DIII-D Research to Prepare for Steady State Advanced Tokamak Power Plants

Criteria for Steady State Fusion and Key Metrics

The challenge for a tokamak steady state reactor is to have sufficient fusion performance to generate net energy, after powering auxiliary systems to sustain the regime non-inductively. Following the approach of [8] we discuss the parameters that matter in developing this solution, and the associated research questions that must be explored to determine whether such a solution will be possible in a reactor.

In the numerator, fusion power scales with volume and the square of plasma pressure, p (provided one is in the regime where fusion cross section rises with the square of temperature, 8–25 kV). In the denominator heating power is re-expressed in terms of the characteristic energy confinement timescale \(\tau = \left\langle p \right\rangle V/P_{aux}\). Thus one arises at the familiar fusion triple product with \(Q \propto nT\tau\).

Thus sufficient field and size can raise Q to the point that no additional heating is required beyond that needed for current drive, which we discuss shortly. However, given limits in device field and scale, one sees that the fusion performance metric, \(G = \beta_{N} H/q_{95}^{2}\) becomes important. Thus higher \(\beta_{N}\), increased confinement scaling factor, H, and particularly lower \(q_{95}\) are levering to performance and heating needs. Also, it should be noted that fusion performance can reach a point that additional heating, offers no benefit to the thermal sustainment, as the plasma ignites (reaches \(Q = \infty\)) or the current drive power alone is enough to maintain energy.

This formalism identifies the key governing plasma physics parameters. The most critical role is played by plasma pressure, as represented by the parameter \(\beta_{N}\). This drives bootstrap fraction, thereby reducing auxiliary current drive needs. It also raises the fusion performance metric, G. High \(\beta_{N}\) thus favors steady state performance as well as fusion gain, and thus represents a key metric to improve the tokamak concept for steady state fusion. Similarly higher field provides the other means to raise pressure (at fixed \(\beta_{N}\)) and achieve ubiquitous benefits to performance and steady state goals. This strongly motivates science and technology programs to raise \(\beta_{N}\) and field respectively to optimize the tokamak concept. For the purposes of this paper we concentrate on the plasma physics aspects—how to make best use of the toroidal field available, considering progress in the underlying physics understanding of this question. We leave technology development such as higher field superconductors to other studies, though their leverage on these issues make them important to pursue also.

The second key consideration is the role of \(q_{95}\). Higher \(q_{95}\) favors higher bootstrap operation, reducing heating and current drive needs. But it also lowers fusion performance, as plasma current is lower. Conversely, a lower \(q_{95}\) will raise the fusion power, but will also require more power to be recycled back into current drive systems to sustain the device. Further, lower \(q_{95}\) increases device risk, as plasma instabilities become more severe with the increased free energy provided by the current profile, leading to disruptions (Fig. 1, left) at low \(q_{95}\) values, but absent at high \(q_{95}\). Thus the choice of \(q_{95}\) requires careful investigation in arriving at optimum reactor efficiency and in the development of robust stability and control strategies. Interestingly, it is found that disruptivity does not depend significantly on \(\beta_{N}\) (Fig. 1, right); current rather than pressure provides a much greater drive of instability in the tokamak concept. Some scenarios, such as high l_i or standard H modes, are more at risk of certain instabilities such as tearing modes, though at high \(q_{95}\) these tend to act on confinement rather that causing a termination.

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The third key consideration is density. Lower density permits more efficient current drive. But higher density is more highly levering for bootstrap current (not discussed in above formalism, but outlined in ref [30]), as increased density gradients directly drive increased bootstrap current (provided collisionality remains low), whereas increased temperature gradient alters particle orbits in ways that can offset the benefits of increased velocity gradient. Considering the role of current profile, this divides the approach between two optimization paths—a high bootstrap solution in which auxiliary current drive needs are minimized, or efficient auxiliary current drive solution at lower density. For the driven current solution, current drive is most efficient in the hottest region of the plasma—the core. This favors a peaked current profile together with low density. This peaked current solution can access high ideal MHD stability, with high \(\beta_{N}\). However, lower density will make compatibility with a divertor solution, which favors higher density radiative techniques, more challenging.

A high bootstrap solution favors a broader current profile and elevated density. Further a broader current profiles also creates higher local \(\beta_{P}\) increasing bootstrap current. Also, the bootstrap current, as it is driven by pressure gradients, forms off-axis, thereby aligning self-consistently with a broad overall current profile. This broad current profile also benefits from a high ideal MHD \(\beta_{N}\) limit thanks to a stabilizing interaction with the surrounding conducting structure of the vessel, thereby self-consistently enabling a high bootstrap solution.

In the high bootstrap approach there is also a balance between \(q_{95}\) and \(\beta_{N}\); a higher current with lower \(q_{95}\) requires higher \(\beta_{N}\) to reach the same bootstrap fraction. The DIII-D program targets plasmas with \(\beta_{N}\) approaching 5 and \(q_{95} \sim5 - 7\) for power plant relevant scenarios, such as those set out in Table 1, which are predicted to reach very high bootstrap fractions in some cases. (We also explore alternate paths at higher \(q_{95}\) and \(\beta_{P}\), or indeed lower bootstrap fraction, for other concepts). However, plasmas that match this in DIII-D are projected to reach a lower bootstrap fraction than equivalent regimes in fusion reactors, due in part to the higher fast ion content from beams (which may ultimately be reduced by increases in other current drive systems), and the slightly more collisional plasmas attainable with the lower field and size of DIII-D. Typically DIII-D has achieved bootstrap fractions of ~ 50–60% to date in such regimes with \(\beta_{N}\) approaching 4 in fully non-inductive regimes, though higher transiently or at higher \(q_{95}\). See [31] for a more in depth discussion of the trade offs identified.

As noted in Eq. (9), confinement factor, H, does not enter into the steady state aspect of the optimization. Nevertheless transport remains important for two key reasons. Firstly, it determines the evolution of the profiles which govern bootstrap generation and stability in steady state solutions. Secondly, as one seeks to optimize the AT concept, particularly to smaller device size, sufficiently good confinement is needed to ensure α heating maintains plasma temperatures—otherwise additional auxiliary heating will be necessary, driving up required size or current to raise the fusion performance in order to power such systems.

We next consider how to get there.

Range of Plasma Scenarios Explored

In recent years DIII-D has pursued four classes of steady-state scenario usually distinguished by current and safety factor profile: (1) High-β_P, (2) High-q_min, (3) High-β Hybrid, and (4) High-l_i. These scenarios represent points on a continuum of discharge parameters, but it is helpful to understand the differences in behavior of these four points. Example profiles are shown in Fig. 5.

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High-β_P scenario discharges on DIII-D typically have q_min = 2–5, with q₉₅= 10–12 [37]. The current density profile is very broad and dominated by bootstrap current (f_BS = I_BS/I_TOTAL > 70%). Elevated q_min means low-order rational surfaces that are prone to tearing mode instability are absent from the plasma. Normalized confinement typically exceeds confinement-scaling predictions due to the presence of a high radius internal transport barrier in density, temperature, and sometimes rotation. This scenario has been studied in DIII-D in preparation for long pulse operation in the EAST tokamak [38] and is in the parameter regime envisioned for a high B_T DEMO such as ACT2 [21].

High-q_min scenario discharges typically have q_min = 1.4–2.3, with q₉₅ = 5–7 [39, 40, 41]. The current profile is also broad, but not as much as the High-β_P scenario. Bootstrap current fraction is typically less than 65%. There is usually weak positive to negative magnetic shear (q₀–q_min < 0.5) designed to reduce turbulent heat transport [42], but internal transport barriers are avoided to ensure a broad pressure profile for high ideal MHD β_N-limits in the range of 4–5, depending on the detailed current profile and plasma boundary shapes. When β_N exceeds the no-wall kink mode limit, the resistive wall mode becomes a potential concern [43]. This scenario is being developed as a primary option for a medium B_T DEMO such as ACT1 [21], and may also be the basis for steady state operation in ITER and nuclear science facilities.

The High-β Hybrid scenario operates at lower q_min just above 1, also with q₉₅= 5–7 [44, 45]. About half of the total current is bootstrap, and half is from on-axis external current drive using NBI and ECCD. Predicted ideal-wall β_N limits of hybrid plasmas are in the range of 4–5, potentially making the highest β_N applications a little more challenging. Stability to low-order tearing modes (e.g. m/n = 2/1) is improved compared to standard H-mode plasmas by the absence of sawteeth and a current profile that is somewhat broader than is predicted by resistive poloidal flux diffusion. Anomalous current profile broadening is thought to be due to the presence of 4/3 or 3/2 tearing modes that convert toroidal magnetic flux to poloidal magnetic flux [46, 47]. As a result, precise external current drive alignment to tailor the current profile is unnecessary, and external current drive can be deposited near the magnetic axis where it is most efficient. Hybrids may also be a viable operating scenario for a range of future steady state devices, depending on how the anomalous current diffusion scales to a reactor, and on how confinement is affected by increased 3/2 island width going to low rotation.

The High-l_i (l_i = internal inductance) scenario consists of a strongly peaked current density profile, with l_i ≈ 1 and q_min ≈ 1 [48]. At high-l_i, the no-wall kink-mode β_N limit can be 4 or even higher; therefore the key advantage of this scenario is that it can run at high β_N without reliance on wall stabilization of modes with n > 0. Strong positive magnetic shear results in high normalized confinement [42]. Like the hybrid, bootstrap current fraction is typically ~ 50%. To sustain high-l_i non-inductively, the current profile must be carefully controlled using significant external current drive in the inner half-radius while limiting bootstrap current in the outer half radius. For DIII-D, projections also aim to tailor the current profile to avoid sawtooth instabilities (which can trigger other instabilities), while maintaining the good core confinement benefits from high magnetic shear by avoiding too high a pedestal and edge bootstrap current. The high-l_i scenario is a key alternative to the other steady state scenarios for future reactors if RWM stabilization proves to be impracticable.

Considering these scenarios, we see they pose some common and some different research needs. Common element include understanding transport, energetic particle and stability physics, as well as current profile evolution in the quest to develop self-consistent steady state solutions. These issue must be understood in plasma configurations where the underlying plasma behavior and phenomena occurring are similar to those expected in a power plant—and thus with relevant β, current profile, rotation, electron heating, collisionality, etc., so that models can be validated that capture the relevant physics for reactor projection. Dissipative divertor, and likely full detachment, combined with radiative impurity mantles within the separatrix, will be necessary to present plasma facing components with a tolerable challenge and eliminate erosion so the device can run continuously for months or years. These considerations also require development of ELM elimination techniques to prevent divertor erosion. Finally a fall back safe plasma quenching technique must be resolved in order to prevent disruptions should control or system failure occur.

