Table of contents

A recently developed imaging neutral particle analyzer (INPA) on the DIII-D tokamak (Du 2018 Nucl. Fusion58 082006) enables fast ion velocity-space tomography of high fidelity at the interrogated phase space. To accomplish this, the spatial and energy depending fast (E < 80 keV) neutral flux towards the INPA stripping foils is calculated with FIDASIM and a newly developed code INPASIM simulates the INPA instrumental response to this neutral flux. Included in INPASIM is the neutral-foil interaction, the Larmor orbit tracing between the foil and the phosphor, the phosphor response to the incident ion flux as well as camera focusing. Benefiting from heavy, localized velocity-space weights and excellent signal to noise, computed tomography using the Ridge regression method is able to successfully reconstruct fine-scale velocity-space structures produced by multiple neutral beams separated by as small as ∼3 keV in tests. Applying the inversion method to a sawtooth crash event reveals a significant profile flattening of confined passing particles across q = 1 flux surface, as well as a redistribution of fast ions into the trapped orbits at the plasma edge close to the last closed flux surface.

Toroidal Alfvén eigenmode (TAE) bursts are often observed in relatively low-magnetic-field experiments in the Large Helical Device (LHD) with tangential nuclear beam injection. During TAE bursts, hole-clump pairs in real space were observed in previous studies. In order to observe the behavior of the energetic particles during TAE bursts in more detail, a tangential E-parallel-B-type neutral particle analyzer (E||B-NPA) was upgraded to improve the time resolution up to 100 kilo samples per second by updating its measurement electronic circuits. Using this high time resolution E||B-NPA, the clump formations are clearly observed in real space. In order to analyze the observed particles with high time resolution, the conditional averaging technique is used. The lost energetic particles with 150 keV were initially observed just before the TAE burst, and the energy decreases faster than the classical slowing down time. The energetic particles transported by the TAE burst were detected with energy slowing down time of 6–8 ms for more than 6 ms after the TAE burst had finished. According to the orbit trace code Lorentz orbit (LORBIT) calculation, the particle pitch angle and radial location (ρ = r/a₉₉) of the energetic particles resonating with the TAE mode frequency are increased by 5° and 0.2, respectively, during TAE bursts. These results are consistent with the observed downward frequency chirping of the magnetic fluctuation. By comparing the energy of the detected particles by E||B-NPA and the corresponding frequency of the magnetic fluctuation, the pitch angles of the resonant particles are considered to be 15°–25° at 150 keV before they are transported by the TAE burst. The frequency chirping of the magnetic fluctuation shows good agreement with the observed clump structure by considering the pitch angle of the resonant particles.

Elliptical (EAE) and toroidal Alfvén eigenmode (TAE) instabilities have been observed in hydrogen-rich JET discharges of the D-(³He)-H ion cyclotron resonance heating (ICRH) scenario, which is characterized by strong absorption of radio frequency waves at very low concentrations of the resonant ³He-ions. In the experiments, core localized TAEs with a frequency f_TAE ≈ 280 kHz with mode numbers n= 3, 4, 5 and 6 were detected. Following the phase with TAE excitation, EAE modes at higher frequencies f_EAE ≈ 550–580 kHz with mode numbers n = 1, 3, 5 were seen. These high frequency modes indicate that a MeV range population of trapped energetic ions was present in the plasma. The experimental evidence of existence of the MeV-energy ³He-ions able to excite the AEs is provided by neutron and gamma-ray diagnostics as well as fast ion loss measurements. The ICRH modelling code calculations confirm the acceleration of ³He-ions to MeV energies. The magnetohydrodynamic (MHD) analysis results are consistent with the experimental data showing that the MeV ³He ions satisfy to resonant conditions interacting with TAE and EAE modes. This experiment demonstrates the efficient plasma heating mimicking the conditions representative for the ITER plasmas and contribute to the understanding of fast-ion interaction with MHD wave modes.

The 2018 operation phase (OP 1.2b) of the stellarator Wendelstein 7-X (W7-X) included, for the first time, neutral beam injection (NBI) to heat the plasma. Since the injection geometry at W7-X is not parallel, this generates both passing and trapped fast particles. During longer phases of NBI injection, with the primary purpose to study the heating efficiency of this system, Alfvén eigenmodes (AEs) were observed by a number of diagnostics, including the phase contrast imaging (PCI) system, the magnetic pick-up coils (Mirnov coils), and the soft x-ray multi-camera tomography system (XMCTS).

