Search

A nonlinear simulation of the energetic particle driven instabilities in the Chinese First Quasi-axisymmetric Stellarator (CFQS) has been conducted for the first time. MEGA, a hybrid simulation code for energetic particles interacting with a magneto-hydrodynamic fluid, was used in the present work. Both the m/n = 3/1 energetic-particle-mode (EPM) like mode and the m/n = 5/2 toroidal Alfvén eigenmode (TAE) were found, where m is the poloidal mode number and n is the toroidal mode number. Four important results were obtained as follows. First, the instability in the CFQS in three-dimensional form was shown for the first time. Second, strong toroidal mode coupling was found for the spatial profiles, and it is consistent with the theoretical prediction. Third, the resonant condition caused by the absence of axial symmetry in CFQS was demonstrated for the first time. The general resonant condition is f mode = Nf ϕ − Lf θ , where f mode, f ϕ , and f θ are mode frequency, particle toroidal transit frequency, and particle poloidal transit frequency, respectively; N and L are arbitrary integers, represent toroidal and poloidal resonance numbers. For EPM-like mode, the dominant and subdominant resonant conditions are f mode = 3f ϕ − 7f θ and f mode = f ϕ − f θ , respectively. For TAE, the dominant and subdominant resonant conditions are f mode = 4f ϕ − 9f θ and f mode = 2f ϕ − 3f θ , respectively. On the one hand, the toroidal resonance numbers are different from the toroidal mode numbers by 2. This indicates that the two-fold rotational symmetry affects the resonance condition. On the other hand, the subdominant resonances satisfy N = n, which is expected for the axisymmetric plasmas and most of the toroidal plasmas including stellarators. Fourth, the nonlinear frequency chirpings in CFQS were demonstrated for the first time. Hole and clump structures were formed in the pitch angle and energy phase space, and the particles comprising the hole and clump were kept resonant with the modes during the mode frequencies chirping.

openaire: EC/H2020/633053/EU//EUROfusion Funding Information: The author (X. D. Du) would like to thank M. Podestà, G. J. Kramer, and R.Nazikian for fruitful discussions. This work was supported by the US DOE under DE-AC05-00OR22725, DE-FC02-04ER54698, DE-AC02-09CH11466, and DE-SC0015878. The ASCOT5 project has received funding from the European Research Council under Grant Agreement No. 647121. This ASCOT5 project has been carried out within the framework of the EUROfusion consortium and has received funding from the Euratom research and training programme under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. The ASCOT5 project was also partially funded by the Academy of Finland projects No. 324759 and No. 298126. We acknowledge the computational resources provided by Aalto Science-IT project. The MEGA simulation used resources of the National Energy Research Scientific Computing Center (NERSC), a U.S. Department of Energy Office of Science User Facility located at Lawrence Berkeley National Laboratory, operated under Contract No. DE-AC02-05CH11231. Publisher Copyright: © 2021 American Physical Society. Fast ion phase-space flow, driven by Alfvén eigenmodes (AEs), is measured by an imaging neutral particle analyzer in the DIII-D tokamak. The flow firstly appears near the minimum safety factor at the injection energy of neutral beams, and then moves radially inward and outward by gaining and losing energy, respectively. The flow trajectories in phase space align well with the intersection lines of the constant magnetic moment surfaces and constant E-(ω/n)Pζ surfaces, where E, Pζ are the energy and canonical toroidal momentum of ions; ω and n are angular frequencies and toroidal mode numbers of AEs. It is found that the flow is so destructive that the thermalization of fast ions is no longer observed in regions of strong interaction. The measured phase-space flow is consistent with nonlinear hybrid kinetic-magnetohydrodynamics simulation. Calculations of the relatively narrow phase-space islands reveal that fast ions must transition between different flow trajectories to experience large-scale phase-space transport.

A synthetic fast-ion loss (FIL) detector and an imaging Heavy Ion Beam Probe (i-HIBP) have been implemented in the 3D hybrid kinetic-magnetohydrodynamic code MEGA. First synthetic measurements from these two diagnostics have been obtained for neutral beam injection-driven Alfvén Eigenmode (AE) simulated with MEGA. The synthetic FILs show a strong correlation with the AE amplitude. This correlation is observed in the phase-space, represented in coordinates (P, E), being toroidal canonical momentum and energy, respectively. FILs and the energy exchange diagrams of the confined population are connected with lines of constant E, a linear combination of E and P. First i-HIBP synthetic signals also have been computed for the simulated AE, showing displacements in the strike line of the order of ∼1 mm, above the expected resolution in the i-HIBP scintillator of ∼100 μm., This work received funding from the European Starting Grant (ERC) from project 3D-FIREFLUC and from the Spanish Ministry of Science under Grant No. FPU19/02267. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.

