Understanding the Internal Magnetic Field Configurations of ICMEs Using More than 20 Years of Wind Observations

Abstract

The magnetic topology, structure, and geometry of the magnetic obstacles embedded within interplanetary coronal mass ejections (ICMEs) are not yet fully and consistently described by in situ models and reconstruction techniques. The main goal of this work is to better understand the status of the internal magnetic field of ICMEs and to explore in situ signatures to identify clues to develop a more accurate and reliable in situ analytical models. We take advantage of more than 20 years of Wind observations of transients at 1 AU to compile a comprehensive database of ICMEs through three solar cycles, from 1995 to 2015. The catalog is publicly available at wind.gsfc.nasa.gov and is fully described in this article. We identify and collect the properties of 337 ICMEs, of which 298 show organized magnetic field signatures. To allow for departures from idealized magnetic configurations, we introduce the term “magnetic obstacle” (MO) to signify the possibility of more complex configurations. To quantify the asymmetry of the magnetic field strength profile within these events, we introduce the distortion parameter (DiP) and calculate the expansion velocity within the magnetic obstacle. Circular-cylindrical geometry is assumed when the magnetic field strength displays a symmetric profile. We perform a statistical study of these two parameters and find that only 35% of the events show symmetric magnetic profiles and a low enough expansion velocity to be compatible with the assumption of an idealized cylindrical static flux rope, and that 41% of the events do not show the expected relationship between expansion and magnetic field compression in the front, with the maximum magnetic field closer to the first encounter of the spacecraft with the magnetic obstacle; 18% show contractions (i.e. apparent negative expansion velocity), and 30% show magnetic field compression in the back. We derive an empirical relation between DiP and expansion velocity that is the first step toward improving reconstructions with possible applications to space weather studies. In summary, our main results demonstrate that the assumed correlation between expanding structure and asymmetric magnetic field is not always valid. Although 59% of the cases could be described by circular-cylindrical geometry, with or without expansion, the remaining cases show significant in situ signatures of departures from circular-cylindrical geometry. These results will aid in the development of more accurate in situ models to reconcile image.

Introduction

Coronal mass ejections (CMEs) are eruptions of magnetized plasma from the solar corona into the heliosphere, which are commonly observed via imaging instruments, such as white-light coronagraphs. Their interplanetary signatures, so-called interplanetary coronal mass ejections (ICMEs), are usually detected via in situ instrumentation with specific imprints on the observations. Sometimes, following an interplanetary shock, we observed a period of a magnetic field with low proton temperature that was stronger than the ambient field, a relatively quiet and smooth rotation of the magnetic field, a helium abundance enhancement, and/or bidirectional electrons. The in situ measured properties of ICMEs (Zurbuchen and Richardson, 2006; Jian et al., 2006) in interplanetary space do not necessarily reflect the initial solar conditions and/or magnetic field structure ejected at the Sun. ICMEs can change significantly because of their internal evolution and interaction with the ambient solar wind. The interplanetary (IP) evolution of CMEs is neither well observed nor well understood, thus challenging our understanding of their magnetic field topology and internal plasma structure at 1 AU. The challenge is compounded by the inconsistencies in reconstructing the ICME in three-dimensions (3D) among models based on in situ measurements (Riley et al., 2004; Al-Haddad et al., 2013; Janvier et al., 2015) and between these models and reconstruction from image-based observations (e.g. Wood et al., 2017).

Most in situ reconstruction techniques rely on the existence of an organized magnetic field topology within the ICME, which is assumed to be a magnetic flux rope configuration. The commonly used in situ term for this structure, “magnetic cloud”, follows a rather strict definition given by Burlaga et al. (1981) that reflects the in situ signatures of an idealized flux rope. However, the reality is different. The IP evolution likely distorts (e.g. Odstrcil and Pizzo, 1999; Lynnyk and Vandas, 2009; Nieves-Chinchilla et al., 2012; DeForest, Howard, and McComas, 2013) or even disrupts the CME internal magnetic structure (Lugaz et al., 2015), resulting in a complex heliospheric structure. The evolution may include interaction of successive CMEs (Gopalswamy et al., 2001; Lugaz et al., 2017) or erosion due to interaction with the ambient solar wind (Dasso et al., 2006; Ruffenach et al., 2012). To allow for such changes, we adopt a less restrictive term, “magnetic obstacle” (MO), to describe the magnetic structure embedded in an ICME. An ICME with an embedded MO follows the general criteria in Jian et al. (2006), but it is limited to the cases that contain a time period with low \(\beta_{\mathrm{p}}\) (ratio between proton thermal pressure and magnetic pressure). This period of time is called the MO, and in some cases, the magnetic field displays a smooth and monotonic change.

In terms of modeling, the MO enables exploration of different magnetic field configurations within ICMEs. For example, in the case of a monotonic \(180^{\circ}\) magnetic field rotation, an MO could consist of a single flux rope. However, in the case of more than \(180^{\circ}\) or more than a rotation, it could be considered as multiple flux ropes (Osherovich, Fainberg, and Webb, 2013), or spheromaks (Vandas et al., 1997). Detailed examples are discussed in Section 2.2.

In the best cases, MOs are well-ordered magnetic clouds (single flux ropes), and they can be readily modeled by a variety of techniques. In general, they are reconstructed by neglecting expansion or cross-section distortion. Lepping, Burlaga, and Jones (1990) developed the most commonly used in situ reconstruction technique. The magnetic structure is assumed to be a static axially symmetric cylinder, and thus it can be approximated by a linear force-free magnetic configuration (Lundquist, 1950; Burlaga, 1988). Following the same geometrical assumptions, but relaxing the force-free requirement, Hidalgo et al. (2000) derived a family of models that attempt to reproduce different physical and geometrical characteristics in the in situ data (Hidalgo, Nieves-Chinchilla, and Cid, 2002; Hidalgo and Nieves-Chinchilla, 2012; Nieves-Chinchilla et al., 2016). It is not yet understood whether any of these models are realistic enough to represent a heliospheric flux rope and if a single model could describe the observed variety of MO signatures.

Sometimes, in situ observations reveal significantly higher speeds in the MO front than in the back. This is usually interpreted as a signature of self-similar expansion (Jian et al., 2006; Dasso et al., 2007; Démoulin et al., 2008; Démoulin and Dasso, 2009; Gulisano et al., 2010; Rodriguez et al., 2016). However, sometimes the plasma speed profile does not decrease as the MO passes over the spacecraft. Gulisano et al. (2010, 2012) classified magnetic clouds as perturbed when the velocity profile displays a strongly distorted profile. In these cases, the deviation from the expected decreasing linear profile is ascribed by the authors to solar wind interactions.

