Determining critical thermal background density to suppress Alfvén eigenmode growth with gyrokinetics simulations in stellarator and tokamak geometries

This work aims to determine the thermal background density for which Alfvén eigenmodes (AEs) are suppressed. AEs resonate with energetic particles in a fusion reactor, degrading confinement [1]. We aim to determine thermal background densities that maintain a fixed fusion power while limiting AE growth. Since AEs have high mode numbers at reactor scale [2], they can be sufficiently localized within a flux tube geometry.

We use the GX [3] code to model AEs. GX solves the gyrokinetic equation, evolving the distribution function of kinetic electrons, ions, and alphas influenced by AEs. In linear simulations, we compute growth rates and evaluate the linear threshold density gradient across thermal background densities. In nonlinear simulations, we compute heat and particle fluxes to determine the critical gradient that prevents saturation in the flux tube domain. Results for linear and nonlinear simulations have been benchmarked against existing work for a tokamak geometry [5]. We analyze the cyclone base case in the Miller geometry as well as simulations in various stellarator equilibria to inform the geometry dependence of the critical density.

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[2] Gorelenkov, N.N. et al (2014) Nucl. Fusion, 54

[3] Mandell, N. R. et al (2024) JPP, 90 (4)

[4] Barnes, M. et al (2010) Phys. Plasmas 17 (5)

[5] Bass, E. M. & Waltz, R. E. (2010) Phys. Plasmas, 17 (11)

[6] Spong, D. A. et al (1992) Phys. Fluids B, 4 (10)