Considering physics emphases for particular scenarios, the high q_min path requires operation substantially above the no wall ideal MHD stability limit, and thus either additional inherent kinetic stabilizing mechanisms or magnetic feedback control. The high l_i path is more reliant on the development of new and more efficient current drive tools—though these are highly levering for all concepts to reduce recirculating power. The hybrid scenario provides a degree of self-optimization for the current profile (through flux pumping) which must be understood. High l_i and hybrid are also more susceptible to tearing modes. Beyond the plasma itself, there also remain many hardware, engineering, diagnostic and control challenges, though we leave these topics to other publications—though do note that there is a strong need for an extensive technology and engineering program to develop solutions. We focus here on the advanced tokamak physics.

Simulation Tools

Theory-based integrated scenario modeling plays an essential role in the development of self-consistent high β_N steady-state scenarios on DIII-D in a repeated cycle of scenario design, experimental implementation, and model validation. At the heart of this is the FASTRAN suite [49, 50], which is an efficient and robust iterative solution procedure to find a steady-state solution (d/dt ~ 0) of core transport, self-consistent with external heating/current drive, MHD equilibrium, ideal MHD stability, and edge pedestal, built upon a modern integrated modeling framework, Integrated Plasma Simulator (IPS). Recently, remarkable progress has been made in improving the individual elements of the FASTRAN modeling, such as a comprehensive theory-based core transport model, TGLF for all transport channels (particle, energy, and momentum), and EPED for edge pedestal to provide the boundary condition of the core transport. Integration of such high-fidelity core transport and edge pedestal models along with the well-established modeling of MHD equilibrium (EFIT), ideal kink stability (DCON, GATO) and external heating/current drive (NUBEAM, TORAY, GENRAY) has substantially advanced our predictive capability for the steady-state operating scenario development without relying on any significant free input parameters.

The FASTRAN modeling reproduces most features of DIII-D high β_N discharges in the stationary condition. Figure 6 shows a comparison of the FASTRAN-predicted stationary profiles at t = ∞ with the measurements during the high β_N phase of an elevated q_min > 1.5 discharge at β_N ~ 3, which was sustained by the off-axis NBI and ECCD longer than 2τ_R. The calculated radial profiles of n_e, T_e, T_i, and Ω reproduce the measurement reasonably well. The predicted plasma current profile (Fig. 6e), to which the discharge would eventually evolve, is close to the estimation by kinetic EFIT equilibrium reconstruction obtained with MSE and the calculated edge bootstrap current as constraint. The proximity of these two profiles both (1) improves confidence that FASTRAN contains most of the important physics, and (2) confirms that the experimental discharge was approaching a stationary state.

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In addition to guiding the DIII-D experiment and H/CD upgrade ("Future Research Requirements and DIII-D’s Role" section), the same FASTRAN modeling has been used to extrapolate the steady-state scenarios developed on DIII-D to future reactors such as ITER [51] and C-AT DEMO [52; journal paper in preparation], thereby identifying gaps between the present-day experiments and future reactors, and further research needs on DIII-D. One such example for the ITER projection is shown in Fig. 7, predicting that fully non-inductive hybrids described in section "Steady State Hybrid with RMP-ELM Suppression" can achieve the Q_fus = 5 ITER steady-state mission.

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It should be noted that in this work, while the transport models can make projections, and do in same cases get good agreement with experiment (Fig. 6), these models remain to be fully validated, particularly with more advanced current profiles and higher \(\beta_{N}\) required for steady state scenarios. This is an area of progress set out in the paper, but also a major research goal of ongoing work set out in section "Future Research Requirements and DIII-D’s Role", with significant discrepancies emerging at high \(\beta_{N}\) and broader profiles, and further work to do to more fully understand electron transport and multi-scale effects.

Steady State Hybrid with RMP-ELM Suppression

Experiments on DIII-D have demonstrated the potential of the hybrid scenario as a regime for high-beta, steady-state plasmas with 1 MA of plasma current driven non-inductively and β_N up to 3.7 sustained for ~ 3 s (~ 1.5 current diffusion time, τ_R) [44, 45]. The hybrid scenario is a long duration, high performance, H-mode regime that operates near q_min≈ 1 with higher confinement and greater stability compared to the conventional H-mode regime. The hybrid scenario in the presence of a small 3/2 NTM has the attractive property of a self-organized current profile that derives from a “flux pumping” mechanism transferring part of the central current drive to an off-axis position [46, 53]. This allows all of the current drive to be located near the plasma center where the efficiency is high without forcing q_min below 1 and triggering significant sawtooth activity.

In steady-state hybrid experiments on DIII-D, the surface loop voltage is driven down to zero for > 1 τ_R when the poloidal β is increased above 1.9 at a plasma current of 1.0 MA, co-NBI power of 11 MW and ECCD power of 3.2 MW. Figure 8 shows that theoretically the central current is strongly overdriven in these steady-state hybrids owing primarily to the efficient on-axis ECCD. Despite this, the measured plasma current profile remains broad and shows no sign of peaking during the ~ 3 s high-beta phase (TRANSP simulations predict that q_min should drop well below 1). The confinement quality is excellent (H_98y2 ~ 1.6) and increases approximately with the square root of density. Stationary operation is sustained at pressures above the calculated ideal no-wall limit and 80–90% of the ideal with-wall MHD limit (the latter calculated to be β_N ~ 4–4.5). High-beta hybrids heated only by NBI typically have TAE/EAE energetic particle modes that increase the beam ion transport. By applying ECCD to achieve complete current drive, these EP modes are replaced by a more benign fishbone-like instability, possibly because ECCD depresses q_min closer to 1, which lessens the beam ion transport.

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The steady-state hybrid scenario with ITER relevant values of beta, collisionality, safety factor and plasma shape has been successfully integrated with ELM suppression by applying an odd parity n = 3 resonant magnetic perturbation (RMP) [51]. Figure 9 shows an ELM suppressed hybrid with I_P = 0.95 MA, β_N = 3.0, β_P = 1.9 and H_98y2 = 1.2 using 3.5 MW of on-axis ECCD and 9.9 MW of co-NBI. The measured surface loop voltage is zero and the modeled non-inductive currents equal the plasma current. Experiments also demonstrated that 0.95 MA hybrids with RMP ELM suppression could be maintained with a flat (and zero) loop voltage profile when the central solenoid current was frozen between 2.5 and 5.5 s. The RMP stabilization of type-I ELMs is predominantly through density pumpout, partially compensated by increased pedestal temperature, which shifts the pedestal from the unstable region for peeling–ballooning modes to the stable region. A new finding in this steady-state hybrid regime from ideal MHD modeling using the GPEC code is the presence of one dominant marginally stable mode in the plasma edge that couples effectively to the n = 3 RMP, producing an edge magnetic perturbation 2–3x the amplitude of the applied vacuum field [54].

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Two different extrapolation methods, ρ* scaling and theory-based modeling from FASTRAN simulations, show that these steady-state hybrids can satisfy the ITER steady-state mission with a fusion gain of Q ≈ 5 and a required current drive power of ≈ 100 MW for 100% non-inductive operation.

High li Scenario

Increased confinement and ideal stability limits at relatively high values of the internal inductance (l_i > 1) enable an attractive scenario for steady state tokamak operation at high β_N. Many of the features of such a discharge have been demonstrated in DIII-D, and the highlights of the most recent experiments [48] are reviewed in this section. The improvements in confinement and stability arise largely as a result of higher poloidal field in the discharge core and larger magnetic shear in the outer half of the plasma when the current density profile is more peaked. Plasmas with high l_i and β_N ≈ 4–5 are predicted by theory to be stable to low toroidal mode number (n) ideal MHD instabilities even without the effect of a conducting vacuum vessel wall [55, 56]. In addition, the β_N limit as determined by the infinite-n ballooning mode is expected to increase with l_i [57]. These features make a high l_i discharge a candidate for a power plant that could either operate stably at β_N ≈ 4 without the requirement for a nearby conducting wall or n ≥ 1 active stabilization coils, or at β_N ≈ 5 with wall stabilization. A more detailed description of the history of the experimental and theoretical study of discharges at high l_i can be found in Ref. [48]. Here, \(l_{i} = \int {dV} B_{P}^{2} /V/\left( {\oint {B_{P} dl} /\oint {dl} } \right)^{2}\) where B_P (T) is the poloidal magnetic field, V (m³) is the plasma volume and the path for the line integrals is the plasma boundary.

Steady-state tokamak operation is optimum with a high fraction of bootstrap driven current (f_BS), but typical bootstrap current density (J_BS) profiles can have limited compatibility with an elevated value of l_i. The dependence of the stability limit to β_N on l_i strengthens as the core pressure profile is broadened [55] and stability limits are highest with high plasma elongation κ and triangularity [34, 56]. A broad core pressure profile and strong discharge shaping both increase J_BS in the outer half of the plasma. In addition, there is a localized peak in the bootstrap-driven current in the H-mode pedestal region at the edge of the plasma as a result of the steep pressure gradient there. As the fraction of I_p resulting from bootstrap current in the outer half of the plasma increases, the maximum value of l_i that can be obtained by tailoring the profile of the externally-driven current density will decrease. Taking this into account, the expectation is that there is an optimum value of l_i [56] where there is a compromise between high l_i and high f_BS: l_i ≈ 1, β_N = 3.5–4.0, and f_BS ≈ 0.5. For fully noninductive operation, about half of the current would be provided by externally-driven current near the axis. Although the total amount of externally-driven current would be relatively large, the required external current drive power could be comparable to what is required for other steady-state scenarios because of increased efficiency for external current drive near the axis.

The significant advantages of high l_i operation are reflected in the most recent DIII-D experimental results [48]. In a double-null divertor configuration, discharges have been produced with β_N ≈ 5 and excellent confinement H_98(y,2) ≈ 1.8, parameters that are in the range required for a high power density reactor. Discharges were obtained with β_N > 4 sustained for 1 s (≈ 0.5τ_R), and with brief, tearing mode-limited phases with β_N > 5 (Fig. 10). High l_i is presently the only method to access β_N this high in conventional aspect ratio tokamaks, although similar β_N values are projected for a scenario with a broad current density profile and q_min > 2 ("Simulation Tools" section).