Another common in situ observation within the MO is the magnetic field compression observed at its front. This asymmetry in the magnetic field strength with respect to the center of the MO is described in several dynamical models as radial and/or axial expansion, which introduces a correction to account for the structure evolution during spacecraft crossing (e.g. Farrugia et al., 1993; Osherovich, Farrugia, and Burlaga, 1993; Berdichevsky, Lepping, and Farrugia, 2003; Hidalgo, 2003; Wang et al., 2015). Other models interpret the asymmetry as evidence of a distorted flux rope cross-section (Hidalgo, Nieves-Chinchilla, and Cid, 2002; Berdichevsky, 2013) or as a signature of a non-cylindrical structure (Marubashi, 1997; Hidalgo and Nieves-Chinchilla, 2012).

In this article, we investigate the assumption that the magnetic field asymmetry is evidence of expansion and explore the possible origins of this asymmetry in magnetic field profiles within ICMEs at 1 AU. Our goal is to assess the information that such observations provide on the global magnetic morphology of ICMEs in order to improve the reliability of the reconstructions. We use a comprehensive catalog of ICMEs with entrained MOs over two solar cycles (1995 – 2015) observed by the Wind spacecraft (Lepping et al., 1995; Ogilvie et al., 1995). To facilitate the analysis, we introduce a new parameter that we call distortion parameter (DiP) to quantify the asymmetry in the magnetic field strength profile.

The article is organized as follows. Section 2 describes the Earth-directed ICME catalog observed by the Wind spacecraft. Section 3 discusses the distortion parameter (DiP). In Section 4 we analyze this parameter, compare it with magnetic field and plasma parameters, and discuss the results. We conclude in Section 5.

Earth-Directed ICMEs (1995 – 2015) Observed by Wind

The Wind mission has been providing in situ plasma, waves, energetic particle, and magnetic field observations since late 1994. Wind is one of a few spacecraft that have acquired data over three solar cycles (SCs); namely, the end of SC22 (November 1, 1994, to May 31, 1996), SC23 (June 1, 1996, to December 31, 2008) and most of SC24 (January 1, 2009, to the present). The SC boundaries have been selected based on the sunspot number. The continuous coverage from a single array of instruments provides researchers a unique opportunity for long-term studies without the burden of intercalibration with other spacecraft and instruments. One focus is the SC variation of ICMEs with embedded MOs in the near-Earth environment (e.g. Hundhausen et al., 1984; Lynch et al., 2003; Huttunen et al., 2005; Lepping and Wu, 2007; Richardson and Cane, 2010; Wu and Lepping, 2011; Kilpua et al., 2011; Dasso, Démoulin, and Gulisano, 2012; Mohamed et al., 2012; Gopalswamy et al., 2014; Wu and Lepping, 2015) and the geomagnetic response (Gopalswamy et al., 2005, 2015; Huttunen et al., 2005; Echer, Tsurutani, and Gonzalez, 2013).

We use the Wind archive to build a catalog of ICMEs with clear signatures of an organized magnetic structure, which are therefore prime candidates for 3D reconstruction modeling. The catalog builds on and expands upon previous catalogs (Lepping et al., 2011, 2015; Nieves-Chinchilla, Hidalgo, and Sequeiros, 2005; Jian et al., 2006; Kilpua et al., 2011; Richardson and Cane, 2010), publicly available lists (Lepping’s list: https://wind.gsfc.nasa.gov/mfi/mag_cloud_S1.html ; Richardson’s list: http://www.srl.caltech.edu/ACE/ASC/DATA/level3/icmetable2.htm ) and visual inspection. Table 1 shows the Earth-directed events observed by Wind in the period 1995 – 2015. The first column lists the events sorted by year. The ICME start time and the MO start time and duration (in hours) follow. The ICME start time is selected using the IP shock followed by the sheath, which consist of heliospheric plasma and magnetic field. This time is marked along with the increase in magnetic field and plasma parameters (proton density, temperature, and speed), or, in the case of no clear signatures, the ICME start time will coincide with the MO start time. The MOs are classified as flux rope(s) (F), when an ordered and monotonic change in the magnetic field is observed and ejecta (E) when no ordered topology is observed, i.e. no rotations or monotonic changes. In the F cases magnetic clouds, events with more than one flux rope, or more complex structures, as described in Section 2.1, are included. The online version provides, for each event, the mean magnetic field and solar wind bulk velocity within the MO interval. The apparent expansion velocity (in Table 1) is included for the F events and described in Section 2.1 below.

Table 1 Catalog of ICMEs observed by Wind from 1995 to 2015. Column: (1) event number; (2) year, (3) ICME – disturbance arrival time, (4) magnetic obstacle start time, (5) duration in decimal hours, (6) mean magnetic field strength, (7) mean magnetic obstacle speed, (8) mean proton density, (9) apparent expansion velocity, (10) distortion parameter (DiP), (11) kind of magnetic obstacle – F means contains flux rope, and E means no clear flux rope.

The online catalog ( http://wind.nasa.gov/ICMEindex.php ) provides a link for each event to a plot with the in situ observations: magnetic field magnitude, magnetic field components (in GSE, geocentric solar ecliptic coordinate system), proton number density, proton thermal speed, proton beta, solar bulk flow speed, and the electron pitch angle distribution parameter (EPP), for 116 and 290 eV electrons (the definition for EEPs can be found in Nieves-Chinchilla et al., 2016). Figures 1 – 5 exhibit examples of ICME events observed by Wind, where the vertical lines indicate the interval of the ICME front and the MO boundaries. The events are also linked to the Integrated Space Weather Analysis System (iSWA, iswa.gsfc.nasa.gov ) for an overview of the heliosphere during the expected transit of the CME to Earth.

Figure 1
figure1

(a) In situ data from the Magnetic Field Instrument (MFI) and the Solar Wind Experiment (SWE) instrument onboard the Wind spacecraft on October 18, 1995. From the top, the magnetic field magnitude and components in GSE coordinate system, proton plasma density, temperature (expressed as a thermal velocity), proton beta, the solar wind bulk velocity, and the electron pitch angle distribution (PAD) parameter (EPP) for 290 eV and 580 eV energy levels are shown. The vertical lines show the interval of the ICME front and MO boundaries. (b) Three combined magnetic hodograms in the GSE coordinate system.

