Kinetic extensions of magnetohydrodynamics for axisymmetric toroidal plasmas

A nonvariational kinetic-MHD stability code (NOVA-K) has been developed to integrate non-Hermitian integro-differential eigenmode equations due to energetic particles in a general flux coordinate (ψ, θ, ζ) system with an arbitrary Jacobian. The NOVA-K code employs the Galerkin method involving Fourier expansions in the generalized poloidal angle θ and generalized toroidal angle ζ directions, and cubic-B spline finite elements in the radial ψ direction. Extensive comparisons with the existing variational ideal MHD codes show that the NOVA-K code coverages faster and gives more accurate results. We have employed the NOVA-K code to study the effects of energetic particles on MHD type modes: (1) the stabilization of ideal MHD internal kink modes and the excitation of "fishbone" internal kink modes; (2) the α-particle destabilization of toroidicity-induced Alfvén eigenmodes (TAE) via transit and/or trapped particle resonances. Analytical theories are also presented to help explain the NOVA-K results. For energetic trapped particles generated by neutral-beam injection (NBI) and ion cyclotron resonant heating (ICRH) a stability window for the n = 1 internal kink mode in the hot particle beta space exists. On the other hand, the trapped α-particles can resonantly destabilize the n = 1 resonant fishbone mode even for total plasma β value smaller than the β threshold value for the n = 1 ideal internal kink mode. Finally, we show that the TAE modes can be destabilizedby α-particles via inverse Landau damping associated with the spatial gradient of the α-particle pressure with very low α-particle β threshold in the order of 10^-4 for major tokamak DT experiments.