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The high l_i, high β_N discharges have not yet been operated with a stationary current density profile as sufficient externally-driven current is not yet available (but planned upgrades are projected to address this—see section "Future Research Requirements and DIII-D’s Role"). Thus the decrease in β_N with time in Fig. 10a occurs because of the decrease in confinement as l_i decreases with constant beam power. In this case, the total calculated noninductively driven current exceeds the total plasma current as a result of the high β_N and the relatively large q₉₅ ≈ 7.5, with bootstrap current fraction f_BS ≈ 0.8, and a negative surface voltage applied by the control system to maintain the target value of I_p. However the l_i is not sustained because the current is not distributed centrally enough to maintain it. Further current drive upgrades and work to control pedestal height are projected to address this.

Discharges in the planned ITER shape, scaled to fit into the DIII-D vacuum vessel, have been studied with q₉₅ ≈ 4.8, l_i ≈ 1, and β_N ≈ 3.5, near the parameter range anticipated for steady-state operation in ITER (Fig. 11). In this case, f_NI < 1 as a result of the lower β_N and q₉₅. Discharge performance was close to the estimated requirement for the ITER steady-state mission with G = β_N H₈₉/q ₉₅ ²  ≈ 0.3 (Fig. 11d).

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A high l_i scenario is a possibility for ITER in the event that the H-mode pedestal pressure is found to be too low to achieve the target fusion gain for the steady-state mission at high q_min > 2. ELM mitigation using 3D magnetic fields, for instance, can reduce the pedestal density and pressure, an effect that would reduce the bootstrap current density near the plasma boundary, leading naturally to increased l_i. The effect of a reduction in the H-mode pedestal pressure was tested in DIII-D by applying n = 3 fields from the internal non-axisymmetric coils. As the n = 3 field amplitude was increased, the pedestal pressure decreased along with the calculated fraction of I_p supplied by bootstrap current in the pedestal region. A corresponding increase in the average value of l_i during the high β_N phase was observed.

The high values of β_N attained at high l_i are close to, but below, the calculated limits set by the ideal n = 1 kink and the ideal infinite-n ballooning instabilities (Fig. 12 [48, 58]). Consistent with the stability calculations, a global, pressure-limiting instability has not yet been clearly observed in the experiment. Instead, in the cases where stability determines the limit to performance, the observed mode is most commonly an m = 2/n = 1 resistive tearing mode (e.g. Fig. 10d–f). In the ITER scaled shape (Fig. 11), the value of β_N that could be sustained for the full discharge duration was limited by the 2/1 resistive mode to a value below the no-wall ideal limit (Fig. 12b).

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A power plant relevant method to form the high l_i equilibrium has been demonstrated. The discharge is begun with an initial, low β_N phase with only inductive heating so that the electron temperature is low and the characteristic timescale for relaxation of the current density profile is very short. The discharge remains in these conditions long enough for the current profile to evolve to a stationary, peaked-on-axis state prior to the application of the external heating and current drive power. There is no requirement for rapid changes in I_p, elongation or radius as used in the past to increase l_i, techniques which would be difficult to implement in a large device with superconducting coils.

Transport code modeling studies have been used to explore how increased current drive and heating powers in DIII-D (13 MW off-axis neutral beam, 9 MW ECCD) could be applied to maintain a stationary, f_NI = 1 high l_i discharge. The FASTRAN framework [49] was used to calculate a stationary current density profile solution using theory-based bootstrap current, current drive and transport models. With the goal of maximizing the stationary value of β_N consistent with the calculated stability limits, the current drive and heating powers, the deposition profiles for the ECCD sources, and the relative fractions of on-axis and off-axis neutral beam powers were varied. The result from this initial modeling study (Fig. 13) is close to the “optimum” solution found in [56] with l_i = 1.07, β_N = 4, f_BS = 0.5, f_NBCD = 0.35, f_ECCD = 0.3, H₈₉ = 2.3, H_98(y,2) = 1.1, and the ideal n = 1 stability limits β_N ≈ 4.1 without a conducting wall and β_N = 4.8 with a wall. All of the available off-axis neutral beam power is used in order to broaden the fast ion pressure profile, thus minimizing the peaking of the pressure profile which reduces the stability limit. The off-axis neutral-beam-driven current density is minimized, though, through choice of the toroidal field direction [59].

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Continued development of a high l_i steady-state scenario requires work in several areas. The onset of the resistive tearing mode, particularly at β_N near the ideal mode limits, must be understood as these modes presently set the observed stability limit. Improved capability to avoid the 2/1 mode would enable the study of discharges with the combination of β_N and q₉₅ that results in f_NI = 1. The understanding of the parameters in the H-mode pedestal region should be refined as the pressure and current density there play significant roles in determining the self-consistent values of l_i and β_N. Finally, development of the capability to provide the required externally driven current near the axis is needed in order to be able to operate high l_i discharges in a stationary, rather than the present transient, manner. In DIII-D, the expectation is that stationary operation would be enabled by an increase in the available ECCD power to approximately 9 MW (see section "Future Research Requirements and DIII-D’s Role"). A method to mitigate the limitations on the current density at the axis imposed by the sawtooth instability [60] would allow more of the current to be driven closer to the axis, increasing efficiency and also providing access to higher values of l_i.

High q _min Scenario

The high q_min scenario focuses on q₉₅ ≤ 6 with q(0)–q_min< 0.5. This approach has been studied at DIII-D because, with broad pressure profiles, it scales to high β_T, and thus high Q, in a power plant. Close to fully non-inductive plasmas with durations approaching the current redistribution timescale, τ_R, have been achieved in DIII-D with 1.5 < q_min < 2 and current density peak value at ρ ≈ 0.3 [39], q₉₅≈ 6.2, and β_N≈ 3.7. These discharges were achieved with all on-axis NBCD and a broad ECCD distributed about the mid-radius. Ideal stability analysis showed that these discharges operate only marginally below the n = 1 kink mode ideal-wall β_N limit (3.7–4), as a result of insufficiently broad current and pressure profiles. Such operational proximity to an ideal MHD limit is understood to risk tearing mode instability—i.e., a 2/1 tearing mode in this case.

The introduction of off-axis neutral beam injection led to improved capability to operate with broader current and pressure profiles to increase β_N limits [40, 41]. Discharges with 1.4 < q_min < 2 and 5 < q₉₅ < 6.2 were explored with β_N ≈ 3.5 for durations lasting up to 2τ_R (3 s). The most interesting cases from an ideal stability point of view had q₉₅≈ 5 and q_min≈ 1.4—an example is shown in Fig. 14. While only 70–75% non-inductive at this q₉₅, these plasmas were nonetheless quasi-stationary, and had predicted n = 1 ideal-wall β_N limits near 4.5. In most discharges with 1.4 < q_min < 2 using off-axis NBI, off-axis fishbones were observed that are likely responsible for some inferred anomalous fast ion transport. Most plasmas with q_min just below 2 (~ 1.8) had the high β_N phase terminated by 2/1 tearing modes.

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Off-axis NBI also clearly improved the ability to sustain plasmas with q_min > 2, but thus far at reduced maximum β_N (~ 3.2) and f_NI, largely as a result of increased fast ion transport caused by unstable Alfven eigenmodes (AE) [61]. AE stability was found to be sensitive to gradients of fast ion β. When a critical gradient is exceeded, multiple overlapping AE resonances cause fast ion redistribution or loss if further beam heating is applied [62] (see section "Energetic Particle Physics"). This lowers the NBI heating and current drive effectiveness and global energy confinement. When the lost heating power is accounted for, power balance analysis showed q_min > 2 plasmas have thermal transport similar to plasmas with lower q_min.

Experiments and modeling have shown a variety of options for improving fast ion confinement in DIII-D q_min > 2 discharges. Modeling predicts, and some experimental evidence confirms, that further broadening of the q-profile can reduce AE-induced fast ion loss [63]. Specifically, increasing q₀ is predicted to eliminate Toroidal AEs by closing off the frequency gap in which they can exist, and increasing the radius of q_min is predicted to lower the impact of Reverse Shear AEs on fast ion confinement by pushing the modes to a region of lower fast ion density. Planned increases in off-axis ECCD and NBCD in the next few years will enable further tests of this. Prompt AE stabilization using ECH applied at ρ_qmin has also been demonstrated [64]. In this case ECH is thought to modify RSAE existence and damping through changes to the local pressure and pressure gradient. Variable NBI voltage and current at fixed power has also been developed. At reduced beam voltage, reduced AE-drive in high-q_min discharges has been shown to result in improved performance. [65, 66]. The physics of these processes is discussed further in section "Energetic Particle Physics".

Other DIII-D experiments have explored properties of q_min> 2 plasmas with broader current profile using a transient technique. Dynamically ramping down the toroidal field induces current density broadly distributed in the outer half radius, effectively mimicking non-inductive current drive sources that will be available after future upgrades [67]. Using this technique, plasmas with q_min> 2 were produced that had excellent normalized global energy confinement (H₈₉ = 2.5) [68]. Using fast RWM magnetic feedback enabled access to β_N = 4. This corresponds to the predicted ideal-wall n = 1 kink mode limit, and indeed quickly growing instabilities consistent with an internal kink were observed. The reasons for the improved energy confinement compared to other q_min> 2 discharges described above still needs to be determined. Possible contributors include: improved thermal confinement from internal transport barriers, increased density and shorter fast ion slowing down time, and broader q-profile.

High β _P Scenario

Experimental and modeling investigations performed in the last few years by an international joint team of scientists working on DIII-D and EAST have made great progress toward developing the high poloidal beta (\(\varepsilon \beta_{P}\) ≥ 1) regime as a basis for the steady state operation of a tokamak fusion reactor [37, 69, 70, 71, 72, 73, 74, 75]. Plasma operation in the high poloidal beta regime ameliorates two key weakness of the tokamak configuration: current disruptions and the need for external current drive. Operating a tokamak at high \(\beta_{P}\) offers low disruptivity because of high safety factor [\(q_{95} \propto \varepsilon \beta_{P} /\beta_{N}\), where \(\beta_{N} = \beta_{T} /\left( {I_{P} /aB_{T} } \right)\), with the toroidal plasma current], and low external current drive requirements because of high self-generated bootstrap current fraction (\(f_{BS} \propto \sqrt \varepsilon \beta_{P}\) assuming constant collisionality). Conversely, since the plasma current is relatively low at high \(\beta_{P}\), maintaining a high fusion power density generally requires operation at high \(\beta_{N}\), and at confinement quality higher than standard H-mode. As discussed in section "Criteria for Steady State Fusion and Key Metrics", operation at high \(\beta_{N}\) does not increase disruptivity—see Fig. 1, taken from the DIII-D disruption database.