Beam modulation effects on Alfvén eigenmode stability have been investigated in a recent DIII-D experiment and show that variations in neutral beam modulation period can have an impact on the beam driven Alfvén eigenmode spectrum and resultant fast ion transport despite similar time-averaged input power. The experiment was carried out during the current ramp phase of L-mode discharges heated with sub-Alfvénic 50–80 kV deuterium neutral beams that drive a variety of Alfvén eigenmodes unstable. The modulation period of two interleaved beams with different tangency radii was varied from shot to shot in order to modify the relative time dependent mix of the beam pitch angle distribution as well as the persistence of a bump-on-tail feature near the injection energy (a feature confirmed by imaging neutral particle analyzer measurements). As the beam modulation period is varied from 7 ms to 30 ms on/off (typical full energy slowing down time of τ slow ≈ 50 ms at mid-radius), toroidicity-induced Alfvén eigenmodes (TAEs) located in the outer periphery of the plasma become intermittent and coincident with the more tangential beam. Core mode activity changes from reversed shear Alfvén eigenmodes (RSAEs) to a mix of RSAE and beta-induced Alfvén eigenmodes. Discharges with 30 ms on/off period do not have a persistent bump-on-tail feature, have the lowest average mode amplitude and least fast ion transport. Detailed analysis of an individual TAE using TRANSP kick modeling (Monte Carlo evolution of the distribution function with probabilistic ‘kicks’ by the AEs) and the resistive MHD code with kinetic fast ions, MEGA, find no strong role of energy gradient drive due to bump-on-tail features. Instead, the observed TAE modulation with interleaved beams is likely a pitch angle dependent result combined with slowing down of the tangential beam between pulses. For the conditions investigated, bump-on-tail contributions to TAE drive were found to be 5% or less of the total drive at any given time.

Spherical tokamak (ST) research in Japan has produced many innovative results: (i) plasma start-up to I p > 70 kA was achieved by electron cyclotron wave (ECW) with N ∥ = 0.75, while electron heating to T e > 500 eV was achieved with N ∥ = 0.26 on QUEST. (ii) The radiofrequency (RF)-induced transport model was combined with the x-ray emission model, and extended magnetohydrodynamics equilibrium with kinetic electrons was developed to interpret fast-electron-dominated lower hybrid wave sustained plasmas on TST-2. (iii) Density as high as 30 times the cutoff density was achieved by electron Berstein wave current drive combined with electron beam injection on LATE. (iv) Multiple plasmoids formed by tearing instability in the elongated current sheet were observed, and flux closure and ion heating by plasmoid-mediated fast magnetic reconnection were observed on HIST. (v) Optimization of ECW-assisted inductive start-up with a vertical field with positive decay index was performed on TST-2. (vi) Stabilization of the vertical displacement event by a set of upper and lower helical field coils was demonstrated on TOKASTAR-2. (vii) A 6 h discharge was achieved by cool-down of the center stack cover on QUEST, where the plasma duration limit was consistent with the wall saturation time estimated by modeling. (viii) Extension of ion heating by plasma merging was achieved on TS-3U, TS-4U, UTST, MAST, and ST40.

In this study a hybrid simulation environment to investigate the lower-hybrid-wave-driven tokamak plasmas is presented, and its application to the spherical tokamak TST-2 is described. These plasma are formed and driven by radio-frequency waves without the use of the central solenoid, and are characterized by low density and low magnetic field. A hybrid simulation environment which is divided into two groups, one using magneto-hydrodynamic (MHD) as well as particle-in-cell (PIC) approaches, and the second group using ray-tracing and Fokker–Planck solvers, is applied to describe the behavior of energetic electrons, bulk plasma, wave propagation, and the wave-particle interaction. Both groups of solvers can be coupled via the energetic-particle velocity distribution function and the equilibrium conditions of magnetic field, pressure, and density profiles to obtain a self-consistent solution. First results show the impact of a self-consistent equilibrium on ray trajectories and current density profiles. Therefore, new insights in lower-hybrid-wave-driven plasmas of TST-2 can be obtained using the proposed hybrid simulation environment.

Kinetic-magnetohydrodynamic hybrid simulations were performed to investigate the linear growth and the nonlinear evolution of off-axis fishbone mode (OFM) destabilized by trapped energetic ions in tokamak plasmas. The spatial profile of OFM is mainly composed of m/n = 2/1 mode inside the q = 2 magnetic flux surface while the m/n = 3/1 mode is predominant outside the q = 2 surface, where m and n are the poloidal and toroidal mode numbers, respectively, and q is the safety factor. The spatial profile of the OFM is a strongly shearing shape on the poloidal plane, suggesting the nonperturbative effect of the interaction with energetic ions. The frequency of the OFM in the linear growth phase is in good agreement with the precession drift frequency of trapped energetic ions, and the frequency chirps down in the nonlinear phase. Two types of resonance conditions between trapped energetic ions and OFM are found. For the first type of resonance, the precession drift frequency matches the OFM frequency, while for the second type, the sum of the precession drift frequency and the bounce frequency matches the OFM frequency. The first type of resonance is the primary resonance for the destabilization of OFM. The resonance frequency which is defined based on precession drift frequency and bounce frequency of the nonlinear orbit for each resonant particle is analyzed to understand the frequency chirping. The resonance frequency of the particles that transfer energy to the OFM chirps down, which may result in the chirping down of the OFM frequency. A detailed analysis of the energetic ion distribution function in phase space shows that the gradient of the distribution function along the E′ = const. line drives or stabilizes the instability, where E′ is a combination of energy and toroidal canonical momentum and conserved during the wave–particle interaction. The distribution function is flattened along the E′ = const. line in the nonlinear phase leading to the saturation of the instability.

