<figure><img src="image_76.png" /><figcaption>**Figure 78.** Magnetic spectrograms showing the TAE activity in two AUG discharges with RMP-induced TAE mitigation / suppression (a) and excitation (b). The RMP time traces are over-plotted in white. The bottom panel shows the temporal evolution of the EP losses measured with the FILD system. Reproduced from [993].</figcaption></figure>

### 8.3.2. EP confinement in tokamaks with 3D fields.
Particle orbits in 3D fields, such as in realistic, non-axisymmetric tokamaks or stellarators, are more complicated than in idealized, axisymmetric tokamaks in several important ways. Trapped orbits may no longer remain centered on a fixed flux surface. As the magnetic field varies along the toroidal direction, the EPs may move radially. EPs with a large pitch may become trapped in the local ripple wells and drift out of the plasma. Passing orbits are not as directly affected by 3D perturbations as trapped orbits. However, over many toroidal turns, passing orbits can trace out drift surface islands, leading to enhanced radial transport [1028].

An important 3D effect compromising EP confinement is that of edge resonant transport layers (ERTLs), as found for AUG [987]. The plasma response to the 3D field perturbation was calculated with the MARS-F code, and the EP orbits were followed using ASCOT [1029]. The computed change of the canonical toroidal momentum $\langle \delta P_{\phi} \rangle$ of particles NBI was used to quantify their transport. The maxima of the computed change in $\langle \delta P_{\phi} \rangle$ are well aligned with resonances between drift and bounce motion of the particles [987] (see figure 79). Exploiting ERTLs may lead to scenarios where optimized RMP fields could be used to

minimize the EP losses.

The 3D field effects on alpha and NBI ion confinement were assessed in the major ITER scenarios (15 MA baseline, 12.5 MA hybrid, 9 MA “advanced tokamak”, and 7.5 MA half-field) [984, 1030], including ferritic inserts, TF coil ripple, TBMs and ELM control coils, using the OFMC code [1031, 1032] and ASCOT. The effect of the plasma responses to ferritic inserts and TBM perturbations was also assessed in [1033]. No significant deterioration of EP confinement due to the error fields from the TF coil ripple, ferritic inserts and TBMs were found in these studies. The key factors influencing the confinement were found to be the edge source rate, the plasma/first wall gap, and the plasma current [963], although for the 15 MA scenario part of load on the target plates in the divertor was found to be shifted to the divertor dome [1034].

However, the ELM control coil perturbation resulted in orders-of-magnitude increases in the power load on the wall up to the MW-range. This was attributed to the field line stochasticity penetrating deeper into the pedestal top, leading to an increase of losses. The mechanism for this large increase in EP transport was found to be a new loss channel for marginally trapped particles caused by a strong toroidal variation of the poloidal field near the X-point, leading to a displacement of banana tips and collisionless transport [1035].

The effect of the ERTLs on the confinement of NBI ions in ITER has been investigated as function of the applied RMP spectrum using ASCOT [1036]. The total EP losses depend on the poloidal spectra of the applied $n = 3$ RMP as well as on the absolute toroidal phase of the applied perturbation with respect to the NBI birth distribution. The absolute toroidal phase of the RMP perturbation does not affect the ELM control capabilities, leading to an expectation that it could be used for NBI confinement optimization in ITER.

### 8.3.3. Stability of 3D MHD equilibria.
As in axisymmetric toroidal equilibria (see section 6), the gaps in the Alfvén continuum indicate the frequency ranges where weakly damped AEs reside. These modes are expected in the gaps or above or below flat branches of the continuum (e.g. in [614]). There are several numerical implementations for 3D equilibria available [1037–1039], including the coupled Alfvén and sound continuum [1040]. For weak 3D error fields, the Alfvén continuum structure changes only mildly. For example, small open gaps driven by toroidal field ripple couplings from discrete coils in the case of DIII-D have been identified [1026]. Also, structures known as continuum crossing gaps can be present in configurations with 3D perturbations [1041]; these were also identified in the DIII-D case with field ripple
<figure><img src="image_77.png" /><figcaption>**Figure 79.** AUG#33143. $\langle\delta P_{\phi}\rangle$ as a function of particle major radius and energy for poloidal RMP phasing of: (a) $\delta\phi_{UL} = 40^{\circ}$, (b) $\delta\phi_{UL} = 160^{\circ}$, (c) $\delta\phi_{UL} = 260^{\circ}$, White contours indicate the particle frequency ratio ($\omega_b/\bar{\omega}_d$). (d) Radial profiles of $\langle\delta P_{\phi}\rangle$ for different $\delta\phi_{UL}$ at energy of $\mathcal{E} = 50$ keV and pitch $\lambda = -0.5$. Note that a negative sign of $\langle\delta P_{\phi}\rangle$ means an outward drift of the particle. Reproduced from [987].</figcaption></figure>

[1026]. For strong 3D error fields, new classes of Alfvén gaps appear. Helical variations in the magnetic field strength produce helicity-induced AEs (HAEs) and toroidal variations lead to mirror-induced AEs (MAEs).

Most of the existing nonlinear MHD implementations were initially developed for axisymmetric equilibria [867, 1042], but have now been extended to full 3D configurations [864, 1043–1046]. They can either consider equilibria with islands [1017, 1043] or with nested flux surfaces from VMEC [1044, 1047]. Nonlinear 3D models using reduced MHD have been developed [1008, 1048–1050].

The interaction of MHD eigenmodes with EP populations has an approximate analytic solution [1051] in 3D configurations, as for idealized tokamaks [478]. This solution is local on a flux surface and allows the determination of the resonance velocity of passing particles with fluctuations such as AEs in a 3D magnetic topology.

In 3D tokamaks and stellarators, there is not only a larger spectrum of eigenmodes, but also a larger number of wave-particle resonances. This is partly due to the more complicated particle orbit topologies [1052] as can be confirmed either analytically [1051] or numerically [1053, 1054] by coupling a drift kinetic

equation perturbatively with a 3D ideal MHD stability model [1055, 1056]. The additional resonances may also lead to a destabilisation of AEs by interaction with the bulk plasma species [1054, 1057].

As for 2D fields, models ranging from full gyrokinetic), kinetic-MHD and reduced models have been used to evaluate the effect of 3D perturbations on AEs. These models originated from modeling either axisymmetric tokamaks or stellarators, but can now be used to describe 3D tokamaks.

8.3.4. Gyrokinetic and kinetic-MHD simulation with 3D fields and reduced models. The most complete description of wave-particle interaction is gyrokinetic simulations (section 7), in which all species can be handled on the same footing. A few codes provide the capabilities to perform global electromagnetic calculations in 3D geometries [1058–1061]. Most of the numerical approaches use PIC paradigms to solve the gyrokinetic equation in a $\delta f$-formulation. The electron dynamics is often solved iteratively starting with a fluid model [1062] or using a pullback scheme [833, 838, 839, 1063], a control variate scheme [1064, 1065], or a fluid electron model.

Recently, progress has been made using a grid-based method for the global electromagnetic
calculation of ITG modes in W7-X [1061]. It showed that turbulence suppression by EPs stemming from ICRF heating, which has been observed for tokamaks [1066], can also be achieved in optimized stellarators [1067]. EP simulations have been performed for an LHD equilibrium with low mode numbers, and a successful benchmark with a kinetic-MHD model has been carried out [1068]. More recently, this approach has been extended to the full LHD radial and poloidal range [1069, 1070]. Fully gyrokinetic models have also been used to calculate drift Alfvén waves in LHD [833].

3D kinetic-MHD models have been successfully applied to study EP effects on MHD modes in tokamaks [1071, 1072], and stellarators [1069, 1070]. Global gyrofluid models have also been developed for 3D systems. This approach is based on the Landau closure [903] which provides an efficient treatment of the effect of parallel resonances. In the FAR3d [904] and TAEFL [1073] models, moment equations of the EP density and parallel velocity have been coupled to a nonlinear reduced resistive MHD model for the bulk plasma. The closure for the fluid equations includes the linear wave-particle resonance effects required for Landau damping/growth. The speed advantage of this model has allowed rapid parameter scans as recently demonstrated for LHD [1074] and TJ-II [1075] plasmas.

For 3D plasma equilibria including magnetic islands, a fully nonlinear resistive MHD model [867] has been coupled to a gyro- or drift kinetic equation for the EPs in the MEGA model [1043, 1076]. Investigations for TAEs in LHD have been made in [1043]. Later, the experimentally observed EGAMs in LHD have been explained and the energy transfer between the bulk plasma and the EPs has been calculated [1077, 1078]. More recently, AE bursts in LHD have been investigated [1079]. Also, orbit-following codes for EPs have been added to a nonlinear resistive MHD model [1048] and successfully benchmarked [1080].

Finally, it has been shown that reduced MHD models are a reliable tool for modeling stable global Alfvén waves in 3D systems and can be used with wave-particle interaction models to assess EP stability [840, 1081, 1082], including FLR and finite $E_\|$ effects [1082]. The continuum damping of global modes in 3D has been quantified [1083, 1084].

Stability calculations for ITER including a realistic wall are found in [1085]. A resistive MHD stability model for tokamaks [1086] has been generalized to 3D and could also be applied to an AUG equilibrium with a helical core [1087].

## 9. Multiscale synergistic interactions between EPs, thermal-plasma- and EP-driven instabilities, and turbulence

This section describes the multiscale interplay between EPs and perturbations, both electrostatic and electromagnetic, ranging from large-scale to small-scale perturbations and including microturbulence. Firstly, we will deal with interactions between EPs, tornado modes, and sawteeth. Secondly, we will deal with the nonlinear wave-particle interactions between EPs and EGAMs (including the EGAM channeling and the EP transport induced by EGAMs) and wave-wave interaction between NTMs and EP-driven AEs and EGAMs; an overview is given of synergistic effects in nonlinear simulations and experiments. Thirdly, the interplay between turbulence and EPs is reviewed. This includes the EP-turbulence interaction mediated by EGAMs and the mechanisms of microturbulence stabilization by EPs (dilution effect, linear stabilization and nonlinear electromagnetic stabilization). We then review the possible role of microturbulence on EP transport, including synergistic effects. An example is the impact of the pitch-angle scattering rate on the nonlinear evolution of AEs, mediated by ICRF heating and microturbulence. In particular, a 2D (toroidal momentum and energy) quasi-linear model implemented in the RBQ code computes the EP distribution function in the presence of AE-induced diffusion, Coulomb collisions and anomalous scattering due to microturbulence.

### 9.1. Interactions between EPs, tornado modes, and sawteeth

A synergistic effect observed in present-day tokamak experiments with significant populations of EPs is an interplay between EPs, sawtooth instability [372,1088], and high-frequency TAEs excited by the EPs inside the $q=1$ magnetic flux surface, called *tornado modes* [373, 1089–1092]. The sawtooth and tornado instabilities are very different in their nature, but they are both affected by EPs and by temporal evolution of the safety factor $q(r)$, so they become coupled through these two essential elements they share.

As already discussed in section 5, the sawtooth [1088] is a global thermal-plasma instability driven by plasma current, and it is associated with the $q=1$ magnetic flux surface. The high-frequency tornado modes are localized in the plasma core inside the $q=1$ surface. They appear one-by-one with decreasing toroidal mode numbers when the on-axis safety factor $q(0)$ decreases through the relevant TAE safety factors of $q = (m + 1/2)/n$ after the sawtooth crash. The tornado modes are excited via resonant interaction with EPs inside the $q=1$ surface. These modes were first observed at TFTR [1089] and then at JT-60U
[1090], where they were nick-named tornado modes due to the temporal evolution of their frequencies.

Figure 80 shows typical magnetic spectrograms and main plasma parameters in JT-60U discharges with both the usual global TAEs localized outside the $q = 1$ radius (left panel) and with the core-localized tornado modes and sawteeth (right panel). Note that the frequencies of the tornado modes change on a rather short timescale compared to the Alfvén scaling $f \sim B/n^{1/2}$ of global TAEs. Note also from the right panel of figure 80 that the tornado modes (top panel) appear just before sawtooth crashes, which suggests a possible role of tornado modes as precursors to sawtooth crashes.

The role of TAE modes in redistributing EPs and causing sawtooth crashes was investigated first on DIII-D [1091]. However, the location of the TAEs could not be identified, leaving open questions. It was shown later for a TFTR discharge [1092] that when the amplitudes of tornado modes excited by EPs become sufficiently high, a significant radial redistribution of the EPs occurs from inside the $q = 1$ radius to outside. This depletion of EPs inside the $q = 1$ radius takes away the stabilizing effect of EPs on sawteeth, which leads to the sawtooth crash. In this way, a relatively minor local redistribution of EPs away from the plasma core can trigger a sawtooth crash, causing global transport with significant modification of the thermal plasma profiles.

Similar studies were performed later on JET confirming the synergistic character of the interaction between sawteeth and tornado modes coupled through the EP population [373, 1093, 1094]. Core TAEs inside the $q = 1$ surface were also implicated in DIII-D monster sawteeth [1095]. This synergy between sawteeth, tornado modes and EP-driven modes has yet to be simulated, so we are lacking a prediction for this phenomenon in ITER. Based on the possible occurrence of tornado modes and sawteeth in ITER, this synergy is likely to occur.

## 9.2. Interactions involving EPs and EGAMs

Linear stability of EGAMs was discussed in section 6.6.3. Here we deal with the nonlinear regime of EGAMs, the possibility to couple energy from EPs to EGAMs to eventually heat the thermal ions instead of the electrons (dubbed EGAM channeling), and on interactions between EPs, EGAMs and other modes.

### 9.2.1. Nonlinear regime of EGAMs and EGAM channeling.
The nonlinear regime of EGAMs has been analyzed since the observation of the $n = 0$ chirping mode in JET [686, 687]. It has been shown that kinetic effects are essential for the generation of second harmonics in the density perturbation [1096].

In nonlinear simulations of non-chirping EGAMs using GYSELA [667], the distribution function was found to flatten during the mode saturation. Such a flattening of the distribution function was also observed in kinetic-MHD MEGA simulations [351], including the formation of holes and clumps [702, 703] at the start of the chirping [550], as anticipated in [686]. Further detailed analysis of the wave-particle nonlinearity effect on the saturation of EGAM including the nonlinear time evolution of the frequency was reported in [1097].

An important aspect of EGAMs is the possible transfer of energy from EPs to thermal ions mediated by the EGAM in collisionless regimes [667, 676]. Although energy transfer appears already in linear regimes [668], the nonlinear transfer from high- to low-$\mu$ (magnetic moment) particles was confirmed from realistic simulations of LHD plasmas, which opened the possibility for EGAM channeling [1078]. Finally, the nonlinear generation of higher harmonics has been observed to play an important role in the EGAM channeling in GYSELA simulations [690] as well as in realistic kinetic-MHD MEGA simulation of LHD discharges [566, 1078]. Figure 81 shows an example of the energy exchange between EPs and thermal ions mediated by EGAMs. The solid lines in the top panel represent the time traces of the energy exchanged between EGAM and both ion species, measured as $\Delta\mathcal{E}_{s,\text{trans}} = \int_0^t dt' \int \mathbf{J}_s \cdot \mathbf{E} dV$, with s the species (either EP or thermal ions), $\mathbf{J}_s$ the current density of species s, and $\mathbf{E}$ the electric field. The dashed line represents the curve for EPs scaled by a factor $k = 0.47$. Therefore, in this example, the efficiency of the energy exchange is $\Delta\mathcal{E}_{i,\text{trans}}/\Delta\mathcal{E}_{f,\text{trans}} \approx 0.47$, i.e. 47% of the energy transferred from EPs to EGAM is subsequently transferred to thermal ions. The bottom panel of figure 81 represents the time trace of the EGAM poloidal velocity, showing a good correlation between the onset of the nonlinear saturation and the exchange of energy between EPs and thermal ions. In that example, the power transferred to the thermal ions through the EGAM was estimated to be $\sim 3.4 \text{ kWm}^{-3}$ [1078]. The energy transfer efficiency depends on $\beta_f$ [566]. In particular, it can reach values up to 60% for $\beta_f = 0.08\%$. EGAM channeling could be an option for the idea of alpha channeling to optimize burning fusion plasmas (see section 10.4).

### 9.2.2. EGAM-induced EP transport.
Since an EGAM is an axisymmetric mode with $n = 0$, it does not change the toroidal canonical angular momentum $P_\phi$ of particles ($n\Delta\mathcal{E} = \omega\Delta P_\phi$) and therefore it has long been believed to have little effect on the transport of EPs. Yet, since $P_\phi$ depends on both the poloidal flux $\Psi$ and the parallel velocity $v_\parallel$, wave-particle interactions can result in EP transport [447] and even
<figure><img src="image_78.png" /><figcaption>**Figure 80.** Comparison of two JT-60U discharges showing (left) low-*n* TAE modes outside the *q* = 1 surface and (right) high-*n* multiple TAE modes inside the *q* = 1 surface (tornado modes). Both discharges have almost the same plasma conditions except for the start time of ICRF and NBI heating. Reproduced from [1090].</figcaption></figure>

<figure><img src="image_79.png" /><figcaption>**Figure 81.** Top panel: The solid lines represent the time evolution of the energy exchange between EGAM and both EP ($\Delta\mathcal{E}_{f,\text{trans}}$) and thermal ions ($\Delta\mathcal{E}_{i,\text{trans}}$). The energy transfer efficiency from EPs to thermal ions mediated by EGAM is measured as $\Delta\mathcal{E}_{i,\text{trans}}/\Delta\mathcal{E}_{f,\text{trans}} \approx 0.47$. The curve for EPs (dashed line) is scaled to show that the energy transfer efficiency from EPs to thermal ions is constant. Bottom panel: Time trace of the poloidal velocity, representing the excitation and nonlinear saturation of the EGAM. Reproduced from [566].</figcaption></figure>

<figure><img src="image_80.png" /><figcaption>**Figure 82.** Trajectory of loss EP computed using the full particle-orbit code SPIRAL. The EGAM radial electric field is represented in the background. Reproduced from [677].</figcaption></figure>

losses when the orbits of counter-passing particles are changed into unconfined trapped particle orbits that intercept the wall [676]. Such a mechanism was corroborated in [677], where the orbits of lost EP detected by FILD were followed (in reverse) using the orbit-following SPIRAL code. Figure 82 illustrates a trajectory calculated using SPIRAL. The initially confined counter-passing particle interacts with the EGAM electric field, becomes trapped and is lost. Further analysis of the EGAM-induced EP transport was given in [1098], where it was shown

that resonances of the form equation 86 can also occur when *l* is fractional. Such transport induced by fractional resonances is in principle only possible for a large amplitude of the perturbations. Later, nonlinear studies of EGAM-induced EP transport were performed in [690] using the EGAM potential self-consistently computed using the GYSELA code.
<figure><img src="image_81.png" /><figcaption>**Figure 83.** Spectrograms of fluctuations from EGAMs on (a) Mirnov signal, (b) SXR signal in the core. (c)–(f) Density fluctuations of Doppler reflectometers with different work frequencies: (c) X-mode, *f* = 34 GHz; (d) O-mode, *f* = 17 GHz; (e) O-mode, *f* = 23 GHz; and (f) X-mode, *f* = 48 GHz. Reproduced from [682].</figcaption></figure>

Integer and fractional resonances were found, as well as a chaotic separatrix interacting with the trapped-passing boundary. The losses modulated at the EGAM frequency and the class of trajectories of lost particles (counter-passing) agreed with observations [677]. The existence of the chaotic separatrix motivated studies of the EGAM-induced EP transport in the radial direction, which was found to be non-diffusive. This non-diffusive radial transport was linked to a super-diffusive poloidal transport governed by rare events called Lévy flights [1099]. The original papers on Lévy processes are [1100,1101], but we recommend the more recent [1102] for an overview.

