Vlasov tokamak equilibria with shearad toroidal flow and anisotropic pressure

TL;DR

This paper develops a numerical method to construct Vlasov equilibrium solutions for tokamaks with sheared toroidal flow and anisotropic pressure, revealing bifurcations related to distribution function symmetry.

Contribution

It introduces a novel approach to solve the Vlasov equilibrium problem with anisotropic pressure and flow by reducing it to a Grad-Shafranov-like equation and analyzing bifurcations.

Findings

Equilibria can have peaked or hollow toroidal current densities.

Bifurcation occurs based on distribution function symmetry.

Steady states depend on distribution function deformation.

Abstract

By choosing appropriate deformed Maxwellian ion and electron distribution functions depending on the two particle constants of motion, i.e. the energy and toroidal angular momentum, we reduce the Vlasov axisymmetric equilibrium problem for quasineutral plasmas to a transcendental Grad-Shafranov-like equation. This equation is then solved numerically under the Dirichlet boundary condition for an analytically prescribed boundary possessing a lower X-point to construct tokamak equilibria with toroidal sheared ion flow and anisotropic pressure. Depending on the deformation of the distribution functions these steady states can have toroidal current densities either peaked on the magnetic axis or hollow. These two kinds of equilibria may be regarded as a bifurcation in connection with symmetry properties of the distribution functions on the magnetic axis.