Experiments and simulations have shown that energy confinement quality higher than standard H-mode (enhancement factor over H-mode confinement scaling H_98y2 > 1) can be achieved and sustained in the high \(\beta_{P}\) regime independently of the plasma rotation, thanks to a key feature of the high \(\beta_{P}\) regime: the high Shafranov shift of the plasma equilibrium, which can provide turbulence suppression via local magnetic shear [76], and can lead to the formation of an internal transport barrier (ITB) in the kinetic profiles at large minor radius [see refs above]. Furthermore, the investigations have addressed several of the outstanding issues previously highlighted in the literature regarding operation with ITBs, by demonstrating ITB formation and sustainment at high Greenwald density fraction, lack of impurity accumulation, sustainment of the large radius, compatibility with a high \(\beta_{N}\) limit, and robustness of the self-organized configuration.

These experimental results have been used to validate MHD, current drive, and turbulent transport models, and to project the high-β_P regime to a reactor. In a burning plasma, it is found that the Shafranov shift alone may not suffice to provide improved confinement (over standard H-mode) without rotation and rotation shear. However, making the core magnetic shear more negative provides a similar turbulence suppression mechanism to Shafranov shift, and can help devices such as ITER and CFETR achieve their steady-state fusion goals.

An example of high \(\beta_{P}\) discharge obtained on DIII-D and illustrating several of these features is shown in Fig. 15. The plasma cross section is a double-null divertor shape with elongation κ ~ 1.9 and average triangularity < δ> ~ 0.6. After an appropriate equilibrium is established (~ 1.7 s) the current in the Ohmic heating coil is clamped, so that the plasma current is forced to relax noninductively. This discharge achieves and maintains \(\beta_{P} \sim\beta_{N}\) ~ 3.3 with \(f_{BS}\) ≥ 70%, an excellent energy confinement quality (H_98y2 ~ 1.5) associated with the formation of an ITB at large minor radius (ρ ~ 0.7) in all channels (density, temperature, rotation, see e.g. [37]), Greenwald density fraction \(f_{Gw}\) ~ 1, and constant radiated power throughout the high \(\beta\) phase. The significant oscillations in the \(\beta\) traces are due to bursty ELM-like events driven by pedestal gradients and dominated by n = 1 [37], rather than higher n as most ELMs. Despite the severity of these perturbations, the ITB and a broad current profile with elevated minimum safety factor q_min≥ 3 are maintained in fully noninductive conditions for about 3 current relaxation times (\(\tau_{R}\) ~ 1 s).

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While the discharge of Fig. 15 has very high q₉₅~ 10, DIII-D experiments have also showed that excellent energy confinement quality can be maintained when q₉₅ is reduced towards reactor relevant values of q₉₅≤ 7, as long as \(\beta_{p}\) is maintained above a threshold value ~ 1.9 for ITB formation (see Fig. 16). With reduced Shafranov shift at lower q₉₅ and β_p, negative magnetic can be utilized to contribute to suppression of turbulence. Reverse shear has been predicted to lower the β_p threshold for the ITB in ITER and CFETR. So far, the extension to lower q₉₅ has been carried out inductively. Future experiments on DIII-D will aim to extend the fully-noninductive high \(\beta_{P}\) regime with ITB to q₉₅~ 6 by operating closer to the \(\beta_{N}\) limit ~ 4.5.

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Radiative Divertor Progress in Advanced Tokamak Plasmas

A significant effort has been made to extend puff-and-pump scenarios to even higher levels of power input in DIII-D. While plasma conditions at lower-to-moderate power input were found to be favorable to successful puff-and-pump radiating divertor applications to the DND, plasma response to higher power input resulted in a more complicated picture. Recent studies [85] have shown that improved energy confinement is possible during gas puffing under certain conditions for near-double null divertor (DND) plasmas, e.g. q₉₅ ≥ 6, P_IN ≥ 13–15 MW, H₉₈ = 1.4–1.8, and β_N = 3.5–4.0. In marked contrast to lower powered high performance plasmas, both τ_E and β_N in high power cases increased and ELM frequency decreased, as density was raised by deuterium gas injection (Fig. 17). This improved performance in the higher power plasmas was tied to higher pedestal pressure, which according to peeling–ballooning mode stability analysis using the ELITE code [87] could increase with density along the kink/peeling stability threshold, while the pedestal pressure gradient in the lower power discharges were limited by the ballooning threshold [85]. This resulted in improved fueling efficiency and ≈ 10% higher τ_E and β_N than is normally observed in comparable high performance plasmas on DIII-D. Applying the puff-and-pump radiating divertor approach at high versus moderate power input was shown to result in a much different evolution in core and pedestal plasma behavior. We have found that injecting deuterium gas into these highly powered DND plasmas can open up a new avenue for achieving elevated plasma performance, including better fueling, but this improved fueling may also have a downside when applied to a radiating divertor approach to divertor heat flux reduction. Just as fueling the main plasma by gas puffing can be less formidable for a DEMO-class plasma, the same also applies to impurity seed “fueling” of the core and, if uncontrolled, an unacceptable drawback is the possibility of deleterious accumulation of these impurities in the core.

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(2) Divertor poloidal flux expansion A second approach in reducing divertor heat flux that has been studied on DIII-D relies on shaping the divertor flux surfaces in advantageous ways. Increasing the poloidal flux expansion at the divertor targets spreads power loading over a wider target (“wetted”) area. One very promising and sophisticated approach that was tested in a high performance regime has been referred to the “Snowflake” divertor configuration [88]. The Snowflake divertor has been shown to be effective in dissipating heat flux at the divertor target for more conventional single-null H-mode discharges in both NSTX [89] and DIII-D [90] at modest power input. We examined a Snowflake-double-null divertor hybrid (SF-DN), which was configured by: (a) adding a second X-point near the outer target of the primary divertor, and (b) preserving the conventional double-null shape in the secondary divertor (Fig. 18b; [91]). The poloidal flux expansion at the outer divertor target of the primary divertor was significantly increased and the incoming power flow to this outer divertor was much more dispersed compared with a more conventional divertor configuration that does not have this second X-point. Compare the conventional DND (Fig. 18a) with the Snowflake-DN hybrid (SF-DN), as shown in Fig. 18b. Both configurations were biased slightly toward the lower divertor. High performance SF-DN plasmas largely mirrored the high performance characteristics of DNDs under both radiating- and non-radiating divertor conditions. This was not unexpected, because these SF-DN and DND plasmas had very similar poloidal cross-sections, upper and lower triangularities, and q₉₅ (≅ 5.0–5.2). Because of their nearly identical lower inner divertor geometry and poloidal flux expansion (≅ 6.6), both SF-DN and DND heat flux profiles at their respective inner divertor targets were similar, both prior to and during the radiating phases (Fig. 18a1, b1). On the other hand, the advantage of the SF-DN was tied to a much larger poloidal flux expansion at its lower outer divertor target, i.e., ≅ 28 for the SF-DN versus ≅ 9 for the DND; the result was a factor of two lower peak heat flux at the outer divertor target with the SF-DN shape, both before and during deuterium gas injection operation (Fig. 18a2, b2). One notes that q_⊥,P at the lower outer divertor target for the SF-DN in the non-radiating divertor case was still lower than q_⊥,P for the corresponding DND in the radiating divertor case. Control of snowflake configurations has been raised as a concern for future reactors, as small vertical perturbations could lead to large strike point motions; on DIII-D, we have found control to be sufficient to maintain appropriate geometry, though this affect does lead to some modest beneficial heat flux spreading.

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Controlling the particle inventory in the SF-DN from the primary divertor was difficult because particle flux in that divertor was spread out, making particle pumping difficult. For single-null Snowflake divertors, this would present a serious obstacle. DIII-D studies have shown for the hybrid SF-DN, however, that adequate pumping from the secondary divertor which has DND shape can provide significant pumping to help compensate for weak pumping in the primary divertor.

More reactor relevant DND plasmas that produce significant power outflow will very likely have peak divertor heat flux levels well above 10 MW/m² and thus require reliable methods of reducing excessive heating to the divertor structures. While several studies at DIII-D have found modest reductions in divertor heat flux under AT DND conditions are possible without acute deterioration in high performance, these experiences suggest, however, that no single approach will be adequate by itself to satisfy the severe requirements for divertor heat flux reduction DEMO-class plasma conditions. Future work will doubtless focus on advantageously combining different approaches to achieve the three goals of significant divertor heat flux reduction, maintenance of plasma performance, and adequate pumping—cognizant at the same time that plasma transport behavior can change as power input changes.

Validation of Current Drive Models

DIII-D experiments on Neutral Beam Current Drive (NBCD) have clearly demonstrated off-axis NBCD as expected from modeling [92, 93, 94]. Off-axis current drive is critical in testing the potential of high bootstrap fraction, steady-state operation with a broad current profile at elevated q, especially for q_min > 2 (section "High q_min Scenario"). For validation of off-axis NBCD physics, the local NBCD profile driven by the new tilted beams was measured in H-mode plasma and compared with modeling under a range of beam injection and discharge conditions such as the toroidal magnetic field direction, beam injection power, plasma beta and ratio of beam injection energy to electron temperature (E_b/T_e).

The full radial profile of NBCD measured by the magnetic pitch angles from the motional Stark effect (MSE) diagnostic (Fig. 19) shows a clear hollow in NBCD with the peak NBCD location at ρ ~ 0.45. This is in good agreement with the classical model calculation using the beam-ion orbit following Monte-Carlo beam ion slowing down code, NUBEAM. (Note that the orbit following nature of NUBEAM means that the calculated NBCD includes the fast-ion bootstrap current. Other analytical expressions have been derived to explicitly calculate the bootstrap current from alpha particles [95] and beam ions [96], with [96] finding the beam-ion bootstrap current is less than one-tenth the bulk bootstrap current at the same pressure gradient.) Time evolution of the MSE signals is consistent with transport simulation with realistic current drive sources. The beam-stored energy estimated using equilibrium reconstruction, neutron, and fast-ion D-alpha data do not show any noticeable anomalous losses of NBCD and fast ions. The measured magnitude of off-axis NBCD (Fig. 20) is very sensitive to the toroidal magnetic field (B_T) direction that modifies the alignment of the off-axis beam injection to the local helical pitch of the magnetic field lines. The NBCD profile for the B_T direction in poor alignment shows substantially reduced NBCD (~ 45%) as well as inward shift of the peak NBCD location (Δρ ~ 0.1). This dependency of the off-axis NBCD efficiency on the B_T direction is crucial to optimum use of the off-axis beams not only in DIII-D but also for application in ITER.

