Calculation of large-aspect-ratio tokamak and toroidally-averaged stellarator equilibria of high-beta reduced magnetohydrodynamics via simulated annealing

Abstract

A simulated annealing (SA) relaxation method is used for calculation of high-beta reduced magnetohydrodynamics (MHD) equilibria in toroidal geometry. The SA method, based on artificial dynamics derived from the MHD Hamiltonian structure, is used to calculate equilibria of large-aspect-ratio and circular-cross-section tokamaks as well as toroidally averaged stellarators. Tokamak equilibria including incompressible poloidal rotations are obtained and the Shafranov shift is seen to increase nearly quadratically in the rotation speed. A mapping procedure between non-rotating and poloidally rotating equilibria is shown to explain a quadratic dependence of equilibria shift on rotation. Calculated stellarator equilibria are seen to agree reasonably with previous results. The numerical results demonstrate the first successful application of the SA method to obtain toroidal equilibria.

arXiv commentsubmitted to Physics of Plasmas

References in corpus (4)

• Structure and structure-preserving algorithms for plasma physics
• Hamiltonian magnetohydrodynamics: symmetric formulation, Casimir invariants, and equilibrium variational principles
• Ideal magnetohydrodynamic equilibria with helical symmetry and incompressible flows
• Simulated annealing for three-dimensional low-beta reduced MHD equilibria in cylindrical geometry

Cited by in corpus (5)

• A Collision Operator for Describing Dissipation in Noncanonical Phase Space
• Dissipative Brackets for the Fokker-Planck Equation in Hamiltonian Systems and Characterization of Metriplectic Manifolds
• Relaxation to magnetohydrodynamics equilibria via collision brackets
• Linear stability analysis via simulated annealing and accelerated relaxation
• A Reduced Ideal MHD System for Nonlinear Magnetic Field Turbulence in Plasmas with Approximate Flux Surfaces