Flow-Induced New Channels of Energy Exchange in Multi-Scale Plasma Dynamics – Revisiting Perturbative Hybrid Kinetic-MHD Theory

Abstract

It is found that new channels of energy exchange between macro- and microscopic dynamics exist in plasmas. They are induced by macroscopic plasma flow. This finding is based on the kinetic-magnetohydrodynamic (MHD) theory, which analyses interaction between macroscopic (MHD-scale) motion and microscopic (particle-scale) dynamics. The kinetic-MHD theory is extended to include effects of macroscopic plasma flow self-consistently. The extension is realised by generalising an energy exchange term due to wave-particle resonance, denoted by δ WK. The first extension is generalisation of the particle’s Lagrangian, and the second one stems from modification to the particle distribution function due to flow. These extensions lead to a generalised expression of δ WK, which affects the MHD stability of plasmas.

Impact of hot particles on resistive wall mode stability in rotating high-beta plasmas

“…where the last term indicates the bulk plasma rotation. The first term in the last equation can be numerically computed by invoking the equilibrium distribution function (7). We would assume V hφ ∼ V h for simplicity, which would be reasonable for hot particles by tangential NBI.…”

“…As seen in equation ( 3), the perturbed total pressure tensor P (1) (resultantly δW K ) depends on f (1) , which is governed by the linearized driftkinetic equation. The nonadiabatic part of the solution to the linearized drift kinetic equation reads [1,5,7,10]…”

“…Here Y l 0 is associated with the conventional perturbed guiding center Lagrangian L 1 , and Y l 1 and Y l 2 are related to the per turbed guidingcenter Lagrangians including the Coriolis (L 2 ) and centrifugal (L 3 ) forces, respectively. Additionally, modification to the equilibrium distribution function (only for bulk particles) leads to generalization of the resonance frac tion λ l → λ l0 + λ l1 , where λ l0 is almost the same as the con ventional one, and λ l1 is a new fraction including the radial derivative d/dr [7]. We remark that the resonant fraction λ l contains the growth rate and real frequency of RWMs, γ and ω r ; however, these are ignored in the present formulation.…”

“…To study the kinetic effects of hot particles on RWM stability, we extend the MINERVA/RWMaC code [13], which consists of a linearized ideal MHD solver equipped with vacuum and wall solvers. A module to compute δW K for bulk particles was developed and has been implemented in the MINERVA/ RWMaC code [7]. This module is modified for the computa tion of the hot particles.…”

“…However, all the above theor etical studies [1,4,5] are based on the hybrid kineticMHD model without plasma rotation. Recently, we have extended the hybrid kineticMHD model to include selfconsistent bulk rotation effects [6,7]. By the term 'selfconsistent', we mean that such rotational effects on the guidingcenter motion as Coriolis and centrifugal accelerations are included, while they are not considered in the previous model.…”