The catalog contains 337 events, 298 of which exhibit a clear organized magnetic structure and plasma parameters. They are therefore good candidates for reconstruction. The remaining 39 events do not exhibit an ordered topology, and we excluded them from the rest of this study. Table 2 lists the statistics of the main parameters of the 298 F events. The average embedded magnetic field varies between 3 nT (August 30, 2012) and 36 nT (July 15, 2000), with an overall average of 11 nT. The solar wind speed varies from \(270~\mbox{km}\,\mbox{s}^{-1}\) (December 12, 2009) to \(962~\mbox{km}\,\mbox{s}^{-1}\) (July 26, 2004), with an overall average of \(434~\mbox{km}\,\mbox{s}^{-1}\).

Table 2 Maximum, minimum and average magnetic field (\(B\)), speed (\(V\)), expansion velocity (\(V_{\exp}\)) and distortion parameter (DiP) for the ICME events observed by Wind in the period 1995 – 2015.

Magnetic Obstacles vs. Magnetic Clouds

The full definition of a magnetic cloud includes (i) an increase in magnetic field, (ii) rotation of the magnetic field direction, and (iii) a decrease in proton plasma temperature (Klein and Burlaga, 1982). This definition is compatible with a flux rope (FR) magnetic configuration as a helical magnetic field wrapped around an axis. A typical example of a magnetic cloud is shown in Figure 1. The event, observed by Wind on October 18, 1995 (291), was initially reported by Lepping et al. (1997) and has been used in several studies, such as Burlaga et al. (1998). Figure 1a displays the magnetic field and proton plasma observations. The ICME extends from 10:40 UT on October 18, 1995 (291, vertical black line) to 02:23 UT on October 20 (293, second dashed line). The ICME period is marked with a horizontal black line at the top of the figure. The magnetic cloud (FR1), marked with a horizontal pink line at the top of the figure, is bounded by the two dashed lines (from 11:19 UT on October 18 to 2:23 UT on October 20) with an increase of the magnetic field strength (top panel) and the complete rotation of the \(B_{z}\) component (second panel from the top). The fourth panel from the top shows the depression in the proton plasma thermal speed in the same interval as the depression in the \(\beta_{\mathrm{p}}\). In the bottom panel, the electron pitch angle distribution parameter (EPP) (Nieves-Chinchilla et al., 2016) displays an increase in the electron intensity aligned with the magnetic field direction in both directions, showing bidirectional electrons at these two energy levels. At the bottom, Figure 1b displays the combined magnetic hodograms of pairs of GSE magnetic field components. Overplotted with a pink line is the hourly data average, and the start time is marked with a red dot. Following the pink line, the magnetic flux rope configuration is confirmed by a 180° rotation of the magnetic field vector in the \(z\) – \(y\) plane (see \(B_{z} - B_{y}\) hodogram).

Deviations from the signatures mentioned in the previous paragraph are known as complex ejecta (Burlaga, Plunkett, and St. Cyr, 2002) that are like a magnetic cloud or like flux-rope-like (Lepping, Wu, and Berdichevsky, 2005; Wu and Lepping, 2015; Gopalswamy et al., 2015). Complex ejecta structures are not identified at 1 AU as magnetic clouds or as corotating streams, and they can be associated with Earth-directed halo CMEs. According to the initial definition, they display irregular in situ signatures that are possibly due to the interaction of successive CMEs. The magnetic-cloud-like or flux-rope-like ejecta were used to denote structures that met some, but not all, of the rules of the magnetic cloud definition. For some authors, the absence of the flux rope signatures can be explained by the spacecraft encountering the MC far from the center, by magnetic flux erosion by reconnection at the front of the MO (e.g. Cane, Richardson, and Wibberenz, 1997; Dasso et al., 2007; Kilpua et al., 2011; Ruffenach et al., 2012), or by interacting CMEs leading to so-called “complex ejecta”. We have included these cases in the catalog and identified a period of time within the ICME where the magnetic pressure dominates the plasma pressure, i.e. low \(\beta_{\mathrm{p}}\). The cases are often reconstructed using flux rope reconstruction techniques. This is the case of the event displayed in Figure 2 and included in the reconstruction analysis by Lepping et al. (2006). The Wind magnetic field and plasma observations in the period between 12:50 UT on February 9 (40) and 18:28 UT on February 11 (42), 1997 (Figure 2), show an increase in magnetic field strength and a depression in proton temperature and \(\beta_{\mathrm{p}}\). The period is marked with a horizontal pink line at the top of the plot. However, no clear rotation in the magnetic field direction is observed in the hodogram, Figure 2b.

Figure 2
figure2

(a) In situ data from the Magnetic Field Instrument (MFI) and Solar Wind Experiment (SWE) instrument onboard the Wind spacecraft on February 10 (40), 1997. From the top, the magnetic field magnitude and components in the GSE coordinate system, proton plasma density, temperature (expressed as a thermal velocity), proton beta, the solar wind bulk velocity, and the electron PAD parameter (EPP) for 580 eV are shown. The vertical lines show the interval of the ICME front and MO boundaries. (b) Three combined magnetic hodograms in GSE coordinate system.

Figure 3 shows the case of an ICME included in Lepping’s list as a case of a single magnetic cloud. The event was the focus of a detailed study by Dasso et al. (2009) as a case of complex ejecta, although the in situ signatures qualify as a magnetic cloud. The event was proposed to be an example of two interacting ICMEs. Figure 3a shows Wind observations in the period May 14 – 17, 2005. The ICME starts at 02:10 UT on May 15, 2005 (horizontal black line at the top of the figure), and the MO extends from 05:31 UT to 22:47 UT on May 16, 2005. According to Richardson’s list, the event extends until 00:00 UT on May 19, 2005. In Figure 3a the two flux ropes reported by Dasso et al. (2009) are marked by dashed lines, and the extension is marked by pink and green horizontal lines at the top of the figure. Below them, with a red line, we show the period of the magnetic cloud reported in Lepping’s list. In Figure 3b the pink line is the hourly average of the data that corresponds to the first flux rope, and the green line is the hourly average of the second flux rope. The red points indicate the start time of each flux rope for all hodograms. The end of the first flux rope is linked with the beginning of the second flux rope as if it were a single flux rope. Therefore, an adequate reconstruction of the event may need an analysis of the CME counterpart at the solar corona.