Alfvén eigenmodes are of great interest for future fusion reactors as it has been shown that the resonant interaction of fast ions with self-excited AEs can lead to enhanced transport of fast ions and potentially to energy losses. This is especially true for so-called gap-modes, Alfvén eigenmodes with frequencies in gaps of the continuous spectrum, since they lack continuum damping. These modes are commonly known to be excited by fast ions, but other destabilizing mechanisms, e.g. the electron-pressure gradient are also possible.

In this article we present a first analysis of the experimentally observed frequencies from the theoretical side. The calculation of shear Alfvén wave continua for selected cases and the assignment of observed frequencies to the gaps of the continuous spectra are presented. Using the ideal-MHD code CKA (Könies A. 2007 10th IAEA TM on Energetic Particles in Magnetic Confinement System), we find gap modes that match the experimental measurements in terms of the observed frequencies. We emphasize the crucial roles played by the coupling of sound and Alfvén waves as well as of the Doppler shift arising as a consequence of the radial electric field in W7-X.

We employ the perturbative gyrokinetic code CKA-EUTERPE (Feh´er 2013 Simulation of the interaction between Alfv´en waves and fast particles), using a slowing-down distribution function for the fast ions as calculated by the Monte-Carlo particle following code ASCOT (Hirvijoki et al 2014 Comput. Phys. Commun. 185 1310–21) to assess the fast-ion drive. We find that the fast-ion drive is insufficient to overcome the background-plasma damping. The fact that unstable modes were observed experimentally may point to problems with the modelling or indicate the existence of other destabilizing mechanisms, e.g. associated with the electron-pressure gradient (Windisch et al 2017 Plasma Phys. Control. Fusion 59 105002) that sensitively depend on the profiles of the background plasma.

The characteristics and excitation conditions of the beta-induced Alfvén-acoustic eigenmode (BAAE) have been investigated during sawtooth-like oscillation in the Experimental Advanced Superconducting Tokamak (EAST). The sawtooth-like events are triggered periodically by the $m = 2/n = 1$ double-tearing reconnection crash (DTRC), and the oscillations with period τ_o≥ 100 ms, where m and n are the poloidal and toroidal mode numbers respectively. The BAAE coexists with beta-induced Alfvén eigenmodes (BAEs) and reversed-shear Alfvén eigenmodes (RSAEs), and the BAAE has similar characteristics to the pairing of BAEs–RSAEs. The radial structures of the BAAE and BAEs are deformed into analogous triangle shapes along the poloidal direction, and the BAAE is located more outward with broadened radial coverage. The frequencies of the BAAE and RSAEs sweep upward synchronously with decreasing $q_{\textrm{min}}$ ($q_{\textrm{min}}$ < 1), and the BAAE can also provide valuable constraint conditions for the q-profile measurements. Furthermore, the mode structure of the BAAE is achieved experimentally with m = 4/n ≈ 4.

The period τ_o of DTRC is an important factor, which can be adopted for evaluating the excitation conditions of BAAE; namely, the BAAE can be excited when τ_o achieves the threshold condition. τ_o increases when the total injected power of neutral beam injection (NBI) and ion cyclotron resonance heating (ICRH) increases, where the NBI beam direction is perpendicular to the plasma current. The gradient of electron temperature at the vicinity of $q_{\textrm{min}}$ increases with τ_o, and the portion of energetic ions in the central region increases as well. Therefore, the BAAE in EAST should be excited by the special distribution of trapped energetic ions through toroidal precessional resonances, and $q_{\textrm{min}} \leq 1$ is also an important constraint condition for the excitation.

Energy and momentum transfer by eigenmodes in tokamaks and stellarators, which arises when eigenmodes are destabilized by superthermal ions in a region that does not coincide with the damping region, is considered. This phenomenon, named spatial channeling (SC), may play an important role in toroidal plasmas. It may affect plasma energy confinement, plasma rotation, heating of the electron and ion components, and features of eigenmodes. The work contains both an overview and new results. In particular, it is found that SC may affect structure of Toroidicity-induced Alfvén Eigenmodes (TAE modes); the analysis is carried out for a low-mode-number TAE. It is concluded that high-frequency modes, with frequencies above and around the ion cyclotron frequency (fast magnetoacoustic modes and Alfvén modes), are more likely to affect plasma energy balance for reasonable values of mode amplitudes than low-frequency Alfvén modes. SC can also have strong influence on sheared rotation for reasonable values of mode amplitudes, and this effect does not depend on mode frequency. The overview is restricted to modes naturally occurring in unstable plasmas.

