Wenjun Deng

The gyrokinetic toroidal code (GTC) capability has been extended for simulating internal kink instability with kinetic effects in toroidal geometry. The global simulation domain covers the magnetic axis, which is necessary for simulating current-driven instabilities. GTC simulation in the fluid limit of the kink modes in cylindrical geometry is verified by benchmarking with a magnetohydrodynamic eigenvalue code. Gyrokinetic simulations of the kink modes in the toroidal geometry find that ion… Show more

The gyrokinetic toroidal code (GTC) capability has been extended for simulating internal kink instability with kinetic effects in toroidal geometry. The global simulation domain covers the magnetic axis, which is necessary for simulating current-driven instabilities. GTC simulation in the fluid limit of the kink modes in cylindrical geometry is verified by benchmarking with a magnetohydrodynamic eigenvalue code. Gyrokinetic simulations of the kink modes in the toroidal geometry find that ion kinetic effects significantly reduce the growth rate even when the banana orbit width is much smaller than the radial width of the perturbed current layer at the mode rational surface. Show less

A marker removal optimization technique is developed for δf particle simulations to optimize the marker distribution so as to save markers and computing time. The technique can be directly applied to single-mode linear simulations. For multi-mode or nonlinear simulations, the technique can still be directly applied if there is one most unstable mode that dominates the simulation and δf does not change too much in nonlinear stage, otherwise special care is needed, which is discussed in detail in… Show more

A marker removal optimization technique is developed for δf particle simulations to optimize the marker distribution so as to save markers and computing time. The technique can be directly applied to single-mode linear simulations. For multi-mode or nonlinear simulations, the technique can still be directly applied if there is one most unstable mode that dominates the simulation and δf does not change too much in nonlinear stage, otherwise special care is needed, which is discussed in detail in this paper. The technique effectiveness, e.g., marker saving factor, depends on how localized δf is. In this paper, the technique is first demonstrated in a simple 2D bump-on-tail simulation, and then generalized to 5D gyrokinetic simulations. The technique saves markers by factors of 4 and 19 in our nonlinear 2D bump-on-tail and 5D toroidal Alfvén eigenmode (TAE) simulations, respectively. The technique can be used for phase space of arbitrary dimension, as long as the equilibrium motion constants can be found. The technique is not limited to particle-in-cell (PIC) simulations but could be applied to other approaches of marker particle simulations such as particle-in-wavelet (PIW) and treecode simulations. Show less

The beta-induced Alfvén eigenmode (BAE) excited by energetic particles in toroidal plasmas is studied in the global gyrokinetic simulations. It is found that the nonlinear BAE dynamics depends on the deviation from the marginality. In the strongly driven case, the mode exhibits a bursting state with fast and repetitive chirping. The nonlinear saturation is determined by the thermal ion nonlinearity and has no clear dependence on the linear growth rate. In the weakly driven case, the mode… Show more

The beta-induced Alfvén eigenmode (BAE) excited by energetic particles in toroidal plasmas is studied in the global gyrokinetic simulations. It is found that the nonlinear BAE dynamics depends on the deviation from the marginality. In the strongly driven case, the mode exhibits a bursting state with fast and repetitive chirping. The nonlinear saturation is determined by the thermal ion nonlinearity and has no clear dependence on the linear growth rate. In the weakly driven case, the mode reaches a nearly steady state with small frequency chirping. The nonlinear dynamics is dominated by the energetic particle nonlinearity. In both cases, the nonlinear intensity oscillation and frequency chirping are correlated with the evolution of the coherent structures in the energetic particle phase space. Due to the radial variation of the mode amplitude and the radially asymmetric guiding center dynamics, the wave-particle interaction in the toroidal geometry is much more complex than the conventional one-dimensional wave-particle interaction paradigm. Show less

A verification and validation study is carried out for a sequence of reversed shear Alfvén instability time slices. The mode frequency increases in time as the minimum (qmin) in the safety factor profile decreases. Profiles and equilibria are based upon reconstructions of DIII-D discharge (#142111) in which many such frequency up-sweeping modes were observed. Calculations of the frequency and mode structure evolution from two gyrokinetic codes, GTC and GYRO, and a gyro-Landau fluid code TAEFL… Show more