9.2.3. Interactions between EPs, EGAMs, NTMs and AEs. Another topic of concern is the interaction between NTMs and other EP-driven modes [1103]. NTMs change the Alfvén continuum and transport EPs, which has immediate consequences for the AE stability. Several examples of such direct interactions in plasmas without EPs have been found. Pairs of BAEs are sometimes found in the presence of magnetic islands [334, 641, 1104, 1105]. Destabilization of BAEs has been attributed to the interaction between tearing modes and geodesic acoustic modes [1106]. A strong interaction between tearing modes and TAEs has also been found in simulations and experiments [635,1107]. These interactions could enhance the transport and loss of EPs. Also TAE wave-wave coupling has been observed experimentally [1108].

Evidence indicates that nonlinear wave-wave interaction among tearing modes and m-BAEs leads to generation of geodesic acoustic modes induced by energetic electrons (eEGAMs) [509], as shown in figure 83. The m-BAE is a standing-wave structure formed by counter-propagating Alfvén waves within a magnetic island [644], when the island is above a certain threshold island width, see also section 6. The EGAMs are localized in the core plasma with a broad radial structure measured by several diagnostics, such as Mirnov probes, soft X-ray arrays and Doppler reflectometers. The *n* = 0 mode can only be observed in plasmas with line averaged densities $n_e < 0.5 \times 10^{19} \text{m}^{-3}$ but the threshold can be increased by auxiliary heating. The squared bicoherence indicates that EGAMs are driven by three-wave resonance among m-BAEs and tearing modes. The radial structures of EGAMs and BAEs have been found to overlap. Therefore, AEs can propagate poloidally into the region of zonal flows (ZFs), then interact with GAMs/ZFs, and finally result in wave energy transfer between the GAMs and AEs.

9.3. Interactions between EPs and turbulence

On the route towards the steady-state production of energy in future fusion devices, understanding and controlling turbulent transport is of prime importance because turbulence limits the confinement of energy and particles. Indeed, experimentally measured
diffusivities [1109] are largely above those predicted by neoclassical theory and in good agreement with the diffusivities computed in gyrofluid and gyrokinetic turbulent simulations [1110], i.e. $\chi_{sim} \sim \chi_{exp} \sim 1 \text{ m}^2\text{s}^{-1}$. Since EPs are ubiquitous in current fusion devices and are a key ingredient to achieve good plasma performance, understanding and predicting the mutual interplay between microturbulence and EPs is an active research topic. It is especially important to assess whether the presence of EPs will have a significant impact on the dynamics of microturbulence or not. In typical conditions of present tokamaks, turbulent transport in the plasma core is dominated by ion-temperature gradient (ITG) driven instabilities for relatively flat plasma density profiles [1111]. Hence most studies have focused on the interaction between EPs and ITG turbulence.

### 9.3.1. Energy transfer from EPs to microturbulence mediated by EGAMs and AEs
When GAMs were excited by EPs at JET for the first time, the possibility to use them as a knob to control turbulence became appealing [686, 687], especially because GAMs are interpreted as the oscillatory component of zonal flows, which are known to play a crucial role in the self-regulation of turbulence [797, 845]. In that context, gyrokinetic electrostatic simulations using GYSELA were performed to study the possibility of controlling turbulence by means of a source of EPs that can drive EGAMs unstable [688]. The EP source in this study accelerated thermal particles, reducing the available energy for the linear destabilization of ITG, and hence reducing turbulence. This is illustrated in the top panel of figure 84 by the solid black line, where the time evolution of the measured $E \times B$ heat flux is plotted. As comparison, a second source injecting the same energy, but without accelerating particles to supra-thermal energies was introduced. In that case, no reduction of turbulence was observed, as shown in figure 84 (dashed blue line). This suggests that EPs were indeed the reason for the turbulence reduction.

However, the source of EPs resulted in the excitation of EGAMs, and a coupling between the EGAM structure and the ITG-avalanches was evident in the temperature gradient, as observed in the bottom panel of figure 84. This coupling leads to an energy channel from the inner to the outer region of the tokamak, increasing the turbulent transport to previous levels. An explanation based on a wave-kinetic equation was proposed in [674], suggesting that EGAMs can trap turbulence clumps and carry them across the transport barrier. Additionally, the transfer of energy from EPs to ITG turbulence via EGAMs was also found to be due to a local three-wave coupling mechanism [689]. The global and local mechanisms

can be concomitant.

<figure><img src="image_82.png" /><figcaption>**Figure 84.** (Top panel) Time trace of the $E \times B$ heat flux in the absence of EPs (blue dashed line) and in the presence of EPs separated into the non axisymmetric and the axisymmetric modes. (Bottom panel) Oscillating part of the temperature gradient, showing the coupling between EGAM oscillations and ITG-avalanches. Reproduced from [688].</figcaption></figure>

Studies were also conducted in the electromagnetic regime using the ORB5 code for the case of BAEs excited by EP [804]. It was shown that the heat fluxes are generally increased, especially for electrons, first at low toroidal mode numbers corresponding to large scales, where BAEs are dominant, and subsequently at high toroidal mode numbers corresponding to smaller scales, where ITG modes are dominant. However, it was also found that TAEs excited by EPs might have a beneficial impact on the stabilization of turbulence, which is discussed in the next subsection.

### 9.3.2. Turbulence stabilization by EPs
Among the first experimental indications that EPs might play a role in the stabilization of turbulence was the observation that the ion stiffness was mitigated at high NBI and ICRF power in hybrid regimes [1112] with internal ion transport barriers (ITB) on JET [1113]. The ion stiffness refers to the degree of sensitivity of the ion heat flux to the mode drive, $\gamma_{drive} \propto R/L_{T_i} \equiv R \frac{\partial}{\partial r} \log T_i$ [1114]. Although this enhanced
confinement was initially thought to be due to low magnetic shear and high rotational flow shear [1115], further experiments with only ICRF $^3$He minority heating in deuterium plasmas have shown that similar ITG stabilization is also obtained in the absence of rotation [1116]. Efforts to explain the fundamental mechanisms underlying the observed stabilization were therefore required.

EPs can contribute already linearly to stabilize ITG modes and thereby reduce turbulent transport in different ways. The first stabilization mechanism is that they dilute the main species, and consequently the background free energy available to drive ITG modes is reduced [1117, 1118]. It was shown in [1118] that the formation and sustainment of an ion ITB in AUG could not be explained by the $E \times B$ shear alone, but required the inclusion of EPs from NBI. Moreover, the existence of such EP-induced ITBs is limited to the thermalization timescale of EPs. The second stabilization mechanism is due to a modification of the resonance between the EP frequency and the wave. For example, the increase of $\alpha_S = -q^2 R \frac{\partial \beta}{\partial r}$ affects the mode stability by changing the wave-particle drift resonance in phase space, known as the Shafranov-shift effect [1119–1121]. Recent analytic calculations accompanied by gyrokinetic simulations with the GENE code [699] were reported in [836], demonstrating the possibility to stabilize ITG modes by means of the modification of the magnetic drift resonance. Moreover, since the linear resonant mechanism requires also that $\eta_f = d \ln n_f / d \ln T_{f,eff}$ is larger than one, mainly EPs generated by ICRF heating have the optimal profiles for this mechanism. Experimental observations of these effects have been made at JET [1116] and AUG [1122]. The third stabilization mechanism is due to electromagnetic fluctuations. Experimental studies of the reduction of ITG-driven turbulence were conducted at JET in the presence of ICRF-accelerated minority energetic hydrogen [1123]. This study found that the increased pressure due to EPs resulted in a transition from electrostatic ITG modes to nearly electrostatic tearing-parity modes and that the EPs locally modify $\alpha_S$ in such a way that the electrostatic ITGs are stable and the kinetic ballooning of Alfvénic modes stays quiescent [1123].

EP-induced stabilization of turbulence has also been investigated extensively in the nonlinear regime. Experimental work on JET [1113, 1115] reported a significant reduction of ion stiffness which might open the possibility of controlling the onset of turbulence by means of EPs. Linear effects alone are not enough to explain the enhanced confinement observed on JET [1114]. This motivated further gyrokinetic simulations with the GENE code [1114],

<figure><img src="image_83.png" /><figcaption>**Figure 85.** Comparison of nonlinear GENE simulations and experimental measurements of ion heat flux as a function of the normalized logarithmic gradient of the ion temperature. This shows that taking into account the EPs facilitates the agreement with experimentally observed reduction of ion stiffness. Reproduced from [1114].</figcaption></figure>

where electromagnetic effects resulted in the nonlinear stabilization of turbulence by EP pressure, which helped explain the heat flux and ion stiffness reduction observed in [1113, 1115]. Figure 85 shows a comparison between nonlinear GENE simulations and the experiments. Nonlinear gyrokinetic simulations predicted the EP-induced stabilization of ITG-driven turbulence in JET [1124–1127] and AUG [1128] discharges. Comparisons of linear and nonlinear electromagnetic gyrokinetic simulations pointed out the key role of EPs generated by NBI and ICRF in enhancing the nonlinear electromagnetic stabilization of ITG modes [1114, 1124–1126, 1128]. The stabilizing effects of fast ions are further enhanced at low magnetic shear [1114], and the rotational flow shear is effective only at outer radii [1129], in agreement with experiments [1115].

First attempts to partially explain the elusive physics behind the enhancement of the nonlinear electromagnetic stabilization due to EPs suggested the possible role of EPs in the nonlinear transfer of energy from ITG modes to zonal flows through mode-mode coupling involving EP-driven marginally-stable modes as nonlinear mediators [1130, 1131]. The experiments at JET with deuterium plasmas with minority $^3$He [1116] corroborated both the linear stabilization via a wave-particle interaction and the nonlinear electromagnetic stabilization. Furthermore, whereas most simulations showing a significant reduction of turbulence by EPs were performed using an equivalent Maxwellian, it was demonstrated that a more realistic modeling of EPs using a non-Maxwellian distribution function still stabilizes ITG turbulence, although in a less significant manner [1132]. Recent simulations
using GENE were performed to extend the analysis of the stabilization of turbulence by EPs to other turbulent regimes such as turbulence driven by the trapped electron mode (TEM), concluding that EPs have little impact on TEM-induced turbulent transport [1133]. Turbulence is also thought to be implicated in a new possibility to control the density profile via anisotropy in the EP distribution [1134].

Recent gyrokinetic simulations of a DIII-D discharge with the GTC code illuminate the complicated relationship between EP-driven AEs, zonal flows, and ITG turbulence [843, 848] (see section 7.3.2). In the simulations, ITG turbulence can scatter the resonant EPs that are nonlinearly trapped by the RSAE, thereby damping the zonal flows generated by the RSAE. Simulations without coupled interactions overestimate both EP and thermal-ion transport, but predicted transport levels are consistent with experiment when coupling between AEs, ZFs, and ITGs are included.

The EP-induced stabilization might be also significant in the presence of alphas in ITER DT plasmas [1135] or in the initial phase of ITER with He³ minority ICRF heating in DT plasmas [1130]. Since most experiments in current devices do not produce fusion-born alpha particles, studying their physics including their impact on turbulence is a challenging task. In that respect, the three-ion ICRF scheme [113] with ³He traces in mixed hydrogen-deuterium plasmas can generate highly energetic (~ MeV) helium ions, which can help in addressing some aspects of the physics of fusion-born alpha and thermal-ion turbulent-transport stabilization. This heating scheme was recently employed in JET with the observation of enhanced thermal-ion confinement even in the presence of linearly unstable EP-driven modes. Nonlinear gyrokinetic simulations corroborated the experimental evidence, explained by the formation of zonal structures due to the excitation of TAEs [139]. This promising result is further discussed in chapter 2 of this volume [14]. Recent analytic and numerical studies indicate that a phase synchronization between trapped electrons and passing energetic ions might also result in the total suppression of ITG-driven turbulence [1136]. Finally, it is to be noted that a new stable impurity-free D-T plasma regime has been recently found, exhibiting high thermal confinement as a result of the zonal flows generated by EP-driven instabilities [52].

Although further investigation is required to provide a full experimental picture, measurements of sheared flows using charge exchange spectroscopy (CXS) diagnostic in the LHD device have been recently reported [1137], indicating a strong correlation between the maximum of the zonal flow and the radial location

of unstable TAEs and EPMs. All these experimental and numerical studies suggest a possible stabilization of turbulence by EPs through the excitation of zonal flows.

9.3.3. *Turbulence-induced EP transport.* Here, we discuss the impact of microturbulence on the transport and confinement of EPs. Since EPs can have large Larmor radii, it has been generally believed that gyro-averaging might lead to negligible EP transport [1138]. Based on this idea, the diffusivity is expected to decrease down to $D_f \sim 0.01 \text{ m}^2\text{s}^{-1}$, which is much smaller than the diffusivity of thermal particles. Recent advances in flux-tube gyrokinetic modeling as well as in experimental measurement techniques made it possible to gain further insight into this important research topic.

First self-consistent flux-tube gyrokinetic simulations were performed to study the alpha particle transport induced by microturbulence with the GYRO code [941]. It was found that alphas might interact significantly with ITG turbulence in the core of a fusion reactor, despite their large Larmor radius. The simulations resulted in density modifications of the order of 15% in the presence of microturbulence [1139]. Later, simulations with the GENE code [699] suggested that the effect observed in [1139] might occur if the Larmor radius of EPs does not exceed the turbulence correlation length and if the poloidal drift velocities are sufficiently small [1140]. The EP transport in the presence of ITG turbulence was also analyzed in [857] using the GTC code [845], showing that the probability density function of the radial excursion is close to Gaussian, suggesting diffusive transport. The diffusivity is found to decrease strongly with energy due to gyro-averaging, in agreement with conventional wisdom. At the same time, gyrokinetic simulations using the GENE code showed that the EP diffusivities are significant for EPs with energies up to 10 times the thermal energy. The particle diffusivity then decreases as $D_f \sim 1/\epsilon_f$ [1141].

In addition, flux-tube gyrokinetic analyses of transport of EPs as passive tracers have been reported in several works [854, 856, 1142, 1143]. Multi-code gyrokinetic analyses were performed using the GKW [1144], GYRO and GS2 [1145, 1146] codes, which mainly focused on impurity transport, but also included transport of alphas [1143]. In these studies, only microturbulence induced by electrostatic fluctuations was included, such as ITG- or TEM-driven turbulence. Moreover, alphas were modelled as passive tracers using a slowing-down distribution function. The derivatives of the EP distribution function with respect to the energy and to the radial coordinate were introduced in the gyrokinetic equation in GS2 and GKW, but not in GYRO. The three codes agreed
well on the transport of alphas in both the linear
and the nonlinear phases. It was again found that
the diffusivity of alphas decreases strongly with their
energy, leading to 20 times smaller diffusivity compared
to thermal helium ash diffusivity in the core of ITER.
The gyrokinetic results for particle transport were
included in ITER transport modeling, concluding that
the electrostatic microturbulent transport of alphas
occurs on a characteristic timescale at least one order
of magnitude larger than the slowing-down time.
According to this multi-code analysis, on the timescale
of the slowing-down process of alphas, electrostatic
microturbulence might not play a significant role
in the modification of the radial profiles of alphas.
Further numerical simulations with the GENE code
computed the diffusivities of EPs as passive tracers
moving in fields with both electrostatic and magnetic
fluctuations [854]. Whereas the electrostatic part
indeed decreases with the energy of EPs as $1/\mathcal{E}_f$, the
magnetic counterpart does not and was found to be
independent of the energy. The explanation that the
gyro-averaging operation might not be valid for EPs
has subsequently been debated in the literature [1147,
1148]. Finally, flux-tube simulations with GENE using
passive highly energetic deuterium in ITER scenarios
concluded that the EP transport can be significant for
intermediate energies on the order of 100 keV, with the
electrostatic fluctuations dominating over the magnetic
fluctuations [856].

From the experimental viewpoint, measurements
in an ITPA joint experiment [1149] have suggested the
possibility of anomalous spatial EP transport induced
by microturbulence. Multi-machine analyses with
measurements of NBCD on four different tokamaks
(AUG, DIII-D, JT-60U and MAST) were done. In
particular, the measured NBCD profile with a neutral
beam injected power of 7.2 MW in the DIII-D tokamak
was compared to calculations assuming various EP
diffusion coefficients. As shown in figure 89, discussed
in the next section, the best fit to one measurement
occurred for an assumed EP diffusion coefficient
of $D_f \simeq 0.3 \text{ m}^2/\text{s}$. A similar comparison was
reported in [1149] for AUG, but in that case the
EP diffusion coefficient required to obtain a match
between the measurements and calculations depended
on the triangularity, suggesting that other unexplored
parameters may play a role.