Figure 3
figure3

(a) In situ data from the Magnetic Field Instrument (MFI) and Solar Wind Experiment (SWE) instrument onboard the Wind spacecraft on May 15 (135), 2005. From the top, the magnetic field magnitude and components in the GSE coordinate system, proton plasma density, temperature (expressed as a thermal velocity), proton beta, the solar wind bulk velocity, and the electron PAD parameter (EPP) for 116 and 290 eV energy levels are shown. The vertical lines show the interval of the ICME front and MO boundaries (see text for a complete explanation). (b) Three combined magnetic hodograms in GSE coordinate system.

This is not the case for the event observed on February 7 (38), 1995 (Figure 4), where the end of the first flux rope does not coincide with the beginning of the second flux rope in any hodogram (Figure 4b). The vertical lines in Figure 4a delimit the ICME (black horizontal line at the top of the figure). The ICME time is set from February 7 (38), 1995, at 19:11 UT to February 10 (41), 1995, at 21:36 UT, and the MO starts on February 8 at 03:21 UT. The first flux rope (FR1) starts with the MO, and it extends to 21:07 UT on the same day. The second flux rope (FR2) starts at 21:36 UT on February 10, 1995, and extends until the end of the ICME. In this case, we speculate that two CMEs interacted here because of the lack of imaging information, but this observation could also be the result of the CME evolution throughout the interplanetary medium. We consider this case to be a unique ICME event, and a more detailed analysis is beyond the scope of this article.

Figure 4
figure4

(a) In situ data from the Magnetic Field Instrument (MFI) and Solar Wind Experiment (SWE) instrument onboard the Wind spacecraft on February 7 (38), 1995. From the top, the magnetic field magnitude and components in the GSE coordinate system, proton plasma density, temperature (expressed as a thermal velocity), proton beta, the solar wind bulk velocity, and the electron PAD parameter (EPP) for 290 and 580 eV energy levels are shown. The vertical lines show the interval of the ICME front and MO boundaries (see text for a complete explanation). (b) Three combined magnetic hodograms in GSE coordinate system.

Finally, Figure 5 shows one more example of an MO embedded in the ICME on September 30 (273), 2006. The ICME starts at 02:52 UT, with the MO extending from 08:23 UT to 22:04 UT (black horizontal line at the top of the figure). This event was cataloged as a magnetic cloud. It displays almost a complete rotation in the three magnetic field components during the MO period (horizontal pink line at the top of the figure). This effect is also observed in the hodograms, which display a rotation of almost \(360^{\circ}\). The inspection of the magnetic field and plasma data does not reveal any evidence of two CMEs interacting or internal reconfiguration processes. In this case then, the magnetic field configuration seems to be more consistent with a more complex magnetic field configuration than with a flux rope or magnetic cloud, i.e. a spheromak or a magnetic bubble, for instance.

Figure 5
figure5

(a) In situ data from the Magnetic Field Instrument (MFI) and Solar Wind Experiment (SWE) instrument onboard the Wind spacecraft on September 30, 2006. From the top, the magnetic field magnitude and components in the GSE coordinate system, proton plasma density, temperature (expressed as a thermal velocity), proton beta and solar wind speed. The vertical lines show the interval of the ICME front and MO boundaries. (b) Three combined magnetic hodograms in GSE coordinate system.

In summary, because of the diversity of the magnetic field configurations, the article focuses on the MOs embedded in ICMEs. The MO could be considered as plasma confined in a closed magnetic loop, and the selection of the boundaries in this article avoids any bias conditioned by a specific flux rope model.

Expansion Velocity

Table 1 includes the expansion velocity (\(V_{\exp}\)) for the F events. This article does not use any reconstruction technique to infer the axis orientation of the magnetic structure, and therefore the \(V_{\exp}\) we include is the expansion velocity projected in the spacecraft trajectory. Thus, the calculated apparent expansion velocity (\(V_{\exp}\)) does not distinguish between different components of the magnetic structure expansion, i.e. radial vs. axial expansion component. For some events, there are no proton plasma measurements, so that we do not include the \(V_{\exp}\) in those analyses. The \(V_{\exp}\) is calculated from a linear fit of the solar wind bulk velocity in the MO interval,

$$ V_{\exp}=\frac{(V_{\mathrm{s}}-V_{\mathrm{e}})}{2} , $$
(1)

where the \(V_{\mathrm{s}}\) (start speed) is the speed obtained from the fit at the front of the structure, and \(V_{\mathrm{e}}\) (end speed) is the speed from the fit at the back of the structure (see Figure 6). In the four cases shown in Figure 6, cases (a) and (c) show bulk velocity profiles implying a large expansion (May 18, 2002, and November 6, 2011). In the case of Figure 6b, the profile in the solar wind bulk velocity suggests a non-expanding structure (October 18, 1998), and contraction in case (d) (May 15, 1997). The analysis of the ICMEs with F events (Table 1) reports a \(V_{\exp}\) ranging from \(-56~\mbox{km}\,\mbox{s}^{-1}\) to \(271~\mbox{km}\,\mbox{s}^{-1}\) with the mean value \(28~\mbox{km}\,\mbox{s}^{-1}\) (Table 2).

Figure 6
figure6

Magnetic field strength and solar wind bulk velocity vs. time for the ICMEs observed by Wind spacecraft on (a) May 18 (138), 2002, (b) October 18 (291), 1995, (c) November 6 (311), 2000, and (d) May 15 (135), 1997. For each figure, the MO is delimited by two black dashed lines with 0 close to the bottom of the first dashed line and 1 close to the bottom of the second dashed line. In each figure, the magnetic field magnitude is displayed in the first panel and the solar wind bulk speed in the bottom panel. At the top, a vertical red line indicates where the DiP value is located according to Equation 3. In the bottom panel, the expected velocity from the linear fit is overplotted on the solar wind bulk speed as the red line. The \(V_{\exp}\) is the result of the half of the difference between the expected value at the front (\({V}_{\mathrm{s}}\)) and rear boundary (\({V}_{\mathrm{e}}\)) of the MO.

