Linear stability of the ITER 15 MA scenario against the alpha fishbone

Abstract

The stability of the n = m = 1 alpha-fishbone kinetic-MHD mode on the ITER 15 MA baseline scenario (ITER Physics Expert Group on Energe Drive and ITER Physics Basis 1999 Nucl. Fusion 39 2471-95) is analyzed using the non-linear hybrid kinetic-MHD code XTOR-K. Quantitative agreement is found between the complex frequencies ω + iγ computed with the linear model in (Brochard G. et al 2018 J. Phys.: Conf. Series 1125 012003) and XTOR-K's linear simulations. Identical precessional resonance positions in phase space are also found between the linear model and XTOR-K. Linear hybrid simulations performed with XTOR-K on the ITER 15 MA scenario reveal that this configuration is likely to be unstable against the alpha fishbone mode. The fishbone thresholds for kinetic-MHD equilibria with flat q profiles with on-axis safety factor just below unity lies between βα,thres/βtot = 6 10%, whereas the expected beta ratio on ITER is βα/βtot = 15 20% (ITER Physics Expert Group on Energe Drive and ITER Physics Basis 1999 Nucl. Fusion 39 2471-95).

En route to realistic modeling of the kinetic-MHD interaction between macroscopic modes and fast particles induced by neutral beam injection in tokamaks

“…The number of particle is integrated over unit surface (x and y directions are subdivided into 100 pieces for the integration). for similar conditions of fast particles of 1 MeV in ITER [20,21]. In this linear study, no resonance is found with passing particles but a resonance with trapped particles destabilize the n = 1 fishbone mode.…”

“…It is likely that the destabilization of fishbones ("fishbone branch" with growth rates increasing with β f p , as observed in Ref. [21]) requires unrealistically large fast particle pressure for this plasma configuration.…”

“…Collision rate and NBI power are enhanced by a factor 10 to obtain in a reasonable time a slowing-down distribution, as explained above. The reason why NBI source #5 is chosen here is that a positive fast particle density gradient ∇n i,f ast > 0 is necessary to obtain the growth of a fishbone mode or the stabilization of a kink mode [20,21]. Otherwise, if a resonance occurs with ∇n i,f ast < 0, no resonant transport is induced and thus the resonance cannot be detected.…”

“…Therefore, as explained in Refs. [20,21], the only resonance available with the n = m = 1 internal kink mode is the precessional resonance characterized by…”

“…For simplicity and for comparisons with the linear model for kink-fishbone stability described in Refs. [20,21], a circular cross-section is chosen. The resolutions taken in radial, poloidal and toroidal directions respectively are: 201, 128 and 32 points.…”