FIDA measurements on DIII-D found evidence
for EP transport when the ratio of EP energy
to temperature was $\mathcal{E}_f/T < 10$ [1150], which
seems consistent with the ordering given by flux-
tube simulations [1141]. The inferred transport
rates in [1150] were found to be of the same order
of magnitude as those predicted by the NUBEAM
module. However, a subsequent DIII-D study

concluded that any EP transport is dwarfed by EP
transport induced by coherent fluctuations [1151].
In the absence of MHD activity, the confinement
of energetic ions was shown to be neoclassical in
plasmas characterized over a wide range of the ratio
$\mathcal{E}_f/T_i$. These conclusions are consistent with the
theoretical predictions that no significant energetic ion
transport by microturbulence is expected in ITER half-
field scenarios for intermediate energies [856]. Basic
physics studies on LAPD confirmed the expected
dependence of EP transport on finite gyroradius [1152]
and turbulence wavenumber [1153]. Studies of cross-
field EP transport in turbulent magnetized plasmas
in TORPEX [1154] concluded that transport can be
super-diffusive due to the intermittent transport of
EPs mediated by turbulent structures elongated in
the parallel direction that propagate radially (the so-
called *blobs*). Such non-diffusivity of EP due to rare
events dominated by Lévy statistics [1100–1102] can be
concomitant with the mechanism described in [1099].

In conclusion, the numerical and experimental
studies performed so far suggest that alphas and other
EPs with energies $\gtrsim 100$ keV in ITER scenarios might
not suffer transport due to microturbulence alone for
most of the slowing-down process. However, further
modeling is required to include global and full-orbit
effects in order to completely assess the impact of
turbulence on EP transport.

9.3.4. *Interaction between EPs, turbulence and AEs.*
Fusion experiments such as ITER are expected to
have a multitude of marginally unstable modes in the
TAE frequency range [576, 579]. It has recently been
shown that when pitch angle scattering is enhanced
above classical Coulomb scattering levels, it will likely
lead to AE amplitudes larger than those expected in
the absence of anomalous processes [858]. Therefore,
any modification of the EP pitch angle scattering rate
could have an impact on the EP transport by means
of the modified AE amplitude. Here, we review two
mechanisms that are known to modify the pitch angle
scattering rate: ICRF heating and microturbulence.

The first possible mechanism has been explored
in TFTR experiments with the ICRF heating as a
mediator, where the enhanced scattering of minority
energetic ions increased the AE amplitude by an
order of magnitude [1155]. However, the effects
of RF injection on the stability of AEs is still
an active research topic, especially when additional
heating and current drive by RF and NBI are used
simultaneously. As discussed in section 3, ICRF can
create super-Alfvénic EPs which can easily destabilize
AEs. The use of external RF injection to alter AE
mode activity has been experimentally studied on
several devices. Results vary greatly, from very weak
effects observed [710] to AE activity suppression [711]. Mixed results have been reported even from the same device and similar plasma conditions (see figure 17 of [712]). Encouraging results were obtained when RF fields were employed to successfully terminate wave chirping excited by energetic electrons trapped in a magnetic dipole field experiment [708]. Nonetheless, more experimental and modeling work is required to fully understand the effects of RF-accelerated EPs on AE stability, especially when a synergy between different heating schemes (e.g. ICRF and NBI) can be expected. This remains an open area of research, especially considering the external heating mix planned for ITER. More specifically, phase-space engineering solutions can be employed, by exploiting the tuning of RF resonances in such a way that it can have the effect of decorrelating the EPs from the AE resonances, thereby extinguishing dangerous AE-induced transport. Guiding-center- or full-orbit- following codes can be specially helpful for that purpose, to find scenarios that maximize the RF effect.

The ability to predict, for a given plasma background, the nature of Alfvénic oscillations (fixed-frequency, leading to diffusive losses, or chirping/avalanching, leading to convective losses) can be of considerable advantage for measures aiming at the mitigation of EP transport. Spherical tokamaks tend to exhibit Alfvénic chirping and avalanching, accompanied by wave amplitude bursting, while conventional tokamaks tend to have Alfvénic waves oscillating with a nearly fixed frequency and a quasi-steady amplitude. To be able to explain this puzzling observation, a criterion for the likelihood of chirping oscillations was developed based on the theory of driven, kinetic instabilities near threshold with dissipation [953, 956] and evaluated for a number of NSTX, DIII-D and TFTR discharges [713, 928] using the stability code NOVA-K. It has been predicted [928] and verified experimentally [474, 714, 1156, 1157] that microturbulence can be a strong mediator between the mode transition from fixed-frequency to chirping and vice versa, due to an enhancement of the EP stochasticity. In spherical tokamaks, particles spend more time on the good curvature region and experience higher relative rotation shear. Therefore, spherical tokamaks naturally exhibit lower anomalous transport compared to conventional tokamaks. For example, on NSTX the total thermal ion diffusivity has been found to be of order of the neoclassical level [1158]. These distinct turbulence features have been found to explain why chirping instabilities are rare in conventional tokamaks and common in spherical tokamaks. Predictions for baseline ELMy, reversed-shear and hybrid scenarios of experiments planned for ITER have also been recently explored [714] and shown to be near the borderline between the fixed-frequency

and the chirping regimes when collisional and microturbulence effects are accounted for. For scenarios in which other resonance decorrelating mechanisms are important, the TAEs and RSAEs would then be expected to exhibit a steady response with no frequency excursions. Experiments with reduced turbulence in DIII-D (using negative triangularity) [474] and in AUG (through impurity accumulation in the core) [1156] observed more prevalence of chirping than in usual operational configurations. The turbulence acts to effectively increase the scattering experienced by the resonant EPs [859] and therefore prevents the chirping and avalanching responses, resulting in diffusive transport. An example of the emergence of chirping correlating with low turbulence is shown in figure 86. It was also found recently that microturbulence may affect AE amplitudes [858], supported by expensive numerical simulations which are available for estimates.

<figure><img src="image_84.png" /><figcaption>**Figure 86.** Correlation of Alfvénic chirping onset with a marked reduction of turbulence, as inferred by the ion heat conductivity calculated by TRANSP. Reproduced from [928].</figcaption></figure>

When microturbulence is accounted for, diffusive losses can dominate the transport and quasilinear
theory is expected to be sufficient to capture the essence of the self-consistent evolution of the EP distribution function. Quasilinear frameworks have been developed [1159] and have been applied to Alfvénic oscillations [927, 1160, 1161]. Recently, the quasilinear framework was extended to the case of a single mode [933], without any resonance overlap, when stochastic processes dominate the wave dynamics over the characteristic wave growth time and make the dynamics increasingly more time-local [931, 932]. The resonance (or window) function that weights the resonance strength in the EP diffusion coefficient was derived self-consistently in [933]. Such a resonance function is shown in figure 87 for the cases of scattering (blue) and Krook (red) collisions. Remarkably, the quasilinear theory that uses the analytically derived window functions has been demonstrated [933] to replicate the same saturation levels of the more complex nonlinear theory near threshold [935]. The resonance function has also been extended to account for dynamical friction [934] and has been applied to the dynamics of self-gravitating systems [1162].

<figure><img src="image_85.png" /><figcaption>**Figure 87.** Plots of the self-consistently derived resonance functions $\mathcal{R}$ in quasilinear theory for the case of scattering (blue) and Krook (red) collisions. In the absence of broadening, the resonance function becomes simply a $\delta$-function at $\Omega = 0$. Reproduced from [933].</figcaption></figure>

One way of prescribing the microturbulence scattering is through the changes in ion canonical toroidal angular momentum $P_\phi$ through the change in the radial position of the EP. Additionally, the classical Coulomb collisions can modify $P_\phi$ directly through the pitch $\chi = v_\parallel/v$. The quasilinear frameworks of [713, 927] have been recently adopted to build a 2D realistic RBQ model with relaxation along the canonical momentum and the energy variables [929, 938]. In a 1D case, shown here for simplicity, RBQ evolves the EP distribution function as

$$ \frac{\partial f}{\partial t} \approx \sum_{k,p} \frac{\partial}{\partial P_{\phi}} D_{kp}(P_{\phi}; t) \frac{\partial}{\partial P_{\phi}} f $$

$$ + \left\langle [1 + R_{Dh}] \frac{\partial P_{\phi}}{\partial \chi} \frac{\partial}{\partial P_{\phi}} \nu_{\chi\chi} \frac{\partial P_{\phi}}{\partial \chi} \right\rangle \frac{\partial(f - f_0)}{\partial P_{\phi}} \quad (97) $$

where the diffusion coefficients due to AEs are $D_{kp}(P_\phi; t) \sim \delta B_\phi^2 \mathcal{R}(\Omega_{kp})$ and $\nu_{\chi\chi} = \nu_\perp (1 - \chi^2)$ for the case of Coulomb collisions with $\nu_\perp$ being the 90° scattering rate [915]. The second term on the right-hand side of equation (97) represents pitch angle scattering due to classical Coulomb collisions ('1' in the square brackets) and due to anomalous scattering due to microturbulence ($R_{Dh}$ in the square brackets) [859]. If $R_{Dh} \gg 1$, the diffusion is dominated by microturbulence, and if $R_{Dh} \ll 1$, it is dominated by collisions. The resonance window function $\mathcal{R}(\Omega_{kp})$ prescribes the weight of the resonant interaction on a $P_\phi$ grid. In the absence of collisions and modes, it is a delta function taken at the perturbative resonance, i.e. $\mathcal{R}(\Omega_{kp}) \rightarrow \delta(\Omega_{kp})$. It broadens within a certain window across the resonance with collisions and mode amplitude. The shape of $\mathcal{R}(\Omega_{kp})$ can be analytically computed self-consistently [933] (see also Ref. [1163]), provided that the degree of marginality makes the resonant dynamics increasingly local in time [931].

In RBQ simulations, equation (97) is supplemented by an equation governing AE amplitude evolution $dC_k^2(t)/dt = 2(\gamma_{L,k}(t) + \gamma_{d,k})C_k^2(t)$, where growth rates, $\gamma_{L,k}(t)$, are computed at each time $t$ using the distribution function $f$, whereas the damping rate, $\gamma_{d,k}$, is fixed in time but needs to be corrected non-perturbatively, so the damping may change as the mode evolves. During the development of the RBQ model, rigorous verification studies were proposed, including the analytically expected amplitude of a saturated mode [841], the dependence of the mode amplitude on the effective pitch angle scattering frequency, and computations of different marginally unstable cases [938].

The scattering window function $\mathcal{R}_{scatt}$ (blue curve of figure 87) has been shown to be critical for realistic modeling of EP relaxation due to AEs. Earlier, a comparison between the quasilinear approach in a model geometry [1161] and the BOT code had been performed using a heuristic, flat-top broadening function. In the BOT code, the Vlasov equation was solved fully nonlinearly in 1D for one resonance in Fourier space [936]. Although the quasilinear and the BOT simulations can agree qualitatively fairly well, they agree quantitatively only in a limited parameter range. RBQ simulations employing the self-consistent resonance window function [933] in tokamak geometry were compared with BOT [858]. The most important difference between the two simulations, which are qualitatively very similar, is the recovery time between the peaks which is about 30 to 50% larger in RBQ than in the BOT code for the same scattering frequency. The experimental point lies near the threshold of
existence and non-existence of steady-state regimes in both RBQ and BOT simulations whereas the AE amplitudes are in a steady-state regime in the DIII-D discharge of interest [881]. Figure 88 illustrates BOT and RBQ results where the DIII-D parameters for an RSAE mode of interest correspond to the red curve, showing that the normalized nonlinear bounce frequency, $\omega_b$, was consistent between the RBQ and BOT simulations. Both models agree fairly well in near-threshold regimes.

Recently, a comprehensive stability analysis of ITER steady-state plasma was performed using the ideal MHD code NOVA, its drift kinetic extension NOVA-C and the 2D quasilinear code RBQ with a novel methodology [588]. Within that study a potentially important effect of AEs on EP confinement was identified which is due to EP density depletion near the plasma center. This effect is connected with the beam-ion and alpha current drive which will be also depleted near the center so that the generation of current drive is required for whole-device modeling (WDM) simulations. A self-consistent analysis of a plasma discharge including this effect is needed to evaluate its consequences on the plasma scenario.

The beam ions injected at 1 MeV lead to stronger AE growth rates in comparison with fusion alpha particles, which are born isotropically. This was not the case in earlier studies of ITER baseline scenario [31] where NBI injected fast ions have much smaller (around ten times smaller) beta. On the other hand, the background microturbulence can enhance EP losses in ITER plasmas, which deserves careful consideration. Present applications of RBQ and NUBEAM to the ITER steady-state case have shown a weak loss of fast ions to the wall at the level of a few percent [588].

## 10. EP current drive and scenario optimization by EP phase-space control

EPs can be very attractive to enhance the performance of fusion reactors by phase-space control and optimization. In this section, several such phase-space control possibilities involving EPs are discussed which have been demonstrated either experimentally or theoretically. Here we understand the term *control* to denote strategies to steer a discharge towards a higher performance by means of actuators affecting either the EPs directly, or indirectly by mediating EP-driven instabilities. There are two possible avenues to suppress or mitigate such instabilities, which both aim for separation of the mode locations and the locations with steep EP gradients: 1) modify the EP distribution to flatten the gradients at the mode location, and 2) modify the background plasma profiles to move eigenmodes away from the region with steep EP gradient (or high EP density).

<figure><img src="image_86.png" /></figure>

<figure><img src="image_87.png" /><figcaption>**Figure 88.** AE amplitude (shown in terms of the nonlinear bounce frequency) vs. time from RBQ1D and BOT for different levels of collisionality, modeling a DIII-D plasma. (Top panel) BOT has the effective frequency rates (going from the bottom figure up) $0.49\gamma_L$, $0.618\gamma_L$, $0.778\gamma_L$ and $0.98\gamma_L$. They correspond to the RBQ scattering rates $\nu_{Col}/2$, $\nu_{Col}$, $2\nu_{Col}$ and $4\nu_{Col}$ of the nominal scattering frequency $\nu_{Col} = 8.9s^{-1}$ computed by NOVA-K (bottom panel). Both figures have the same color coding for the corresponding scattering frequencies, i.e. the red curve is the nominal (collisional) scattering frequency. A much larger value of the scattering frequency curve, $10\nu_{Col}$, is added for RBQ simulations as blue dashed like. Reproduced from [858].</figcaption></figure>

Both avenues have been explored in recent years on several tokamaks and stellarators [127, 562, 1164-1166]. Promising actuators to this end are variable NBI and ICRF sources that change the gradients in the EP distribution, localized ECRF heating affecting the slowing down of EPs, localized ECCD to change the helicity of the magnetic equilibrium and hence the existence criteria and damping of AEs, and externally applied 3D magnetic perturbations to change the EP distribution and hence the wave drive [1166]. In this section, these phase-space control schemes are considered from the perspective of their effects on AEs and on EP confinement as well as on the overall fusion reactor performance with the goal to optimize plasma scenarios in burning plasma conditions. We start by reviewing EP current drive, since it can make an important contribution to the overall current drive and can be an important control knob for scenario optimization.
## 10.1. EP current drive

In addition to the essential role of EPs in heating burning plasmas, they can also generate noninductive current drive [20]. Different noninductive current drive schemes have been reviewed in [1167]. Fully noninductive discharges at high pressure are being studied extensively at EAST [1168]. The ITER NBI system [1169] has two heating NBIs with the possibility to add a third. Heating NBIs also drive current and introduce plasma rotation due to the oblique NBI beam path with respect to the magnetic field. Additional current drive schemes planned in ITER are ICCD and ECCD.

To calculate the EP current drive (NBCD or ICCD) for the purpose of scenario optimization accurately, we need to know the EP phase-space distribution function, which may or may not be captured accurately in whole device models (WDMs) such as TRANSP. The EP current drive is found from the first moment of the phase-space distribution function on the equilibrium timescale, which is much longer than the timescale associated with the Alfvén wave period. Thus, the current density is related to the phase-space distribution functions of all species in the plasma, including the EPs, according to

$$ \mathbf{J} = \sum_{s} Z_{s} e \int (\mathbf{v}_{\parallel} + \mathbf{v}_{\text{dr}}) f_{s} \frac{2\pi B}{\sqrt{2m^{3}(\mathcal{E} - \mu B)}} d\mu d\mathcal{E}, \quad (98) $$

where $2\pi B/\sqrt{2m^3(\mathcal{E} - \mu B)}$ is the Jacobian.

The calculation of the EP current drive should include the screening effect by thermal electrons which is not trivial since the electron gyromotion needs to be resolved. For example, the EP current screening by thermal electrons leads to so-called Ohkawa current [1171] which depends on the effective plasma charge $Z_{\text{eff}}$ and modifies only the parallel component of the EP current. However, the parallel currents do not appear in the Grad-Shafranov equation used to calculate plasma equilibria, and thus the Ohkawa current does not enter the calculation of plasma equilibria explicitly.

Equation (98) suggests that the most useful and straightforward way to compute the EP current drive is to compute the EP distribution function in COM space. The representation of EP phase-space distributions in various coordinate system is not trivial since the COM space Jacobian diverges at the trapped-passing boundary [1172, 1173]. The current drive is quite sensitive to the details of the distribution function [1174], so it needs to be accurate enough in at least the following three requirements. First, the model needs to accurately represent the balance between the passing and trapped EPs since the bounce average of the trapped-EP contribution to the parallel component of the current is much smaller than the passing-EP contribution. Second, the model needs to accurately

represent the balance between the low- and high-energy EPs, since high-energy EPs cause more current than low-energy EPs. Third, the model needs to accurately represent the Ohkawa current [1171] in the calculation of the parallel component of EP current drive, as already mentioned.