A transition from an interchange mode to a non-resonant mode is found in the nonlinear magnetohydrodynamic simulation for the partial collapse in a large helical device (LHD) plasma with a net toroidal current. This transition can occur when the magnetic shear is weak and the rotational transform is close to unity in the core region. In this transition, the mode number of the dominant Fourier component is reduced. As a result of the nonlinear evolution, the (m, n) = (1, 1) component can be dominant, where m and n are the poloidal and the toroidal mode numbers, respectively. This transition is considered to be a candidate to explain the observation in the LHD experiments with the net toroidal current that show partial collapses are caused by the (1, 1) mode.

Energetic particle transport by a magnetohydrodynamic (MHD) instability driven by helically trapped energetic particles is studied for a high-performance Large Helical Device plasma with kinetic-MHD hybrid simulations. It is observed in the simulation that an MHD mode with poloidal/toroidal mode numbers ????/????=2/1driven by helically trapped energetic particles causes a significant redistribution of perpendicular energetic particle pressure profile. The frequency of the MHD mode decreases rapidly at the saturation of the instability and changes sign, which indicates a reversal of the mode propagation direction. It is found that the helically trapped energetic particles interacting strongly with the MHD mode change the precession drift direction at the same time as the reversal of the MHD mode propagation direction. The helically trapped energetic particles with the precession drift reversal are transported rapidly in the radially outward direction before the original precession drift direction is recovered. The precession drift reversal and the outward transport are caused by interaction with the electric field of the MHD mode. The vast majority of trapped energetic particles which interact strongly with the MHD mode experience precession drift reversal, leading to a significant redistribution of the perpendicular energetic particle pressure profile.Numerical computations were performed on the Plasma Simulator (NEC SX-Aurora TSUBASA) of NIFS with the support and under the auspices of the NIFS Collaboration Research program (No. NIFS20KNST169), the JFRS-1 of the International Fusion Energy Research Centre, and the Supercomputer Fugaku of the RIKEN Center for Computational Science (Project ID: hp210178). This work was supported by MEXT as Program for Promoting Research studies on the Supercomputer Fugaku (Exploration of burning plasma confinement physics).

A new kinetic-magnetohydrodynamic hybrid simulation model where the gyrokinetic particle-in-cell simulation is applied to both thermal ions and energetic particles is presented. Toroidal Alfvén eigenmodes (TAEs) destabilized by energetic ions in tokamak plasmas are simulated with the new simulation model. Energy channeling from energetic ions to thermal ions through Alfvén eigenmodes (AEs) is demonstrated by the simulation. The distribution function fluctuations and the resonance condition are analyzed for both thermal ions and energetic ions. The strong energy transfer between the particles and the AE and the strong particle transport occur when the following conditions are satisfied at the resonance location in phase space: (1) the poloidal resonance number is close to the poloidal mode number of the AE, (2) the AE has a substantial amplitude, (3) the distribution function has a substantial gradient along the E ′ = const. line, where E ′ is a conserved variable for the wave-particle interaction. While the distribution function fluctuations for energetic ions are consistent with the resonance condition with the TAEs, the distribution function fluctuations for thermal ions do not satisfy the resonance condition when the bulk plasma beta is 1%. This indicates that the resonance does not play an important role in the interaction between thermal ions and the TAE for the relatively low bulk plasma temperature. On the other hand, when the bulk plasma beta is 4%, the resonance between thermal ions and the TAEs become important leading to Landau damping.

Toroidal Alfvén eigenmodes excited by energetic particles (EPs) and their transition to energetic particle modes are investigated using a three-dimensional nonlinear kinetic-magnetohydrodynamic hybrid simulation code. Both the symmetric chirping inside the Alfvén continuum gap for upward and downward directions and the asymmetric chirping affected by the Alfvén continuum are found in the simulations depending on the EP drive and the mode damping. For weak drive and damping, symmetric frequency chirping is observed with a chirping rate consistent with the Berk–Breizman theory (Berk et al 1997 Phys. Lett. A 234 213). For moderate drive and damping, upward chirping is dominant because downward chirping is interrupted by interaction with the Alfvén continuum. For strong drive and damping, two branches of frequency chirping are found for different poloidal harmonics. The dominant chirping is downward into the Alfvén continuum and the other is an upward chirping inside the Alfvén continuum gap. The creation and the propagation of holes and clumps are found in EP phase space, which is qualitatively consistent with the Berk–Breizman theory.