Solar Cycle Properties of the ICMEs with a Magnetic Obstacle Embedded

Table 3 summarizes the statistics, the average and standard deviation of the properties by SC. The 14 events (5% of the total) observed in SC22, from 1995 to the end of May 1996, are not included in the table. The 165 SC23 events (55%) extend from May 1996 to the end of 2008. The remainder are 119 SC24 events (40% of the total). We report in this article in Table 3 and Figure 7 the values obtained based on our criterion to select the MO embedded in the ICME. Figure 7 displays the histograms comparing the MO parameters in both SCs; SC23 is shown in red and SC24 in blue. Based on the MO definition, the number of events observed per SC increased by a factor of \({\sim}\,2.5\) in SC23 and by \({\sim}\,2 \) in SC24 relative to the numbers reported by Gopalswamy et al. (2015) in a survey of ICMEs with magnetic cloud signatures. The mean duration of the MO events in SC24 is 26 hours, 2 hours longer than our results in SC23, Figure 7a – b. For SC24, Gopalswamy et al. (2015) found a mean duration of 18 hours, 8 hours less than our results. The differences in the mean values for duration are caused by the difference in the statistical population and the difference in MO boundary choice, in the case of Gopalswamy et al. (2015) this choice restricted to the magnetic field component rotation. The MO average speed is \(431~\mbox{km}\,\mbox{s}^{-1}\) in SC23 vs. the \(401~\mbox{km}\,\mbox{s}^{-1}\) in SC24 (Figure 7c – d). This indicates that the current SC24 is weaker than SC23. This is extensively discussed in Gopalswamy et al. (2015). In the case of the magnetic field strength (Figure 7e – f), the value calculated is the mean value in the MO interval and shows a decline in SC24 with respect to SC23. Similarly, in the case of the expansion velocity (Figure 7g – h), the values decline from SC23 to SC24, as observed by Gopalswamy et al. (2015). Conversely, however, the mean density values remain similar in both SCs. Finally, the dynamic pressure calculated from the mean proton density and bulk velocity (Figure 7k – l) falls \({\sim}\,7\%\) in SC24.

Figure 7
figure7

Comparison of the MOs properties between SC23 (red) and SC24 (blue). (a) Duration (hr) for SC23 and (b) duration (hr) for SC24. (c) Solar wind average speed (\(\mbox{km}\,\mbox{s}^{-1}\)) for SC23 and (d) solar wind average speed (\(\mbox{km}\,\mbox{s}^{-1}\)) for SC24. (e) Mean magnetic field strength (nT) for SC23 and (f) mean magnetic field strength (nT) for SC24. (g) Expansion velocity (\(\mbox{km}\,\mbox{s}^{-1}\)) for SC23 and (h) expansion velocity (\(\mbox{km}\,\mbox{s}^{-1}\)) for SC24. (i) Density (\(\mbox{cm}^{-3}\)) for SC23 and (j) density (\(\mbox{cm}^{-3}\)) for SC24. (k) Dynamic pressure (pPa) for SC23 and (l) dynamic pressure (pPa) for SC24.

Table 3 Number of events, average number of events per year, duration, mean magnetic field strength (\(B\)), speed (\(V\)), density (\(N\)), dynamic pressure (\(q\)), and expansion velocity (\(V_{\exp}\)) in Solar Cycle 23 (SC23) and 24 (SC24).

Figure 8 compares the yearly ICME averages in SC22 (green), SC23 (red), and SC24 (blue). The ICME peak occurs earlier in SC23 (1998) than in SC24, which exhibits a bell-shaped profile with a maximum in the fourth year (i.e. 2012). The average yearly rate is 13 for SC23 and 17 for SC24 (Table 3). The event duration (second panel from the top) does not differ significantly between or within the two cycles, giving 24 vs. 26 hours on average for SC23 and SC24, respectively. The dynamic pressure (third panel from the top) resembles a bimodal distribution for SC23, but is less well pronounced for SC24. Average MO speed (fourth panel) and average magnetic field strength (bottom panel) display little SC dependence. The \(V_{\exp}\) shows a double distribution with the first maximum around the SC23 maximum (2001) and the second maximum in 2004, coinciding with the maximum of the solar wind speed (fourth panel).

Figure 8
figure8

Annual statistics of some properties of the magnetic structures in SCs 22 (green), 23 (red), and 24 (blue). In order from top to bottom: occurrence, duration, dynamic pressure, solar wind bulk flow speed, apparent expansion velocity, and magnetic field magnitude. The standard deviation is indicated as the error bar for the solar wind speed and magnetic field strength.

Definition of the Distortion Parameter

We introduce the distortion parameter (DiP) to quantify the effect of cross-section distortion in the MO that is due to the interaction with the solar wind. The parameter is derived from the temporal average of the magnetic field,

$$\begin{aligned} \bigl\langle B(t)\bigr\rangle _{t}=\frac{1}{T_{\mathrm{d}}} \int_{t_{\mathrm{s}}}^{t} B(t)\,\mathrm{d}t , \end{aligned}$$
(2)

where \(B(t)\) is the magnetic field magnitude, \(T_{\mathrm{d}}=t_{\mathrm{end}}-t_{\mathrm{start}}\) is the MO time duration. Then, the DiP is the fraction of \(T_{\mathrm{d}}\) where 50% of the \(\langle B(t) \rangle\) total is accumulated. In other words, the DiP is such that

$$\begin{aligned} \frac{\int_{0}^{\mathrm{DiP}\cdot T_{\mathrm{d}}} B(t')\,\mathrm{d}t'}{\int_{0}^{T_{\mathrm{d}}} B(t')\,\mathrm{d}t'}=0.5 , \end{aligned}$$
(3)

where \(t'=t-t_{\mathrm{start}}\).

Figure 6a – d (top panel in each figure) displays the magnetic field magnitude with the magnetic structure (MO) enclosed within two dashed black vertical lines. The red vertical line shows the portion of time (from 0 at the front to 1 at the rear) where the magnetic field cumulative integral has reached 50% of its total value (the DiP). By definition, DiP varies from 0 to 1. Values \({<}\,0.5\) imply compression at the front. An example is shown in Figure 6a for the event on May 18, 2002, with an \(\mathrm{DiP}=0.34\). For an \(\mathrm{DiP}>0.5\), the compression lies at the back, and the DiP approaches 1 for higher compressions. An example was observed on November 6, 2000 (Figure 6c), with an \(\mathrm{DiP}=0.55\) (compression at the rear edge). Symmetric MOs would have an \(\mathrm{DiP} \sim 0.5\). One observed event on October 18, 1995 is shown in Figure 6b with an \(\mathrm{DiP}=0.52\).