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Turbulent Transport in High β Scenarios

Transport is expected to be modified in high β scenarios through two principle effects. Firstly the turbulence can be reduced when local magnetic shear is increased on the outboard ballooning side. This naturally occurs in high l_i and high q_min scenarios. In the high l_i, a high average magnetic shear arises, driving up local shear. In the high q_min this is also found to occur as the weakening of the average magnetic shear near the q_min point is associated with stronger local shear on the outboard side. Geometric effects such as shaping and Shafranov shift can strongly increase these effects further. Secondly, higher β increases electromagnetic effects in the turbulence. It is important to assess behavior with electron heating, which further changes the character of the turbulence (favoring lower k ITG and TEM modes) in ways expected for burning plasma devices. The DIII-D program has made significant progress in assessing these issues, finding favorable transport properties for high β regimes.

Effect of Current Profile

While turbulent transport is known to generally degrade as the electron-to-ion temperature ratio increases from below 1 to near unity [97], recent experiments in steady-state scenario plasmas on DIII-D have shown that negative central magnetic shear (NCS) mitigates the transport degradation observed during electron cyclotron heating [98]. In these studies, systematic comparisons are made of core turbulence and transport at high T_e/T_i as the magnetic shear is varied by adjusting the early heating power, plasma current ramp rate and L–H transition time. For plasmas with positive magnetic shear (PS), both the ion and electron thermal diffusivities increase by ≈ 3 × near the mid-radius when T_e/T_i is raised from 0.8 to 1.1. Both the ion and electron thermal transport increase less with higher T_e/T_i for NCS plasmas, and the drop in H_98y2 during ECH is also significantly smaller (5% vs. 18%) for NCS plasmas compared to PS plasmas. The T_e/T_i dependence of transport observed on DIII-D is consistent with that observed on JT-60U, but the DIII-D studies permit deeper investigation of the underlying physics [99].

These DIII-D experiments have provided a more comprehensive physics understanding of the transport dependence at high T_e/T_i between positive and negative magnetic shear through measurements of the plasma turbulence. As seen in Fig. 21, the low-k broadband turbulent fluctuations increase less in NCS plasmas compared to PS plasmas with increased T_e/T_i [98]. Furthermore, a clear difference in the behaviour of low-k and intermediate-k fluctuations is seen, with low-k electron temperature fluctuations at ρ ~ 0.6 increasing with electron heating in NCS plasmas and intermediate-k electron density fluctuations around ρ = 0.65–0.7 decreasing with higher T_e/T_i in both PS and NCS plasmas. Linear simulations using the GKV electromagnetic gyrokinetic Vlasov code find that the growth rates of low and higher-k modes increase less with electron heating for NCS plasmas than for PS plasmas, and the dominant mode switches from ITG to TEM in the PS region as T_e/T_i is increased. These experimental and theoretical results encourage the development of Advanced Tokamak scenarios with NCS current profiles to mitigate the increase in thermal transport at higher T_e/T_i.

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To understand the effect of q profile on bootstrap fraction, systematic scans of the current profile in DIII-D, were made using an off-axis injecting neutral beam installed in 2011. These revealed that the ion and electron thermal diffusivities scale differently with the q profile [100]. As seen in Fig. 22, the electron heat channel improved with higher q_min, whereas more power was expelled through the ion channel as q_min increased. As a consequence, confinement did not improve with higher q_min values. These core transport experimental trends did not seem to match well with the TGLF model, which fits linear turbulent modes to predicted saturation levels from the GYRO non-linear code. Far infrared (FIR) chord integral fluctuation measurements showed low-k density fluctuations rising as q_min rose. The effects of this ion transport degradation on the profiles was observed to impact the bootstrap and non-inductive current fractions achievable for each type of q profile. In addition, higher q₉₅ was found to lower pedestal height, while higher q_min was found to raise core temperatures and broaden profiles. Thus, the maximum bootstrap fraction is not found at the maximum q_min as expected.

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These observations highlight the importance of deeper investigation of transport dependencies to resolve physics models and map the path to high performance fully non-inductive operation, motivating upgrades to DIII-D to increase current profile flexibility, as discussed in section "Future Research Requirements and DIII-D’s Role".

Effect of High β

Reaching high bootstrap fraction fully non-inductive plasmas, requires operation at high poloidal beta, β_P, the pressure relative to poloidal field. This has a natural synergy with transport optimization as high β_P increases local shear, stabilizing turbulence. Recent experiments on DIII-D show an internal transport barrier (ITB) spontaneously forms [37] with high bootstrap current leading to improved energy confinement. This is largely a result of turbulence suppression from a large outward shift of the core plasma that increases the local magnetic shear on the outboard ballooning side of the plasma.

Using both gyrokinetic stability analysis and quasi-linear turbulent transport predictive modeling [101], it is found that plasma discharges with high bootstrap fraction can self-organize into a state with either a strong internal transport barrier (ITB) and a weak edge transport barrier (ETB), or a weak ITB with a strong ETB. The weak ITB state can be triggered to switch into a state with a strong ITB state by its large edge localized modes (called ELMs). The strong ITB type is more persistent due to its smaller ELMs. Both types of discharges show improved energy confinement over the standard ITER98pb(y,2) scaling by up to 80%. However, it is noteworthy that discharges with the strong ITB achieve the highest energy confinement. Transport differences between the two discharges are partially controlled by the kinetic ballooning mode instability (KBM). Thus self-organization occurs by interactions between the bootstrap current, magnetic shear, and the KBM stability, while at lower bootstrap fraction the ITB collapses and the energy confinement drops (Fig. 23). It should be noted that even these smaller ELMs are unlikely to be sufficiently small for ITER, and almost certainly not for a fusion reactor, where the steady state exhaust is already a major challenge. Thus ELM control development for steady state regime remains essential,

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A deeper analysis of these discharges [102] reveals the electron transport in the core to be enhanced by electromagnetic effects that develop at high β and multiscale effects. The importance of including these effects is highlighted in Fig. 24, where DIII-D data [73] is compared with transport models using either only electrostatic or also electromagnetic effects. In the electromagnetic simulations it is found that ion scale turbulence suppresses electron scale fluctuations due to zonal flow mixing. A new saturation model in TGLF that incorporated this effect improved accuracy of temperature predictions, with the electromagnetic effects reducing temperature gradients, to achieve a better match to experiment as shown in Fig. 24 [74]. These effects, and discrepancies with experiment become more pronounced at higher q₉₅; there is clearly much further work to do to resolve transport models for high β advanced tokamak plasma configurations. Not least direct perturbative measurement of fluctuations in relevant configurations could directly validate the processes involved. And, as we set out in section "Burning Plasma Relevant Conditions", increases in ECH and current drive capability will permit exploration of this physics in more reactor relevant dominantly electron heated steady state regimes.

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Stability

From the viewpoint of MHD stability, the greatest difference between steady state advanced tokamak scenarios and more conventional scenarios is that most AT scenarios operate at high normalized beta (β_N), requiring a nearby (distance ~ 30–40% of minor radius) conducting wall for stability to long wavelength kink modes. The steady state hybrid scenario typically is very near the no-wall, ideal-MHD stability limit [45, 51], while the high-q_min and high-β_P scenarios significantly exceed it [41, 103]. Only the high-ℓ_i scenario [48] achieves high β_N without wall stabilization. The broad profiles of pressure and current density that are preferred for maximizing the bootstrap current are in addition favorable for wall stabilization, and DIII-D’s off-axis neutral beam injection (a capability added in 2011) contributes to broadening of these profiles [40, 50, 100]. As shown by the blue data points in Fig. 25, high-q_min advanced tokamak discharges in DIII-D often significantly exceed the no-wall stability limit, indicating the influence of wall stabilization [68].In the case of a real wall with finite conductivity, the ideal kink mode is predicted not to be fully stabilized, but instead is converted to a resistive wall mode (RWM) with a growth rate and real frequency of the order of the inverse resistive time of the wall. In high-q_min experiments, for example, slowly growing instabilities consistent with the RWM are often observed to cause beta collapse or termination of the discharge at high β_N, as indicated by the yellow points in Fig. 25. Understanding the conditions for “passive” stability of the RWM above the simple ideal-MHD, no-wall limit has been an important challenge for AT research.

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A key development of the past decade has been the prediction and experimental confirmation of the role of kinetic damping in the stability of the RWM, superseding earlier models of RWM damping that invoked sound waves or Landau damping. The passive stability of the RWM at high β_N is now understood to result from resonant wave-particle interactions [104, 105, 106], including the transit frequency of passing particles as well as the bounce and precession frequencies of trapped particles. The plasma’s ExB flow Doppler-shifts these frequencies into resonance with the near-zero frequency of the RWM. In a DIII-D experiment [107] that actively probed the stability of the mode, the RWM was excited with a 20 Hz magnetic perturbation while the plasma rotation was varied using the neutral beam torque. The measured amplitude and phase of the plasma response agree well with the predictions of the MISK model [106] (Fig. 26). The two minima in the amplitude, indicating stronger damping of the stable mode, are attributed to resonant damping at the precession drift frequency and the bounce frequency of trapped ions. Other MISK calculations show that the passively stable points above the no-wall limit in Fig. 25 are consistent with stabilization by kinetic damping [68].

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Reducing the plasma-wall distance can also improve wall stabilization. In high-β_P experiments in DIII-D, ELMs are found to trigger a transient n = 1 external kink that leads to a temporary collapse of the H-mode edge pedestal or a disruption [37]. The kink and the ELM that drives it both typically evolve on a sub-millisecond time scale, shorter than the time constant of the vessel wall, and thus the instability behaves as an ideal-wall kink mode. Reducing the plasma-wall distance improves the stability of the discharge, consistent with ideal-MHD stability calculations using GATO [37, 70].

