Kinetic construction of the high-beta anisotropic-pressure equilibrium in the magnetosphere

Abstract

A theoretical model of the high-beta equilibrium of magnetospheric plasmas was constructed by consistently connecting the (anisotropic pressure) Grad-Shafranov equation and the Vlasov equation. The Grad-Shafranov equation was used to determine the axisymmetric magnetic field for a given magnetization current corresponding to a pressure tensor. Given a magnetic field, we determine the distribution function as a specific equilibrium solution of the Vlasov equation, using which we obtain the pressure tensor. We need to find an appropriate class of the distribution function for these two equations to be satisfied simultaneously. Here, we consider the distribution function that maximizes the entropy on the submanifold specified by the magnetic moment. This is equivalent to the reduction of the canonical Poisson bracket to the noncanonical one having the Casimir corresponding to the magnetic moment. The pressure tensor then becomes a function of the magnetic field (through the cyclotron frequency) and flux function, satisfying the requirement of the Grad-Shafranov equation.

Axisymmetric hybrid Vlasov equilibria with applications to tokamak plasmas

“…It remains an open question whether and under what conditions, additional, approximate constants of motion exist within the framework of full-orbit Vlasov description (see [19] and references therein for a discussion on the existence of an approximate third integral of motion in axisymmetric potentials). In certain scenarios, it may be pertinent to consider adiabatic constants, such as the magnetic moment µ as explored in [20]. It is worth noting that in the context of the hybrid model and the present analysis, some assumptions made in [20], such as p ϕ ≈ ψ, can be justified due to the presence of the significant d −2 i factor, especially in systems like the magnetosphere.…”

“…In certain scenarios, it may be pertinent to consider adiabatic constants, such as the magnetic moment µ as explored in [20]. It is worth noting that in the context of the hybrid model and the present analysis, some assumptions made in [20], such as p ϕ ≈ ψ, can be justified due to the presence of the significant d −2 i factor, especially in systems like the magnetosphere. However, in this paper, which focuses on laboratory plasmas, we will not adopt this assumption.…”