We find 92 events (31% of the total) with an \(\mathrm{DiP}>0.5\) (compression at the back), Table 4. Sixty-nine percent (207 events) of the F events have compression signatures at the front. The DiP values range from 0.19 (event on November 07, 2004) to 0.67 (event on February 18, 2014). The histogram in Figure 9a demonstrates the prevalence of compression at the front. Figure 9b shows the mean DiP value by year and the standard deviation. In general, the yearly DiP does not have strong SC variation. It seems that compression at the front is more common in both SCs with bimodal trend (SC23 and SC24). Around the minimum of SC22 and SC23 (1995 – 1997 and 2007 – 2009), the DiP value indicates more symmetric profiles (\(\mathrm{DiP} \sim 0.5\)) or compression at the back of the structure (1996 and 2007).

Figure 9
figure9

(a) Histogram for DiP values obtained for the whole set of events observed by Wind in the period 1995 – 2015 with a bin value of 0.05. (b) SC variation of the DiP. The standard deviation is indicated as the error bar for the DiP means.

Table 4 Statistics of events according to different ranges of distortion parameter (DiP) and expansion velocity (\(V_{\exp}\)).

Analysis and Discussion

DiP vs. Expansion

In situ observations of the magnetic structures within ICMEs sometimes exhibit an asymmetry in the magnetic field strength profiles and in the solar wind speed. This fact can be considered as the effect in the magnetic field observations that is due to the time-delay factor of passing over the front of the ICME long before passing over the back of the ICME. Thus, in an expanding flux rope, the field will weaken during the time the spacecraft passes through it, resulting in a decrease in field strength from the front to the back of the MO and in an apparent compression of the field near the front. Under this premise, the assumption of a circular cylindrical geometry with the inclusion of the expansion, when needed, could be enough to develop a reliable reconstruction technique.

In general, the mean values of the DiP and \(V_{\exp}\) (\(\mathrm{DiP}=0.47\) and \(V_{\exp}=28~\mbox{km}\,\mbox{s}^{-1}\), Table 2) appear to justify the circular cylindrical (symmetry) assumption and non-expanding structure in modeling. However, the range of values in both parameters suggests that there are significant deviations from the mean values (\(\mathrm{DiP}=[0.19,0.67]\), \(V_{\exp}=[-56, 271]~\mbox{km}\,\mbox{s}^{-1}\)) that require a closer look. For our analysis, we considered symmetric all events within an \(\mathrm{DiP}=0.5\pm 0.07\), where \({\pm}\, 0.07\) is the mean error bar for the yearly DiP values. In that case, there are 207 symmetric events (69%, Table 4). For \(V_{\exp}\), we considered non-expanding events those with \(-18~\mbox{km}\,\mbox{s}^{-1} \leq V_{\exp} \leq +18~\mbox{km}\,\mbox{s}^{-1}\), where \({\pm}\, 18~\mbox{km}\,\mbox{s}^{-1}\) is the mean error bar for the yearly \(\langle V_{\mathrm{sw}} \rangle\) values. There are 126 such events (42%). About \(35\%\) (103 events) meet both conditions in the DiP and \(V_{\exp}\) and hence make the best candidates for non-expanding circular-cylindrical modeling. Only one-third of the total number of ICMEs reported are consistent with the assumptions of the vast majority of models used for their reconstruction.

Figure 10a tests the validity of this assumption by plotting the DiP vs. the apparent expansion velocity (\(V_{\exp}\)). At first glance, the figure shows that the vast majority of the events have positive expansion and that most expansion velocities lie below \(50~\mbox{km}\,\mbox{s}^{-1}\). This could be consistent with the prevalence of front compression (\(\mathrm{DiP}< 0.5\)) and expanding structure (\(V_{\exp} > 0~\mbox{km}\,\mbox{s}^{-1}\)).

Figure 10
figure10

(a) Distortion parameter vs. MO expansion velocity (\(V_{\exp}\)). The \(V_{\exp}\) interval extends from \(-100~\mbox{km}\,\mbox{s}^{-1}\) to \(300~\mbox{km}\,\mbox{s}^{-1}\). The negative value of the expansion velocity represents compression. The DiP interval reaches from 0 to 1, with a symmetric magnetic field profile giving an \(\mathrm{DiP}= 0.5\), magnetic field strength compression in the front with an \(\mathrm{DiP}<0.5\), and magnetic field compression in the back with an \(\mathrm{DIP}>0.5\). (b) Quadratic fit of DiP vs. \(V_{\exp}\) for cases in quadrants A1 and A3.

Only 19 events show high expansion velocities with \(V_{\exp}\geq 100~\mbox{km}\,\mbox{s}^{-1}\). Some events, however, show symmetry in the magnetic field strength in spite of high \(V_{\exp}\) (e.g. the event on May 23, 2002, with an \(\mathrm{DiP}=0.48\) and \(V_{\exp}= 245~\mbox{km}\,\mbox{s}^{-1}\); or the event on April 05, 2010, with an \(\mathrm{DiP}=0.46\) and \(V_{\exp}=130~\mbox{km}\,\mbox{s}^{-1}\)), which is contrary to our expectations. The mean value of the \(V_{\exp}\) for this extreme group of events is \(V_{\exp}=150~\mbox{km}\,\mbox{s}^{-1}\), whose mean DiP value is 0.38, \(\mathrm{DiP}_{\min}=0.23\) (event on May 15, 2005), \(\mathrm{DiP}_{\max}=0.48\). Therefore, all events show compression in the front, but at least one shows an almost symmetric magnetic field profile, which contradicts the expected effect of the \(V_{\exp}\) on the magnetic field strength.

We divided Figure 10a in four quadrants, A1 to A4. The case with expansion (\(V_{\exp}>0\)) and compression in the front (\(\mathrm{DiP}\le 0.5\)) corresponds to A1. These events represent the expected profile: as \(V_{\exp}\) increases, so does the compression in the front. As shown in Table 5, around 59% (177 events) correspond to this hypothesis. The first line in Table 5 indicates the SC variation of the \(V_{\exp}\) and DiP of A1 events. The mean value of \(V_{\exp} = 44~\mbox{km}\,\mbox{s}^{-1}\), but the \(V_{\exp}^{\mathtt{{SC23}}}\) is greater than the mean value in SC24, in agreement with the trend for the full dataset. SC23 and SC24 have a similar percentage of A1 events, 60% (SC23) and 58% (SC24). For the DiP value, the A1 events exhibit a similar value in each SC (\({\sim}\, 0.43\)).

Table 5 Statistics of events and average parameters (\(V_{\exp}\) and DiP) by area and solar cycle.

