High-resolution magnetohydrodynamic equilibrium code for unity beta plasmas

• Published in: Journal of computational physics Vol. 216; no. 1; pp. 275 - 299
• Main Authors: Gourdain, P.-A., Leboeuf, J.-N., Neches, R.Y.
• Format: Journal Article
• Language: English
• Published: Amsterdam Elsevier Inc 20-07-2006; Elsevier
• Subjects: Beta; Computational techniques; Convergence; Equilibrium; Exact sciences and technology; High; Magnetic properties; Magnetohydrodynamics; Mathematical methods in physics; Mathematical models; Multigrid; Physics; Plasma; Plasmas; Shafranov; Simulated annealing; Stability; Tokamak; Unity; Tokamak; High; Plasma; Magnetohydrodynamics; Unity; Multigrid; Shafranov; 65N55; Equilibrium; Beta; Algorithms; Positions; Magnetohydrodynamics; Plasma; Tokamak; High; Beta; Unity; Equilibrium; Multigrid; Shafranov; Calculation; MHD equilibrium; Current density; Calculation methods
• ISSN: 0021-9991; 1090-2716
• DOI: 10.1016/j.jcp.2005.12.005

There is great interest in the properties of extremely high-β magnetohydrodynamic equilibria in axisymmetric toroidal geometry and the stability of such equilibria. However, few equilibrium codes maintain solid numerical behavior as beta approaches unity. The free-boundary algorithm presented herein utilizes a numerically stabilized multigrid method, current density input, position control, magnetic axis search, and dynamically adjusted simulated annealing. This approach yields numerically robust behavior in the spectrum of cases ranging from low to very high-β configurations. As the convergence time depends linearly on the total number of grid points, the production of extremely fine, low-error equilibria becomes possible. Such a code facilitates a variety of intriguing applications which include the exploration of the stability of extreme Shafranov shift equilibria.