Abstract
Pressure anisotropy is a commonly observed phenomenon in tokamak plasmas, due to external heating methods such as neutral beam injection and ion-cyclotron resonance heating. Equilibrium models for tokamaks are constructed by solving the Grad–Shafranov equation; such models, however, do not account for pressure anisotropy since ideal magnetohydrodynamics assumes a scalar pressure. A modified Grad–Shafranov equation can be derived to include anisotropic pressure and toroidal flow by including drift-kinetic effects from the guiding-centre model of particle motion. In this work, we have studied the mathematical well-posedness of these two problems by showing the existence and uniqueness of solutions to the Grad–Shafranov equation both in the standard isotropic case and when including pressure anisotropy and toroidal flow. A new fixed-point approach is used to show the existence of solutions in the Sobolev space
$H_0^1$
to the Grad–Shafranov equation, and sufficient criteria for their uniqueness are derived. The conditions required for the existence of solutions to the modified Grad–Shafranov equation are also constructed.
Funder
Simons Foundation
Australian Research Council
Publisher
Cambridge University Press (CUP)
Reference23 articles.
1. Tokamak plasma equilibrium problems with anisotropic pressure and rotation and their numerical solution
2. Plasma equilibrium with fast ion orbit width, pressure anisotropy, and toroidal flow effects
3. Toroidal Containment of a Plasma
4. Grad, H. & Rubin, H. 1958 Hydromagnetic equilibria and force-free fields. In Proceedings of the Second United Nations International Conference on the Peaceful Uses of Atomic Energy, vol. 31. pp. 190–197. United Nations Publication.
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