Energetic Particle Modes Research Articles

Nonlinear simulations of energetic particle-driven instabilities interacting with Alfvén continuum during frequency chirping

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.

Modeling of the ECCD injection effect on the Heliotron J and LHD plasma stability

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 (). In the ctr-ECCD simulations, the EPM/AE growth rate decreases only below a given , 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.

Summary of the 16th IAEA technical meeting on energetic particles in magnetic confinement systems—theory of plasma instabilities

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.

Magnetohydrodynamic hybrid simulation of Alfvén eigenmodes in Heliotron J, a low shear helical axis stellarator/heliotron

Alfvén eigenmodes destabilized by energetic particles in Heliotron J, a low magnetic shear helical axis stellarator/heliotron with four toroidal equilibrium field periods, are investigated with MEGA, a hybrid simulation code for energetic particles interacting with a magnetohydrodynamic fluid. The objectives of this study are to validate the MEGA simulation results on Alfvén eigenmodes in Heliotron J, and to clarify the properties of Alfvén eigenmodes. The experimentally observed global Alfvén eigenmode (GAE) was reproduced with MEGA simulations based on the experimental bulk plasma temperature and density profiles. Beside GAE, GAE was also observed with lower amplitude and linear growth rate. The frequency and spatial location of GAE are close to those of the experimentally observed energetic particle mode (EPM). For GAE, it was found that the three-dimensional spatial profile of the GAE was primarily composed of n = 2 harmonics while the contribution from the other toroidal mode numbers such as n = 2 ± iNfp was weak, where ‘i’ and ‘Nfp’ are arbitrary integer and toroidal field period, respectively. This indicates that the coupling of harmonics with the same toroidal mode number through toroidicity is dominant for the GAE spatial profile, and the coupling with the different toroidal mode numbers through helicity and bumpiness has minor effects. For GAE, the coupling of harmonic through toroidicity is weaker than that of GAE. The non-linear evolutions of the GAE and GAE destabilized by energetic particles with a bump-on-tail distribution and a slowing-down distribution were compared. Weak dependence of the linear growth rate for both and modes on charge-exchange time were implied.

Effect of ECH/ECCD on energetic-particle-driven MHD modes in helical plasmas

The effect of electron cyclotron heating (ECH) and electron cyclotron current drive (ECCD) on energetic-particle (EP)-driven magnetohydrodynamic (MHD) modes is studied in the helical devices LHD, TJ-II and Heliotron J. We demonstrate that EP-driven MHD modes, including Alfvén eigenmodes (AEs) and energetic particle modes (EPMs), can be controlled by ECH/ECCD. In the LHD device, which has a moderate rotational transform and a high magnetic shear, co-ECCD enhances toroidal AEs (TAEs) and global AEs (GAEs), while counter-ECCD stabilizes them, which improves the neutron rate compared with the co-ECCD case. Counter-ECCD decreases the core rotational transform and increases the magnetic shear, strengthening the continuum damping on the shear Alfvén continua (SAC). In the TJ-II device, which has a high rotational transform, moderate magnetic shear and low toroidal field period, helical AEs (HAEs) appear when the HAE frequency gap of the SAC is changed by counter-ECCD combined with a bootstrap current and neutral-beam-driven current. On the other hand, both co- and counter-ECCD are effective in stabilizing GAEs and EPMs in the Heliotron J device, which has a low rotational transform and low magnetic shear. The experimental results indicate that the magnetic shear has a stabilizing effect regardless of its sign. Modeling analysis using the FAR3d code shows that the growth rates are reduced by both co- and counter-ECCD in Heliotron J, reproducing the experimental results. ECH only affects EP-driven MHD modes, and the experimental results show that the effect depends on the magnetic configuration. In Heliotron J, some modes are stabilized with an increase in ECH power in the low-bumpiness magnetic configuration, while some modes are destabilized in the high- and medium-bumpiness magnetic configurations.