The multiphase simulations are conducted with the kinetic-magnetohydrodynamics hybrid code MEGA to investigate the spatial and the velocity distributions of lost fast ions due to the Alfvén eigenmode (AE) bursts in the Large Helical Device plasmas. It is found that fast ions are lost along the divertor region with helical symmetry both before and during the AE burst except for the promptly lost particles. On the other hand, several peaks are present in the spatial distribution of lost fast ions along the divertor region. These peaks along the divertor region can be attributed to the deviation of the fast-ion orbits from the magnetic surfaces due to the grad-B and the curvature drifts. For comparison with the velocity distribution of lost fast ions measured by the fast-ion loss detector (FILD), the ‘numerical FILD’ which solves the Newton–Lorentz equation is constructed in the MEGA code. The velocity distribution of lost fast ions detected by the numerical FILD during AE burst is in good qualitative agreement with the experimental FILD measurements. During the AE burst, fast ions with high energy (100–180 keV) are detected by the numerical FILD, while co-going fast ions lost to the divertor region are the particles with energy lower than 50 keV.

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 − p r o f i l e 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.

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 (Eion/EEP) 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.

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 Alfven 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.

Energetic electron effects on an energetic-ion driven toroidal Alfvén eigenmode (TAE) are investigated via hybrid simulations of an MHD fluid interacting with energetic particles. Both energetic electrons and energetic ions described by drift-kinetic equations are included in the present work. It is found that the TAE can be effectively stabilized by off-axis peaked energetic electrons which are located near the mode center, while the centrally peaked energetic electrons fail to stabilize the mode. It is confirmed that the spatially localized pressure profile of energetic electrons causes the stabilization of TAE. The stabilized TAE has a more localized mode structure accompanied by a significant reduction in the energetic ion driving rate. The small change of mode frequency and dissipation rate indicate the stabilization mechanism is different from the so-called pressure gradient stabilization that drives the TAE into continuum. The results suggest that the strong plasma non-uniformity induced by the energetic electron beta profile may be responsible for the change of mode structure. It is also found that this stabilizing effect is more effective for a high-n TAE. Moreover, it is numerically verified that the positive (negative) pressure gradient at the TAE center will increase (decrease) the mode frequency. The wave-particle interactions are also analysed for a case with energetic electrons peaked at the inner side of the TAE center. It is found that the power transfer to a resonant barely trapped energetic electron, which taps energy from the wave, can be comparable to the power transfer from a resonant energetic ion. This suggests that if a sufficient number of resonant barely trapped electrons are present, they might stabilize energetic-ion driven TAE through the wave-particle interaction.

This article is a tutorial review of the interaction between energetic particles and Alfven eigenmodes (AEs) which is one of the important research issues for fusion burning plasmas. The destabilization mechanism of AEs is a kind of inverse Landau damping through the resonant interaction with energetic particles. The important properties of the AE instability, such as resonance condition, conserved variable during the interaction, and particle trapping by the AE, are explained. The time evolution of AEs is classified into various types, steady state, frequency splitting, frequency chirping, and recurrent bursts. Berk and Breizman presented both a one-dimensional weakly nonlinear theory for marginal stability and a reduced simulation model that qualitatively explain the various types of time evolution. Berk–Breizman’s theory and reduced simulation model are introduced, and their limitations and the future works are discussed in this article. In addition, energetic particle transport by AEs is illustrated with surface-of-section plots. The particle trapping by the AE creates phase space islands and leads to the local flattening of the energetic particle spatial profile. The resonance overlap of multiple AEs and the overlap of higher-order resonances of a single AE lead to the emergence of stochasticity in phase space and the global transport of energetic particles.

Energetic-particle-driven geodesic acoustic modes (EGAMs) observed in a Large Helical Device experiment are investigated using a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid. The frequency chirping of the primary mode and the sudden excitation of the half-frequency secondary mode are reproduced for the first time with the hybrid simulation using the realistic physical condition and the three-dimensional equilibrium. Both EGAMs have global spatial profiles which are consistent with the experimental measurements. For the secondary mode, the bulk pressure perturbation and the energetic particle pressure perturbation cancel each other out, and thus the frequency is lower than the primary mode. It is found that the excitation of the secondary mode does not depend on the nonlinear MHD coupling. The secondary mode is excited by energetic particles that satisfy the linear and nonlinear resonance conditions, respectively, for the primary and secondary modes.

Comprehensive computer simulations of the Alfven eigenmode burst, which is the synchronized sudden growth of multiple Alfven eigenmodes (AEs) interacting with energetic particles, were conducted with continuous neutral beam injection, collisions, and particle losses. It is found that the energetic-particle distribution in phase space reaches a 'critical distribution' with a stairway structure where a resonance overlap triggers the Alfven eigenmode burst. Before the burst, the gradual growth of the AEs associated with the beam injection broadens the resonant regions in phase space forming the distribution into a stairway shape. When the distribution reaches the 'critical distribution,' a resonance overlap triggers multiple resonance overlaps leading to the synchronized growth of AEs and the collapse of the distribution. For another run with the beam deposition power reduced to one-half, the energetic-particle distribution function just before the Alfven eigenmode burst is close to that for the original beam power. This result indicates that the critical distribution for the Alfven eigenmode burst is present.

