Numerical simulations of global Alfvén eigenmodes excitation and stabilization in NSTX-U

Abstract

Three-dimensional nonlinear simulations of Alfvén eigenmodes in the subcyclotron frequency range show a robust physical stabilizing mechanism via modest off-axis beam injection, in agreement with experimental observations from the National Spherical Torus Experiment (NSTX-U). Experimental results from NSTX-U have demonstrated that neutral beam injection from the new beam sources with large tangency radii deposits beam ions with large pitch, which can very effectively stabilize all unstable Global Alfvén Eigenmodes (GAEs). Beam-driven GAEs have been linked to enhanced electron transport in NSTX, and the ability to control these modes will have significant implications for NSTX-U, ITER, and other fusion devices where super-Alfvénic fast ions might be present. Nonlinear simulations using the HYM code have been performed to study the excitation and stabilization of GAEs in the NSTX-U right before and shortly after the additional off-axis beam injection. The simulations reproduce the experimental finding, namely, it is shown that off-axis neutral beam injection reliably and strongly suppresses all unstable GAEs. Before additional beam injection, the simulations show unstable counter-rotating GAEs with toroidal mode numbers and frequencies that match the experimentally observed modes. Additional off-axis beam injection has been modeled by adding beam ions with large pitch and varying density. The complete stabilization occurs at less than 7% of the total beam ion inventory. New analytical theory of GAE (de)stabilization has also been derived, suggesting a different interpretation for the GAE stabilization mechanism compared to previous publications.

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

“…The global Alfvén eigenmodes in these simulations appeared in two flavors: co-and counter-propagating rela- δB in the core where the fluctuation was largest, and their dispersion which generally scaled with the shear Alfvén dispersion ω ∝ k v A . Counter-GAEs were routinely observed in NSTX 7 and NSTX-U 9 experiments with these basic characteristics, and previous comparisons between HYM simulations and experimental measurements have revealed close agreement between the frequency of the most unstable counter-GAE for each n. 34 All counterpropagating modes which appeared in these simulations were determined to be GAEs, even though cntr-CAEs have also been observed in NSTX experiments. 7 This may be attributed to the initial value nature of these simulations, which are dominated by the most unstable mode.…”

“…Notably, the effect of finite injection energy of NBI distributions is included consistently, yielding a previously overlooked instability regime. 34 Terms to all orders in ω/ω ci , k /k ⊥ , and k ⊥ ρ ⊥b are kept for applicability to the entire possible spectrum of modes. Analysis was restricted to 2D velocity space, neglecting the influence of plasma non- uniformities.…”

“…A detailed simulation study of multi-beam effects on CAE/GAE stability is a compelling next step, especially when considering the very robust stabilization of GAEs found with the off-axis, tangential beam sources on NSTX-U. 9,34,56 While this paper focused on the influence of fast ion parameters, the stability properties also depend on the equilibrium profiles, which could be explored in future work. Development of a complete nonlocal analytic theory including both fast ion drive and relevant background damping sources would be the next step forward for the local theory used here which works well qualitatively but does not give reliable values for the total growth rate.…”

“…In reality, ∆λ increases at lower energies due to pitch angle scattering, as accounted for in Ref. 34, but this effect was not included in this study. Characteristic profiles of beam density calculated by the global transport code TRANSP 35 and Monte Carlo fast ion module NUBEAM 36 motivate the ad-hoc form of f 3 (p φ , v).…”

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].…”