Destabilization of beta-induced Alfvén eigenmodes by energetic trapped electrons in tokamak

The stability of high torodial mode number (n) beta-induced Alfvén eigenmodes excited by precessional resonance of magnetically trapped energetic electrons in low magnetic-shear tokamak plasma is investigated. The dispersion relation of the energetic-electron beta-induced Alfvén eigenmodes (e-BAE) is derived and solved analytically and numerically. It is found that the contribution of the trapped energetic electrons to the e-BAE dispersion relation is limited to the ideal MHD structure of the BAE. Numerical results show that, for typical equilibrium parameters, the e-BAE can be destabilized by the energetic electrons, and the mode frequency is consistent with the experimental observation. Varying the background plasma parameters can lead to transitions between e-BAEs and energetic particle modes. Moreover, the dependence of the e-BAE frequencies and growth rates on energetic electron parameters shows that the growth rates monotonically increase(decrease) with the energetic electron density(the normalized energetic electron density scale length), and the frequencies are not much affected. The frequency and growth rate are sensitive to the energetic electron temperature, and there exists a maximum growth rate.

Effect of the tangential NBI current drive on the stability of pressure and energetic particle driven MHD modes in LHD plasma

The aim of the present study is to analyze the stability of the pressure gradient driven modes (PM) and Alfvén eigenmodes (AE) in the large helical device (LHD) plasma if the rotational transform profile is modified by the current drive of the tangential neutral beam injectors (NBI). This study forms a basic search for optimized operation scenarios with reduced mode activity. The analysis is performed using the code FAR3d which 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 for density and parallel velocity moments of 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. On-axis and off-axis NBI current drive modifies the rotational transform which becomes strongly distorted as the intensity of the neutral beam current drive (NBCD) increases, leading to wider continuum gaps and modifying the magnetic shear. The simulations with on-axis NBI injection show that a counter (ctr-) NBCD in inward shifted and default configurations leads to a lower growth rate of the PM, although strong n = 1 and 2 AEs can be destabilized. For the outward shifted configurations, a co-NBCD improves the AEs stability but the PM are further destabilized if the co-NBCD intensity is 30 kA T−1. If the NBI injection is off-axis, the plasma stability is not significantly improved due to the further destabilization of the AE and energetic particle modes (EPM) in the middle and outer plasma region.

Re-splitting [formula omitted] method for electro-magnetic gyrokinetic particle-in-cell (PIC) simulation of tokamak plasmas

A new method based on a re-splitting δf technique is proposed to mitigate the cancellation problem in electro-magnetic gyrokinetic PIC simulation. This new scheme, together with the pull-back mitigation (PBM) scheme (Mishchenko et al., 2014), have recently been implemented in the GEM code (Chen et al., 2003). These two algorithms are systematically compared with the original GEM algorithm for the simulation of the ion temperature gradient (ITG) mode, the kinetic ballooning mode (KBM), the toroidal Alfvén eigenmode (TAE) and the energetic particle mode (EPM). The three algorithms agree well for all of these modes. Moreover, both the re-splitting method and PBM can mitigate the cancellation problem and improve the computational efficiency.

Numerical study of transition between even and odd toroidal Alfvén eigenmodes on EAST

Linear simulations of toroidal Alfvén eigenmodes (TAEs) driven by energetic particles (EPs) on EAST (Experimental Advanced Superconducting Tokamak) are performed using the hybrid-kinetic MHD model implemented in NIMROD code. The EAST equilibrium is reconstructed using the EFIT code based on the experimental measurement. The “slowing down” distribution is adopted for modeling the equilibrium distribution of the energetic ions from the deuterium neutral beam injection on EAST. The frequency, the dominant poloidal mode number, the radial location and the detailed 2D mode structure of the TAE/RSAE (Reverse Shear Alfvén Eigenmode)/EPM (energetic particle mode) modes are consistent between the eigenvalue analysis and the NIMROD simulation. As the β fraction of EP increases, a transition between even and odd TAEs occurs, along with that between the ballooning and antiballooning mode structures. When the β fraction of EP is close to the transition threshold, both types of TAEs coexist.