A verification and validation study is carried out for a sequence of reversed shear Alfvén instability time slices. The mode frequency increases in time as the minimum (qmin) in the safety factor profile decreases. Profiles and equilibria are based upon reconstructions of DIII-D discharge (#142111) in which many such frequency up-sweeping modes were observed. Calculations of the frequency and mode structure evolution from two gyrokinetic codes, GTC and GYRO, and a gyro-Landau fluid code TAEFL are compared. The experimental mode structure of the instability was measured using time-resolved two-dimensional electron cyclotron emission imaging. The three models reproduce the frequency upsweep event within ±10% of each other, and the average of the code predictions is within ±8% of the measurements; growth rates are predicted that are consistent with the observed spectral line widths. The mode structures qualitatively agree with respect to radial location and width, dominant poloidal mode number, ballooning structure, and the up-down asymmetry, with some remaining differences in the details. Such similarities and differences between the predictions of the different models and the experimental results are a valuable part of the verification/validation process and help to guide future development of the modeling efforts. Show less

The effect of bulk pressure on the nonlinear dynamics of energetic particle modes (EPM) in a neutral-beam-driven JT-60U discharge is examined through nonlinear hybrid (MHD + particle) simulations with realistic values of the plasma beta and in realistic flux surface geometry. In the scenario studied, the linear EPM growth rate is 20% higher in the finite-beta compared to the zero-beta case, but compressibility stabilizes the mode by roughly the same amount. In the finite-beta case, the… Show more

The effect of bulk pressure on the nonlinear dynamics of energetic particle modes (EPM) in a neutral-beam-driven JT-60U discharge is examined through nonlinear hybrid (MHD + particle) simulations with realistic values of the plasma beta and in realistic flux surface geometry. In the scenario studied, the linear EPM growth rate is 20% higher in the finite-beta compared to the zero-beta case, but compressibility stabilizes the mode by roughly the same amount. In the finite-beta case, the nonlinear frequency shift and the radial spreading/propagation of the mode are affected by the beta-induced gap in the shear Alfvén continuum. Although the evolution of the modes is affected by bulk pressure, compressibility and geometry, the overall energetic ion transport during the first few 100 Alfvén times following the saturation of the EPM is comparable in all cases studied. Show less

Linear properties of the reverse shear Alfvén eigenmode (RSAE) in a well-diagnosed DIII-D tokamak experiment (discharge #142111) are studied in gyrokinetic particle simulations. Simulations find that a weakly damped RSAE exists due to toroidal coupling and other geometric effects. The mode is driven unstable by density gradients of fast ions from neutral beam injection. Various damping and driving mechanisms are identified and measured in the simulations. Accurate damping and growth rate… Show more

Linear properties of the reverse shear Alfvén eigenmode (RSAE) in a well-diagnosed DIII-D tokamak experiment (discharge #142111) are studied in gyrokinetic particle simulations. Simulations find that a weakly damped RSAE exists due to toroidal coupling and other geometric effects. The mode is driven unstable by density gradients of fast ions from neutral beam injection. Various damping and driving mechanisms are identified and measured in the simulations. Accurate damping and growth rate calculation requires a non-perturbative, fully self-consistent simulation to calculate the true mode structure. The mode structure has no up–down symmetry mainly due to the radial symmetry breaking by the density gradients of the fast ions, as measured in the experiment by electron cyclotron emission imaging. The RSAE frequency up-sweeping and the mode transition from RSAE to TAE (toroidal Alfvén eigenmode) are in good agreement with the experimental results when the values of the minimum safety factor are scanned in gyrokinetic simulations. Show less

A nonlinear gyrokinetic simulation model incorporating equilibrium current has been formulated for studying kinetic magnetohydrodynamic processes in magnetized plasmas. This complete formulation enables gyrokinetic simulation of both pressure-gradient-driven and current-driven instabilities as well as their nonlinear interactions in multi- scale simulations. The gyrokinetic simulation model recovers the ideal magnetohydrodynamic theory in the linear long wavelength regime including ideal and… Show more

A nonlinear gyrokinetic simulation model incorporating equilibrium current has been formulated for studying kinetic magnetohydrodynamic processes in magnetized plasmas. This complete formulation enables gyrokinetic simulation of both pressure-gradient-driven and current-driven instabilities as well as their nonlinear interactions in multi- scale simulations. The gyrokinetic simulation model recovers the ideal magnetohydrodynamic theory in the linear long wavelength regime including ideal and kinetic ballooning modes, kink modes and shear Alfvén waves. The implementation of this model in the global gyrokinetic particle code has been verified for the simulation of the effects of equilibrium current on the reversed shear Alfvén eigenmode in tokamaks. Show less

Global gyrokinetic particle simulations of reversed shear Alfvén eigenmode (RSAE) have been successfully performed and verified. We have excited the RSAE by initial perturbation, by external antenna, and by energetic ions. The RSAE excitation by antenna provides verifications of the mode structure, the frequency, and the damping rate. When the kinetic effects of the background plasma are artificially suppressed, the mode amplitude shows a near-linear growth. With kinetic thermal ions, the mode… Show more