Active feedback stabilization of the RWM can extend the regime of stable operation very close to the ułtimate limit of ideal-wall stability boundary. Active stabilization of the n = 1 RWM was applied to some of the high-q_min discharges in Fig. 25, using simple proportional gain with internal non-axisymmetric control coils and internal poloidal field sensors. As shown by the magenta points, active stabilization yields a significant extension of the stabilized regime to higher β_N [68]. Some of the RWM instabilities that occur during feedback control are the result of an unstable n = 2 RWM, which was not addressed by the control scheme. Other DIII-D experiments to measure the stable plasma response [108, 109] have shown that multiple n = 1 and n = 2 modes may be excited at high β_N near the no-wall limit. These observations indicate that multi-mode feedback control is a frontier for future development.

Advanced state-space control algorithms can improve the robustness of a feedback system by improved filtering of noise and disturbances [110], and have been employed in NSTX [111] to extend the range of stabilized operation to higher β_N and β_N/ℓi. A linear quadratic Gaussian (LQG) controller was developed and tested in DIII-D. Initial results show that the LQG controller is more efficient than simple proportional control in suppressing an “artificial RWM” magnetic field pattern created by other coils. Notably, its performance in maintaining stability above the no-wall limit using more reactor relevant external control coils matched that of a proportional gain controller using internal coils—a significant development [112]. This suggests that with further work, it may be possible to translate the learning and physics advances being developed with internal coils, as discussed above, to practical reactor relevant external coils.

AT plasmas are also subject to tearing modes, which often become the performance-limiting instability when kink modes are avoided using the strategies discussed above. In steady-state hybrid discharges, resistive modeling with DCON and PEST3 predicts improved stability to tearing modes with broader current density and pressure profiles [44]. In such discharges, a “flux pumping” dynamo process maintains a broad current density profile and also reduces or eliminates sawteeth as seeding events for neoclassical tearing modes (NTMs), both contributing to better stability against m/n = 2/1 NTMs than for conventional H-mode discharges [45, 51]. In high-q_min discharges above the no-wall stability limit, tearing stability is closely linked to the approach to ideal-MHD stability limits. Broadening the pressure and current density profiles is predicted to improve both ideal and resistive stability limits [100]. Off-axis electron cyclotron current drive (ECCD) is found to improve stability to the 2/1 tearing mode, but insensitivity to the exact radial location indicates that the mechanism is likely to be modification of the tearing stability index ∆′ rather than direct stabilization by localized current drive at the q = 2 surface [100, 113]. Raising q_min above 2 eliminates the 2/1 tearing mode, but 3/1 modes can still occur [68]. High-ℓ_i discharges are also often limited by 2/1 tearing modes. As in the high-q_min case, pre-emptive ECCD near the q = 2 surface helps to avoid 2/1 modes, again probably through modification of profiles and not direct stabilization [48].

Remaining challenges for the stability of AT scenarios include the validation of kinetic damping models in the various specific AT scenarios, particularly at higher β_N and at low rotation, and with decreased energetic particle fraction. The development and validation of state-space controllers, including multi-mode control, will improve stability while minimizing the control power. The capabilities of RWM stabilization with external coils should be pursued. Tearing modes remain a significant issue for most scenarios, and the challenge is to develop capabilities of stability prediction and profile control that will enable confident design and operation of passively stable discharges.

Energetic Particle Physics

Energetic particles (EP) provided by the eight 80 kV neutral beams in DIII-D play critical roles in heating, current drive, momentum input and plasma stability, enabling critical studies of these interactions. The presence of these energetic particles introduces challenges as these particles can excite a variety of Alfvén eigenmodes (AE) and other instabilities, which in turn can lead to a range of transport mechanisms and other effects. The resultant fast ion transport and loss can reduce performance, redistribute currents or cause localized heating and damage of first wall components. AT scenarios on DIII-D can have high fast ion content (β_fast/β_total) up to 40% and are often observed to have a variety of unstable energetic particle driven instabilities which limit the achievable performance. Several scenarios are typified by reversed or broad/weakly reversed magnetic shear with relatively high q_min. These scenarios are particularly susceptible to Alfvén eigenmode activity and are the focus of this section.

Transport of Energetic Particles and Predictive Tools

Neutral beam injection into reversed magnetic shear DIII-D plasmas, like those characteristic of various AT scenarios, produces a variety of Alfvénic activity including toroidicity induced Alfvén eigenmodes (TAE) [114], reversed shear Alfvén eigenmodes (RSAE) [115, 116], ellipticity induced Alfvén eigenmodes (EAE) [117], beta induced Alfvén eigenmodes [118], beta induced Alfvén acoustic eigenmodes (BAAEs) [119], and linearly coupled RSAEs and TAEs [120]. By studying these modes during the discharge current ramp phase, when incomplete current penetration results in a high central safety factor and strong drive due to enhanced coupling to multiple higher order resonances [121], a great deal has been learned about the physics of the eigenmodes and their impact on fusion plasmas.

Work in this area has progressed rapidly due in large part to advances in diagnostics for both fast ions and the eigenmodes themselves. For example, measurements of the confined fast ion profile are now routinely available from Fast Ion D_α measurements FIDA [122] and full eigenmode structures are routinely measured by Electron Cyclotron Emission (ECE) [123, 124]. Many of the predictions for linear properties of the typical eigenmodes mentioned above have been observed experimentally and are now well understood. An example is shown in Fig. 27, where ECE measurements as well as ideal MHD predictions from the NOVA [125] code for RSAEs and TAEs are given [120]. The RSAEs are clearly localized near q_min and the TAEs are seen for radii outside of q_min extending to the plasma edge. These are the most common Alfvén eigenmodes modes observed in DIII-D AT plasmas. The NOVA results shown here exhibit close agreement with the measured spatial structure of the temperature perturbation for both the n = 3 RSAE and TAE, including the oscillatory structure of the solutions in the radial direction, and predicted mode frequencies were within 10% of calculations.

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Data from fast ion diagnostics on several devices worldwide indicate that during periods of strong Alfvénic activity the central fast ion population is significantly depleted relative to expectations based on neoclassical diffusion alone [126]. An example of the observed fast ion profile flattening is shown in Fig. 28, where the fast ion pressure profile inferred from equilibrium reconstructions is given along with FIDA measurements and the classical TRANSP prediction [126]. Throughout this time period the neutron rate is approximately 50% of that predicted by TRANSP, but consistent with a large radial transport of the beam ions (DB = 5 m²/s, inset). In addition to impacting heating, torque and overall performance, this large transport has been shown to have a similar effect on the neutral beam current drive (NBCD) profile, something which can have serious implications for steady-state scenario development [62, 126, 127, 128]. Interestingly, there are examples where EP instability induced fast ion transport was actually found to benefit performance by redistributing central NBCD causing a reduction in central magnetic shear and the formation of an internal transport barrier [127]. Subsequent fast ion transport experiments have identified critical gradient-like or stiff behavior of the fast ion profile where above a phase space dependent threshold, EP transport rises sharply [62, 129]. An example is shown in Fig. 29, where measured FIDA profiles become clamped above a critical beam power due to an increasing level of Alfvén eigenmode activity (not shown), and the measured neutron deficit (panel b) is found to increase abruptly from classical levels above ~ 3 MW injected power.

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This large deficit in the central fast ion population is a common feature of discharges with multiple Alfvén eigenmodes and has generated both concern and interest worldwide. In 2010, the EP deficit in DIII-D was explained using guiding center calculations in the presence of a spectrum of modes [130, 131] using the ORBIT code [132] and mode structures from the ideal MHD code NOVA, matched to experiment. It was found that the measured mode amplitudes were just above the threshold for stochastic transport due overlap of multiple wave particle resonances of the central fast ion population. This was well described in self-consistent coupled mode-EP simulations (Fig. 30) [133, 134, 135].

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EP Behavior in AT Scenarios

AT scenarios with elevated q profiles like those discussed above, are more susceptible to EP driven instabilities and fast ion transport. The reason is two-fold. First, elevated q_min allows fast ions to drive energetic particle instabilities more effectively through higher order resonances [121, 130, 136]. These are particularly important in DIII-D plasmas, since the 80 keV beam energies are not able to fulfill the fundamental wave-particle resonance condition at normal operation fields. Second, scenarios with elevated q_min often have weak or reversed magnetic shear, and these types of q-profiles result in wider modes with weaker continuum interaction that are capable of interacting with the energetic particle population over a larger radial range. At even weaker poloidal field like that in DIII-D high-β_P discharges, fast ion loss boundaries can be present in the core of the plasma and allow energetic particles to be lost to the vessel wall [41, 137].

Figure 31 compares the q-profiles obtained during the high-β_N phases of a pair of consecutive AT discharges. Both use the same boundary shape and have density profiles with the same shape, but the q_min~ 2 case is approximately 10% lower density at all radii. The crosspower density fluctuation spectra between the two most central interferometer chords shows significantly more TAE activity in the plasma with q_min ~ 2 than q_min ~ 1, with average amplitude of coherent modes in the TAE band about four times higher. These cause additional transport of energetic particles, with plastic scintillator neutron counts 43% lower and a 17% energy deficit relative to TRANSP predictions (panel b), typical for such high q_min AT plasmas. [138, 139].

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High β_P scenarios like those discussed in section "High β_P Scenario" are also susceptible to EP driven instabilities and fast ion transport. For example Fig. 32 shows that the diffusivity level required to match the measured neutron emission roughly tracks the AE mode activity. As the density increases, the fast ion slowing down time decreases, reducing fast ion content (thereby reducing the AE instability drive), and the distances travelled by displaced fast ions before thermalization. Both effects lead to reduced fast ion losses. Calculations of the Alfvén continuum indicate that during the high density phase, the core TAE gap is relatively closed [139], which may also contribute to the reduced AE activity and resulting lower fast ion transport [37].

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It should be noted that other scenarios such as steady-state hybrid plasmas (with q_min~ 1–1.3) are also susceptible to EP transport, and, depending on q_min, they can have either AEs or Fishbones that cause significant transport and limit performance [51].

