Certain developments on the equilibrium of magnetized plasmas

TL;DR

This paper presents new theoretical and computational developments in the equilibrium analysis of magnetized plasmas, including generalized equations, extended codes, and Hamiltonian formulations for various plasma configurations.

Contribution

It introduces a generalized Grad-Shafranov equation for helically symmetric plasmas with anisotropy and flow, extends the HELENA code for such conditions, and formulates Hamiltonian methods within extended MHD for equilibrium derivation.

Findings

Derivation of a generalized Grad-Shafranov equation for anisotropic, flowing plasmas.

Extension of the HELENA code to include pressure anisotropy and flow parallel to magnetic fields.

Development of Hamiltonian formulations and Energy-Casimir principles for extended MHD equilibria.

Abstract

Recent results will be presented on steady states of magnetically confined plasmas obtained by conventional and Hamiltonian methods. The presentation consists of three parts. The first one concerns the derivation of a generalized Grad-Shafranov equation describing helically symmetric equilibria with pressure anisotropy and incompressible plasma flow of arbitrary direction with application to straight-stellarator configurations [1]. The impact of pressure anisotropy and flow on the equilibrium characteristics is also examined. In the second part the axisymmetric equilibrium code HELENA is extended for pressure anisotropy and flow parallel to the magnetic field and ITER-pertinent equilibria are constructed. In the third part the Hamiltonian formulation of helically symmetric plasmas is established within the framework of extended MHD, a simplified two-fluid model including Hall-ion and electron-inertia contributions [2,3]. Four families of Casimir invariants are obtained and they are used to construct Energy-Casimir variational principles for deriving generalized extended MHD equilibrium equations with arbitrary flow. The system is then cast into the form of Grad-Shafranov-Bernoulli equations. In addition, an example of an incompressible double-Beltrami equilibrium will be presented in connection with a straight-stellarator configuration.