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Bao, J.

Publications and source records attributed to Bao, J..

Saturation of Fishbone Instability by Self-Generated Zonal Flows in Tokamak Plasmas

Gyrokinetic simulations of the fishbone instability in DIII-D tokamak plasmas find that self-generated zonal flows can dominate the nonlinear saturation by preventing coherent structures from persisting or drifting in the energetic particle phase space when the mode frequency down-chirps. Results from the simulation with zonal flows agree quantitatively, for the first time, with experimental measurements of the fishbone saturation amplitude and energetic particle transport. Moreover, the fishbone-induced zonal flows are likely responsible for the formation of an internal transport barrier that was observed after fishbone bursts in this DIII-D experiment. Finally, gyrokinetic simulations of a related ITER baseline scenario show that the fishbone induces insignificant energetic particle redistribution and may enable high performance scenarios in ITER burning plasma experiments. Published by the American Physical Society 2024

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Verification and validation of linear gyrokinetic and kinetic-MHD simulations for internal kink instability in DIII-D tokamak

Here, verification and linear validation of the internal kink instability in tokamak have been performed for both gyrokinetic (GTC) and kinetic-MHD codes (GAM-solver, M3D-C1-K, NOVA, XTOR-K). Using realistic magnetic geometry and plasma profiles from the same equilibrium reconstruction of the DIII-D shot #141216, these codes exhibit excellent agreement for the growth rate and mode structure of the internal kink mode when all kinetic effects are suppressed. The simulated radial mode structures, obtained from linear simulations, are in reasonable agreement with the normalised electron cyclotron emission measurement after adjusting, within the experimental uncertainty, the safety factor q = 1 flux-surface location in the equilibrium reconstruction. Compressible magnetic perturbations strongly destabilize the kink, while poloidal variations of the equilibrium current density reduce the growth rate of the kink. Furthermore, kinetic effects of thermal ions are found to decrease the kink growth rate in kinetic-MHD simulations, but increase the kink growth rate in gyrokinetic simulations, due to the additional drive of the ion temperature gradient and parallel electric field. Kinetic thermal electrons are found to have negligible effects on the internal kink instability.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Gyrokinetic particle simulations of interactions between energetic particles and magnetic islands induced by neoclassical tearing modes

Interactions between energetic particles (EPs) and neoclassical tearing mode (NTM) islands in the DIII-D tokamak are studied using the global gyrokinetic toroidal code (GTC). GTC simulations find that the EP radial profile is partially flattened within the magnetic island regions and that there are stochastic regions in the particle phase space. Radial particle flux is induced mainly around the magnetic island regions and decreases with time to almost zero when the initial EP distribution achieves a new steady-state in the absence of EP sources. Stochastic regions of magnetic field lines induced by the superposition of multiple islands have weak effects on the particle flux when the width of stochastic regions is smaller than the EP drift orbit width. In conclusion, the perturbed parallel EP current induced by the magnetic islands has weak stabilizing effects on the linear growth rate of the NTM instability in this DIII-D experiment.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Kinetic particle simulations in a global toroidal geometry

The gyrokinetic toroidal code has been upgraded for global simulations by coupling the core and scrape-off layer regions across the separatrix with field-aligned particle-grid interpolations. A fully kinetic particle pusher for high frequency waves (ion cyclotron frequency and beyond) and a guiding center pusher for low frequency waves have been implemented using cylindrical coordinates in a global toroidal geometry. The two integrators correctly capture the particle orbits and agree well with each other, conserving energy and canonical angular momentum. As a verification and application of this new capability, ion guiding center simulations have been carried out to study ion orbit losses at the edge of the DIII-D tokamak for single null magnetic separatrix discharges. The ion loss conditions are examined as a function of the pitch angle for cases without and with a radial electric field. We report the simulations show good agreement with past theoretical results and with the experimentally observed feature in which high energy ions flow out along the ion drift orbits and then hit the divertor plates. A measure of the ion direct orbit loss fraction shows that the loss fraction increases with the ion energy for DIII-D in the initial velocity space. Finally, as a further verification of the capability of the new code, self-consistent simulations of zonal flows in the core region of the DIII-D tokamak were carried out. All DIII-D simulations were performed in the absence of turbulence.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Cross-separatrix simulations of turbulent transport in the field-reversed configuration

Recent local simulations of the field-reversed configuration (FRC) have reported drift-wave stability in the core and instability in the scrape-off layer (SOL). However, experimental measurements indicate the existence of fluctuations in both FRC core and SOL, with much lower amplitude fluctuations measured in the core. With the updated cross-separatrix capabilities of the simulation code used in this paper, nonlinear turbulence simulations find that linear instabilities grow in the SOL, generating fluctuations which spread from SOL to core. After saturation of the linear instabilities, a balance of the inward spread and local damping in the core is achieved. The steady state toroidal wavenumber spectrum shows lower amplitude core fluctuations and larger SOL fluctuations with amplitude decreasing towards shorter wavelengths, which are consistent with experimental measurements.

Lau, C. K.↗

Verification and validation of integrated simulation of energetic particles in fusion plasmas

Here, we report on verification and validation of linear simulations of Alf´ven 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 Alf´ven 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. Due to uncertainty in the experimentally measured minimum safety factor (q min ) and the sensitivity of the RSAE’s frequency to q min , the average difference in frequency between simulated and measured is df/f = 14.7%, 22.6%, for n = 4 and 5, respectively. If qmin is adjusted slightly, within experimental errors, an agreement of within 4.5% and 3.1%, for n = 4 and 5 respectively, is found for all codes. 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. Using a calculated fast ion profile that takes into account the action of the spectrum of multiple unstable modes, a toroidal Alf´ven eigenmode (TAE) with n = 6 is found to be unstable in the outer edge, consistent with the experimental data. Variations of the real frequencies and growth rates of the TAE are slightly larger than those of the RSAE. Lastly, 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 simulations of Alf´ven eigenmodes is the first step to determine an integrated simulation of energetic particles confinement in burning plasmas incorporating multiple physical processes with kinetic effects of both energetic and thermal particles on an equal footing.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Global simulation of ion temperature gradient instabilities in a field-reversed configuration

We investigate the global properties of drift waves in the beam driven field-reversed configuration (FRC), the C2-U device, in which the central FRC and its scrape-off layer (SOL) plasma are connected with the formation sections and divertors. The ion temperature gradient modes are globally connected and unstable across these regions, while they are linearly stable inside the FRC separatrix. The unstable global drift waves in the SOL show an axially varying structure that is less intense near the central FRC region and the mirror throat areas, while being more robust in the bad curvature formation exit areas.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗

Nonlinear saturation of kinetic ballooning modes by zonal fields in toroidal plasmas

Kinetic ballooning modes (KBMs) are widely believed to play a critical role in disruptive dynamics as well as turbulent transport in magnetic fusion and space plasmas. While the nonlinear evolution of the ballooning modes has been proposed as a mechanism for “detonation” in various scenarios such as the edge localized modes in tokamaks, the role of the kinetic effects in such nonlinear dynamics remains largely unexplored. In this study, global gyrokinetic simulation results of KBM nonlinear behavior are presented. Instead of the finite-time singularity predicted by ideal magnetohydrodynamic theory, the kinetic instability is shown to develop into an intermediate nonlinear regime of exponential growth, followed by a nonlinear saturation regulated by spontaneously generated zonal fields. In the intermediate nonlinear regime, rapid growth of localized current sheets, which can induce magnetic reconnection, is observed.

70 PLASMA PHYSICS AND FUSION TECHNOLOGY↗