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

Abstract

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.

Stellarator and tokamak plasmas: a comparison

“…Here ψ measures the toroidal flux and α = θ − ιϕ labels the different field lines on each flux surface. A configuration with vanishing bounce-averaged drift, ∂J/∂α = 0, is called omnigenous [44], and if the contours of constant magnetic field strength are poloidally, but not toroidally, closed one speaks of quasi-isodynamic configurations [45,46]. W7-X is the first stellarator to approach quasi-isodynamicity (close to the axis at high beta) but substantially more quasi-isodynamic designs have been found in recent years [47], although exact quasi-isodynamicity is impossible to achieve [48].…”

Intrinsic Ambipolarity and Rotation in Stellarators

“…Quasisymmetry is a special case of omnigeneity, which means that there is no net (timeaveraged) drift of particles off flux surfaces [12][13][14]. Omnigenous configurations therefore have low neoclassical transport, but it is not immediately clear whether they can support plasma rotation.…”

Radial drift invariant in long-thin mirrors

“…... , where primes refer to differentiation with respect to z, we also find that 1,2 A are determined by…”

“…Oscillatory "banana" excursions from a magnetic surface is tolerable, but an average radial drift would quickly ruin the confinement. The concept of omnigenity was introduced by Hall and McNamara [1] to analyze the radial particle confinement in mirror machines by a bounce averaged procedure. In their approach, omnigenity is determined in an average sense [2], allowing for oscillatory guiding center excursions from a given magnetic surface.…”