Three-dimensional equilibrium of the anisotropic, finite-pressure guiding-center plasma: Theory of the magnetic plasma

Theoretical and numerical methods now give a complete solution to the problem of finite-β plasma equilibrium in mirror magnetic wells and toroidal devices. The equilibria can be made consistent on all of the progressively longer time scales of the guiding-center fluid model, including the particle magnetic drifts and the Coulomb scattering equilibrium of a neutral injected plasma. The theory of equilibrium in the guiding-center fluid model of a finite-β plasma with an arbitrary, anisotropic pressure tensor can be formulated as a classical magnetostatic system: ∇⋅B = 0, ∇×H = 0, B = H + 4πM(B). The plasma magnetization is found explicitly in terms of three physically distinct components related to the laws of conservation of magnetic moment, of longitudinal invariant, and of the sign of the velocity along B of particles that do not undergo mirror reflection. A condition is derived upon the field geometry whereby a large class of special equilibria can be found in which all particles on a given line drift on the same surface, the omnigenous surface. Such systems allow a specially simple connection between particle and fluid models in the guiding-center fluid theory. The usefulness of the theory is exemplified by application to the problem of a finite-β plasma in a magnetic well. Finally, a brief treatment of stability in terms of the energy principle is given. The omnigenous equilibria have particularly simple stability criteria.