Energetic particle driven geodesic acoustic modes (EGAMs) in the Large Helical Device (LHD) plasmas are investigated using MEGA code. MEGA is a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic (MHD) fluid and in the present work, both the energetic particles and bulk ions are described by the kinetic equations. The low frequency EGAMs are reproduced. Also, the energy transfer is analyzed and the bulk ion heating during the EGAM activity is observed. The ions obtain energy when the energetic particles lose energy, and this indicates that an energy channel is established by EGAM. The EGAM channeling is reproduced by simulation with realistic parameters for the first time. The heating power to bulk ions is 3.4 kW/malt;supagt;3alt;/supagt;. It is found that the sideband resonance is dominant during the energy transfer from EGAM to the bulk ions, and the transit frequencies of resonant bulk ions are one-half of the EGAM frequency.

The linear stability analysis of resistive ballooning modes in Large Helical Device plasmas has been carried out by numerical simulation based on the kinetic magnetohydrodynamic (MHD) model where thermal ions are simulated with the drift-kinetic model. Due to the curvature drift and the gradient B drift, the orbit of trapped ions not only deviates from the magnetic surface but also has the precession motion in the poloidal and toroidal directions. Even when the trapped ions remain well inside the radial profile of the MHD mode, the response of the trapped ions is weakened when the precession drift frequency of the trapped ions with respect to the mode phase is close to or larger than the linear growth rate of the instability. This results in the suppression of the ion perpendicular pressure perturbation to the magnetic field leading to the reduction of the linear growth rate.

Comprehensive magnetohydrodynamic (MHD) hybrid simulations with neutral beam injection and collisions were conducted to investigate the Alfven eigenmode (AE) bursts and the fast-ion losses in the large helical device (LHD) for the realistic conditions close to the experiments. It is found in the simulation of the slowing-down time scale that the AE bursts take place repetitively accompanied by fast-ion redistribution and losses leading to lower saturation levels of stored fast-ion energy than those in a classical calculation where the MHD perturbations are neglected. The fast-ion loss rate caused by the AE burst has the quadratic dependence on AE amplitude, which was observed in the LHD experiment. The majority of the lost fast ions are counter-passing particles whose velocity and pitch-angle are close to those of the beam injection. The second component of the lost fast ions is transit particles whose velocity is close to thermal velocity. The loss of the counter-passing particles occurs mainly during the AE bursts, while the transit particles are lost both during the AE bursts and the quiescent periods with larger loss rate than that in the classical calculation. The initial location of the lost counter-injected particles spreads from the plasma edge to the plasma center, while only the particles initially located in the peripheral region are lost for the co-injected beam.

The aim of this study is to analyze the destabilization of Alfven Eigenmodes (AE) by multiple energetic particles (EP) species in DIII-D and LHD discharges. We use the reduced MHD equations to describe 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 particles species, including the effect of the acoustic modes, diamagnetic currents and helical couplings. We add the Landau damping and resonant destabilization effects using a closure relation. The simulations with multiple NBI lines show three different regimes: the non damped regime where the multi beam AEs growth rate is larger compared to the growth rate of the AEs destabilized by the individual NBI lines, the interaction regime where the multi beam AEs growth rate is smaller than the single NBI AEs and the damped regime where the AEs are suppressed. Operations in the damped regime requires EP species with different density profile flatness or gradient locations. In addition, the AEs growth rate in the interaction regime is further reduced if the combined NBI lines have similar beam temperatures and the beta of the NBI line with flatter EP density profile increases. Then, optimization trends are identified in DIII-D high poloidal beta and LHD low density / magnetic field discharges with multiple NBI lines as well as the configuration requirements to operate in the damped and interaction regimes. DIII-D simulations show a decrease of the n=2 to 6 AEs growth rate and n=1 AE are stabilized in the LHD case. The helical coupling effects in LHD simulations lead to a transition from the interaction to the damped regime of the n=2,-8,12 helical family., arXiv admin note: text overlap with arXiv:1807.04380, arXiv:1906.05700