Potential for Control or Avoidance of AEs to Improve AT Scenarios

Comparison of cases with high and low fast ion transport has suggested ways to improve the q_min ~ 2 scenario [63] that the DIII-D EP program has begun to explore experimentally. For example, if the negative magnetic shear region can be expanded so that the q_min radius is moved outwards where there are fewer fast-ions, then the drive of RSAEs (and perhaps other EP modes) should be greatly reduced, as shown in Fig. 33, to suppress the core TAEs [63, 140]. Also, the drive for AEs can be altered by varying the radial gradient in the fast ion pressure profile grad-β_fast [129, 136] to keep it below a critical threshold [139] through variation of density and NBI power as well as NBI injection geometry. In 2010, two beams on DIII-D were modified to allow off-axis injection as opposed to central deposition. The result is the capability to create flat or potentially off-axis peaks in the fast ion pressure profile and thus completely stabilize the RSAEs (Fig. 34). At the beginning of the 2019 DIII-D experimental campaign, the amount of off-axis NBI power available to DIII-D will be doubled, allowing the exploration of high q_min AT scenarios with broader, more stable beam ion profiles. To the extent that neutral beams or other externally controllable sources of fast ions such as ICRH tail acceleration are available in a fusion power plant, the potential will exist for tailoring of the fast ion profile to reduce (or possibly enhance) fast ion transport and optimize performance. The actual 3.5 MeV alpha fusion product profile, however, will be more difficult to control directly and may ultimately drive instabilities that limit performance.

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Experiments carried out on DIII-D also show that localized electron cyclotron heating (ECH) can drastically alter beam driven AE activity including, in some cases, the stabilization of RSAEs and improve fast ion confinement [64, 141, 142]. Similar experiments have been carried out on several devices, altering AE activity in Heliotron J [143] the TJ-II stellarators [144] and on ASDEX Upgrade [145]. The suppression occurs when ECH is deposited near q_min in DIII-D experiments (Fig. 35), when only the very end of RSAE chirps are visible.

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In 2017, an engineering upgrade to the neutral beam system on DIII-D enabled time-dependent programming of both the beam voltage and current [65, 66]. This has enabled the injected beam ion population to evolve with plasma characteristics in order to navigate the AE space, to optimize heating and AE stability in real time, and thus discharge performance [66]. This raises the exciting prospect of exploring how to tune EP populations with subtle changes to manage the plasma EP stability.

International Context

New plasma research capabilities are needed to resolve the path to a steady state fusion reactor. Many devices around the world exploit co-injected neutral beams to reach high performance, heating the ions and driving favorable rotation, unlike in a fusion reactor. The push to operate with reactor relevant wall materials, though important to study, has forced facilities to high collisionality, as they use gas puffing to drive ELMs to flush impurities from the core; on present scale devices, this forces the pedestal to the reactor-irrelevant ballooning limited part of the operational space, and the core to elevated collisionality [146]. Flexibility to access high β_N and vary current and pressure profiles is also limited, while reactor compatible current drive tools (which must be more efficient than present technologies, and solve antenna loading and plasma facing component issues) have yet to be developed. The world’s facilities are well suited to explore improved divertor concepts with the highly flexible MAST-U and beam-upgraded TCV facilities coming on line in 2018, and tungsten divertors on JET, ASDEX Upgrade and WEST (where the divertor can be heated). However, integration of closed divertor approaches with high performance fully non-inductive cores remains elusive.

In this context, the DIII-D facility focuses on exploring the core advanced tokamak physics and its compatibility with reactor relevant plasma exhaust solutions. On the core it will exploit its high configuration flexibility to develop reactor relevant scenarios and resolve scientific questions. In parallel it is assessing improved divertor concepts and underlying divertor physics to project how to detach plasma exhaust from plasma facing components while maintaining AT configurations.

DIII-D Plans

The DIII-D facility is now being redeveloped to access regimes at reactor like physics parameters and plasma configurations directly, in order to address the relevant physics at the performance levels required and resolve the techniques needed for future fusion reactors. Starting in 2018, major improvements in current drive tools, electron heating, 3D fields and divertors are foreseen, providing capabilities that will complement those elsewhere around the world. The below described elements represent a coherent package of facility developments proposed for the next DIII-D operating period from 2019 to 2024. Further gaps to a fusion reactor, facility potential and more speculative long term possibilities are reserved to a discussion in section "Further Gap Issues to Fusion Reactors".

Fully Non-inductive Steady State Regimes

A foundational element of the steady state approach is to demonstrate that self-consistent fully non-inductive solutions can be sustained at required performance levels, and to understand what the performance limits and required control tools are. DIII-D is being upgraded with large rises in flexibly deposited current drive and increases in available heating power to access the full range of potential high β steady state reactor configurations to determine the path and the physics basis. It is also pioneering new current drive technologies to proof out the tools that will be required in a steady state fusion reactor.

In 2018, DIII-D neutral beam systems will be re-oriented to double off-axis current drive power. Two of the 8 beams will be toroidally steerable, allowing all power to be injected in the plasma current direction to assess high β_N limits, as well as enabling rotation variation at lower current drive levels. Beam energy rises will increase current drive and electron heating. This will be augmented by increases to 9 MW electron cyclotron current drive power, to be used to finely tune the current profile for performance and stability control thanks to its precise deposition control.

These developments will broaden current profiles and remove rational q flux surfaces (Fig. 36) to access projected-stable configurations. Simulations predict transport and stability limits will rise to reach β_N ~ 5 fully non-inductively (Table 2), comparable to ARIES-AT parameters, with flexibility to explore the roles of current, pressure and fast ion profile, with modeled solutions ranging from peaked current so-called ‘high l_i’ scenarios, to the broad current ‘high q_min’ shown here. This will enable tests of (1) kinetic damping and resistive MHD close to ideal MHD β limits, (2) probing and control of energetic particle driven instabilities, (3) assessment of the role of current profile in high β electromagnetically driven turbulence, and (4) compatibility of advanced profiles with fully non-inductive sustainment and performance limiting physics.

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Table 2

Existing best stationary high q_min plasma (inductive) compared to FASTRAN/IPS simulations of DIII-D operating points with upgrades. q₉₅ = 5–6. f_NI≡ total noninductive current/I_P

Case	On-axis NBI (MW)	Off-axis NBI (MW)	ECH (MW)	Transport limited βN	Ideal MHD limited βN
Shot 147,634 qmin ~ 1.5	7.5	3.3	3.5	3.5 (fNI = 0.75)	3.7 (with wall limita)
Predicted qmin > 2	9.5	10.7	9	5.1 (fNI = 1.0)	4.9 (with wall limit)
Predicted qmin ~ 1 “high li”	7	13b	9	4	4.1 (no-wall limit)

^aLimit predicted by FASTRAN with the ~ 6 s, partially inductive discharge taken to t = ∞

^bWith unfavorable B_T direction for off-axis current drive. Off-axis NBI broadens pressure only in this case

DIII-D will also assess the physics of three promising new current drive technologies, which simulations indicate could lead to much greater efficiency in future reactors, also addressing coupling and antenna issues—potential game changers in required scale and performance of the device. These are top launch ECCD, ultra-high harmonic fast wave (Helicon) [151, 152], and high-field side lower hybrid current drive (HFS LHCD) [153]. Helicon has, in fact, already demonstrated good coupling in low power tests on DIII-D [152] and is proceeding to a 1 MW installation in 2019, alongside proof of principle top launch ECCD tests. HFS LHCD is planned soon after. Projections indicate these could substantially improve current drive and further broaden profiles on DIII-D (Fig. 37) to further study transport, stability and energetic particle physics, raising ideal MHD β_N limits to values approaching 6, and thereby fostering potentially more robust margins for ideal and resistive MHD stability.

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This work will establish the potential for fully non-inductive high β_N scenarios with stationary current and pressure distributions that are consistent with current drive sources, and macroscopic and Alfvénic stability.

Burning Plasma Relevant Conditions

The critical further step in developing a steady state core is to project regimes to burning plasma conditions. Rotation, collisionality, T_e/T_i and energetic particle content all play crucial roles in determining the structure, magnitude and channels of turbulent transport, modifying fluctuations from fine scale instabilities to large structures (Fig. 38), and altering pinch and diffusive effects. These parameters are also critical determinants of ideal MHD β_N limits through kinetic resonances with plasma rotation and energetic particle interactions [107]. Collisionality and rotation can further play important roles in pedestal stability and height.

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To address these issues DIII-D plans progressive increases in electron and torque-free heating. A second pair of beams will be made toroidally steer able to enable full-power balanced torque operation. Combining with the planned upgrade to 9 MW ECH, which increases electron heating and current drive, simulations predict this will enable fully non-inductive plasmas with advanced tokamak profiles (Fig. 39 with q_min > 1.5) and burning plasma relevant parameters (T_e/T_i ≈ 1, low ν* and rotational shear) at β_N ~ 4 and q₉₅ = 6. Additional helicon or HFS LHCD improves on this further, replacing lost neutral beam current drive with further off-axis currents to study the influence of advanced tokamak profiles on transport and stability up to β_N ~ 5 in torque free H-modes (Fig. 40). The increased ECH also permits evaluation of reactor relevant dominant electron heating and thus burning plasma transport processes at low rotation in these regimes. Separately, these current drive tools enable operation at higher density to study coupled electron–ion turbulence at T_e ~ T_i and zero torque.

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This will enable development of validated models to predict burning plasma performance, with assessments of how these parameters impact critical gradients for drift wave induced turbulent transport in all channels. Research will evaluate how scenarios can be adapted to loss of ExB shear stabilization, and how optimization of the magnetic shear profile may be used to compensate. ECH will also enable precise perturbative tests of turbulence and pedestal behavior. Kinetic MHD stabilization physics will be advanced by varying the influence of fast ions using variable beam geometry, voltage, and by increasing β_thermal/β_fast using ECH.

Control of Instabilities and ELMs

Sustained operation of tokamak fusion plasmas requires control and mitigation of deleterious transient events. Plasma instabilities, including edge-localized modes (ELMs) and core, tearing, or global instabilities that lead to disruptions, could prevent reactors achieving their mission through damage to the facility or de-rated operation to avoid potential damage.

The heating and current drive tools discussed in section "Fully Non-inductive Steady State Regimes" will be highly important in exploring and understanding how to stabilize instabilities. One aspect is to assess the physics and develop control of global plasma stability at high β_N, where kinetic stabilization mediates a dissipative interaction of the pressure driven kink with the resistive wall, into which the broader current profiles achievable will that displace the eigenmodes more deeply. Toroidally steerable, variable-voltage neutral beams and ECH will also vary ion velocity distribution and rotation to explore the resonant interaction of this mode with orbital frequencies of trapped ions behind this kinetic damping effect.

A second crucial aspect will be the understanding of tearing mode influence, where even with the 2/1 surface removed, there remain concerns over the incidence of higher m/n modes (5/2, 3/1). Are these a manifestation of proximity to ideal MHD limits, or likely to occur more broadly across the operating space? If the latter, can current drive techniques be developed to maintain passive stability or actively remove modes when they occur? Exploring the high β_N stability space will be a crucial research goal, benefiting from both the broad regime access and the local perturbative capabilities with ECCD.