As an example of the effects of these requirements, a recent study fitted the radial dependence of the current drive by adjusting the radial diffusion [1170]. Although the fit only partially satisfies our three requirements for the diffusion coefficients, it shows how sensitive the current drive is to the magnitude of the radial diffusion. This study varied the ad hoc diffusion coefficient, which is fairly moderate, uniformly over velocity space for two discharge with different NBI power levels. For the high power discharge, anomalous diffusion at a moderate level ($D_b \sim 0.3 \text{ m}^2/\text{s}$) was used to fit the current drive to the reconstructed NBI current profile (figure 89 (b)). The fitted diffusion magnitude already provides some constraints for the choice of the distribution function parametrization.

However, for the AE-induced relaxation of EP distribution function and similar wave-particle interactions, the multidimensionality of the problem should not be overlooked. The current drive was later simulated using the kick model which includes both the diffusive and convective motion of all EPs in the presence of MHD instabilities (see section 7). The internal kink-like mode and several TAEs with mode numbers $n = 1$ to $n = 6$ were included. Figure 90 illustrates that the kicks in COM space are substantially different for the kink mode and the TAEs. The figure suggests that the uniform ad hoc diffusion [1170] may not be appropriate to describe the current drive because a mode with a given frequency interacts differently with the various groups of EPs, which have different characteristic orbital frequencies.

An important question on the path to burning plasma operations is how to optimize plasma discharges to achieve optimum burning plasma conditions. The EP contribution to this goal could be critical due to the effects of AEs and other modes on the current drive efficiency. Given the importance of the current drive for the plasma scenario and the availability of the power from fusion products, NBI or ICRF, the benefits of current drive control could be significant for the overall reactor performance.

The difficulty of the current drive problem in the presence of EPs lies in both its accurate diagnostic and its accurate modeling. The EP current density in the plasma center from NBI heating was measured by velocity-space tomography based on FIDA measurements at EAST [225]. The modeling tools need to accurately resolve the EP distribution function in COM space and in time which can
<figure><img src="image_88.png" /><figcaption>**Figure 89.** Effects of ad hoc anomalous EP diffusion on off-axis NBCD profiles at DIII-D. The measured NBCD profile fits best with the theoretical calculation with $D_b = 0$ and $0.3 \text{ m}^2/\text{s}$ at (a) $P_{\text{NB}} = 5.6 \text{ MW}$ and (b) $7.2 \text{ MW}$, respectively. Reproduced from [1170].</figcaption></figure>

<figure><img src="image_89.png" /><figcaption>**Figure 90.** Illustration that EP transport in different parts of phase space depends on the instability. The probability density function $p(\Delta E, \Delta P_\zeta)$ for “kicks” in energy and canonical angular momentum resulting from (a) a kink-like mode and (b) TAEs for fast particles with energy $\mathcal{E} = 80 \text{ keV}$, $P_\zeta = 0$ and $\Lambda = \mu B_0 / \mathcal{E} = 0.5$. (c)–(d) Root mean square of energy kicks for (c) kinks and (d) TAEs at $\mathcal{E} = 80 \text{ keV}$ in different parts of phase space. Reproduced from [1174].</figcaption></figure>

be addressed by initial value simulations but not necessarily by the reduced models. To a large extent, EP current drive is not properly calculated by present common models which needs to be addressed for integration into the whole device modeling tools such as TRANSP [916] for predictive simulations of future burning plasma devices.

## 10.2. Actuators changing linear stability properties

AEs in burning plasmas could produce significant transport of the EP population to the wall, which could degrade the fusion performance and could cause localized heat loads from EP impact. External

actuators to control AEs in burning plasmas are being developed in present fusion devices to mitigate this risk. These can act on the gradients in the EP distribution affecting the mode drive, or on the magnetic helicity affecting the Alfvén continuum damping and the existence of AEs in the Alfvén continuum. In practice, these control strategies are interrelated and cannot be changed individually. For example, changes in the kinetic profiles ($T_e, n_e$) directly change both the wave drive and the damping. Changes in the $q$-profile affect not only the Alfvén continuum and hence the continuum damping but also the EP distribution and hence the wave drive. Experiments in present tokamaks and stellarators together with
numerical simulations allow us to develop control techniques applicable to future burning plasmas, which we will review in the following [1166]: variable ICRF and NBI, ECRF, ECCD, and RMPs.

### 10.2.1. Toroidally asymmetric ICRF waves.
As discussed in section 2, the changes in particle toroidal canonical angular momentum and energy of a particle interacting with an ICRF wave are related by $\Delta P_{\phi} = (n/\omega)\Delta\mathcal{E}$. ICRF heating increases the energy of EPs, so we always have $\Delta\mathcal{E} > 0$. The mode number can be large for ICRF heating ($n \sim 30$), and the spatial transport can be significant despite the high wave frequency. This allows flattening of the spatial profiles or moving steep gradients away from the mode location. Toroidally asymmetric waves can have positive or negative toroidal mode numbers $n$. The particles can thus be transported either in the positive or in the negative direction of $P_{\phi}$, corresponding to inward or outward transport in the poloidal flux coordinate $\psi$ [1175-1177]. This control knob on the transport of ICRF-accelerated EPs has been demonstrated on JET where the energetic $^3$He density profile could be modified selectively. Measured $\gamma$-ray emission profiles showed clearly that peaked EP profiles were obtained for ICRF waves with +90° phasing, corresponding to an inward EP transport, and flattened EP profiles were obtained for ICRF heating with -90° phasing, corresponding to an outward EP transport. Toroidally asymmetric waves can further be used to induce plasma rotation, which may be of significant interest for scenario optimization [1178].

### 10.2.2. Variable NBI.
As discussed in section 2, NBI heating generates highly anisotropic EP distributions. As the operational parameters of the various NBI sources can be controlled, the EP population from NBI heating can be changed quite substantially. This allows, e.g., changing the gradients in the EP population or changing the EP phase-space densities at the wave-particle resonances that cause the AE drive, which has been experimentally demonstrated by varying the heating power, voltage, and torque [1179, 1180], the toroidal rotation shear [1181], the energy and pitch of the injected particles [598, 621] and the spatial gradients of the EP distribution [561, 1182].

For example, experiments in NSTX-U changed the AE activity by using either inboard or outboard NBI heating, significantly modifying phase-space distribution of the NBI ions [621]. Whereas the in-board NBI heating at NSTX-U typically excites GAEs, the outboard (more tangential) NBI stabilizes GAEs [621] as figure 91 demonstrates. Resonant EPs are stabilizing for $k_{\perp}\rho_{Lf} < 1.9$ but destabilizing for $1.9 < k_{\perp}\rho_{Lf} < 3.9$ according to the Doppler-shifted

ion cyclotron resonance model. The stabilization is thought to be due to an increase in the phase-space density of low pitch, deeply passing particles with small Larmor radii as suggested by analytic theory, experiments, and kinetic-MHD simulations with the HYM code [77]. The kinetic-MHD simulations carried out with the HYM code [1183] suggest that stabilization is due to the reduction of the anisotropy of the NBI ion distribution function by the increase in the passing particle population.

<figure><img src="image_90.png" /><figcaption>**Figure 91.** a) Mirnov coil color-coded spectrogram showing counter-propagating GAE activity at NSTX-U. Dominant modes are n=-10 (green) and n=-11 (blue). b) Power of on-axis (green) and off-axis (red) NBIs. Reproduced from [621].</figcaption></figure>

### 10.2.3. Electron cyclotron current drive.
ECCD is a promising tool to control AEs as it can locally change the magnetic shear and hence the AE damping. The AE activity observed in tokamaks and stellarators depends on the Alfvén continuum with its gaps given by the magnetic equilibrium and the thermal plasma profiles [32]. In tokamaks, TAEs do not exist if the plasma pressure gradient is larger than a threshold given by the magnetic shear $S$, the aspect ratio $\epsilon$, and the Shafranov shift $\Delta'$ according to

$$ \alpha = -R_0 q^2 \frac{d\beta}{dr} > \alpha_{\text{crit}} = (\epsilon + 2\Delta') + S^2. \qquad (99) $$

The tokamak confinement principle requires large plasma currents, which makes it rather difficult to change the local magnetic shear by targeted, localized ECCD. Additionally, ECCD also heats the plasma, and the effects of heating and current drive are difficult to distinguish. Stellarators, on the contrary, have small plasma currents, so ECCD can generate a significant part of the total plasma current, which makes the effect of ECCD on AE activity readily observable. In Heliotron J, ECCD with $N_{\parallel} = 0.15$ fully suppressed
<figure><img src="image_91.png" /><figcaption>**Figure 92.** Temporal evolution of the magnetic activity in Heliotron J as measured by a magnetic pick-up coil in a discharge without ECCD, i.e. $N_\| = 0$ (a) and with ECCD and $N_\| = 0.15$ (b). Temporal evolution of plasma stored energy (c), line-averaged electron density (d), plasma current (e), and Lyman $\alpha$ line for the case with $N_\| = 0$ (red) and $N_\| = 0.15$ (blue) (f). Reproduced from [1184].</figcaption></figure>

GAEs driven by NBIs as figure 92 shows [1184]. In fact, the basic physics mechanisms for mitigation or suppression of EP-driven modes have been confirmed in several experiments in non-axisymmetric devices, e.g. in TJ-II, Heliotron J and LHD [1185–1187]. In those studies, either NBI or ECCD were used to modify the current profile and local pressure, shifting the mode frequencies into the Alfvén continuum.

#### 10.2.4. ECRF heating.
ECRF heating has been used to affect AE dynamics in different ways in tokamaks [127, 309, 921, 1166]. ECRF heating is a highly localized form of heating and allows targeted heating in a narrow region around the ECRF resonance, so individual modes can be targeted. ECRF heating changes the kinetic plasma profiles very locally, and many different types of interaction can be exploited. Since AEs are highly sensitive to the $q$-profile, the electron density profile and the temperature profile, ECRF has a strong impact on the AE drive and damping and hence on the stability. This idea was corroborated in experiments in DIII-D and AUG. In discharges with early NBI heating and elevated, reversed $q$-profiles, ECRF heating mitigated [1188] or even suppressed RSAEs [127, 1189]. The localized ECRF power deposition profile was varied in several

otherwise nominally identical shots to investigate the impact on the RSAE activity at DIII-D. The power was deposited in the plasma center near the magnetic axis (figure 93a), at the $q_{min}$ position (figure 93b), or at the outer mid-plasma radius. The AE activity was strong for ECRF heating near the magnetic axis, whereas it was fairly weak for ECRF heating at the $q_{min}$ location, and RSAEs were almost suppressed (figure 93). The RSAEs were completely suppressed when ECRF heating is applied at the $q_{min}$ location at AUG, in agreement with the DIII-D results.

<figure><img src="image_92.png" /><figcaption>**Figure 93.** Windowed crosspower spectra of vertical and radial CO2 interferometer data at DIII-D for 1.9 MW ECRF heating deposition at (a) the plasma center #128564, (b) at $q_{min}$ #128560. Overlayed white curves are a typical RSAE and the local TAE frequency plus toroidal rotation frequency at $q_{min}$. Reproduced from [1188].</figcaption></figure>

It is important to remember that the demonstrated control of RSAE activity by ECRF heating at AUG and DIII-D comes from several simultaneous effects, which are interrelated. The localized ECRF heating has an impact on the mode drive, on the damping, and on the ideal eigenmode itself. The AE stability depends on different damping mechanisms such as electron collisional damping [498] and electron Landau damping [444], as well as on continuum damping [1190] through changes to the modes and the continuum induced by changes in the pressure or plasma rotation [1181, 1191]. The mode drive is also affected since the electron drag on EPs depends on $T_e$, modifying the gradients in the EP distribution. Finally, the AEs themselves are affected via coupling to sound waves due to changes in $T_e$ or $T_i$ [1192].

In experiments at DIII-D, the ECRF power deposition, the current ramp rate, the ECRF injection
timing, and NBI power were varied to study any
changes in the RSAE activity [309]. The impact
of ECRF heating on the AE activity was found to
be sensitive to all these parameters. RSAEs were
even observed to be more unstable for ECRF heating
near q_min in some cases, which is in contrast to
the observations in the original experiments, where
they were more unstable for ECRF heating near
the magnetic axis. The existence of RSAEs that
sweep in frequency strongly depends on the ratio of
the minimum frequency of the RSAEs (including a
pressure-dependent upshift from the GAM frequency
at q_min) to the TAE frequency. When these frequencies
are similar, no RSAEs are found, whereas TAEs still
exist. Typical frequency-sweeping RSAEs are highly
sensitive to gradients in the plasma pressure, and may
no longer be an eigenmode of the system. When
the electron beta increases due to ECRF heating,
the RSAE frequency increases and may exceed the
characteristic TAE frequency so that RSAEs can no
longer sweep, resulting in reduced EP transport. Finite
pressure effects can explain many of these observations
[309], but they cannot account for the strong impact of
ECRF heating on NBI-driven AEs in AUG and DIII-D.

Furthermore, additional factors are found to be
important and must be experimentally characterized
further. For example, modulated ECRF heating which
leads to rapid modulations of TAEs [484]. A second
example is that RSAEs are absent in a discharge
after T_e profiles have relaxed so that the plasma is
apparently similar to that in another discharge where
RSAEs were observed [1193].

A plasma scenario of particular interest for steady-
state, high-performance discharges is the so-called
high-q<sub>min</sub> scenario, in which the minimum safety factor
profile value remains near or above q<sub>min</sub> ~ 2. This
prevents the development of potentially disruptive
tearing modes [1194]. As a downside, a higher q<sub>min</sub>
can make the scenario more susceptible to AEs for
which the growth rate increases as q<sub>min</sub>². Such scenarios
can lead to a deterioration of the overall plasma
performance [1194, 1195].

Recent experiments on DIII-D [127, 309, 1165,
1196], AUG [1166] and KSTAR [921, 1197] have
further demonstrated the potential of AE mitiga-
tion/suppression strategies for improving the overall
plasma performance.

As an example, low-frequency AE mitigation/suppression schemes for plasma scenario optimization have been extensively tested in DIII-D experiments [1164, 1165] (figure 94).

Another study was aimed at developing scenarios
where the q_min location is shifted away from the core
toward the plasma mid-radius or slightly higher, e.g.
using the off-axis NBI as an external actuator to

<figure><img src="image_93.png" /><figcaption>**Figure 94.** DIII-D scenario optimization shot to mitigate AE excitation and improve plasma performance by applying core ECCD, along with off-axis NBI, to move *q*<sub>min</sub> inward to the location of reduced beam pressure gradient. Reproduced from [1165].</figcaption></figure>

tailor the current density profile [1164]. The idea in
those experiments is that the unstable modes, that
are potentially detrimental for core EP confinement
(e.g. RSAEs), are pushed towards the plasma edge
in regions with lower EP density, which quenches the
associated EP loss channel. A significant reduction
in AE driven EP transport was found and agreed
with predictions of critical gradient models discussed
in section 7 [1164].

A stabilizing effect of ECRF heating was observed
on TJ-II, which was attributed to an increased
damping at higher temperatures, but the reason was
not obvious [1193]. Experiments on TCV showed
an increase in mode activity with increasing ECRF
heating and NBI [1198], which in that case was
attributed to an increase in the slowing-down time
of NBI ions resulting in an increase in EP density.
As a general conclusion, those effects are usually well
captured by codes such as TRANSP, and competition
between drive and damping can be investigated
through AE stability codes.

<figure><img src="image_94.png" /><figcaption>**Figure 95.** Example of AE mitigation and suppression by ECRF heating on KSTAR. The top panel shows the toroidal mode number spectrum from Mirnov coils at the vessel wall. The ECCD power deposition location is varied from $\rho = 0.56$ to $\rho = 0.29$ between 5 s and 5.5 s, resulting to suppression of TAEs after $\approx 6.5$ s. The bottom panels show the evolution of mode amplitude for $n = 1-4$, with negligible amplitude detected in the TAE frequency range after 6.5 s. Reproduced from [1197].</figcaption></figure>

It should be noted that ECRF heating could affect AE activity via other mechanisms. First, ECRF heating has an impact on microturbulence which is thought to affect the AE saturation and the impact on the EP profile [851]. Second, ECRF heating can have an impact on the horizontal polarization of flux surfaces which can form a potential hill for RSAEs, eliminating RSAEs at fairly low ECRF power [1199, 1200]. Since the effect depends on changes in the electron distribution function, RSAE were suppressed for timescales similar to the electron-electron collision time. Hence, the AE response to ECRF heating modulation [484] as well as to wave polarization should be studied further.

For ITER and future fusion reactors, the feasibility of AE control schemes through ECRF heating is intriguing. The ITER ECRF heating system is primarily designed for heating, current drive, and NTM control [1201, 1202]. At present, no active investigations on the use of ECRF heating or ECCD for AE mitigation control have been performed, and it is unclear if the timescales and hardware

capabilities for mirror steering of the ECRF heating system are compatible with such demanding, multi-task operations at ITER [1203].

#### 10.2.5. Externally applied RMPs.
Externally applied RMPs are routinely used in tokamaks to stabilize the plasma against MHD activity such as ELMs [1204–1206] or RWMs [426] as discussed in section 8. Externally applied RMPs have been used in NSTX to mitigate TAEs and GAEs by modifying the EP phase-space distribution [992, 1207]. Perturbations of size $\delta B/B \approx 0.01$ at the plasma boundary reduced the mode amplitude, increased the mode bursting frequency, and decreased the frequency chirp. Furthermore, the magnetic perturbation can modify weakly bursting modes temporarily to a saturated continuous mode. Figure 96 shows the impacts of RMP blips on the GAE activity in an NBI heated discharge. Experiments at AUG have corroborated that RMPs can be used to control strong TAEs driven by NBIs.

#### 10.2.6. Sensors for real-time control
For real-time control, accurate rapid detection of AEs or fast-ion properties are required. Various methods to detect unstable AEs have been tested on DIII-D using ECE [1208–1210] and interferometer [1211, 1212] signals. Real-time control of neutral-beam populations based on calculations using the RABBIT code [943] are being developed on AUG [944, 945] and DIII-D.