Overview of physics studies on ASDEX Upgrade

The ASDEX Upgrade (AUG) programme, jointly run with the EUROfusion MST1 task force, continues to significantly enhance the physics base of ITER and DEMO. Here, the full tungsten wall is a key asset for extrapolating to future devices. The high overall heating power, flexible heating mix and comprehensive diagnostic set allows studies ranging from mimicking the scrape-off-layer and divertor conditions of ITER and DEMO at high density to fully non-inductive operation (q95 = 5.5, ) at low density. Higher installed electron cyclotron resonance heating power 6 MW, new diagnostics and improved analysis techniques have further enhanced the capabilities of AUG.Stable high-density H-modes with MW m−1 with fully detached strike-points have been demonstrated. The ballooning instability close to the separatrix has been identified as a potential cause leading to the H-mode density limit and is also found to play an important role for the access to small edge-localized modes (ELMs). Density limit disruptions have been successfully avoided using a path-oriented approach to disruption handling and progress has been made in understanding the dissipation and avoidance of runaway electron beams. ELM suppression with resonant magnetic perturbations is now routinely achieved reaching transiently . This gives new insight into the field penetration physics, in particular with respect to plasma flows. Modelling agrees well with plasma response measurements and a helically localised ballooning structure observed prior to the ELM is evidence for the changed edge stability due to the magnetic perturbations. The impact of 3D perturbations on heat load patterns and fast-ion losses have been further elaborated.Progress has also been made in understanding the ELM cycle itself. Here, new fast measurements of and Er allow for inter ELM transport analysis confirming that Er is dominated by the diamagnetic term even for fast timescales. New analysis techniques allow detailed comparison of the ELM crash and are in good agreement with nonlinear MHD modelling. The observation of accelerated ions during the ELM crash can be seen as evidence for the reconnection during the ELM. As type-I ELMs (even mitigated) are likely not a viable operational regime in DEMO studies of ‘natural’ no ELM regimes have been extended. Stable I-modes up to have been characterised using -feedback.Core physics has been advanced by more detailed characterisation of the turbulence with new measurements such as the eddy tilt angle—measured for the first time—or the cross-phase angle of and fluctuations. These new data put strong constraints on gyro-kinetic turbulence modelling. In addition, carefully executed studies in different main species (H, D and He) and with different heating mixes highlight the importance of the collisional energy exchange for interpreting energy confinement. A new regime with a hollow profile now gives access to regimes mimicking aspects of burning plasma conditions and lead to nonlinear interactions of energetic particle modes despite the sub-Alfvénic beam energy. This will help to validate the fast-ion codes for predicting ITER and DEMO.

A measure of fast ion beta at marginal stability in the reversed field pinch

Energetic ions are well confined in the core of the reversed field pinch and a substantial population develops rapidly during tangential neutral beam injection. A saturated fast ion density is observed within several milliseconds and coincides with the onset of energetic particle mode activity. First measurements of the fusion product profile determine the fast ion density and pressure profiles, the latter of which when combined with neutral particle analysis of the energy distribution. These are key measurements in explaining the limiting behavior of the fast ion profile in response to a combination of effects. Tearing mode activity affects the fast ion profile, and the fast ions noticeably influence the core-most tearing mode. The nonlinear situation settles into a marginally stable state where the EPM transports fast ions down a steep gradient to a region where their confinement is limited by stochastic orbit and charge exchange losses. In the state at marginal stability (achieved in one set of experimental conditions with full 1 MW neutral beam power), a critical fast ion beta gradient is measured that limits the core , or nearly four times the core thermal , but less than a strictly classical calculation predicts.

Low-frequency fishbone driven by passing fast ions in tokamak plasmas

Low-frequency fishbone instability driven by passing fast ions via wave-particle resonance is studied within the framework of energetic particle mode (EPM), where and are toroidal transit frequency and poloidal transit frequency of passing fast ions respectively. The effects of finite orbit width of energetic particles are responsible for the low-frequency fishbone of EPM type. It is found that magnetic shear at the q = 1 radius plays an important role in the instability whereas the effect of background plasma beta is weak. In particular, for the case of co-injection of beam ions, there exists a critical magnetic shear below which the beam ion beta threshold for EPM excitation is very small. For moderate or higher magnetic shear, the beam ion beta threshold is much higher, on order of a few percent. These results are consistent with the observation of the low-frequency fishbone in the HL-2A tokamak.

Frequency chirping in the Alfvén continuum

A new kinetic code, CHIRP, shows how long range frequency chirping emerges from the energetic particle (EP) excitation of Alfvénic instability. Both a perturbative toroidal Alfvén eigenmode (TAE) and a non-perturbative energetic particle mode (EPM) can be driven unstable due to the EP pressure gradient. These instabilities produce phase space chirping structures in the form of holes or clumps. The code calculates the nonlinear resonant EP response of the poloidally coupled Alfvén wave equations, while the background plasma is assumed to respond linearly to the generated fields. At moderate EP pressure gradient, only TAEs are excited, that produce chirping structures that have only moderate frequency change which do not reach the continuum frequency. Larger pressure gradients excite an EPM mode that emerges in the lower continuum, which then chirps rapidly downward with its amplitude growing appreciably in time. An adiabatic theory was developed that accurately describes the late time evolution of the rapid frequency chirping. The strong correlation between the adiabatic theory and simulation is compatible with the view that the bulk of the EPM-trapped particles evolve in accordance with the conservation of their action.