Global gyrokinetic particle simulations of reversed shear Alfvén eigenmode (RSAE) have been successfully performed and verified. We have excited the RSAE by initial perturbation, by external antenna, and by energetic ions. The RSAE excitation by antenna provides verifications of the mode structure, the frequency, and the damping rate. When the kinetic effects of the background plasma are artificially suppressed, the mode amplitude shows a near-linear growth. With kinetic thermal ions, the mode amplitude eventually saturates due to the thermal ion damping. The damping rates measured from the antenna excitation and from the initial perturbation simulation agree very well. The RSAE excited by fast ions shows an exponential growth. The finite Larmor radius effects of the fast ions are found to significantly reduce the growth rate. With kinetic thermal ions and electron pressure, the mode frequency increases due to the elevation of the Alfvén continuum by the geodesic compressibility. The nonperturbative contributions from the fast ions and kinetic thermal ions modify the mode structure relative to the ideal magnetohydrodynamic (MHD) theory. The gyrokinetic simulations have been benchmarked with extended hybrid MHD-gyrokinetic simulations. Show less

Electrostatic drift wave turbulence in tokamak plasmas with reversed magnetic shear is studied using global gyrokinetic particle simulations. The linear eigenmode of the ion temperature gradient (ITG) instability exhibits a mode gap around the minimum safety factor (qmin) region, particularly when qmin is an integer, due to the rarefaction of rational surfaces. The collisionless trapped electron mode (CTEM) instability is suppressed in the negative-shear region due to the reversal of the… Show more

Electrostatic drift wave turbulence in tokamak plasmas with reversed magnetic shear is studied using global gyrokinetic particle simulations. The linear eigenmode of the ion temperature gradient (ITG) instability exhibits a mode gap around the minimum safety factor (qmin) region, particularly when qmin is an integer, due to the rarefaction of rational surfaces. The collisionless trapped electron mode (CTEM) instability is suppressed in the negative-shear region due to the reversal of the toroidal precessional drift of trapped electrons. However, after nonlinear saturation, the ITG gap is filled up by the turbulence spreading and the CTEM fluctuation propagates into the stable negative-shear region. The steady state turbulence occupies the whole volume without any identifiable gap or coherent structures of the heat conductivity, perturbed temperature, or zonal flows in the qmin location or the reversed shear region. Our finding indicates that the electrostatic drift wave turbulence itself does not support either linear or nonlinear mechanism for the formation of internal transport barriers in the reversed magnetic shear when qmin crossing an integer. Show less

Electron transport in burning plasmas is more important since fusion products first heat electrons. First-principles simulations of electron turbulence are much more challenging due to the multi-scale dynamics of the electron turbulence, and have been made possible by close collaborations between plasma physicists and computational scientists. The GTC simulations of collisionless trapped electron mode (CTEM) turbulence show that the electron heat transport exhibits a gradual transition from… Show more

Electron transport in burning plasmas is more important since fusion products first heat electrons. First-principles simulations of electron turbulence are much more challenging due to the multi-scale dynamics of the electron turbulence, and have been made possible by close collaborations between plasma physicists and computational scientists. The GTC simulations of collisionless trapped electron mode (CTEM) turbulence show that the electron heat transport exhibits a gradual transition from Bohm to gyroBohm scaling when the device size is increased. The deviation from the gyroBohm scaling can be induced by large turbulence eddies, turbulence spreading, and non-diffusive transport processes. Analysis of radial correlation function shows that CTEM turbulence eddies are predominantly microscopic but with a significant tail in the mesoscale. A comprehensive analysis of kinetic and fluid time scales shows that zonal flow shearing is the dominant decorrelation mechanism. The mesoscale eddies result from a dynamical process of linear streamers breaking by zonal flows and merging of microscopic eddies. The radial profile of the electron heat conductivity only follows the profile of fluctuation intensity on a global scale, whereas the ion transport tracks more sensitively the local fluctuation intensity. This suggests the existence of a nondiffusive component in the electron heat flux, which arises from the ballistic radial E X B drift of trapped electrons due to a combination of the presence of mesoscale eddies and the weak de-tuning of the toroidal precessional resonance that drives the CTEM instability. On the other hand, the ion radial excursion is not affected by the mesoscale eddies due to a parallel decorrelation, which is not operational for the trapped electrons because of a bounce averaging process associated with the electron fast motion along magnetic field lines. ... Show less