<figure><img src="image_95.png" /><figcaption>**Figure 96.** AE mitigation at NSTX via externally applied 3D fields. (a) RMP coil current per turn, (b) $D_\alpha$-light, (c) SXR emission from the plasma pedestal, (d) neutron rate, (e) spectrogram of Alfvén activity from a magnetic pick-up coil and (f) bandpass filtered magnetic pick-up coil signal. Reproduced from [992].</figcaption></figure>
### 10.3. Scenario optimization exploiting low- and high-frequency AEs

The basic relation between changes in energy and canonical toroidal angular momentum $n\Delta\mathcal{E} = \omega\Delta P_\phi$ suggests we can target transport in energy and in $P_\phi$ selectively through low- or high-frequency waves. EP-driven Alfvénic instabilities with frequencies well below the ion cyclotron frequency transport EPs primarily along the $P_\phi$ direction with $\Delta\mathcal{E}$ relatively small. For usual EP energies the magnetic flux term of $P_\phi$ dominates, so $P_\phi \propto \Psi_{\text{pol}}$ suggests transport in the radial direction. Conversely, at higher frequencies, $n\Delta\mathcal{E} = \omega\Delta P_\phi$ suggests that $\Delta\mathcal{E}$ is now large whereas the change in $P_\phi$ can be small for small mode numbers $n$.

As a result, the low-frequency AEs are mostly driven by the EP radial density gradients whereas high-frequency AEs are mostly driven by the EP energy gradients. Furthermore, the low-frequency AEs lead to primarily radial redistribution of EPs, leading to relaxed EP drive from spatial gradients, whereas the high-frequency AEs lead to primarily energy redistribution of EPs, leading to relaxed drive from energy gradients. Nevertheless, as already discussed, asymmetric ICRF waves with $n \sim 30$ can still cause significant radial transport. These considerations lead to avenues of scenario optimization via high- and low-frequency AEs.

The high-frequency Alfvénic modes on the order of the ion cyclotron frequency can tap into the EP energy and to a lesser extent the EP toroidal momentum, which is proportional to approximately the square of the minor radius of the confined ion position. Given that both the high-frequency CAE and high-frequency GAE type of instabilities reach primarily the EP kinetic energy, they can provide a opportunities to improve the plasma performance by influencing the EP velocity distribution function. This in turn modifies the stability of EP-driven modes. The linear properties of high-frequency instabilities were discussed in section 6. High-frequency GAEs [615] and CAEs [1183] can channel their energy to the plasma through the excitation of kinetic Alfvén waves (KAW). Such channeling is important in particular for the ICE problem, i.e. it provides an additional damping mechanism not considered earlier. KAW excitation leads to CAE damping through the electron Landau damping by inducing $E_\|$ due to the small perpendicular wavelength of KAWs. This particular damping mechanism is new and had not been accounted for in ICE theory [589, 590]. However, these mechanisms exploiting high- and low-frequency AEs need to be better understood and verified for the active plasma optimization of a fusion reactor.

### 10.4. Alpha channeling

Alphas are born at 3.5 MeV, which is far above the critical energy in fusion plasmas, and thus the largest part of the fusion alpha energy heats the electrons rather than the fuel ions, as described in section 2.4. However, the fusion reactivity is mostly determined by the fuel ion temperature, rather than the electron temperature. Alpha channeling has been suggested theoretically as an attractive option for directly transferring energy from alphas or other EPs to thermal ions in fusion reactors for several decades [633, 1213]. The advantage is that this would be faster than the usual collisional energy transfer mechanisms and would avoid slowing down on electrons, which can add a further loss channel before transferring the energy to thermal ions. Several mechanisms have been proposed that would facilitate alpha channeling. The simplest involves either linear [1214] or nonlinear [1215] damping of Alfvénic waves (driven unstable by alphas) on thermal ions. Beyond this, a variety of wave-wave coupling schemes have been proposed [1216–1218], some of which involve antenna launching of external waves that would serve as catalysts for such processes. Coupling mechanisms that rely on minority ions have also been suggested [1219]. While some limited attempts have been made to check for alpha channeling in DT experiments [1217, 1220], clear evidence for significant ion heating has not been forthcoming. However, evidence of rapid ion heating correlated with EP driven waves in LHD has recently been reported [1221].

Some analyses based on the solution of the steady-state Fokker-Planck equation for the alpha distribution in slab [1222] and full toroidal [1223] geometries indicated that significant extraction of alpha energy using alpha channeling might be possible, provided there is sufficient control over Alfvénic turbulence to remove the helium ash. However, the practical feasibility of alpha channeling in an ITER-like plasma is still debated [1216]. Simulations were performed using a mode with resonances in the ion cyclotron range to extract energy from the alphas and using either a low-frequency mode or microturbulence for ash removal. It was found that any combination of mode amplitudes and diffusion by microturbulence capable of extracting energy from the alphas and ejecting ashes also causes significant alpha energy fluxes to the walls. Despite these discouraging results, alpha channeling remains an intriguing subject for improving the performance of fusion reactors, requiring further experimental and modeling work.

Alpha channeling can also be considered in a broader sense in order to optimize plasma discharges by using the fusion-born charged products not only for plasma heating. For example, the alpha energy
may also be used to amplify the plasma waves that drive current. It was also suggested to use Alfvénic instabilities to redistribute EPs in order to reduce the central magnetic shear [1224]. In that case, the formed steady-state internal transport barrier can be sustained as was demonstrated in DIII-D experiments. Another possibility for alpha channeling is EGAM channeling discussed in subsection 9.2.

## 11. EPs in ITER reduced-field scenarios before DT

The 2016 ITER baseline configuration and research plan foresaw a fairly long operation period in hydrogen and helium plasmas heated by NBI, ICRF and ECRF. This non-nuclear period minimized the activation of the machine by DD fusion neutrons in the early operational phases [4, 5]. In the new 2024 ITER baseline, this period has been significantly shortened and only RF heating will be applied [6]. After a brief period of hydrogen and helium operations, ITER will commence deuterium operations.

The new start-up phase will demonstrate L-mode operation at full magnetic field and full current (5.3 T, 15 MA). H-mode access is easier to achieve at reduced fields and will be attempted at half field and current (2.65 T, 7.5 MA), or possibly even at 1/3 field, 1/3 current, (1.8 T, 5 MA) in ITER. It would be advantageous to attempt H-mode access in deuterium since the L-H transition power threshold is lower than in hydrogen, but deuterium should be avoided in the start-up phase to minimize the activation of the machine. The reduced-field scenarios are further discussed in chapter 6 of this volume [18].

The plasmas in the early operation phases of ITER will be heated mostly by ECRF heating with an additional 10 MW ICRF heating which can generate EPs. As NBI heating had a prominent role in the non-nuclear phase of the original 2016 ITER baseline, the EP related work for these scenarios has had its focus on NBI heating. Therefore, the review in this section pays much attention to NBI physics, which will play a lesser role in the new plan but will be nevertheless be important just before the DT phase where obviously safe operations is also required, despite the brevity of operation phase.

At reduced field and current, the EP confinement will be worse than at full field and current due to the wider drift orbit widths. Furthermore, the reduced fields cause a relatively stronger magnetic field ripple. Additionally, the lower current leads to lower plasma density, which increases NBI shinethrough that can lead to localized power loads on the plasma-facing components and, in the worst case, result in local melting.

We will first discuss NBI shinethrough and then EP confinement in MHD-quietcent plasmas with external 3D perturbations and various MHD modes, as well as ICRF heating scenarios at reduced field. Microturbulence is not expected to be a particular concern for half-field scenarios (see section 9). Finally, conclusions based on existing results are given and needs for more detailed studies are identified.

### 11.1. NBI shinethrough power loads in reduced-field scenarios

ITER will have two heating NBIs and one diagnostic beam. The heating NBIs will each inject 16.5 MW at 870 keV for hydrogen and at 1 MeV for deuterium (see section 2). In addition to heating, they also drive current and plasma rotation. The diagnostic beam will operate with hydrogen and inject up to 2 MW at up to 100 keV.

Empirical scaling relationships suggest that H-mode access will be easier at the lower densities of the reduced field scenarios. To reduce shinethrough, the NBI injection energy needs to be decreased from the nominal energy of 1 MeV, which also decreases the available NBI power according to the perveance relationship $P_{NBI} \propto \epsilon_{inj}^{2.5}$. In addition, the injected species plays a significant role: the shinethrough is stronger for hydrogen NBIs than for helium NBIs for the same NBI parameters. To consider worst-case scenarios, shinethrough studies have therefore mainly considered hydrogen beams and plasmas.

Most of the shinethrough hits four special panels designed to withstand extra power loads in horizontal rows 15S and 16S (figure 97). The computed shinethrough power on these panels has been found to be within the allowed power limits even at low densities. However, a small portion of the shinethrough can pass through the 10 mm wide horizontal gap between the rows and can hit blanket shield block 16DS [1169, 1226]. Since the shield blocks are not designed to be replaced during the lifetime of ITER, it is crucial to ensure benign shinethrough loads in this gap (<0.8 MW/m²).

Early work on wall load patterns was based on an analytic beam model [1169]. Later, more detailed simulations using the beamlet-based NBI code BBNBI [1227] were performed for the 1/3-field hydrogen plasma scenario for two different kinetic profiles [1225, 1228]. One was at 50% of the Greenwald density (0.5 $n_{GW}$) with temperature profiles corresponding to about 40 MW auxiliary heating, and the other at 0.9 $n_{GW}$ with over 50 MW of auxiliary heating. At 0.5 $n_{GW}$, the NBI injection energy had to be reduced to 530 keV, which gives a beam power of 4.7 MW. At 0.9 $n_{GW}$, the NBIs can be injected at 745 keV [1169], which gives a beam power of 11.15 MW.
<figure><img src="image_96.png" /><figcaption>**Figure 97.** Power densities of NBI shinethrough losses from 9.4 MW, 530 keV beams off-axis beams (left figure) and on-axis beam s(right figure) in 5 MA and 1.8 T hydrogen plasmas, as calculated by BBNBI/ASCOT. The power is the total power from the two beam boxes. Reproduced from [1225].</figcaption></figure>

At $0.5 n_{\text{GW}}$, the highest power loads of about 1 MW/m² were found predominantly on the shinethrough panels in row 15S for the on-axis beam and on the shinethrough panels in row 16S for the off-axis beam. The high-power shinethrough footprint is smaller for the on-axis beam. The load on the critical horizontal gap is benign at about 0.2 MW/m². The structures adjacent to shinethrough panels in row 15S also receive a benign shinethrough load of tens of kilowatts. At $0.9 n_{\text{GW}}$, the high-power shinethrough footprint from the on-axis beam and the off-axis beams become similar in size. This results in higher loads on both the TBM frame and on the diagnostic port, reaching up to 100 kW/m². The power density on the sensitive horizontal gap between rows 15S and 16S then approaches the power limit of 0.8 MW/m².

A helium plasma in the 1/3-field scenario at $n = 0.4 n_{\text{GW}}$ with hydrogen injection at various power levels and corresponding changes in the injection energy was studied in [1229]. Both the total and peak shinethrough power loads were found to have the same dependence on the injection energy, $P_{\text{shinethrough}} \propto \mathcal{E}_{\text{inj}}^4$, which is stronger than the perveance relation $P_{\text{NBI}} \propto \mathcal{E}_{\text{inj}}^{2.5}$. These larger loads for higher energy particles are explained by their higher probability to pass through the plasma without ionization. The total shinethrough power fraction is 19% (2.3 MW) for the nominal injection energy of 580 keV and power of 12 MW. While the peak power loads on the dedicated shinethrough panels remained well below the design limit of 4.7 MW/m², the distribution of the load was not confined to these panels. The peak power limit, 0.3 MW/m², for the adjacent TBM port (to the left of shinethrough panels in figure 97) and the diagnostic port (to the right) was reached for the diagnostic port just due to the shinethrough.

The same study also considered the half-field

scenario with a helium plasma at $n = 0.4 n_{\text{GW}}$ with hydrogen injection at 16.5 MW at 870 keV. The total shinethrough power fraction was only slightly higher than in the 1/3-field case at 21% (3.5 MW), and the power load distribution was very similar both qualitatively and quantitatively. More recently, shinethrough was studied for a wider plasma parameter range, for hydrogen injection into hydrogen and helium plasmas, and the shinethrough fraction was fitted as a function of the plasma parameters [1230]. Since its impact on the shinethrough is different for on-axis and off-axis beam configurations, this work considered also the density peaking factor as a variable. Further work is needed to investigate the shinethrough of deuterium NBI on deuterium plasmas.

## 11.2. EP confinement in MHD-quietcent reduced-field scenarios with external perturbations

In the non-nuclear phase, the EPs are generated by auxiliary heating only. ICRF heating can produce EPs in the plasma core, and NBIs can produce co-going EPs. Despite the wider drift orbits in the low-current scenarios, prompt losses are still expected to be small assuming axisymmetry. Neoclassical transport is also expected to be benign. However, the EP transport and loss channels due to 3D effects and MHD activity are expected to be stronger in the half-field scenarios than in the full-field scenarios. In this subsection, we will discuss the effect of the unavoidable magnetic field ripple in the half- and 1/3-field scenarios, including the wall power loads.

EPs in the standard ITER magnetic configurations with 3D effects have been discussed in section 8. The ITER 15 MA baseline scenario is close to axisymmetric due to the ferritic inserts optimized for that scenario: the TF ripple at the outboard midplane sep-
aratrix is reduced to 0.3%, except for near the NBI
ports (0.6%). However, while the ferritic inserts com-
pensate the TF ripple at the full field, the ferritic ma-
terial saturates already at magnetic fields below 2 T.
Therefore, the ferritic inserts overcompensate the TF
ripple at the lower fields, so that their effect can turn
into ripple enhancement. Indeed, in the 1/3-field sce-
nario, the TF ripple phase is reversed, and the ripple
strength at the outboard midplane separatrix can reach
~1.3%, which is larger than the unmitigated ripple in
the baseline scenario (~1.1%) [1225] and could com-
promise the good EP confinement. The maximum TF
ripple for the half-field and full-field scenarios are sim-
ilar, but the phase of the ripple relative to the position
of the inserts is also reversed.

Therefore, while the EP confinement is predicted
to be very good in the main operating phases
(15 MA baseline, 12.5 MA hybrid, and 9 MA “advanced
tokamak” scenarios) [1034], it was less clear in the
half- and 1/3-field scenarios. Nevertheless, EP losses
in ITER due to TF ripple mitigated by ferritic inserts
in reduced field scenarios have been found to be
acceptable [1231]. The ferritic inserts reduce both the
total power loss and the peak power flux to the wall
by an order of magnitude both in full-field and in the
half-field scenario compared to a case without ferritic
inserts.

The losses of hydrogen beam ions in hydrogen
plasma in the 1/3-field scenario were estimated in
ASCOT simulations at *n* = 0.4 *n*<sub>GW</sub> and at *n* =
0.9 *n*<sub>GW</sub> [1228]. For the 735 keV beams at *n* =
0.9 *n*<sub>GW</sub>, only 65 kW of the beam power of nearly
20 MW was lost (0.3%). For the 530 keV beams at
*n* = 0.4 *n*<sub>GW</sub>, 270 kW of the beam power of 9.4 MW
was lost (3%).

The effect of the three pairs of TBMs (recently
reduced to two pairs) on the 3D magnetic field and the
EP confinement was assessed by including a numerical
model for the magnetization of the European helium-
cooled pebble bed TBMs [1030]. The initial study
addressed beam ions and alphas in the ramp-up and
flat-top phases of the 15 MA baseline scenario, where
the losses with and without TBMs were compared.
While the wall load increased by about a factor three, it
was still benign at only tens of kW. The divertor loads
remained unaffected. No evidence for non-diffusive
channelling, possibly leading to hot spots, was found.
Instead, the diffusive loss channels were intensified due
to the TBM perturbation, allowing ions from deep in
the plasma to escape. The TBMs caused no significant
changes in the slowing-down density profiles.

The fusion alpha results in the study indicated
that the presence of TBMs enhances the ripple
diffusion of banana particles, but the increase is less
than an order of magnitude. ICRF-heated ions were

not included in this study, but the effect should be
similar to the part of the alpha population on similar
orbit types.

The effect of ELM control coil perturbation was
assessed at several full-field scenarios and the half-
field scenario [963]. Introducing the ELM control coils
was found to decrease the beam-ion confinement even
for the 15 MA baseline scenario. The power loads
increased by an order of magnitude which can be
attributed to the field line stochasticity penetrating
deeper than the pedestal top. In contrast to the
TBM perturbation, ELM control coils mainly affect
the power loads on the divertor. Including the plasma
response was found to intensify the losses in the
plasma periphery, where both the baseline and half-
field scenarios feature the largest number of beam ions.
Up to 4% of the beam power could be lost. This power
load increased due to a new loss channel for marginally
trapped ions [1035].

11.3. Effects of MHD modes on EPs in reduced-field scenarios

The interaction between EPs and thermal-plasma
driven MHD modes was described in section 5. For
ITER, such studies have considered the main operating
scenarios and fusion alphas, e.g. [370] and [371],
where the latter included also the 3D structure of the
magnetic field.

Nevertheless, a recent study [499] assessed the
excitation of TAEs by beam ions for reduced field and
current, together with the effect of these modes on the
EP transport (figure 98). Due to lower field and still
relatively high beam energies, the beam ions are super-
Alfvénic. NOVA-K simulations found that modes with
a wide range of toroidal mode numbers *n* are excited,
and that the most unstable ones were around *n* =
20. These modes reduce the computed mainly beam-
target neutron production (which is proportional to
the EP density) by up to 30% as a result of beam
ion redistribution. It thus appears that, in these
conditions, TAEs will be a concern.

The study also considered how a sawtooth
redistributes EPs in helium plasmas. A monster
sawtooth in these plasmas has a sawtooth period of
around 10 s. Although there is a significant drop
in the neutron production after a monster sawtooth
crash, the time average of the neutron production
is not significantly altered. This is because the EP
distribution rapidly recovers between two sawtooth
crashes.