Energetic-particle-driven geodesic acoustic modes (EGAMs) channeling in the Large Helical Device (LHD) plasmas are systematically investigated for the first time using MEGA code. MEGA is a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. In the present work, both the energetic particles and the bulk ions are described kinetically. The EGAM profiles in the three-dimensional form is illustrated. Then, EGAM channeling behaviors are analyzed under different conditions. During the EGAM activities without frequency chirping, EGAM channeling occurs in the linear growth stage but terminates in the decay stage after the saturation. During the EGAM activities with frequency chirping, EGAM channeling occurs continuously. Also, low-frequency EGAM makes the energy transfer efficiency ($E_{\mathrm{ion}}/E_{\mathrm{EP}}$) higher, and this is confirmed by changing the energetic particle pressure, energetic particle beam velocity, and energetic particle pitch angle. Moreover, higher bulk ion temperature makes the energy transfer efficiency higher. In addition, under a certain condition, the energy transfer efficiency in the deuterium plasma is lower than that in the hydrogen plasma.

The imaging neutral particle analyzer (INPA) is a scintillator-based diagnostic that provides energy and radially resolved measurements of confined fast ions. To verify operation, understanding and modeling of the diagnostic performance, distributions of deuterium beam ions in low density, nearly MHD-quiescent plasmas are measured on the DIII-D tokamak using the INPA. The distribution is altered by changing the pitch-angle scattering rate with electron cyclotron heating (ECH). Experimental images are mostly reproduced with simulation of core fast ions charge exchanging with injected beam and edge cold neutrals in classical cases. Image comparisons between the experiment and simulation show agreement with less than 25% discrepancies near the beam injection energy of 50 keV. Other strong passive signals, observed in a localized region on the image, are suggested to come from charge exchange between cold neutrals and fast ions around the plasma boundary.

Significant variations in MHD activity and fast-ion transport are observed in the DIII-D high-beta, steady-state hybrid discharges with a mixture of electron cyclotron (EC) waves and neutral beam injection (NBI). When electron cyclotron heating (ECH) or current drive (ECCD) is applied, Alfvén eigenmodes (AEs) are usually suppressed and replaced by low-frequency bursting modes. The analysis of a recently compiled database of hybrid discharges suggests that the change of the fast-ion pressure especially the perpendicular pressure is the main factor responsible for the instability transition although the transition in some discharges can also be explained by a slight drop of the safety factor $q_{\textrm{min}}$. The lower ratio of fast-ion injection speed v_inj to Alfvén speed v_alfven and slight drop of $q_{\textrm{min}}$ during ECCD also facilitate the transition. The database shows that AEs mainly occur when the fast-ion fraction $P_{f}/P_{\rm total}$ is less than 0.53 and $v_{\rm inj}/v_{\rm alfven}$ is greater than 0.50, while low-frequency bursting modes appear in the opposite regime. Here, P_f and P_total are the central fast-ion pressure from classical prediction and total plasma pressure, respectively. The correlation with $q_{\textrm{min}}$ is weaker, and $q_{\textrm{min}}$ is around unity in all the cases. The reason why the instability transition correlates with $P_{f}/P_{\rm total}$ and $v_{\rm inj}/v_{\rm alfven}$ is that they can significantly modify the drive of low-frequency bursting modes and AEs. The explanation is supported by the observation that low-frequency bursting modes are rarely seen in the hybrids with NBI only, with EC waves and counter-NBI, or with high plasma density. A careful check of the low-frequency bursting modes suggests that they are mainly chirping (neoclassical) tearing modes (referred to as chirping (N)TMs), i.e. the mode frequency firstly jumps up from the steady (N)TM frequency, then chirps down, and finally returns to the steady (N)TM frequency. Occasionally, the (N)TMs are fully stabilized and replaced with pure fishbones. The resonance condition calculation and 'Kick' model simulations suggest that (N)TMs and fishbones can interact through modification of the fast ion distribution in phase space, which influences the drive.