Experimental characterization of Alfvén modes in a field-reversed configuration plasma

High power neutral beam injection into the C-2U advanced field-reversed configuration (FRC) stimulates at least three distinct energetic particle modes, none of which have been linked to a performance limitation. Here we present an experimental characterization of one mode in particular, a high frequency mode () observed in the decaying phase of the FRC. The mode is reminiscent of the compressional Alfvén eigenmodes observed in spherical tokamaks: its frequency scales with the edge Alfvén velocity and it co-propagates with injected beam ions perpendicular to the magnetic field. There are multiple pieces of evidence that the mode resides outside of the FRC and therefore likely has little to no effect on the confinement properties of the FRC itself.

Energetic-particle-modified global Alfvén eigenmodes

Fully self-consistent hybrid MHD/particle simulations reveal strong energetic particle modifications to sub-cyclotron global Alfvén eigenmodes (GAEs) in low-aspect ratio, NSTX-like conditions. Key parameters defining the fast ion distribution function—the normalized injection velocity v0/vA and central pitch—are varied in order to study their influence on the characteristics of the excited modes. It is found that the frequency of the most unstable mode changes significantly and continuously with beam parameters, in accordance with the Doppler-shifted cyclotron resonances which drive the modes, and depending most substantially on v0/vA. This unexpected result is present for both counter-propagating GAEs, which are routinely excited in NSTX, and high frequency co-GAEs, which have not been previously studied. Large changes in frequency without clear corresponding changes in the mode structure are signatures of an energetic particle mode, referred to here as an energetic-particle-modified GAE. Additional simulations conducted for a fixed MHD equilibrium demonstrate that the GAE frequency shift cannot be explained by the equilibrium changes due to energetic particle effects.

Role of Helium–Hydrogen ratio on energetic interchange mode behaviour and its effect on ion temperature and micro-turbulence in LHD

In the Large helical device, a change of energetic particle mode is observed as He concentration is varied in ion-ITB type experiments, having constant electron density and input heating power but with a clear increase of central ion temperature in He rich discharges. This activity consists of bursty, but damped energetic interchange modes (EICs, Du et al 2015 Phys. Rev. Lett. 114 155003), whose occurrence rate is dramatically lower in the He-rich discharges. Mechanisms are discussed for the changes in drive and damping of the modes with He concentration. These EIC bursts consist of marked changes in the radial electric field, which is derived from the phase velocity of turbulence measured with the 2D phase contrast imaging (PCI) system. Similar bursts are detected in edge fast ion diagnostics. Ion thermal transport by gyro-Bohm scaling is recognised as a contribution to the change in ion temperature, though fast ion losses by these EIC modes may also contribute to the ion temperature dependence on He concentration, most particularly controlling the height of an ‘edge-pedestal’ in the profile. The steady-state level of fast ions is shown to be larger in helium rich discharges on the basis of a compact neutral particle analyser (CNPA), and the fast-ion component of the diamagnetic stored energy. These events also have an influence on turbulence and transport. The large velocity shear induced produced during these events transiently improves confinement and suppresses turbulence, and has a larger net effect when bursts are more frequent in hydrogen discharges. This exactly offsets the increased gyro-Bohm related turbulence drive in hydrogen which results in the same time-averaged turbulence level in hydrogen as in helium.

Observation of enhanced radial transport of energetic ion due to energetic particle mode destabilized by helically-trapped energetic ion in the Large Helical Device

A deuterium experiment was initiated to achieve higher-temperature and higher-density plasmas in March 2017 in the Large Helical Device (LHD). The central ion temperature notably increases compared with that in hydrogen experiments. However, an energetic particle mode called the helically-trapped energetic-ion-driven resistive interchange (EIC) mode is often excited by intensive perpendicular neutral beam injections on high ion-temperature discharges. The mode leads to significant decrease of the ion temperature or to limiting the sustainment of the high ion-temperature state. To understand the effect of EIC on the energetic ion confinement, the radial transport of energetic ions is studied by means of the neutron flux monitor and vertical neutron camera newly installed on the LHD. Decreases of the line-integrated neutron profile in core channels show that helically-trapped energetic ions are lost from the plasma.