This paper reports verification and validation of linear simulations of Alfvén eigenmodes in the current ramp phase of DIII-D L-mode discharge #159243 using gyrokinetic, gyrokinetic-MHD hybrid, and eigenvalue codes. Using a classical fast ion profile, all simulation codes find that reversed shear Alfvén eigenmodes (RSAE) are the dominant instability. The real frequencies from all codes have a coefficient of variation of less than 5% for the most unstable modes with toroidal mode number n = 4 and 5. The simulated RSAE frequencies agree with experimental measurements if the minimum safety factor is adjusted, within experimental errors. The simulated growth rates exhibit greater variation, and simulations find that pressure gradients of thermal plasmas make a significant contribution to the growth rates. Mode structures of the dominant modes agree well among all codes. Moreover, using a calculated fast ion profile that takes into account the diffusion by multiple unstable modes, a toroidal Alfvén eigenmode (TAE) with n = 6 is found to be unstable in the outer edge, consistent with the experimental observations. Variations of the real frequencies and growth rates of the TAE are slightly larger than those of the RSAE. Finally, electron temperature fluctuations and radial phase shifts from simulations show no significant differences with the experimental data for the strong n = 4 RSAE, but significant differences for the weak n = 6 TAE. The verification and validation for the linear Alfvén eigenmodes is the first step to develop an integrated simulation of energetic particles confinement in burning plasmas incorporating multiple physical processes.

Alfvén waves are electromagnetic perturbations inherent to magnetized plasmas that can be driven unstable by a free energy associated with gradients in the energetic particles' distribution function. The energetic particles with velocities comparable to the Alfvén velocity may excite Alfvén instabilities via resonant wave–particle energy and momentum exchange. Burning plasmas with large population of fusion born super-Alfvénic alpha particles in magnetically confined fusion devices are prone to excite weakly-damped Alfvén eigenmodes (AEs) that, if allowed to grow unabated, can cause a degradation of fusion performance and loss of energetic ions through a secular radial transport. In order to control the fast-ion distribution and associated Alfvénic activity, the fusion community is currently searching for external actuators that can control AEs and energetic ions in the harsh environment of a fusion reactor. Most promising control techniques are based on (i) variable fast-ion sources to modify gradients in the energetic particles' distribution, (ii) localized electron cyclotron resonance heating to affect the fast-ion slowing-down distribution, (iii) localized electron cyclotron current drive to modify the equilibrium magnetic helicity and thus the AE existence criteria and damping mechanisms, and (iv) externally applied 3D perturbative fields to manipulate the fast-ion distribution and thus the wave drive. Advanced simulations help to identify the key physics mechanisms underlying the observed AE mitigation and suppression and thus to develop robust control techniques towards future burning plasmas. This work has been carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014–2018 and 2019–2020 under grant agreement No 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission. Support by US DOE and ITER-CN is also acknowledged. The support from the FP7 People: Marie-Curie Actions (Grant No. 321455) and the Spanish Ministry of Economy and Competitiveness (Grants No. RYC-2011-09152, No. FIS2015-69362-P) is gratefully acknowledged. The work of AVM was funded by the Russian Science Foundation, project 14-22-00193, and was partly supported by the Competitiveness Program of NRNU MEPhI.

Fast particles in fusion plasmas may drive Alfvén modes unstable leading to fluctuations of the internal electromagnetic fields and potential loss of particles. Such instabilities can have an impact on the performance and the wall-load of machines with burning plasmas such as ITER. A linear benchmark for a toroidal Alfvén eigenmode (TAE) is done with 11 participating codes with a broad variation in the physical as well as the numerical models. A reasonable agreement of around 20% has been found for the growth rates. Also, the agreement of the eigenfunctions and mode frequencies is satisfying. However, they are found to depend strongly on the complexity of the used model. © EURATOM 2018.

The confinement of energetic ions generated by neutral beam injection (NBI) and ion cyclotron resonance frequency heating is studied using GNET simulation code, in which the drift kinetic equation ...

Energetic ion-driven magnetohydrodynamic instabilities such as Alfven eigenmodes (AEs), energetic particle modes (EPMs), and their impacts on energetic ion confinement are being studied on the Larg...

Energetic-particle driven instabilities have been extensively observed in both tokamaks and stellarators. In order for such devices to ultimately succeed as D-T fusion reactors, the super-Alfvenic 3.5 Mev fusion-produced alpha particles must be sufficiently well confined. This requires the evaluation of losses from classical collisional transport processes as well as from energetic particle-driven instabilities. An important group of instabilities in this context are the discrete shear Alfven modes, which can readily be destabilized by energetic particles (with velocities of the order of vAlfven) through wave-particle resonances. While these modes in three-dimensional systems have many similarities to those in tokamaks, the detailed implementation of modeling tools has required development of new methods. Recent efforts in this direction will be described here, with an emphasis on reduced models (© 2010 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)