We report on the impact of anisotropy to tokamak plasma configuration and stability. Our focus is on analysis of the impact of anisotropy on ITER pre-fusion power operation 5 MA, B = 1.8 T ICRH scenarios. To model ITER scenarios remapping tools are developed to distinguish the impact of pressure anisotropy from the change in magnetic geometry caused by an anisotropy-modified current profile. The remappings iterate the anisotropy-modified current-density profile to produce the same q profile with matched thermal energy. The analysis is a step toward equilibria that are kinetically self-consistent for a prescribed scenario. We find characteristic detachment of flux surfaces from pressure surfaces and an outboard (inboard) shift of peak density for $T_{\parallel}>T_\perp$ ( $T_{\parallel} < T_\perp$). Differences in the poloidal current profile are evident, albeit not as pronounced as for the spherical tokamak. We find that the incompressional continuum is largely unchanged in the presence of anisotropy and the mode structure of gap modes is largely unchanged. The compressional branch however exhibits significant differences in the continuum. We report on the implication of these modifications.

In this work, energetic-ion confinement and loss due to energetic-ion driven magnetohydrodynamic modes are studied using comprehensive neutron diagnostics and orbit-following numerical simulations for the Large Helical Device (LHD). The neutron flux monitor is employed in order to obtain global confinement of energetic ions and two installed vertical neutron cameras (VNCs) viewing different poloidal cross-sections are utilized in order to measure the radial profile of energetic ions. A strong helically-trapped energetic-ion-driven resistive interchange mode (EIC) excited in relatively low-density plasma terminated high-temperature state in LHD. Changes in the neutron emission profile due to the EIC excitation are clearly visualized by the VNCs. The reduction in the neutron signal for the helical ripple valley increases with EIC amplitude, which reaches approximately 50%. In addition to the EIC experiment, orbit-following simulations using the DELTA5D code with EIC fluctuations were performed to assess the energetic-ion transport and loss. Two-dimensional temporal evolution results show that the neutron emissivity at the helical ripple decreases significantly due to the EIC. The rapid reduction in neutron emissivity shows that the helically-trapped beam ions immediately escape from the plasma. The reduction in the VNC signals for the helical ripple valley and the total neutron emission rate increase with increasing EIC amplitude, as observed in the experiment. Calculated line-integrated neutron emission results show that the profile measured by VNC1 has one peak, whereas the profile measured by VNC2 has two peaks, as observed in the experiment. Although the neutron emission profile for VNC2 has a relatively wide peak compared with the experimental results, the significant decrease in neutron signal corresponding to the helical ripple valley was successfully reproduced.

Alfvén eigenmodes (AEs) driven by energetic electrons were investigated via hybrid simulations of an MHD fluid interacting with energetic electrons. The investigation focused on AEs with the toroidal number n = 4. Both energetic electrons with centrally peaked beta profile and off-axis peaked profile are considered. For the centrally peaked energetic electron beta profile case, a toroidal Alfvén eigenmode (TAE) propagating in the electron diamagnetic drift direction is found. The mode is mainly driven by deeply trapped energetic electrons. It is also found that a few passing energetic electrons spatially localized around rational surfaces can resonate with the mode. For the off-axis peaked energetic electron beta profile case, an AE propagating in the ion diamagnetic drift direction is found when a $q\mathrm{-profile}$ with weak magnetic shear is adopted. The destabilized mode is an elliptical-Alfvén-eigenmode-type (EAE-type) mode which has a spatial profile peaking at the rational surface and a frequency close to the second Alfvén frequency gap. It is found that passing energetic electrons and barely trapped energetic electrons are responsible for this EAE-type mode destabilization. The saturation levels are compared for a TAE with the same linear growth rate among energetic electron driven mode and energetic ion driven mode with isotropic and anisotropic velocity space distributions. The saturation level of TAE driven by trapped energetic electrons is comparable to that driven by energetic electrons with isotropic velocity space distribution where the contribution of trapped particles is dominant. It is found that the trapped energetic ion driven TAE has a larger saturation level than the passing energetic ion driven TAE, which indicates the difference in particle trapping by the TAE between trapped and passing energetic ions.

