonstrated that donut-shaped distributions are due to betatron deceleration and the spatial dependence of electron pitch angle distributions in these structures. The characteristic donut-shaped distribution of electrons is considered to be related to whistler waves by Ahmadi et al. (2018).

Fig. 35
figure 35

Electron pitch angle distributions from MMS1. (a) Magnetic field strength. The three horizontal gray lines mark the maximum, mean, and minimum magnetic field strength in the interval. (b-g) Electron pitch angle distributions. The black lines represent the local cones. (h-k) The zoom-in pitch angle spectra of 52 eV electrons with magnetic field strength on the top. The black solid and dashed lines indicate the local cones determined from the mean and maximum magnetic field strength, respectively. (From Yao et al. 2018b)

Before MMS, the mirror mode/magnetic dip/peak structures observed in the magnetosheath are on the MHD scale, from tens to thousands of proton gyroradius, corresponding to temporal scales of seconds to tens of minutes. Yao et al. (2018a) reported an electron scale magnetic peak observed by MMS in the Earth’s magnetosheath, with a scale of ∼7 electron gyroradii and a duration of ∼0.18 s (Fig. 36). An electron vortex is found in the plane perpendicular to the magnetic field line and is self-consistent with the magnetic peak. A technique was developed to distinguish flux ropes and mirror mode peaks which both have bipolar magnetic signatures. The analysis result shows that this small scale magnetic peak is not a flux rope which generally has a toroidal bipolar magnetic field in the plane perpendicular to the rope axis, but rather a magnetic bottle like structure which has a radial bipolar magnetic field in the plane perpendicular to the bottle axis. The mechanism generating the electron scale magnetic bottle like structure is still unclear (e.g., Treumann and Baumjohann 2018; Yao et al. 2019a) and new theories need to be developed to understand such small-scale phenomena.

Fig. 36
figure 36

A kinetic scale magnetic peak observed by MMS in the magnetosheath. (a, b) Ion and electron differential energy fluxes (c) Magnetic field strength and components in GSE coordinates (d) Ion and electron number density (e) Ion and electron bulk velocity (f) Magneticfield magnitude of MMS1-MMS4. MMS1 observations of magneticfield and plasma data. (g) Magneticfield strength and components in GSE coordinates (h) Ion and electron number density (i, j) Ion and electron bulk flow velocity in the in GSE coordinates (k, l) Ion and electron temperature (m-q) Magnetic field and ion and electron bulk flow velocity in LMN coordinates. (From Yao et al. 2018a)

Yao et al. (2017) presented a series of kinetic scale magnetic holes (KSMHs) observed by MMS in the magnetosheath, which exhibit diamagnetic electron vortices in the plane perpendicular to the magnetic field (see also Huang et al. 2017). The scale size of KSMHs is tens of electron gyroradii, similar to that of magnetic peaks. Liu et al. (2019c) reported a KSMH (which they called a magnetic cavity) embedded in a larger scale magnetic hole (Fig. 37). Using particle sounding technique on the KSMH, they found that it has a circular cross section and is a magnetic bottle in 3D.

Fig. 37
figure 37

(Left) Cross-section of the electron scale magnetic cavity obtained using the sounding technique. (Right) The electron scale magnetic cavity is embedded in a proton scale magnetic cavity. (From Liu et al. 2019c)

KSMHs have been observed not only in the magnetosheath but also in the plasma sheet (Ge et al. 2011; Gershman et al. 2016; Sun et al. 2012; Sundberg et al. 2015; Yao et al. 2016; Zhang et al. 2017). KSMHs in the plasma sheet also have a spatial scale similar to that of magnetic peaks. Additionally, KSMHs in the plasma sheet have properties similar to that of magnetic peaks, i.e., electron vortices (Gershman et al. 2016; Zhang et al. 2017) and propagation relative to the plasma flow (Yao et al. 2016). Therefore, magnetic peaks and KSMHs could be physically related structures. Using a PIC simulation, Haynes et al. (2015) reported KSMHs within decaying turbulence showing an azimuthal diamagnetic current associated with the magnetic field depression. An Electron MagnetoHydroDynamics (EMHD) model of the slow-mode soliton has been developed to explain the formation of KSMHs (Ji et al. 2014; Li et al. 2016b), and the observed amplitude, size, and propagation velocity agree well with the theory of EMHD solitons (Yao et al. 2017). A detailed comparison among theories, simulations, and satellite observations is required to fully understand the physics of KSMHs.