The opposite effect on the DiP value is expected for negative \(V_{\exp}\), i.e. the magnetic field strength should increase at the back of the magnetic structure as it should have been compressed. This is the case for the A3 quadrant. Only 8% of the events fall within this area. The events do not show any trend with speed. A visual analysis of individual A3 events suggests that they are affected by interaction with the solar wind or with other solar wind transients. In terms of SC variation, there is a significant increase of cases in SC24, but the \(V_{\exp}\) and DiP mean values are similar in SC23 and SC24 (Table 5).

The A1 and A3 quadrants therefore represent the events with the expected trend between \(V_{\exp}\) and DiP (67% of total). Visual inspection of Figure 10a shows that most of the events are concentrated in the region between \(\mathrm{DiP}= 0.5\) and the dashed diagonal line in A1, which corresponds to an \(\mathrm{DiP}= 0.5-V_{\exp}/(200~\mbox{km}\,\mbox{s}^{-1})\).

We attempt to quantify this trend with an empirical fit (Figure 10b),

$$ \mathrm{DiP} = \exp\bigl(-0.69-3.39\times 10^{-3}\times V_{\exp}+ 7.55\times 10^{-6}\times V _{\exp}^{2} \bigr) . $$
(4)

This empirical relation could aid in predicting the effects of expansion and ambient interactions in the compression of the magnetic field entrained in Earth-directed CMEs.

The two remaining quadrants, A2 and A4, show counterintuitive behavior. The A2 events (22%) have positive \(V_{\exp}\) but show compression at the back. The A4 quadrant events (10%) have negative \(V_{\exp}\) but show compression at the front. In the A2 quadrant, the mean DiP value is 0.54 and is similar across SCs. The percentage of A2 cases is 26% for SC23 and 17% for SC24, so there are slightly more events in SC23. For the A4 cases, the DiP mean value is 0.45. Nine percent of the SC23 and 12% of the SC24 events are A4 cases. In the case of the \(V_{\exp}\), the values in A4 are similar to A3 (quadrants with negative \(V_{\exp}\)) in SC23 but slightly lower in the SC24. In the case of A2, the mean \(V_{\exp}\) value is \(23~\mbox{km}\,\mbox{s}^{-1}\), slightly lower than the mean value for the whole set of events considered in the study. How can we explain the geometry in these cases?

Scenarios and Interpretations

We offer a set of likely scenarios and interpretations for these results in Figure 11. In Figure 11a – d we show a schematic flux rope cross-section with the axis perpendicular to the page in the cases (a), (c), and (d), and with the cross-section perpendicular to the page in (b). In sketch (a), we represent the events in the A1 quadrant. In this case, the in situ magnetic field data show compression at the front and expansion in the back. As we demonstrated previously, this effect becomes more pronounced as the \(V_{\exp}\) increases. Note, however, that events with low DiP but a relatively small expansion, such as the event on September 17, 2011, with a very low \(\mathrm{DiP}=0.32\) and \(V_{\exp}\sim 2~\mbox{km}\,\mbox{s}^{-1}\) may not fit this scenario very well and might instead be interpreted as a highly distorted structure. In general, as the apparent \(V_{\exp}\) increases, the effect of the expansion is an important factor for reconstructing the structure. This might therefore justify the ad hoc inclusion of expansion in the flux rope reconstruction. However, the immediate questions would be how the inclusion of the expansion could affect the reconstruction parameters, or in other words, what the \(V_{\exp}\) threshold value is when this effect becomes important. According to Lynnyk and Vandas (2009), the comparative analysis of magnetic clouds using static and dynamic models revealed that the modified model with expansion provides better fits in 70% of the cases in events with expansion speeds \({\leq}\, 38~\mbox{km}\,\mbox{s}^{-1}\). The results were not conclusive for high expansion speeds. We have found that 56% of the events have \(V_{\exp}\) within \(0\,\mbox{--}\,38~\mbox{km}\,\mbox{s}^{-1}\), whereas 26% have \(V_{\exp}>38~\mbox{km}\,\mbox{s}^{-1}\).

Figure 11
figure11

Suggested interpretations for the four quadrants (A1 – A4) in the DiP vs. expansion velocity plot in Figure 10a. (a) A1 (\(\mathrm{DiP}< 0.5\), \(V_{\exp} > 0~\mbox{km}\,\mbox{s}^{-1}\)) may reveal the effect of compression at the front (pink area) and expansion at the back (green area) of the MO represented as a flux rope with the axis perpendicular to the page. The blue ellipses sketch notional field lines. (b) A2 (\(\mathrm{DiP}>0.5\), \(V_{\exp}>0~\mbox{km}\,\mbox{s}^{-1}\)) suggests compression at the back of the MO (green area) and expansion in the front (pink) due to the curvature of the MO axis. The MO (blue) is shown with the cross-section perpendicular to the page and a curved axis. The dark blue lines symbolize the magnetic field lines. (c) A3 (\(\mathrm{DiP}>0.5\), \(V_{\exp}<0~\mbox{km}\,\mbox{s}^{-1}\)) is the opposite configuration to A1 with expansion in the front (pink) and compression in the back, possibly due to interaction with trailing transient structures or ambient solar wind. (d) A4 (\(\mathrm{DiP}<0.5\), \(V_{\exp}<0~\mbox{km}\,\mbox{s}^{-1}\)) may represent events distorted on both ends. A possible observational scenario is shown with the same labeling as in the previous panels. In this scenario, the geometrical effect of the distortion could be a reliable interpretation.

The A3 quadrant shows the opposite effect—compression at the back of the magnetic field strength with negative \(V_{\exp}\). As mentioned previously, visual inspection of these events sometimes shows effects from the interaction with other solar transient structures or with the ambient solar wind (illustrated in Figure 11c). The effect of the solar wind-CME interaction imprints signatures in the magnetic field and plasma such as internal interplanetary (IP) shocks (event on February 18, 2014). In this case, the cross-section distortion is a reasonable assumption for modeling purposes.

The A2 quadrant (Figure 11b) corresponds to a stronger magnetic field at the back (\(\mathrm{DiP}>0.5\)) with expansion (\(V_{\exp}> 0~\mbox{km}\,\mbox{s}^{-1}\)). A plausible although not unique interpretation in this case is that the curvature of the flux rope produces a stronger field near the back of the MO. In the A4 quadrant, the magnetic field is stronger near the front of the MO, although a negative \(V_{\exp}\) indicates that the structure is contracting. This may occur if the spacecraft crosses an asymmetric or distorted structure with a highly inclined trajectory and large impact parameter (Figure 11d).