NIMROD calculations of energetic particle driven toroidal Alfvén eigenmodes

Toroidal Alfvén eigenmodes (TAEs) are gap modes induced by the toroidicity of tokamak plasmas in the absence of continuum damping. They can be excited by energetic particles (EPs) when the EP drive exceeds other dampings, such as electron and ion Landau damping, and collisional and radiative damping. A TAE benchmark case, which was proposed by the International Tokamak Physics Activity group, is studied in this work. The numerical calculations of linear growth of TAEs driven by EPs in a circular-shaped, large aspect ratio tokamak have been performed using the Hybrid Kinetic-MHD (HK-MHD) model implemented in the NIMROD code. This HK-MHD model couples a δf particle-in-cell representation of EPs with the 3D MHD representation of the bulk plasma through moment closure for the momentum conservation equation. Both the excitation of TAEs and their transition to energetic particle modes (EPMs) have been observed. The influence of EP density, temperature, density gradient, and position of the maximum relative density gradient, on the frequency and the growth rate of TAEs are obtained, which are consistent with those from the eigen-analysis calculations, kinetic-MHD, and gyrokinetic simulations for an initial Maxwellian distribution of EPs. The relative pressure gradient of EP at the radial location of the TAE gap, which represents the drive strength of EPs, can strongly affect the growth rate of TAEs. It is demonstrated that the mode transition due to EP drive variation leads to not only the change of frequency but also the change of the mode structure. This mechanism can be helpful in understanding the nonlinear physics of TAE/EPM, such as frequency chirping.

Nonlinear gyrokinetic simulation of fast ion-driven modes including continuum interaction

Energetic particle transport in toroidal magnetic confinement fusion devices can be enhanced by the particles' interaction with electromagnetic global modes. This process has been modelled numerically. The most extensive work has been with reduced models, which may use a simplified description of the bulk plasma, assuming a perturbative approximation for mode structure evolution, restrict simulation to the linear phase, or some combination. In this work, nonlinear non-perturbative simulations are performed using a fully gyrokinetic and reduced models of the bulk plasma. Previous linear investigation of a simple model tokamak case is extended to show that, at least under some conditions, dramatic qualitative differences in mode structure and saturated mode amplitude can exist due to non-perturbative response in the linear and nonlinear phases that depends upon the bulk plasma physics. This supports analytical work which has shown that the non-perturbative energetic particle response should depend upon the magnetic geometry and kinetic physics. It is also shown that energetic particle modes that dominate in the linear phase can be subdominant to a non-perturbative toroidal Alfvén eigenmode-based global structure in the nonlinear phase.

Suppression of fast-ion-driven MHD instabilities by ECH/ECCD on Heliotron J

Experiments of suppressing fast-ion-driven MHD instabilities such as energetic particle modes (EPMs) and global Alfvén eigenmodes (GAEs) have been made using a second harmonic x-mode electron cyclotron heating and current drive (ECCD) in the helical-axis heliotron device, Heliotron J. ECCD experiments show that the GAEs destabilized by fast ions of neutral beam injection with the observed frequency around 140 kHz are fully stabilized, and the EPMs with the observed frequency around 90 kHz are suppressed when the EC-driven plasma current flowing in the counter direction reaches approximately 0.7 kA. The low magnetic shear under the vacuum condition is modified into positive magnetic shear when counter-ECCD is applied, and the amplitude of GAEs and EPMs decreases with an increase in EC-driven plasma current. These results indicate that magnetic shear plays a key role in controlling GAEs as well as EPMs. The comparison of the calculation of shear Alfvén spectra with experimental results shows that the increasing continuum damping rate with an increase in local magnetic shear by EC-driven current is important for both EPMs and GAEs. Moreover, the increase in plasma current leads to the inward movement of GAEs. This effect would also contribute to suppression of GAEs because the continuum damping rate increases more and more toward the core. Steady ECH is also found experimentally to be effective for controlling the amplitude of both GAEs and EPMs. The amplitude of EPMs, and especially for GAEs, decreases with an increase in the ECH power under fixed density conditions.