Some Toroidal Equilibria for Plasma under Magnetoelectric Confinement

Abstract

A powerful negative bias tends to arise spontaneously by the loss, from a toroidal plasma, of suprathermal ions such as Ohmic or cyclotron heating runaway ions or fusion-product protons and alpha particles, whose Larmor radius is vastly larger than that of the electrons also scraped off at the limiting plasma aperture. By this mechanism, strong ion-confining electric fields may be expected to appear at the plasma surface in all toroidal configurations including stellarators, tokamaks, floating rings, etc. Electrons, restricted to their surfaces of constant total energy, are then also confined. A drift-kinetic description is given of a neutral plasma under such “magnetoelectric confinement” for the interesting special case of purely toroidal magnetic field (i.e., symmetric torus with zero rotational transform). Particle diffusion and the approach to quasisteady state with ambipolar particle loss are discussed. Particular attention is paid to the construction of a two-parameter family of equilibria with density profiles approximating those which, in the succeeding paper, are found favorable to stability.