Regarding the EP-driven modes, a significant
change is expected due to the inclusion of novel
ICRF three-ion schemes (section 3). In particular,
instabilities will be driven by ICRF-heated ions which,
in JET, has resulted in a rich spectrum of modes [38].
<figure><img src="image_97.png" /><figcaption>**Figure 98.** Impact of (a) sawtooth- and (b) TAE-induced mixing of EPs on the neutron rate for an ITER 7.5 MA/2.65 T helium H-mode plasma at $n/n_G = 0.5$ with 33 MW of H$_0$-NBI and 20 MW of ECRF heating with $c_{Be} = 10\%$. Reproduced from [499].</figcaption></figure>

## 11.4. ICRF heating scenarios at half field

During the early operational phases at ITER, the ICRF system will focus on demonstrating ion cyclotron wall cleaning (ICWC), evaluating ICRF coupling, and testing the compatibility of ICRF with a full-tungsten first wall. Additionally, it may be used for early studies of EP physics, modeling, and EP diagnostics, particularly targeting AEs and the impact of MeV-range EPs. Key AE characteristics for modeling, such as the toroidal mode number and the location of the mode, can be obtained from Mirnov coils and ECE measurements. If additional diagnostics, such as gamma-ray measurements, are available, they could strongly improve benchmarking modeling against EP measurement data, in support of future ITER experiments involving alphas.

A range of efficient ICRF scenarios based on plasma mix and magnetic field is available at ITER. Hydrogen minority heating in deuterium plasmas, suitable for a half-field ITER operation ($B_0 = 2.65$T, $f \approx 40$ MHz, $n_H/n_e \approx 2-5\%$), is particularly robust for testing ICRF heating in H-mode plasmas at half-field. By changing the hydrogen minority concentration, one can change the ratio of electron-to-bulk-ion heating, test RF coupling and assess impurity production, critical for evaluating the potential to extend ICRF power to 20 MW in future ITER phases.

However, the 10 MW of ICRF power available during the early operational phases may be insufficient to destabilize AEs with hydrogen minority heating in ITER, unless targeting very low density plasmas. JET experiments typically require at least 4-5 MW of ICRF power to destabilize AEs with H minority heating. Given the large size of ITER compared to JET, optimizing the absorbed RF power per resonant ion is crucial for driving AEs with EP generated by ICRF heating. This goal can be achieved using three-

ion ICRF scenarios, validated on various tokamaks, which are effective in generating MeV-range EPs and destabilizing AEs. Unlike typical minority heating scenarios that require resonant ion concentrations of a few percent, three-ion scheme scenarios can be tailored to channel ICRF power to a very small population of resonant ions with concentrations below $\sim 0.5\%$.

## 11.5. Future work on ITER reduced-field scenarios

In this section, we have summarized the work dedicated to EPs in operating scenarios with reduced field and current. The beam shinethrough has been analyzed in detail to guarantee the integrity of the device for NBI heated plasmas. The confinement of beam ions can be assumed to be very good in the absence of MHD and external perturbations such as ELM control coils. The corresponding neutron rates have been estimated [499].

However, much of the existing work needs to be updated following the changes in the ITER baseline, requiring further EP studies at reduced field and current. Effects of ELM mitigation coils and various low-frequency modes on EP confinement need to be studied in detail, as well as effects of EP-driven modes, e.g. using the three-ion scheme or NBI-ICRF heating synergistic effects. With the new ITER baseline, shinethrough of deuterium NBIs should also be assessed. The beam power is not necessarily critical for accessing H-mode due to the increase of ECRF power, but for the sake of safe operation of the NBI system in the reduced-field scenarios, its shinethrough limits should be assessed.

Furthermore, control strategies or possible actuators to affect instabilities have never been addressed for half- or 1/3-field scenarios. The non-nuclear phase with its reduced field and current gives a good test platform to test the actuators planned for nuclear phase. In particular, one of the candidates to mitigate AEs is
ECCD. This approach relies on the ability to modify the *q*-profile (section 10), which ought to be easier for reduced current and high ECRF heating power. A numerical assessment of this would be highly desirable in the near future.

# 12. Runaway electrons

Runaway electrons (RE) have long been a spotlight topic in plasma research. They now attract increased attention as a part of ITER mission considerations. The toroidal current and the associated magnetic energy are greater in ITER than in any present-day tokamak. It is, therefore, of grave concern when highly energetic runaway electrons become the dominant carriers of the current. This concern pertains immediately to the disruption events in which the unmitigated runaways can produce significant localized melting of plasma-facing components.

The disruptions are commonly described macroscopically in the framework of MHD that needs amendments to cover the runaways. The presence of runaways brings kinetic physics into the problem and calls for a kinetic-MHD approach that combines the MHD treatment of the bulk plasma with kinetic modeling of the runaway population in a self-consistent way. The construction of such an integrated model is an overarching goal of the ongoing theoretical and experimental studies of runaway physics. This section describes the status of these studies with an emphasis on recent advances.

The latest review paper on runaway electrons highlights the prevailing physics themes of the last 20 years [36]: the hot-tail mechanism of runaway production, RE interaction with impurity ions, the role of synchrotron radiation in runaway kinetics, RE transport in presence of magnetic fluctuations, microinstabilities driven by REs in magnetized plasmas, and vertical stability of the plasma with REs. It also includes a discussion of the runaway issues for ITER and the strategy of RE mitigation.

The need to minimize the impact of RE on ITER motivates the continuous development of new numerical tools (especially for synthetic diagnostic). This effort complements the dedicated experimental work on the present-day tokamaks such as JET [257], ASDEX [1232, 1233], MST [1234], COMPASS [1235, 1236], EAST [1237], DIII-D [256], and J-TEXT [1238]. It is unfortunate that the results of the ongoing experiments themselves are not immediately scalable to next-generation tokamaks, which raises concerns regarding capabilities of disruption mitigation systems (DMS) and runaway control, as summarized in [1239, 1240]. Nevertheless, these results are essential as a testbed for the theoretical conjectures,

phenomenological extrapolations and code validation. Diagnostics of runaway electrons in present tokamaks and burning plasmas in ITER is discussed in section 4, and impact of runaway electrons on MHD stability is discussed in chapter 4 of this volume [16].

## 12.1. RE formation during disruptions

Runaway electron formation during disruption is of grave concern for ITER. The disruption event involves a thermal quench (TQ), a current quench (CQ), and, sometimes, a runaway plateau. The TQ refers to the rapid loss of the plasma kinetic energy, the CQ to the decay of the plasma current, and the runaway plateau is a regime when runaway electrons carry most of the current.

### 12.1.1. Thermal Quench.
Reference [1241] offers a thorough statistical analysis of the TQ triggerings in JET. Two phenomena can cause rapid electron cooling: global MHD events that enhance heat transport via stochastization of magnetic field lines and impurity influx resulting in strong radiative losses. Cooling of bulk electrons reduces the plasma conductivity whereas the toroidal current cannot change significantly on the fast TQ timescale. A strong inductive electric field builds-up as a result. In a post-TQ plasma, this field is up to three orders of magnitude greater than the critical Connor-Hastie field for runaway production. Note that, in the absence of ongoing heat losses, Ohmic reheating after the TQ precludes RE production [36]. Such events were observed in tokamaks [1242].

A so-called hot-tail mechanism of RE generation is the prevailing candidate for primary RE generation during TQ in ITER. It considers partial survival and acceleration of the hot pre-TQ plasma electrons [1243]. Its first analytic descriptions involved an assumption that the distribution of plasma electrons remains Maxwellian during the cooling process [1244, 1245]. This assumption, however, does not hold for a rapidly cooling plasma. A more appropriate model, which assumes collisional drag on a cold background to dominate the evolution of the pre-TQ electron distribution function, was suggested in [1246]. This model is referred to as the “hot-tail model” and has been used to make predictions for ITER (for example [1247]) or to analyse recent experiments [1248, 1249].

The hot-tail RE generation has been modeled numerically in [1250–1252] based on the electron kinetic equation. In [1250], the evolution of the hot-tail distribution function was calculated self-consistently with the inductive electric field and the energy balance of the cold background, assuming that the impurity line-radiation is the dominant energy loss mechanism. The trends observed in [1250] are in general agreement with [1246]. Reference [1252] provides a more recent
numerical study of the analytic model [1246] with an improved description of runaway electron scattering.

For a significant hot-tail population, [1250] predicts a ‘prompt conversion’ regime, in which super-thermal electrons carry most of the current with minimal friction. That limits the inductive electric field. A distinctive feature of this regime is the absence of multi-MeV electrons. A detailed comparison of the model [1250] with experimental observations of the prompt conversion in DIII-D has been reported in [1253]. Reference [1254] reports experimental observation of super-thermal electron populations in DIII-D in comparison with the kinetic hot-tail simulations as well. While the theoretical predictions agree with the observations qualitatively, the calculated hot-tail generation is one to two orders of magnitude lower than the one inferred from experiments. These disagreements are likely due to incompleteness of the physics models used for the hot-tail calculations - a complete model should include the effects of radial transport and inhomogeneities of material injection that triggered the TQ. Kinetic modeling of RE generation in AUG plasma also suggests lack of essential physics in these simplified models [1255], in particular - the radial transport. This calls for self-consistent RE-kinetics and MHD calculations.

12.1.2. Strong avalanche during current quench. The plasma becomes more resistive during TQ. The plasma current then decays during the CQ on the $\tau = \frac{L}{R}$ timescale, where $L \approx 2\pi Al_i/c^2$ is the plasma inductance, A is the major radius, and $l_i$ is the internal plasma inductance coefficient (typically of order unity), and R - is the plasma resistance. Because the “wall time” in ITER is very long - 0.5 s, only the poloidal magnetic field energy inside the wall can dissipate faster than 0.5 s. The plasma current will then be taken over by the wall.

Avalanche generation of RE can slow down the current decay in ITER. Reference [1256] provides the following simplified expression for the avalanche growth rate in a very strong electric field:

$$ \frac{1}{j_{\text{re}}} \frac{\partial j_{\text{re}}}{\partial t} \approx \frac{1}{\sqrt{Z + 5 \ln \Lambda}} \frac{eE}{mc}, \quad (100) $$

where $j_{\text{re}}$ is the RE current density, E is the electric field and $\ln \Lambda$ and Z are the Coulomb logarithm and the effective charge as “seen” by the relativistic particles. The inductive electric field E during disruption can be estimated as $E = -\frac{L}{2\pi A} \dot{I}$, where I is the total current.

Integrating equation (100) using the above expression for E provides a relation for the ultimate RE current $I_{\text{re}}(\infty)$ as long as it is smaller than the

initial plasma current $I(0)$ [1257],

$$ \ln \frac{I_{\text{re}}(\infty)}{I_{\text{re}}(0)} = \frac{l_i}{\sqrt{Z + 5 \ln \Lambda}} \frac{I(0) - I_{\text{re}}(\infty)}{I_A}, \quad (101) $$

where $I_A = \frac{4\pi mc}{e\mu_0} = 17$ kA is the Alfvén current. A very large initial plasma current $I(0) = 15$ MA in ITER yields a very strong amplification (a few tens of e-folds) of the initial RE current $I_{\text{re}}(0)$. Equation (101) shows that large amplification of the RE current is insensitive to the CQ scenario and its details such as duration or plasma resistivity evolution.

Note that the avalanche theory proposed in [1256] does not treat the effect of partially ionised impurities in detail. It simply uses the sum of free electron density and half of the bound electron density in the definition of the critical electric field to account for the bound electrons (see section 3.2.2 in [36]). This simplification underestimates the avalanche growth rate. Reference [1258] suggests two improvements: to separately evaluate collisional frequencies (i.e. Coulomb logarithms) for free and bound electrons and to count both free and bound electrons in the description of knock-on collisions. The resulting modified avalanche formula is given by equation (30) in [1258]. Yet, the Coulomb logarithms used in [1258] and subsequently in [1247] for collisions with free electrons and scattering are inaccurate because they are based on a fully classical model (see the discussion in section 3.1 in [1259]). More accurate collisional rates based on the Thomas-Fermi model are given in [1260] (see also sections 3.2 and 3.3 in [36]). A further refinement has been discussed in [1261, 1262], where the collision frequencies have been evaluated using the density functional theory. The derived frequencies agree with the Thomas-Fermi model within the range of their validity, i.e. for atoms with $\alpha Z \ll 1$, where $\alpha \approx 1/137$. Section 4 of [1262] shows a reasonable agreement of the results with those of [1247] when the ambient plasma characteristics are similar (i.e. the ambient temperature is taken to be constant as in [1247]). In particular, at sufficiently high deuterium density ($\sim 4 \cdot 10^{21} \text{m}^{-3}$) the generation of runaways is found to be fully suppressed. This result is in agreement with the original estimate for the RE suppression density given in [1256] (i.e. “Rosenbluth density” $n_{\text{DT}} = 3 - 5 \cdot 10^{21} \text{m}^{-3}$).

In addition, recombination increases the avalanche rate due to the increase of the $n_{\text{bound}}/n_{\text{free}}$ ratio [1262]. However, the ionization balance in [1262] relies on the collisional-radiative model [1263] that implies the plasma to be Maxwellian and transparent to line-radiation. Reassessment of the ionization balance in [1264] gives increased ionization levels for the plasma with minority runaways.

There are some effects of the finite aspect ratio and plasma shaping on the avalanche rate, but none
of them appears to be of primary importance. As shown in the seminal work [1256], toroidicity reduces the avalanche rate by a neoclassical factor $(1+1.46\sqrt{\epsilon}+1.72\epsilon)^{-\frac{1}{2}}$, where $\epsilon$ is the aspect ratio. Reference [1265], however, suggests that poloidal asymmetry of the electric field enhances the avalanche rate when the inductive field is sufficiently strong, which counteracts the reduction of the avalanche rate with the aspect ratio. References [1266, 1267] report a small reduction of the avalanche rate due to plasma elongation. Reference [1268] discusses parametric dependence of avalanche on radial transport. A newly developed numerical framework [1269] should permit further improvements in such studies. Reference [1270] studies spatial transport in axisymmetric configurations and concludes that it is most important in small to mid size devices, and become insignificant in larger tokamaks. Reference [1271] highlights the critical role of the avalanche source on the surface heating of plasma facing components due to deconfined runaway electrons.

## 12.2. Plateau and Mitigation

When REs overtake most of the current, the electric field drops to the near-threshold value for the RE avalanche. This phase of RE evolution and the value of the threshold electric field deserve special attention because they correspond to the long-term RE current decay [1272].

The RE spectrum now peaks at very high energies where radiative processes such as synchrotron and bremsstrahlung play a significant role. Because of that, the threshold electric field exceeds the critical Connor-Hastie electric field $E_c$ [1273] determined by the purely collisional slowing-down. Refs. [1274–1276] consider bremsstrahlung as a limiting mechanism for RE energy gain. Bremsstrahlung can be significant in the presence of high-Z impurities. However, the combined effect of pitch angle-scattering and synchrotron radiation leads to faster energy losses in ITER-like disruption scenarios [1277–1280].

Synchrotron losses cause accumulation of the pre-existing runaways around the stable phase-space attractor when the electric field eventually drops to the near-threshold level [1277,1281]. Figure (99) shows an example of such a quasi steady-state distribution function. This distribution function has a leak into the cold bulk. The resulting decay time depends exponentially on the strengths of the inductive electric field. This feature and the exponential growth of the population at higher electric fields ensure that the inductive electric field remains close to the threshold during the entire RE current decay. Experimental observation of such a non-monotonic distribution function in DIII-D was reported in [1282].

<figure><img src="image_98.png" /><figcaption>Figure 99. Example of RE distribution function in the near-threshold regime. Parameters correspond to $E/E_c = 4$, $Z = 10$, and the ratio of radiation to collisional times is $\nu_{drag}\tau_{rad} = 5$. The avalanche generation is switched off. Reproduced from [36].</figcaption></figure>

A rigorous kinetic treatment [36, 1277, 1281] provides the following estimate for the threshold electric field in the limit of small "over-criticality" parameter $\alpha$:

$$ \frac{E_0}{E_c} \approx 1 + \frac{\alpha \sqrt{2}}{\sqrt[6]{1 + 8\alpha^2}}, \qquad (102) $$

where $\alpha \equiv (Z_{eff} + 1)/\sqrt{\nu_{drag}\tau_{rad}}$, $\nu_{drag}$ is the collisional frequency at the characteristic momentum, and $E_c = \frac{mc}{|e|}\nu_{drag}$ equals the Connor-Hastie field when the plasma is fully ionized. References [1283, 1284] confirm the threshold using the adjoint Fokker-Planck equation method. Reference [1285] also reports an agreement with the threshold equation (102). It uses a fully conservative knock-on operator that enables an accurate calculation of the avalanche growth rate in this near-threshold regime. References [1270, 1280, 1286–1288] are consistent with the above results. They highlight the vortex structure in the momentum phase space around the attractor. The resulting threshold electric field value is reported to agree with [1284] as well [1288].

In presence of high-Z impurities, $Z_{eff}$ and $\nu_{drag}$ should be calculated accordingly (see discussion in section 12.1.2). Reference [1289], in which this threshold field is called "effective critical field", considers the effect of partially ionized impurities carefully. It also includes the effect of bremsstrahlung losses. A good agreement between the results of [1289] and equation (102) is reported in section 7 of [36] for ITER-relevant impurity densities. At very high densities, such as $10^{21}m^{-3}$, bremsstrahlung needs to be taken into account, and equation (102) becomes inaccurate.

### 12.2.1. Benign termination.
Plasma current decay during CQ can trigger vertical displacement events
(VDEs) in ITER. These events create damaging stresses on the plasma facing components. The current decay rate during the VDE is roughly

$$ \frac{dI}{dt} \approx \frac{2\pi R}{L_i} E_0. \qquad (103) $$

Inductive coupling between the plasma and the vessel relates the plasma current to the vertical position of the plasma [36, 1290]. Evolution of the current profile during VDEs often leads to MHD instabilities [1291–1294]. In a plateau regime with high background density, these instabilities can cause fast and localized loss of RE to the wall. It is highly desirable to avoid this scenario in ITER because of the potential damage the localized RE losses can cause to the wall.