A further critical element is the use of 3-D fields to control instabilities such as ELMs, where significant progress has been made on DIII-D. However, present capabilities have limited harmonic flexibility to toroidal mode numbers of n = 1 or 2, whereas the optimal fields for ELM and rotation control have n = 3 or 4. Simulations developed [D.W. Weisberg et al., in preparation, 2018] in the DIII-D program predict that at these higher n it will be possible to vary the plasma response to independently control interactions in different parts of the plasma, thus controlling rotation profile, locked modes and ELMs independently. These simulations predict that much more efficient coil sets for 3-D control are possible. A projected 12 coil midplane (‘M’) array (Figs. 41, 42) will test this physics, providing the first detailed spectral optimization studies for ELM and rotation control with n = 3 or 4 fields. This will help understand how best to deploy 3-D field configurations to control ELMs and minimize hot spots for steady state fusion reactors, where such techniques are likely to require coils to be located outside the vessel for protection. The approach here is to exploit DIII-D flexibility to resolve the physics of the interaction and understand the optimization, so that a simplified external coil approach can be developed for a fusion power plant. This coil set will also help understand the optimization for ITER, which has a coil arrays that the new DIII-D set would closely emulate.

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This enhanced 3-D coil set coupled with upgraded 3-D diagnostics will also be able to probe the plasma response to applied field in order to measure RWM dissipation physics at n up to 6, and develop advanced active control techniques at β_N approaching the ideal-wall limit (Fig. 25) to project a path to high β_N ideal MHD stable operation.

Should reactor systems fail, safe means to quench a fusion plasma are needed. Present techniques inject particles at the edge, limiting assimilation and allowing dangerous runaway electron beams to grow. DIII-D plans to develop ‘inside-out’ disruption mitigation using low-Z shell pellets filled with dust to deposit particles to the core. Modeling (Fig. 43 [156]) indicates this will dramatically improve all aspects of the disruption: 100% impurity assimilation assures high radiation fraction for rapid thermal quench; decay of the plasma current occurs more slowly (reducing induced forces) due to a still-warm plasma edge, while stochasticity generated in the core dissipates incipient runaway electrons. Particle and radiative diagnostics will be deployed to validate models of the quench and runaway dissipation, to develop predictive understanding.

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Core–Edge Integration

A fundamental issue for a steady state reactor is to find a solution that simultaneously delivers high core performance and has compatibility with the divertor and wall. Fusion reactor cores will operate at low collisionality, ν^*, due to their high field and current [ν^* ~ n_e/(I _P ² B _T ² shaping²) ~ n _e ³ /P²], while divertor protection requires a high absolute density dissipative divertor with a high degree of radiation to spread heat and reduce particle energies; a state known as ‘detachment’ This must also provide sufficient pumping for helium ash removal and steady-state density maintenance. However, such dissipative techniques and wall interactions can lead to neutral and impurity influxes that adversely affect the core and pedestal performance. Conversely, access to high power low collisionality cores can lead to divertor and wall fluxes that are particularly challenging to deal with.

Part of the solution is to alleviate this tension by improving behavior in each region. For instance, closed divertors, such as the promising ‘small angle slot’ (SAS) configuration [H. Guo et al., in preparation], would facilitate detachment at lower upstream density, with neutral dynamics optimized to reduce particle energies at all radii (Fig. 44) and somewhat trap neutrals in the divertor region to reduce core fueling), while simultaneously controlling heat flux and erosion—a great challenge facing steady-state fusion reactors. Alternately, a super-H mode pedestal raises pressure (noting ν _ped ^*  ~ n _e ³ /P²) to achieve a high density, low ν^* pedestal solution [157] that may facilitate high density divertor detachment access. Planned power upgrades and increased PF shaping flexibility will help explore such optimizations and the interactions between the two regions. Further, planned installation of more closed configurations in both the main upper and lower pumped divertors will enable investigation of higher density detached states at high power and particle flux with increased neutral and photon opacity compared to present capabilities, in order to explore the interaction of detached radiating divertor regimes with both divertor geometry and the plasma core.

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Core–edge interactions will be explored through new profile, turbulence and neutrals diagnostics, exploiting relevant low ν^* access to assess governing pedestal physics. Compatibility and interaction of impurities arising from the wall and radiative mantle techniques with core performance will be assessed, utilizing perturbative impurity transport techniques, facilitated by a new laser blow off system and a hot tile test facility, as well as changes to wall and divertor materials. Siliconization and a subsequent SiC main wall tile arrays will provide a low carbon environment to assess impurity and radiative divertor dynamics, as well as a potentially interesting candidate reactor wall material. The planned helicon and HFS LHCD upgrades discussed in section "Fully Non-inductive Steady State Regimes" are also projected to enable higher density variants of the fully non-inductive β_N ~ 5 plasmas discussed earlier to assess core-divertor solutions (Fig. 45).

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Further Gap Issues to Fusion Reactors

The capabilities discussed above will position DIII-D well to validate physics models and develop technical solutions for phenomena from the core to the edge at reactor relevant parameters for each region, developing a valuable projective physics understanding. Nevertheless, it is instructive to consider what further physics gaps lie in the path to a steady state solution, and what steps (on DIII-D or elsewhere) may be valuable to develop a fuller confidence and resolve techniques and predictive models for future reactors. Two key themes emerge: (i) to access more reactor-relevant physics behaviors, and (ii) to understand the interaction between different regions and parts of the solution (e.g. high opacity plasma edge, coupled electron–ion turbulence, or super-Alfvénic ion distributions). In many cases these interactions are highly non-linear, and so important to explore in order to resolve models and be able to project integrated reactor solutions at relevant parameters.

The most critical aspect is to reconcile the core and the edge. Core and edge are strongly and non-linearly coupled, with, for instance, leakage of neutrals and impurities from closed divertor solutions impacting pedestal behavior, while requirements for pedestal performance place strong challenges on the divertor. Understanding what combined state they reach, and how they non-linearly interact, requires both regions to be in reactor relevant physics regimes. However, pedestal behavior is governed by collisionality, ν^*, while a dissipative divertor solution requires radiation, primarily governed by absolute divertor density and parallel heat flux. From the basic scaling for collisionality, ν^* ~ n _e ³ /P², (assuming a fixed mapping between divertor and pedestal density for simplicity) divertor and core cannot simultaneously operate in reactor relevant physics regimes (n_e and ν^* respectively) unless they are also at reactor-relevant absolute pressure. Techniques such as super-H and divertor closure can modify the mapping from divertor to pedestal top to alleviate the challenge, but further progress is needed to close the gap in n_e and ν^* to study a reactor-like integrated dynamic. Further, this divertor-pedestal interaction is itself altered by increasing pedestal opacity as reactor-like densities are approached, where pedestal profiles become more strongly dependent on transport and pinch effects, making exploration of higher density pedestals particularly important.

Shaping is a key lever to raise pedestal pressure; for example with higher triangularity (a rise in triangularity to 0.9 is possible with removal of the upper inner cryopump in DIII-D, Fig. 46), pedestal stability and height is improved, also increasing plasma volume and current carrying capacity, and thus overall parameter range. Combined with appropriate heating and current drive choices, a significant rise in performance in steady state conditions is projected (Fig. 47) in FASTRAN integrated modeling projections (see section "Simulation Tools"), with a tripling of pedestal height and stored energy over present steady state regimes on DIII-D. ITER-like ν _ped ^* values would be obtained at double the present accessible density. This could help decouple ν^* and density to explore high performance cores with high power more dissipative divertor configurations, and begin to understand the changes in pedestal dynamic with increasing opacity. The decoupling of ν^* from Greenwald density fraction would also help to resolve the physics and critical parameters for density limit—a key enabling parameter for reactor performance and divertor dissipation. These developments would bring DIII-D close to ITER in ν^*–density space (Fig. 48), though a speculative further step to raise toroidal field to 2.5T would require careful analysis, and possibly further buttressing and cooling of the structure.

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Higher density steady state regimes would also close the gap on other key metrics of fusion regime relevance. Exploring the parameters in the 2.2T projection of Fig. 47 further, we see increased bootstrap fraction will enable exploration of high performance regimes that are closer to self-sustainment. This is due to the lower (and more reactor-like) fast ion fraction, which will in turn help test energetic particle physics and ideal MHD limits in more reactor relevant ways. High density will also lead to increased electron–ion collisionality to explore more equilibrated transport dynamics, and thus capture turbulent transport interactions in reactor-like electron–ion coupled regimes. This would be a significant step in testing physics over a wider range of more reactor relevant parameters to understand projection, helping close and understand key physics gaps toward future D-T fusion reactors, that is possible within present facility limits.

A further gap remains in the above argument, associated with pedestal opacity. While the above developments can enable higher density access with low collisionality pedestals, they will do so at relatively low opacity. Penetration depths for neutral ionization, Δ_CX, scale predominantly with density (Δ_CX = 1.91E17 T _ped ^0.425 /n_ped [Loarte, private communication]). At present maximum field in DIII-D, 2.17T, Δ_CX is comparable to pedestal width for reactor-relevant ν _ped ^*  < 0.2, and significant influence of neutrals is observed on pedestal structure. Penetration depths can be reduced by raising density of course, but at the expense of raising ν _ped ^* , and thus potentially altering pedestal transport mechanisms. But Δ_CX reaches half the width at 3T and a third at 4T. Closing this gap would enable a facility to explore a low collisionality, transport-governed pedestal while at the same time achieving high density detached conditions. This effectively goes further down the path of understanding how non-linear interactions govern an integrated solution, rather than constraining some aspects of the model separately, and relying on the model to project integrated solutions. At 4T ITER-like absolute pedestal pressures are projected to fully explore the pedestal divertor dynamic, with thermal Q_DTeq ~ 1, reducing projection to reactors in a range of parameters. An advanced closed divertor would be combined with this with structure optimized to promote detachment at all radii, to develop and study detachment in the resulting high heat flux scenarios. Parallel heat flux is projected to rise a factor of 3 from 0.8 GW/m² in steady states accessible now, to 2.9 GW/m² at 2.5 T and an ITER-like 5.2 GW/m² at 4T. Such a step would require a major investment in a new facility or major upgrade to DIII-D (new vessel and TF set), but would be a powerful tool to explore reactor scenario optimization in D–D before construction of a D-T device.