Summary and Conclusions

The configuration of the magnetic field embedded in ICMEs is subject to considerable uncertainties. Not only there is disagreement among imaging, modeling, and in situ reconstructions, but consensus is lacking even among in situ models. The latter necessitates a rethinking of the definition of the magnetic structure entrained in the ICMEs. In this article, we offer a broader definition of the MO, defined as the interval within the ICME where the magnetic pressure dominates the plasma pressure while at the same time the magnetic direction changes monotonically. This pattern of change in the magnetic field can be interpreted as a flux rope (known as a magnetic cloud), but also with more complex and diverse topologies, as discussed in Section 2.1.

Currently, in situ reconstructions of the MO rely on a circular cylindrical geometry as a good approximation to the observed data. This geometric assumption requires a symmetric profile for the observed magnetic field strength profile. However, observations often show asymmetry with compression at the obstacle front. This can be considered as the effect in the magnetic field observations that is due to the time-delay factor of passing over the front of the ICME long before passing over the back of the ICME. The primary goals of this study were to quantify the relationship between the observed asymmetry in the ICME-MO magnetic field strength and the expansion velocity and to explore any other possible causes.

We defined the apparent expansion velocity (\(V_{\exp}\)) and distortion parameter (DiP). The \(V_{\exp}\) was obtained from the linear fit of the solar wind bulk velocity within the MO interval, and the DiP evaluates the magnetic field strength asymmetry within the same interval. Using these parameters, we addressed two questions: 1) Can we find any relationship between the in situ observed magnetic field strength asymmetry and the apparent \(V_{\exp}\)? 2) Can we quantify the flux rope distortion or effect of the curvature?.

The study was carried out using the set of 337 ICME events observed at 1 AU by Wind. We only analyzed the events with organized magnetic topology (298 events). The study covers a period between 1995 – 2015, extending to three SCs (SC22 to SC24). We find that MOs in ICMEs are more prevalent during SC24 than SC23, and they have a shorter duration. Consistently with previously cited works, SC24 shows weaker signatures than SC23, although the parameters reported here differ from those in previous studies. The differences are mainly the consequence of the choice of the MO boundaries.

The results of the more detailed analysis of the DiP and apparent \(V_{\exp}\) are summarized as follows:

  • \(\text{About }\)18% of the events have negative \(V_{\exp}\), \({\sim}\,30\%\) show compression in the back, and 41% of the events do not meet the initial hypothesis of positive \(V_{\exp}\) and an \(\mathrm{DiP}<0.5\) (magnetic field compression at the front of the MO). Therefore, a significant number of events do not meet the profile expected by the reconstruction models.

  • To assess the applicability of the widely used circular-cylindrical assumption, we considered as symmetric events those within a \(\mathrm{DiP}=0.5\pm 0.07\) and velocities \(V_{\exp}\) within \({\pm }\,18~\mbox{km}\,\mbox{s}^{-1}\). The number of such cases represents \({\sim}\,35\%\) of the total number of events. Although the mean values for the DiP and \(V_{\exp}\) are 0.47 and \(28~\mbox{km}\,\mbox{s}^{-1}\), the deviations from these values are significant. The range for \(V_{\exp}\) extends from −56 to \(271~\mbox{km}\,\mbox{s}^{-1}\) and that of the DiP reaches from 0.19 to 0.67. In other words, a significant number of ICMEs show large expansion signature or contraction, and magnetic field compression at the leading boundary but also in the rear boundary.

Regarding the relationship between the magnetic field strength compression and apparent \(V_{\exp}\), we find:

  • \(\text{About }67\%\) of the events follow the expected trend between apparent expansion velocity and magnetic field strength, i.e. 59% of the events show an asymmetry in the magnetic field compression at the leading edge of the MO with apparent expansion velocity, and the remaining \({\sim}\, 8\%\) of cases show an asymmetry in the trailing edge of the MO with negative expansion velocity. We derived an empirical relation between the DiP and \(V_{\exp}\) (Equation 4) that quantifies the degree of distortion in the magnetic field strength according to the observed expansion velocity. This provides a first approach to implementing the effect of the expansion in the reconstruction and forecasting techniques. However, this empirical approach is still a very preliminary approximation and needs to account for other effects such as curvature or geometrical distortions.

Regarding the flux rope distortion or effect of the curvature, our findings are:

  • \(\text{About }22\%\) of the cases show \(V_{\exp} > 0~\mbox{km}\,\mbox{s}^{-1}\) but have compression at the back (\(\mathrm{DiP}>0.5\)). A possible geometrical interpretation is the effect of the curvature (Figure 11b). It is also found that \({\sim}\, 10\%\) of the events have negative expansion velocity and front compression at the leading edge of the MO (\(\mathrm{DiP}<0.5\)).

  • Therefore, \({\sim}\, 32\%\) of the ICMEs do not follow the expected profile of expansion with compression at the front. In these cases, geometrical effects such as curvature or cross-section distortion could provide more robust reconstructions.

Finally, this article presents an endeavor to provide insights into the configuration of the magnetic structure embedded within ICMEs in order to develop more reliable reconstruction techniques that can reconcile models based on in situ data with white-light observations. The study takes advantage of \({\sim}\,20\) years of Wind observations. We considered only ICMEs with well-organized magnetic topology, and the results we obtained suggest that there is no unique geometry or assumption for modeling the MOs.

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Acknowledgements

This research has made use of the Wind plasma and magnetic field data throughout. We thank to the Wind team and the NASA’s Space Physics Data Facility (SPDF) to make the data available. The work of N. Al-haddad and T. Nieves-Chinchilla is supported by the National Science Foundation under AGS-1433086 grant. The work of T. Nieves-Chinchilla, A. Vourlidas, M.G. Linton, and J.C. Raymond is supported by the NASA LWS program through ROSES NNH13ZDA001N. T. Nieves-Chinchilla thanks to Leila Markus, Anna Chulaki, Lynn Wilson III, and Charlie Farrugia the discussions and comments to the article.

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Earth-affecting Solar Transients

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Nieves-Chinchilla, T., Vourlidas, A., Raymond, J.C. et al. Understanding the Internal Magnetic Field Configurations of ICMEs Using More than 20 Years of Wind Observations. Sol Phys 293, 25 (2018). https://doi.org/10.1007/s11207-018-1247-z

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Keywords

  • Coronal mass ejection
  • Flux rope
  • Solar wind