Recent experiments on JET and DIII-D demonstrate benign termination of large runaway beams [257, 1291, 1295, 1296]. In these experiments, a megaampère runaway beam terminates without excessive heat loads onto the plasma facing components.

The key to the harmless termination scenarios is a massive deuterium injection into the runaway beam. This technique promotes recombination and expulsion of the high-Z material from the plasma [1297]. The enhanced heat conduction with $D_2$ drops the bulk electron temperature below the ionization threshold to allow recombination. The ambient plasma density then falls below the measurable value ($\approx 10^{18} m^{-3}$). The subsequent MHD event has a short Alfvén time. Infrared camera observations [1296] and modeling [1293] show that such instability scatters REs on a large area, minimizing the localized damage to the wall. When REs are lost, the thermal plasma carries the current. The low impurity content in such plasmas precludes the regeneration of REs, and the plasma current decays resistively. Currently, not all aspects of this benign termination scenario are well understood, and further research is needed to assess the feasibility of such a technique in ITER.

### 12.2.2. Synchrotron emission.
The diagnostic techniques for RE include measurements of soft x-ray emission, hard x-ray emission, and synchrotron emission. The latter has received increased attention in recent years. The numerical codes SOFT (Synchrotron-detecting Orbit Following Tool) [1298] and KORC (Kinetic Orbit Runaway electron Code) [1299] have been developed for synthetic diagnostic and comparison of the simulations with experimental data. The SOFT code follows guiding center orbits whereas KORC has a full orbit capability. Synchrotron emission provides information about the runaway beam position, energy spectrum and pitch-angle distribution of the runaway electrons. Synthetic diagnostic is essential for analyzing experimental data because it is yet unfeasible to infer the runaway parameters from the data via an inver-

sion procedure. In Alcator C-Mod [1300], ten-channel motional Stark effect (MSE) diagnostic detected synchrotron radiation. In TCV [1301], visible images were recorded using the multispectral imaging system Multi-Cam that distributes incoming light over four channels with different narrowband filters. In DIII-D [1302], polarized full cross section images were recorded. Although the collected data are not sufficiently complete for accurate reconstruction of the runaway electron distribution function, the observed polarization of synchrotron emission indicates that the characteristic pitch-angles of the runaway electrons exceed those predicted by theory in the absence of runaway scattering by collective modes. Synchrotron emission was used in [1303] for the reconstruction of the runaway electron current profile in DIII-D post-disruption plateau plasmas.

### 12.3. Waves for RE mitigation

There are ongoing attempts to use perturbed fields in plasmas to control runaway electrons. The perturbations can be generated by external antennas or by the runaways themselves (via kinetic instabilities). Depending on spatial scales and frequencies of the perturbed fields, these fields can either cause radial transport of the runaways to the wall or enhance pitch-angle scattering of the runaway electrons. The potential benefit from enhanced scattering is the enhancement of runaway energy losses via synchrotron radiation.

The radial transport of the runaways is predominantly due to the low-frequency perturbed fields (below the electron gyrofrequency). In this case, the guiding center approximation holds for the runaways. The unperturbed guiding center orbits in a tokamak have three constants of motion ($P_\phi, \mathcal{E}, J_\perp$) and are characterized by the toroidal and poloidal frequencies $\omega_\phi(P_\phi, \mathcal{E}, J_\perp)$ and $\omega_\theta(P_\phi, \mathcal{E}, J_\perp)$. The perturbed field resonates resonances with these frequencies when

$$ \omega - n\omega_\phi(P_\phi; \mathcal{E}; J_\perp) - l\omega_\theta(P_\phi; \mathcal{E}; J_\perp) = 0, \qquad (104) $$

where $\omega$ is the perturbation frequency, $n$ is the toroidal mode number and $l$ is an integer. This resonance condition suggests what particles are most sensitive to perturbations. However, such particles still do not move far from their equilibrium orbits unless the resonances overlap [740] to give rise to global diffusion.

The frequencies of MHD perturbations are commonly much smaller than $\omega_\phi(P_\phi, \mathcal{E}, J_\perp)$ and $\omega_\theta(P_\phi, \mathcal{E}, J_\perp)$ for relativistic electrons. These nearly static perturbations do not change the particle energy significantly. They change the toroidal angular momentum $P_\phi$, and they thereby transport particles across the equilibrium magnetic surfaces. The resonances given by equation (104) are closely related
to rational magnetic surfaces, but not exactly due to the drift-orbit excursions. Consequently, stochastic diffusion of magnetic field lines does not necessarily cause the same diffusion of the fast electrons. As shown in [1304], the drift-orbit-averaged diffusion coefficient for passing particles is formally a sum of delta-functions located at discrete resonances, which precludes global transport of particles unless nonlinearity of the perturbed motion mixes the resonances into a continuous array [740]. However, the resonances with low to moderate n and l often require impractically large perturbations to overlap. Such resonances form isolated phase space islands separated by KAM surfaces. The resulting transport is then a combination of convection within the islands and diffusion across the KAM surfaces. The corresponding advection-diffusion transport model [1305] can reasonably replicate the results of direct numerical simulations, but the free parameters in this model limit its predictive capability.

Depending on input parameters, one finds global stochasticity or co-existence of stochastic areas and nested magnetic surfaces [1306]. The co-existence of destroyed and undestroyed magnetic surfaces suggests that the electrons may escape in short pulses through statistically formed ‘turnstiles’ [1307]. That complicates predictions of the REs losses even when the codes simulate saturated regimes of plasma instabilities rather than just pre-specified perturbations.

Simulations of existing experiments with nonlinear MHD codes NIMROD [1308, 1309] and JOREK [1048] indicate that the MHD modes do produce high-order resonances needed to randomize magnetic surfaces globally [1293]. However, it is still unfeasible for the existing codes to simulate the randomized field directly, because of severe resolution requirements and the need for a kinetic rather than MHD description of the emerging short scales. This difficulty motivates numerous sensitivity studies of the fast electron transport to prescribed fluctuations [854, 1305, 1310–1318]. Such studies involve Monte Carlo simulations with either guiding center codes such as ANTS [1312], ASCOT [1319] or, more recently, a full orbit code KORC [631] and MARS-F [1320]. One of the topics of interest is whether resonant magnetic perturbations produced by external coils can be used to facilitate runaway losses [1312, 1321]. This is a viable option for medium-size or small machines, such as DIII-D [1322], AUG [1323], TEXTOR [1324] or COMPASS [1325], but does not look practical for an ITER-size device in which the required short scale perturbations decay too quickly with the distance from the coils.

Besides the externally imposed resonant magnetic perturbations and those resulting from bulk plasma instabilities, the guiding center resonance equation (104)

appears to be responsible for the excitation of recently observed low-frequency CAEs by the runaways themselves [1326]. Excitation of these modes signifies that the driving electrons have the pitch-angles characteristic of trapped particles and that their distribution over parallel momentum has a positive slope. It is unlikely that these electrons carry most of the runaway current, and it is, therefore, difficult to expect a great benefit from enhancing their radial losses, but it is conceivable that they can serve as a diagnostic tool in the spirit of MHD-spectroscopy [302] that proved very informative for energetic ions.

### 12.3.1. Self-excited waves.
Pitch-angle scattering and synchrotron losses of the runaways can raise the critical electric field for runaway multiplication and limit the runaway energy gain (see subsection 12.2). It is, therefore, natural to consider micro-instabilities to enhance the scattering rate. Strongly anisotropic distribution of the REs is prone to high frequency and short wavelength kinetic instabilities. These instabilities are generally tractable within the WKB approximation, in which case the wave frequency satisfies a local dispersion relation, and the wave-particle resonance condition is

$$ \omega - k_{\parallel}v_{\parallel} - \frac{N\omega_c}{\gamma} = 0, \qquad (105) $$

where N is an integer. The dominant resonances for the runaway electrons are the Cherenkov resonance (N = 0) and the anomalous Doppler resonance (N = 1).

Excitation of whistler modes via anomalous Doppler resonance is of particular interest. These modes change primarily the electron pitch-angles rather than the radial positions. The resulting losses of runaway energies can be faster than the runaway transport to the walls.

In the early tokamaks, such as TM-3, T-6, TFR and others, the “fan” instability [1327, 1328] was observed frequently in the presence of runaway electrons. More recently, observations of runaway-driven instabilities were reported in Refs. [707, 1329–1331]. Linear stability theory reveals that collisional damping is essential for the modes of interest [1332]. This damping precludes excitation of kinetic instabilities by REs for post-disruption ITER parameters with electron temperature less than about 20 eV. Such instability can however develop at higher temperatures and lower plasma densities as in the recent DIII-D experiments [1329]. Although the importance of collisional damping is already seen from local analysis, an experimentally relevant stability assessment must be non-local because the wave packets perform multiple bounces within the plasma during their amplification. A ray-tracing code
COIN (convective instability) [1332] addresses this aspect, which enables runaway stability assessment for present day machines as well as for ITER. The resulting instability thresholds have been confirmed in [396] with the use of a ray tracing code GENRAY [1333, 1334].

Related to potential benefits from kinetic instabilities is the idea of injecting ECRF waves for RE mitigation [1335]. The obstacles in implementation of this idea are the cutoff frequency issue and the collisional dissipation of the injected waves. Also, the spectrum of the injected waves needs to be sufficiently broad to resonate with (affect) a large fraction of runaway electrons.

Nevertheless, the injection of ECRF waves tends to be beneficial even without their direct impact on runaway electrons. First, high-power ECRF heating may help to keep the bulk electrons sufficiently warm to alleviate drastic drop of the Spitzer conductivity during thermal quench. Second, the ECCD may help to prevent the runaway build-up because the thermal quench and the resulting drop in Spitzer conductivity would not necessarily create a very strong inductive electric field in the presence of ECCD. The population of current-carrying electrons tends to be super-thermal in the presence of ECCD, and the collisional slowing down force for these electrons is therefore relatively insensitive to the bulk electron temperature. There are encouraging experimental results [1336, 1337] in support of this concept.

Experimental observations of runaway-driven micro-instabilities always exhibit nonlinear behavior of the excited waves rather than their linear growth. Intermittent bursts of the waves and chirping phenomena seen in the experiments [707] are beyond the scope of linear analysis. These phenomena are reminiscent of nonlinear scenarios for kinetic instabilities driven by energetic ions, and they are likely to have interesting diagnostic applications. Recent quasi-linear simulations within an idealized spatially uniform model [1338] exhibit a strong effect of the excited waves on the RE electron spectrum. This model predicts an increase of the avalanche threshold field above the Connor-Hastie value, which is qualitatively consistent with DIII-D observations. However, the nonlinear theory is not yet ready for predictive modeling of ITER conditions.

## 13. Summary and Outlook

The era of burning plasma physics is approaching with the construction of the ITER tokamak as well as the design or construction of several other devices that currently aim at operating burning plasmas: CFETR, SPARC, STEP, and BEST. Burning plasmas are by definition predominantly self-heated by energetic alphas, leading to a high degree of plasma self-

organization. Scenario optimization in future burning plasma devices for fusion power generation hence calls for a clear understanding of the physics of alphas, and more generally of EPs. The recent DT campaigns on JET have provided an opportunity for testing some of the most important diagnostics and validating the modeling aspects of fusion-born alphas and alpha-driven instabilities [39–54].

The interactions between EPs and a zoology of thermal-plasma-driven and EP-driven instabilities, EPMs, turbulence and 3D effects need to be understood in the qualitatively new regime of burning plasmas. Even in present devices containing non-active or weakly burning plasmas, our predictive capabilities of wave drive and damping and EP transport are challenged when several modes are concurrently destabilized and when synergistic interactions take place. In addition to the ongoing work on these topics on present devices, we will need to carefully diagnose the wave drive and damping as well as EP transport and losses in the future large-scale devices capable of sustaining burning plasmas, both in their non-active and active phases. Such experiments in tokamaks able to sustain burning plasmas will provide the experimental basis to validate our increasingly sophisticated simulation and modeling tools that will be used to guide and even accelerate future research programmes towards their mission goals, as well as to design and optimize future fusion power plants. High-fidelity physics models will capture the scientific community’s knowledge of EP behaviour, whilst reduced or surrogate models, perhaps constructed with the help of machine learning (ML), will bring super-computer modeling capabilities to desktop computers and enable rich EP physics effects to be included in routine predictive simulations and interpretive analysis.

On the EP diagnostics frontier, substantial progress has been made since the last update of the ITER Physics Basis [20]. Several high-resolution EP diagnostics have been developed that can provide a wealth of experimental data. These include EP diagnostics sensitive to the EP phase-space distribution function as well as fluctuation diagnostics sensitive to modes interacting with the EPs. Advances in fast digitization techniques and techniques to exploit fast digitization have significantly improved fluctuation diagnostics on major tokamaks and will be available at ITER. An example is the two-color toroidal interferometer and polarimeter (TIP) which has demonstrated high-resolution spectra of several AEs and low-frequency modes such as NTMs. The TIP to be installed on ITER will be able to detect AEs even in the plasma core and will likely be the workhorse of fluctuation diagnostics on
ITER. ECE diagnostics, microwave reflectometry, and magnetic pick-up coils will also provide high-resolution fluctuation measurements at ITER.

Several high-resolution confined and lost EP diagnostics can now give us detailed experimental access to the EP phase-space distribution. For example, gamma-ray emission from nuclear reactions can now not only identify what reaction is taking place by identifying peaks in the spectra, but can also resolve the Doppler broadening of these peaks, giving diagnostic access to the velocities causing the Doppler broadening. Diamond NES detectors can provide high-resolution measurements of energy spectra of DT neutrons, directly characterizing the fusion reaction. As for fluctuation diagnostics, fast digitization methods have increased the time resolution and the spectral resolution of CTS measurements substantially. FIDA, INPA, FILD, and ICE diagnostics have been deployed on several medium-sized tokamaks and stellarators and provide high-resolution measurements on confined and lost EP populations. The ICE detectors are hoped to provide the experimental basis needed to understand the relation between EPs and ICE emission. For example, accurate measurements of the polarization of the ICE are needed, as well as a forward model that can predict when ICE occurs as well as the ICE spectrum. Understanding ICE is particularly important in view of the limited set of EP diagnostics foreseen for ITER. At ITER, CTS and GRS are the only foreseen diagnostics to measure confined alphas, and FILD and possibly ICE could diagnose lost alphas.

The leading tokamaks have been, or are being, equipped with rich sets of high-resolution EP diagnostics which have motivated the development of tomographic inversion procedures, allowing the measurement of 2D EP velocity distribution functions. Multi-view sets of high-resolution EP diagnostics with more than 20-30 installed lines-of-sight have even allowed the measurement of 3D EP phase-space distribution functions. Such measurements will be improved in the coming years through the installation of new EP diagnostics aided by physics-based prior information, such as collisional physics and wave-particle interaction physics. The final goal in this direction is the development of integrated data analysis procedures that combine information from many diagnostics, including those for EPs, perhaps even including fluctuation diagnostics, to obtain a more holistic determination of the plasma state, including EPs. This data-led approach, including prior assumptions, provides the experimental basis to continually challenge our codes and physics understanding. For ITER, such an approach allows the maximum amount of information to be extracted from the restricted set of EP diagnostics installed. Whilst such approaches often make use of sampling techniques

and are computationally expensive, the use of neural networks trained as part of the many evaluations necessary to infer the plasma state, together with increased exploitation of accelerator technologies such as GPUs, is expected to allow more and more routine use of such advanced data interpretation techniques. This further supports the execution of research programmes conducted around the world as part of the common focus on the realisation of fusion as an energy source.

On the EP physics theory frontier, there has been significant progress and increased sophistication in both the modeling and simulation of EP-driven phenomena and in the validation of these models with experiments. As fusion research gravitates towards the burning plasma regime, the dependence on modeling becomes even more critical since the EP characteristics of future devices do not generally overlap with those of current experiments, and there will be a significant gap in time before validation becomes possible in DT burning plasma devices.

There are several future directions in EP simulation efforts in preparation for this new era. First, existing models need to continue to improve both in physics fidelity and computational efficiency. Some of the new physics topics that need to be explored include: coupling between core plasma microturbulence, EP-driven turbulence, and zonal flows; introduction of multiple EP species (e.g., beams, alphas, ICRF tails) and study of the synergistic interactions between them; extension of nonlinear simulations to longer timescales where alpha and external EP source variations become important; inclusion of 3D equilibrium effects in the EP instability models and exploration of optimization possibilities; and a more detailed modeling of the effects of EP deposition on plasma-facing components.

A second avenue is the incorporation of full EP turbulence and physics models into integrated modeling frameworks. The practical motivation for this is the need for a more self-consistent physics design of future devices and reliable prediction of regimes where EP heat loads on plasma-facing components will become problematic. Additionally, interfaces to EP analysis tools will increasingly need to be accessible to non-experts in EP physics. Integrated full discharge simulations will also be needed to evaluate the range of regimes that the plasma must pass through during startup and shutdown. If regimes are encountered on startup with strong EP instability and poor confinement, then more external power will be required for startup; this can significantly increase the cost of a reactor in comparison to the case where more optimal EP turbulence minimizing startup trajectories are followed. During shutdown the plasma will likewise pass through multiple parameter regimes; care will be needed to control this phase to avoid sudden and
intense EP losses to the wall. The scientific motivation
is that while EP physics has often in the past been
compartmentalized and focused on just a few time
slices from carefully curated discharges, the reality is
that EP phenomena are continuously evolving and are
coupled to and affected by the surrounding plasma
environment. Taking this into account is likely to lead
to new insights and correlations with the dynamics of
the surrounding plasma that have not been noticed in
the more focused approaches that are currently in use.
To support integrated modeling frameworks, there will
be a continuing need to evaluate trade-offs between
the computationally efficient reduced EP models vs.
computationally intensive high fidelity EP models.