Dedicated experiments were conducted in mixed H-D plasmas in JET to demonstrate the efficiency of the 3-ion ICRF scenario for plasma heating, relying on injected fast NBI ions as the resonant ion component. Strong core localization of the RF power deposition in the close vicinity of the ion-ion hybrid layer was achieved, resulting in an efficient plasma heating, generation of energetic D ions, strong enhancement of the neutron rate and observation of Alfvénic modes. A consistent physical picture that emerged from a range of fast-ion measurements at JET, including neutron and gamma-ray measurements, a high-energy neutral particle analyzer and MHD mode localization analysis, is presented. The possibility to moderate the fast-ion energies with the ratio P_ICRF/P_NBI and the choice of the NBI injectors is demonstrated. An outlook of possible applications of the 3-ion scenarios, including a recent example of its use in mixed D-³He plasmas in JET and promising scenarios for D-T plasmas, are presented.

For understanding the physics of energetic particles, the deuterium experimental campaigns started in Large Helical Device (LHD) from March 2017. To investigate the behavior of energetic particles, a Fast-ion D Alpha (FIDA) diagnostic was installed on the LHD. In the FIDA diagnostic, the Doppler-shifted D alpha light from fast-neutrals are utilized as signals of energetic particles, where these fast-neutrals are produced by the charge exchange process between fast-ions in the plasma and actively injected neutrals by neutral beam (NB). The advantages of the FIDA diagnostic are the velocity and the spatially resolved measurement of fast-ions at the crossing point between its line of sight (LOS) and the incident line of NB. The most recent FIDASIM is enhanced to simulate signals produced in three-dimensional magnetic configurations. The new version of FIDASIM uses the fast-ion distribution function produced by GNET as input to simulate FIDA signals at LHD. In order to validate the new version of the code, measurements of radial profiles of fast-ions using the FIDA diagnostic are performed in magnetohydrodynamic (MHD)-quiescent plasmas. The measured spectra are in good agreement with the theoretical prediction by 3D-supporting FIDASIM at the center of the plasma (R= 3.5 m∼3.7 m, r_eff/a₉₉= −0.28∼0.05) on the LHD when the line averaged electron density is n_{e_avg} < 1.23 × 10¹⁹ m⁻³. On the other hand, the measured spectra are in disagreement with the theoretical prediction by 3D-supporting FIDASIM at even the center of the plasma when the line averaged electron density is n_{e_avg} ≥ 1.23 × 10¹⁹ m⁻³.

The aim of the study is to analyze the stability of the energetic particle modes (EPM) and Alfven Eigenmodes (AE) in Helitron J and LHD plasma if the electron cyclotron current drive (ECCD) is applied. The analysis is performed using the code FAR3d that solves the reduced MHD equations describing the linear evolution of the poloidal flux and the toroidal component of the vorticity in a full 3D system, coupled with equations of density and parallel velocity moments for the energetic particle (EP) species, including the effect of the acoustic modes. The Landau damping and resonant destabilization effects are added via the closure relation. The simulation results show that the n = 1 EPM and n = 2 global AE (GAE) in Heliotron J plasma can be stabilized if the magnetic shear is enhanced at the plasma periphery by an increase (co-ECCD injection) or decrease (ctr-ECCD injection) of the rotational transform at the magnetic axis ($\rlap{-} \iota_{0}$). In the ctr-ECCD simulations, the EPM/AE growth rate decreases only below a given $\rlap{-} \iota_{0}$, similar to the ECCD intensity threshold observed in the experiments. In addition, ctr-ECCD simulations show an enhancement of the continuum damping. The simulations of the LHD discharges with ctr-ECCD injection indicate the stabilization of the n = 1 EPM, n = 2 toroidal AE (TAE) and n = 3 TAE, caused by an enhancement of the continuum damping in the inner plasma leading to a higher EP β threshold with respect to the co- and no-ECCD simulations.

This report summarizes the contributions presented at the 16th IAEA Technical Meeting on Energetic Particles in Magnetic Confinement Systems—Theory of Plasma Instabilities, held in Shizuoka, Japan, 3–6 September 2019. The meeting brought together about 100 experts from nuclear fusion research sites worldwide to discuss the physics of energetic particles and plasma instabilities, at the first joint meeting from the two scientific disciplines. The main topics of the meeting were: alpha particles physics; transport of energetic particles; effects of energetic particles in magnetic confinement fusion devices; collective phenomena such as Alfvén eigenmodes, energetic particle modes and others; runaway electrons and disruptions; diagnostics for energetic particles; control of energetic particles confinement; multiscale physics and instabilities in burning plasmas.