Simulations of energetic particle driven instabilities in CFQS

Abstract

A nonlinear simulation of the energetic particle driven instabilities in the Chinese First Quasi-Axisymmetric Stellarator (CFQS) has been conducted for the first time. MEGA, a hybrid simulation code for energetic particles interacting with a magneto-hydrodynamic (MHD) fluid, was used in the present work. Both the m/n=3/1 energetic-particle-mode (EPM) like mode and the m/n=5/2 toroidal Alfvén eigenmode (TAE) were found, where m is the poloidal mode number and n is the toroidal mode number. Four important results were obtained as follows. First, the instability in the CFQS in three-dimensional form was shown for the first time. Second, strong toroidal mode coupling was found for the spatial profiles, and it is consistent with the theoretical prediction. Third, the resonant condition caused by the absence of axial symmetry in CFQS was demonstrated for the first time. The general resonant condition is fmode=Nfφ-Lfθ, where fmode, fφ, and fθ are mode frequency, particle toroidal transit frequency, and particle poloidal transit frequency, respectively; N and L are arbitrary integers, represent toroidal and poloidal resonance numbers. For EPM-like mode, the dominant and subdominant resonant conditions are fmode=3fφ-7fθ and fmode=fφ-fθ, respectively. For TAE, the dominant and subdominant resonant conditions are fmode=4fφ-9fθ and fmode=2fφ-3fθ, respectively. On the one hand, the toroidal resonance numbers are different from the toroidal mode numbers by 2. This indicates that the 2-fold rotational symmetry affects the resonance condition. On the other hand, the subdominant resonances satisfy N=n, which is expected for the axisymmetric plasmas and most of the toroidal plasmas including stellarators. Fourth, the nonlinear frequency chirpings in CFQS were demonstrated for the first time. Hole and clump structures were formed in the pitch angle and energy phase space, and the particles comprising the hole and clump were kept resonant with the modes during the mode frequencies chirping.

Effects of the resonance modification by electron cyclotron current drive on the linear and nonlinear dynamics of energetic particle driven magnetohydrodynamics modes in Heliotron J

“…MEGA [19], a hybrid EP-MHD code, has been used to study the linear and nonlinear interactions between EPs and MHD modes in tokamak [20,21], LHD [22], Heliotron J [23,24] (HJ), and CFQS [25]. In MEGA, the MHD plasma is represented by nonlinear MHD equations in cylindrical coordinates, while EP is represented by the drift kinetic equation.…”