Analytical field-reversed equilibria derived from self-consistent particle orbits – Part I

An analytical approach to the calculation of a special class of field-reversed plasma equilibria is presented. The equilibria analysed are those of an infinite cylindrical plasma layer consisting of monoenergetic ions of fixed canonical angular momentum and 'cold' space-charge-neutralizing electrons immersed in a uniform field. An equation for the self-consistent orbits of the ions is derived and solved for field-reversing (and field-enhancing) equilibria characterized by the dimensionless parameters a/a₀, ratio of plasma outer radius to ion gyroradius in the vacuum field, and s/a, ratio of inner to outer plasma radius. It is shown that field reversal is not possible for a/a₀ < 2.0; strong field reversal requires both a/a₀≫2.0 and s/a≪1.0. The analytical approach is then generalized to permit the inclusion of additional particle groups (ions or energetic electrons) and/or base fields with a radial gradient. Applications of the generalized solutions are to be discussed in a subsequent paper.