Effects of fast ions on the magnetohydrodynamic (MHD) instabilities in a Large Helical Device (LHD) plasma with the central beta value (=pressure normalized by the magnetic pressure) 4% have been investigated with hybrid simulations for energetic particles interacting with an MHD fluid. When fast ions are neglected, it is found that the dominant instability is an ideal interchange mode with the dominant harmonic m/n = 2/1, where m, n are respectively the poloidal and toroidal numbers. The spatial peak location of the m/n = 2/1 harmonic is close to the ι = 1/2 magnetic surface located at r/a = 0.29, where ι is the rotational transform and r/a is the normalized radius. The second unstable mode is a resistive interchange mode with m/n =3/2 that peaks at r/a = 0.65 nearby the ι = 2/3 surface, which grows more slowly than the m/n = 2/1 mode. The nonlinear coupling of the m/n = 3/2 and 2/1 mode results in the growth of the m/n = 5/3 mode and other modes leading to the global reduction and flattening of the pressure profile. When fast ions are considered with the central beta value 0.2% and the total pressure profile is kept the same, the ideal interchange mode with m/n = 2/1 located close to the plasma center is stabilized while the resistive interchange mode with m/n = 3/2 located far from the plasma center is less affected. The stabilization is attributed to the reduction of bulk pressure gradient, which is the dilution of the free energy source, because the energy transfer between the fast ions and the interchange modes is found to be negligible. For higher fast-ion pressure, Alfvén eigenmodes are destabilized by fast ions.

In recent years, fusion research has become exceedingly popular in the Asian region. Many toroidal devices are currently operated for fusion research in universities and institutes. The long pulse operation of a high-performance plasma is also possible in four superconducting devices, which are EAST (Institute of Plasma Physics Chinese Academy of Sciences (ASIPP), China), KSTAR (National Fusion Research Institute (NFRI), Korea), LHD (National Institute for Fusion Science (NIFS), Japan) and SST-1 (Institute for Plasma Research (IPR), India). The world's largest superconducting tokamak, JT-60SA (National Institutes for Quantum and Radiological Science and Technology (QST), Japan), and middle-size tokamak, HL-2M (Southwestern Institute of Physics (SWIP), China), have now been constructed for the upcoming operation. Based on the progressive development of fusion research in Asian region an international collaboration on critical physics for the steady state operation of high-performance plasmas has been carried out among China, Japan and Korea during past five years through the A3 foresight program. Recent fusion research activities in the Asian region and the results of the collaboration are briefly reported with future prospects for international collaboration.

Kinetic-MagnetoHydroDynamic (MHD) hybrid simulations are carried out to study fast ion driven toroidal Alfvén eigenmodes (TAEs) on the Experimental Advanced Superconducting Tokamak (EAST). The first part of this article presents the linear benchmark between two kinetic-MHD codes, namely MEGA and M3D-K, based on a realistic EAST equilibrium. Parameter scans show that the frequency and the growth rate of the TAE given by the two codes agree with each other. The second part of this article discusses the resonance interaction between the TAE and fast ions simulated by the MEGA code. The results show that the TAE exchanges energy with the co-current passing particles with the parallel velocity |ν| ≈ V a0/3 or |ν| ≈ V A0/5 where V A0is the Alfvén speed on the magnetic axis. The TAE destabilized by the counter-current passing ions is also analyzed and found to have a much smaller growth rate than the co-current ions driven TAE. One of the reasons for this is found to be that the overlapping region of the TAE spatial location and the counter-current ion orbits is narrow, and thus the wave-particle energy exchange is not efficient.

This chapter reviews the progress accomplished since the redaction of the first ITER Physics Basis (1999 Nucl. Fusion 39 2137-664) in the field of energetic ion physics and its possible impact on burning plasma regimes. New schemes to create energetic ions simulating the fusion-produced alphas are introduced, accessing experimental conditions of direct relevance for burning plasmas, in terms of the Alfvénic Mach number and of the normalised pressure gradient of the energetic ions, though orbit characteristics and size cannot always match those of ITER. Based on the experimental and theoretical knowledge of the effects of the toroidal magnetic field ripple on direct fast ion losses, ferritic inserts in ITER are expected to provide a significant reduction of ripple alpha losses in reversed shear configurations. The nonlinear fast ion interaction with kink and tearing modes is qualitatively understood, but quantitative predictions are missing, particularly for the stabilisation of sawteeth by fast particles that can trigger neoclassical tearing modes. A large database on the linear stability properties of the modes interacting with energetic ions, such as the Alfvén eigenmode has been constructed. Comparisons between theoretical predictions and experimental measurements of mode structures and drive/damping rates approach a satisfactory degree of consistency, though systematic measurements and theory comparisons of damping and drive of intermediate and high mode numbers, the most relevant for ITER, still need to be performed. The nonlinear behaviour of Alfvén eigenmodes close to marginal stability is well characterized theoretically and experimentally, which gives the opportunity to extract some information on the particle phase space distribution from the measured instability spectral features. Much less data exists for strongly unstable scenarios, characterised by nonlinear dynamical processes leading to energetic ion redistribution and losses, and identified in nonlinear numerical simulations of Alfvén eigenmodes and energetic particle modes. Comparisons with theoretical and numerical analyses are needed to assess the potential implications of these regimes on burning plasma scenarios, including in the presence of a large number of modes simultaneously driven unstable by the fast ions. © 2007 IAEA, Vienna.

