Hybrid simulations of sub-cyclotron compressional and global Alfvén eigenmode stability in spherical tokamaks

Abstract

A comprehensive numerical study has been conducted in order to investigate the stability of beam-driven, sub-cyclotron-frequency compressional Alfvén eigenmodes (CAEs) and global Alfvén eigenmodes (GAEs) in low-aspect-ratio plasmas for a wide range of beam parameters. The presence of CAEs and GAEs has previously been linked to anomalous electron temperature profile flattening at high beam powers in NSTX experiments, prompting a further examination of the conditions necessary for their excitation. Linear simulations have been performed with the hybrid MHD–kinetic initial value code in order to capture the general Doppler-shifted cyclotron resonance that drives the modes. Three distinct types of modes were found in the simulations—co-CAEs, cntr-GAEs, and co-GAEs—with differing spectral and stability properties. The simulations revealed that unstable GAEs are more ubiquitous than unstable CAEs, which is consistent with experimental observations, as they are excited at lower beam energies and generally have larger growth rates. Local analytic theory is used to explain key features of the simulation results, including the preferential excitation of different modes based on beam injection geometry and the growth rate dependence on the beam injection velocity, critical velocity, and degree of velocity space anisotropy. The background damping rate is inferred from the simulations and analytically estimated for relevant sources absent from the simulation model, indicating that co-CAEs are closer to marginal stability than modes driven by the cyclotron resonances.

Application of simulations and theory of sub-cyclotron frequency modes to DIII-D

“…Calculated growth rates and real frequencies for the n = −16 GAE are shown in figure 2(b), where the estimated stability threshold is n b /n 0 ≈ 0.02. In contrast to previous NSTX simulations [18,20]…”

“…New GAE/CAE analytic theory [19][20][21] shows that previously derived [3,23] instability conditions for counterpropagating GAE: 2 < k ⊥ ρ i < 4 and for CAE: 1 < k ⊥ ρ i < 2 are valid only when the beam injection velocity is very large compared to the resonant velocity v 0 v ,res (implying that ω/ω ci ≈ 1). The new theory shows that the instability is driven by the velocity space gradients (specifically, ∂F 0 ∂λ > 0 for counter-propagating GAEs, where λ = μB 0 /ε is the pitch related parameter), and predicts for most cases that the linear growth rate is largest for small values of k ⊥ (k ⊥ ρ i < 1).…”

“…Previous numerical and theoretical studies of the beam driven GAEs and CAEs have been focused on reproducing and understanding the NSTX(-U) results, and a good agreement with the observed toroidal mode numbers, frequencies and saturation amplitudes has been demonstrated by 3D numerical simulations using the HYM code [18][19][20]. A theoretical analysis of beam-driven CAEs in MAST has also been carried out [8].…”

“…A theoretical analysis of beam-driven CAEs in MAST has also been carried out [8]. A new analytic theory of GAE/CAE excitation has been developed and successfully applied to analyze the simulation results and the experimental observations [19][20][21][22]. In particular, the range of unstable GAE frequencies and recently discovered stabilization of GAEs by the new beam sources in NSTX-U experiments [2] have been explained [19].…”

Benchmarking the Scrape-Off-Layer Fast Ion (SOLFI) particle tracer code in a collisionless magnetic mirror with electrostatic potential drop

“…These fast ions are an important particle, momentum, and energy source for the core plasma [7][8][9][10][11]. They also influence the plasma macroscopic stability through excitation of Alfvén eignemodes [12][13][14][15][16], and through strong interaction with MHD activities [10,[17][18][19]. Because of the interplay between their large orbit sizes and the high mirror ratio inherent to the low aspect ratio ST magnetic geometry, fast ions in STs possess unique transport properties that can be difficult to simulate [20].…”