Such small structures have been found to contain a rich set of exciting physical processes, including different kinds of ion and electron distributions, electron or ion vortices, various types of waves, and even particle acceleration and declaration. For example, Yao et al. (2017) found that the flux of lower energy particles decreases in the center of the structure while the higher energy particle flux increases, indicating a non-adiabatic behavior. Liu et al. (2020f) found that these structures can shrink due to increases in the surrounding magnetic field strength and this shrinkage can induce an electric field. They suggested that this non-adiabatic behavior of the particles is related to the shrinking of the structure while propagating to the magnetopause where the magnetic pressure is higher. Qualitatively distinct from adiabatic acceleration mechanisms (e.g., betatron and Fermi acceleration), this process indicates a new type of non-adiabatic acceleration, and has been confirmed by the observed electron distributions and test particle simulations (Liu et al. 2020f). This discovery in space physics also has implications for understanding energy conversion in astrophysical plasmas, the origin of cosmic high-energy particles, and plasma turbulence. Large scale mirror mode structures in the magnetosheath often contain intense bursts of narrow-band whistler mode waves with a center frequency of ∼100 Hz, called “lion roar” (Smith et al. 1969; Smith and Tsurutani 1976; Giagkiozis et al. 2018), which are characteristic high-frequency waves in the magnetosheath. The growth of whistler waves generated in mirror mode structures was examined by PIC simulations (Ahmadi et al. 2016) and was further compared with MMS observations (Ahmadi et al. 2018). On kinetic scales, Yao et al. (2019b) presented observations of whistler mode waves, electrostatic solitary waves, and electron cyclotron waves inside KSMHs in the magnetosheath (Fig. 38). They suggested that the free energy to excite these waves comes from electron temperature anisotropy or beams in KSMH structures. Additionally, a higher wave occurrence rate at the center of the magnetic dips than at their edges indicates that these waves may originate from KSMHs. These observations suggest that electron scale magnetic peaks (Stawarz et al. 2018; Yao et al. 2020a) and KSMHs (Yao et al. 2019b, 2020b; Liu et al. 2020f) may play important roles in transporting particles and dissipating energy in turbulent plasmas.

Fig. 38
figure 38

Three type of waves in kinetic scale magnetic holes in the magnetosheath. (a) Magnetic field strength (b, c) Power spectral densities of the electric and magnetic fields overplotted with the electron cyclotron frequency (solid line) and ion plasma frequency (dashed line) (d) Wave normal angle (e) Magnetic field in field-aligned coordinates and their hodograph during the time interval marked by two vertical dashed lines in above panels. BP1 and BP2 are the magnetic field in two perpendicular directions. (f-h) Same as (a-c) (i, j) Parallel electric field and an expanded view of the parallel electric field (k-m) Same as (a-c). The black solid lines in (m) indicate the electron cyclotron frequency and 3 times of the electron cyclotron frequency. The black dash line is the ion plasma frequency. (n) Parallel electric field (o) Hodographs of the electric field (From Yao et al. 2019b)

2.7 Transient Processes in the Foreshock, Bow Shock, and Magnetosheath at Other Planets

The transient phenomena discussed in the previous sections were discovered at the terrestrial bow shock, and some of them have also been observed at other planets. Table 4 summarizes the transient phenomena observed at various solar system bodies. Based on our current understanding of the formation mechanisms of these phenomena, we expect them to exist at all planets. ULF waves have been observed at Mercury (Russell 1989), Venus (Greenstadt 1986; Orlowski et al. 1995), Mars (Delva and Dubinin 1998), Jupiter (Khurana and Kivelson 1989), Saturn (Orlowski et al. 1995), comets Halley and Giacobini-Zinner (Le et al. 1989). SLAMS have been detected at Venus (Collinson et al. 2012b), Jupiter (Tsurutani et al. 1993), and comet Giacobini-Zinner (Tsurutani et al. 1993). Despite the known physical processes and the easy identification of these events, many fields in the rows of Table 4 for SLAMS, ULF waves, and mirror mode structures are still empty.

Table 4 Transient phenomena observed at various solar system bodies. “+”: observed phenomenon

As mentioned in Sect. 2.3.1, HFAs have been observed at all planets in the solar system. Signatures of SHFAs have been recorded at Venus, Mars, and Saturn. It is important to note that these phenomena were observed at the bow shock of both magnetized and unmagnetized planets. Hence, these phenomena are universal. We expect the other transient events to be universal phenomena as well. Furthermore, the foreshock ULF waves, SLAMS, foreshock cavitons, and SHFAs are related phenomena (Schwartz and Burgess 1991; Kajdič et al. 2011; Omidi et al. 2013b). The foreshock ULF waves have been observed at all planets in the solar system. Hence, we expect the related events to exist at other planets too. Despite this expectation, there is no observation of density holes, foreshock bubbles, transient, local ion foreshock, foreshock cavitons, or foreshock compressional boundaries at other planets yet (Table 4). Fortunately, simulations can help to predict the occurrence pattern and properties of these structures at other planets. For example, Omidi et al. (2017b) performed hybrid simulations of the solar wind-Venus interaction and theoretically predicted the occurre