Fortunately, two already mentioned trends will
help with this challenge. One is the advent of GPUs
(graphics processing units) and the associated progress
in massively parallel scientific computations. The other
is the increasing use of machine learning methods
which allow the construction and training of rapidly
evaluated surrogate models that can encapsulate the
results from the more computationally intensive high
fidelity EP models in a form that will be of use
within the integrated plasma simulation frameworks.
Examples for the use of neural networks are the
detection of AEs and other MHD modes in DIII-
D [1211, 1212] and TJ-II [1339, 1340], which could
eventually allow real-time detection and control of
such modes, and the tomographic reconstruction
and uncertainty quantification of FILD and INPA
measurements at ASDEX Upgrade [244]. In future
devices such as ITER, the dominance of alpha heating,
the lack of direct external control over the alpha
source, and the limited number of diagnostics available
in a nuclear environment will lend substantial value
to continued development of high-fidelity EP physics
simulation tools.

The experimental and simulation tools need to
be used in concert to comprehensively map out the
physics of EPs, including wave-particle interactions
and synergistic interactions among modes and between
modes and turbulence, as well as the associated EP
transport. The most important thermal-plasma-driven
instabilities interacting with EPs are currently thought
to be sawteeth, NTMs, KBMs, ELMs, and RWMs.
The most important EP-driven instabilities are the
zoology of AEs, ranging from the high-frequency modes
in the ion cyclotron frequency range (e.g., GAEs
or CAEs), via the intermediate-frequency modes in
Alfvén frequency range (e.g., TAEs, EAEs, or RSAEs),
down to low-frequency modes in the diamagnetic
frequency range (e.g., BAEs, BAAEs, LFAMs, or
EGAMs) and their kinetically modified branches. At
high EP pressure, these EP-driven modes can overcome
continuum damping and form distinct EPM branches

with properties depending on the EP population. Simulations with predictive capabilities call for global, nonlinear kinetic models and codes, which are being developed, but also for reduced modeling based on the progress of our EP physics understanding. Whereas the behavior of isolated EP-driven modes is fairly well understood, their interplay when several modes are active, their nonlinear evolution, and their interaction with turbulence, in particular synergistic effects between turbulence and EP-driven instabilities, are clear targets for future research. Additionally, 3D effects due to deviations from axisymmetry need to be accounted for in linear and nonlinear modeling and simulation.

It is sometimes advantageous to operate burning
plasma devices at reduced plasma current and
magnetic field in their early operational phases, e.g.
to reduce electromagnetic loads due to disruptions.
Such reduced-field and current scenarios require careful
consideration due to the possibilities of enhanced
NBI shine-through at low density and EP losses
associated with larger orbit widths. This is one of the
many aspects that must be taken into account when
commissioning devices to full operation and will need
to be reflected in the ITER Research Plan as well as
those of other future devices.

It has become recognized that EPs form an
integral part of plasma scenario optimization for
burning plasmas. Plasma scenarios can be optimized
by means of actuators modifying either the EP
distribution function itself or the existence, drive or
damping of EP-driven modes, thereby modifying the
EP transport. EP phase-space modification has been
demonstrated using ECRF heating, ECCD, ICRF
heating, ICCD, NBI heating, NBCD, and RMPs as
actuators, with varying degrees of understanding and
control. Synergistic effects in the plasma such as
the interaction between AEs and turbulence or the
suppression of turbulence by means of EPs have also
been explored. Various ICRF schemes can selectively
heat electrons or ions or accelerate EPs into the MeV-
range, such as the novel three-ion scheme, 2nd or 3rd
harmonic heating, or minority heating. Experiments
have also demonstrated that EP current drive can
be a significant actuator for scenario optimization.
However, while there are several external actuators
to control AEs in present devices and some of
them might be applicable to control AEs in burning
plasmas, systematic studies in present devices as well
as integrated prospective modeling activities for future
burning plasmas are still needed. Demonstrating that
any of these control schemes has the efficacy and
efficiency to be useful in ITER and other burning
plasmas remains at the forefront of current research.

Finally, runaway electrons driven and accelerated
during the current quench phase of disruptions are an area of concern for ITER and constitute an existential threat to the tokamak concept. ITER must necessarily approach regime in which runaways may appear with caution, and new capabilities such as shattered pellet injection, disruption prediction and avoidance based on machine learning, high-power ECRF and ECCD actuators, and diagnostics for runaway electrons are being prepared. In similarity with alpha particle physics, runaway electron physics in ITER will enter new regimes that cannot be fully tested on existing tokamak experiments. In the runaway simulation and modeling area, comprehensive models have been developed based on classical physics, but the effects of the variety of instabilities that strong runaway beams are likely to drive have not yet been consistently integrated into the predictive modeling paradigm. Since runaway-electron instabilities may provide mitigating effects through enhanced scattering of runaways, improved understanding of their role will be an important future development in the continuing search for runaway electron control mechanisms.

In this review, we have outlined our current understanding of EP physics on the path to burning plasmas. We have discussed what we currently consider the most significant EP research topics on that path, summarized the state-of-the-art, and called for future research. Progressing on these current research topics will require pushing the frontier of our understanding of EP physics deeper into yet uncharted territory, by developing new theoretical understanding, by more powerful simulations, and by better controlled and diagnosed experiments in present devices and in future burning plasma devices.

## Acknowledgments

We greatly appreciate the tremendous effort and help of the Guest Editors in charge of this chapter, David Campbell and Ambrogio Fasoli, and the entire team of guest editors for this Nuclear Fusion Special Issue. We also thank all the Members and Experts of the ITPA Topical Group for Energetic Particle Physics who have participated in discussions of this manuscript at ITPA EP meetings over the last 4 years for their valuable comments and suggestions.

The views and opinions expressed herein do not necessarily reflect those of the ITER Organization. Authors from institutes in the EU (M. Salewski, P. Aleynikov, B. Bilato, S. Briguglio, R.J. Dumont, M.V. Falessi, M. Fitzgerald, M. García-Muñoz, T. Hayward-Schneider, Ye.O. Kazakov, V.G. Kiptily, A. Könies, T. Kurki-Suonio, Ph. Lauber, S.A. Lazerson, A. Mishchenko, D. Moseev, M. Nocente, M. Podestà, S.E. Sharapov, A. Snicker, G. Vlad, X. Wang. D.

Zarzoso, and F. Zonca) received funding within the framework of the EUROfusion Consortium, funded by the European Union via the Euratom Research and Training Programme (Grant Agreement No 101052200 — EUROfusion). The views and opinions expressed are however those of the authors only and do not necessarily reflect those of the European Union or the European Commission. Neither the European Union nor the European Commission can be held responsible for them. M. Salewski was partially supported by the Villum Synergy grant no. VIL50096 from the Villum Foundation. A. Snicker was partially funded by the Academy of Finland projects No. 353370 and No. 324759. The Swiss contribution to this work has been funded by the Swiss State Secretariat for Education, Research and Innovation (SERI). B.N. Breizman was supported by U.S. DOE contracts DEFG02-04ER54742 and DESC0016283. W. Heidbrink was partially supported by U.S. DOE grant DE-SC0020337. V.N. Duarte, E. Fredrickson, N.N. Gorelenkov and M. Podestà were supported by DOE contract No. DE-AC02-09CH11466. D. Zarzoso received financial support from the AIM4EP Project (ANR-21-CE30-0018), funded by the French National Research Agency (ANR). D. A. Spong was supported by the U.S. Department of Energy, Office of Science, Office of Fusion Energy Sciences, under Award DE-AC05-00OR22725.

## Acronyms

<table><tr><td>AC</td><td>Alfvén continuum</td></tr><tr><td>AE</td><td>Alfvén eigenmode</td></tr><tr><td>AITG</td><td>Alfvénic ion temperature gradient mode</td></tr><tr><td>ALE</td><td>abrupt large event</td></tr><tr><td>AUG</td><td>ASDEX Upgrade</td></tr><tr><td>BAAE</td><td>beta-induced Alfvén-acoustic eigenmode</td></tr><tr><td>BAE</td><td>beta-induced Alfvén eigenmode</td></tr><tr><td>BGK</td><td>Bernstein-Greene-Kruskal</td></tr><tr><td>CAE</td><td>compressional Alfvén eigenmode</td></tr><tr><td>c.c.</td><td>complex conjugate</td></tr><tr><td>CD</td><td>current drive</td></tr><tr><td>CGL</td><td>Chew, Goldberger and Low</td></tr><tr><td>CGM</td><td>critical gradient model</td></tr><tr><td>CTS</td><td>collective Thomson scattering</td></tr><tr><td>COM</td><td>constants of motion</td></tr><tr><td>CQ</td><td>current quench</td></tr><tr><td>CXRS</td><td>charge-exchange recombination spectroscopy</td></tr><tr><td>DD</td><td>deuterium-deuterium</td></tr><tr><td>DMS</td><td>disruption mitigation system</td></tr><tr><td>DT</td><td>deuterium-tritium</td></tr><tr><td>EAE</td><td>ellipticity-induced Alfvén eigenmode</td></tr><tr><td>e-BAE</td><td>electron-driven beta-induced Alfvén eigenmode</td></tr></table>
<table>
  <tr>
    <td>EC</td>
    <td>electron cyclotron</td>
  </tr>
  <tr>
    <td>ECE</td>
    <td>electron cyclotron emission</td>
  </tr>
  <tr>
    <td>ECEI</td>
    <td>electron cyclotron emission imaging</td>
  </tr>
  <tr>
    <td>ECRF</td>
    <td>electron cyclotron radio-frequency</td>
  </tr>
  <tr>
    <td>ECCD</td>
    <td>electron cyclotron current drive</td>
  </tr>
  <tr>
    <td>EGAM</td>
    <td>energetic-particle-driven geodesic acoustic mode</td>
  </tr>
  <tr>
    <td>eEGAM</td>
    <td>energetic-electron-driven geodesic acoustic mode</td>
  </tr>
  <tr>
    <td>ELM</td>
    <td>edge-localized mode</td>
  </tr>
  <tr>
    <td>EP</td>
    <td>energetic particle</td>
  </tr>
  <tr>
    <td>EPM</td>
    <td>energetic particle mode</td>
  </tr>
  <tr>
    <td>ERTL</td>
    <td>edge resonant transport layer</td>
  </tr>
  <tr>
    <td>EWM</td>
    <td>energetic-particle-driven wall modes</td>
  </tr>
  <tr>
    <td>DIP</td>
    <td>dispersion interferometer polarimeter</td>
  </tr>
  <tr>
    <td>FFCW</td>
    <td>fixed-frequency continuous wave</td>
  </tr>
  <tr>
    <td>FIDA</td>
    <td>fast-ion D-alpha</td>
  </tr>
  <tr>
    <td>FILD</td>
    <td>fast-ion loss detector</td>
  </tr>
  <tr>
    <td>FLR</td>
    <td>finite Larmor radius</td>
  </tr>
  <tr>
    <td>FMCW</td>
    <td>frequency-modulated continuous wave</td>
  </tr>
  <tr>
    <td>FW</td>
    <td>fast magnetosonic wave</td>
  </tr>
  <tr>
    <td>FWI</td>
    <td>fast wave interferometer</td>
  </tr>
  <tr>
    <td>GAE</td>
    <td>global Alfvén eigenmode</td>
  </tr>
  <tr>
    <td>GAM</td>
    <td>geodesic acoustic mode</td>
  </tr>
  <tr>
    <td>GGAM</td>
    <td>global geodesic acoustic mode</td>
  </tr>
  <tr>
    <td>GPU</td>
    <td>graphics processing unit</td>
  </tr>
  <tr>
    <td>GRS</td>
    <td>gamma-ray spectroscopy</td>
  </tr>
  <tr>
    <td>HAE</td>
    <td>helicity-induced Alfvén eigenmode</td>
  </tr>
  <tr>
    <td>HFSR</td>
    <td>how-field-side reflectometer</td>
  </tr>
  <tr>
    <td>H-mode</td>
    <td>High-confinement mode</td>
  </tr>
  <tr>
    <td>HpGe</td>
    <td>high-purity germanium</td>
  </tr>
  <tr>
    <td>HXR</td>
    <td>hard x-ray</td>
  </tr>
  <tr>
    <td>i-BAE</td>
    <td>ion-driven beta-induced Alfvén eigenmode</td>
  </tr>
  <tr>
    <td>IC</td>
    <td>ion cyclotron</td>
  </tr>
  <tr>
    <td>ICCD</td>
    <td>ion cyclotron current drive</td>
  </tr>
  <tr>
    <td>ICE</td>
    <td>ion cyclotron emission</td>
  </tr>
  <tr>
    <td>ICRF</td>
    <td>ion cyclotron range of frequencies</td>
  </tr>
  <tr>
    <td>IIH</td>
    <td>ion-ion hybrid</td>
  </tr>
  <tr>
    <td>IMAS</td>
    <td>integrated modelling and analysis suite</td>
  </tr>
  <tr>
    <td>ITB</td>
    <td>internal transport barrier</td>
  </tr>
  <tr>
    <td>ITER</td>
    <td>International Thermonuclear Experimental Reactor</td>
  </tr>
  <tr>
    <td>ITG</td>
    <td>ion-temperature gradient</td>
  </tr>
  <tr>
    <td>ITPA</td>
    <td>International Tokamak Physics Activity</td>
  </tr>
  <tr>
    <td>KAM</td>
    <td>Kolmogorov-Arnold-Moser</td>
  </tr>
  <tr>
    <td>KAW</td>
    <td>kinetic Alfvén wave</td>
  </tr>
  <tr>
    <td>KBM</td>
    <td>kinetic ballooning mode</td>
  </tr>
  <tr>
    <td>KTAE</td>
    <td>kinetic toroidal Alfvén eigenmode</td>
  </tr>
  <tr>
    <td>LaBr</td>
    <td>lanthanum bromide</td>
  </tr>
  <tr>
    <td>LFAM</td>
    <td>low-frequency Alfvén mode</td>
  </tr>
  <tr>
    <td>LFSR</td>
    <td>low-field-side reflectometer</td>
  </tr>
  <tr>
    <td>LH</td>
    <td>low-confinement to high-confinement</td>
  </tr>
  <tr>
    <td>L-mode</td>
    <td>low-confinement mode</td>
  </tr>
  <tr>
    <td>MAE</td>
    <td>mirror-induced Alfvén eigenmode</td>
  </tr>
</table>

<table>
  <tr>
    <td>m-BAE</td>
    <td>magnetic-island-driven beta-induced Alfvén eigenmode</td>
  </tr>
  <tr>
    <td>MES</td>
    <td>motional Stark effect</td>
  </tr>
  <tr>
    <td>NAE</td>
    <td>non-circular triangularity-induced Alfvén eigenmode</td>
  </tr>
  <tr>
    <td>NGAE</td>
    <td>non-conventional global Alfvén eigenmode</td>
  </tr>
  <tr>
    <td>NES</td>
    <td>neutron emission spectroscopy</td>
  </tr>
  <tr>
    <td>NBCD</td>
    <td>neutral beam current drive</td>
  </tr>
  <tr>
    <td>NBI</td>
    <td>neutral beam injection</td>
  </tr>
  <tr>
    <td>NNBI</td>
    <td>negative-ion neutral beam injection</td>
  </tr>
  <tr>
    <td>NPA</td>
    <td>neutral particle analyzer</td>
  </tr>
  <tr>
    <td>MHD</td>
    <td>magnetohydrodynamic</td>
  </tr>
  <tr>
    <td>NTM</td>
    <td>neoclassical tearing mode</td>
  </tr>
  <tr>
    <td>PIC</td>
    <td>particle in cell</td>
  </tr>
  <tr>
    <td>PNBI</td>
    <td>positive-ion neutral beam injection</td>
  </tr>
  <tr>
    <td>PoPola</td>
    <td>poloidal polarimeter</td>
  </tr>
  <tr>
    <td>RBQ</td>
    <td>resonance broadening quasilinear</td>
  </tr>
  <tr>
    <td>RE</td>
    <td>runaway electrons</td>
  </tr>
  <tr>
    <td>RF</td>
    <td>radio-frequency</td>
  </tr>
  <tr>
    <td>RMP</td>
    <td>resonant magnetic perturbation</td>
  </tr>
  <tr>
    <td>RSAE</td>
    <td>reversed-shear Alfvén eigenmode</td>
  </tr>
  <tr>
    <td>RWM</td>
    <td>resistive wall mode</td>
  </tr>
  <tr>
    <td>SAW</td>
    <td>shear Alfvén wave</td>
  </tr>
  <tr>
    <td>SAWC</td>
    <td>shear Alfvén wave continuum</td>
  </tr>
  <tr>
    <td>SSNPA</td>
    <td>solid-state neutral particle analyzer</td>
  </tr>
  <tr>
    <td>SW</td>
    <td>slow magnetosonic wave</td>
  </tr>
  <tr>
    <td>SXR</td>
    <td>soft x-ray</td>
  </tr>
  <tr>
    <td>TAE</td>
    <td>toroidicity-induced Alfvén eigenmode</td>
  </tr>
  <tr>
    <td>TBM</td>
    <td>test blanket module</td>
  </tr>
  <tr>
    <td>TEM</td>
    <td>trapped electron mode</td>
  </tr>
  <tr>
    <td>TF</td>
    <td>toroidal field</td>
  </tr>
  <tr>
    <td>TIP</td>
    <td>toroidal interferometer and polarimeter</td>
  </tr>
  <tr>
    <td>TM</td>
    <td>tearing mode</td>
  </tr>
  <tr>
    <td>TQ</td>
    <td>thermal quench</td>
  </tr>
  <tr>
    <td>Q</td>
    <td>power amplification factor</td>
  </tr>
  <tr>
    <td>VDE</td>
    <td>vertical displacement event</td>
  </tr>
  <tr>
    <td>WDM</td>
    <td>whole-device model</td>
  </tr>
  <tr>
    <td>WKB</td>
    <td>Wentzel-Kramers-Brillouin</td>
  </tr>
  <tr>
    <td>ZC</td>
    <td>zonal current</td>
  </tr>
  <tr>
    <td>ZF</td>
    <td>zonal flow</td>
  </tr>
  <tr>
    <td>ZFS</td>
    <td>zonal field structure</td>
  </tr>
  <tr>
    <td>ZS</td>
    <td>zonal state</td>
  </tr>
</table>

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