The interaction between pressure driven modes and magnetic islands generated by a resonant magnetic perturbation (RMP) in the large helical device (LHD) is numerically analyzed. In this analysis, three-dimensional treatment is essential in the equilibrium and dynamics calculations, because the equilibrium pressure profile is deformed by the RMP. The deformation changes the linear mode structure from the interchange type to the ballooning-like type that is localized around the X-point of the island in the equilibrium magnetic field including the RMP. This mode causes a pressure collapse in the nonlinear evolution, which spreads from the X-point to the core. Therefore, the spatial phase of the collapse is fixed to the island geometry. The fixed phase agrees with the LHD experimental results with a natural error field.

A new simulation method that improves the conservation properties of δ f particle simulation for the collisionless Boltzmann equation is presented. When the distribution function is divided into a reference distribution specifi ed in advance and a variation distribution, the time evolution of the variation distribution is described by an advection termin the phase space and a source term associated with the reference distribution. The time evolution of the Klimontovich distribution function of the δ f method was investigated. It is shown that the errors in the Monte Carlo estimate of the source term in the δ f method deteriorate the conservation properties. In the new simulation method, errors in the Monte Carlo estimate of the source term are corrected with a complementary fl uid model. An example of the complementary fl uid model is presented for bump-on-tail instability. The simulation results are compared with those of the conventional δ f method. It is demonstrated that particle, momentum, and energy are well conserved with the new simulation method.

Alfven eignemode experiments have been carried out by using the negative-ion-based neutral beam in JT-60U. For bursting instabilities in the frequency range of Alfvn Eigenmodes, two types of mode activity have been observed. In one type called Abrupt Large-amplitude Event (ALE), enhanced transport of the energetic ions was detected. The enhanced transport showed the clear energy dependence based on measurements performed using a natural diamond detector. In another type of bursting event called the fast Frequency Sweeping (fast FS) mode, frequency up-down chirping is observed on the time-scale of a few ms, much faster than equilibrium changes in the background plasma. This frequency chirping was well reproduced by the non-linear simulation code, MEGA, for magnetohydrodynamics (MHD) with energetic particles. The slow up-frequency sweeping of the Reversed-Shear-induced Alfven Eigenmode (RSAEs), due to the slow evolution of qmin was also observed. These experiments were analyzed by using the NOVA-K code. It is shown that the most unstable modes are localized around the minimum in the magnetic safety factor (qmin) in the analysis.

A new simulation method that improves the conservation properties of δf particle simulation for the collisionless Boltzmann equation is presented. When the distribution function is divided into a reference distribution specified in advance and a variation distribution, the time evolution of the variation distribution is described by an advection term in the phase space and a source term associated with the reference distribution. The time evolution of the Klimontovich distribution function of the δf method was investigated. It is shown that the errors in the Monte Carlo estimate of the source term in the δf method deteriorate the conservation properties. In the new simulation method, errors in the Monte Carlo estimate of the source term are corrected with a complementary fluid model. An example of the complementary fluid model is presented for bump-on-tail instability. The simulation results are compared with those of the conventional δf method. It is demonstrated that particle, momentum, and energy are well conserved with the new simulation method.

Recent energetic particle physics research in JT-60U and JFT-2M is reported. Alfven eigenmodes (AEs) are investigated in reversed-shear (RS) plasmas in JT-60U where frequency sweeping (FS) modes are observed to follow the q-profile evolution. The RS-induced AE model can explain the FS of the modes within the context of an evolving q-profile. Enhanced energetic ion transport is also investigated with the appearance of modes in the toroidicity-induced AE range of frequency in JT-60U using a multi-channel neutron profile monitor and in JFT-2M using a lost ion probe. Additionally, the ripple loss in the complex toroidal field ripple due to ferritic steel inserts in JFT-2M is shown and compared with model analysis. The simulation code developed to predict ripple loss in JFT-2M will be of use in estimating the heat flux in the complex ripple field of a future device such as ITER.

Recurrent bursts of toroidicity-induced Alfven eigenmodes (TAE) are studied using a self-consistent simulation model. Bursts of beam ion losses observed in the neutral beam injection experiment at the Tokamak Fusion Test Reactor [K. L. Wong et al., Phys. Rev. Lett. 66, 1874 (1991)] are reproduced using experimental parameters. It is found that synchronized TAE bursts take place at regular time intervals of 2.9 ms, which is close to the experimental value of 2.2 ms. The stored beam energy saturates at about 40% of that of the classical slowing down distribution. The stored beam energy drop associated with each burst has a modulation depth of 10%, which is also close to the inferred experimental value of 7%. Surface of section plots demonstrate that both the resonance overlap of different eigenmodes and the disappearance of KAM surfaces in phase space due to overlap of higher-order islands created by a single eigenmode lead to particle loss. Only co-injected beam ions build up to a significant stored energy even though their distribution is flattened in the plasma center. However, they are not directly lost, as their orbits extend beyond the outer plasma edge when the core plasma leans on a high field side limiter. The saturation amplitude is deltaB/B~2×10^?2, which is larger than would appear to be compatible with experiment. Physical arguments are presented for why the stored energetic particle response observed in the simulation is still plausible.