Equilibrium and Stability of Plasma in Arbitrary Mirror Fields

Abstract

It is shown that an appropriate choice of variables can greatly simplify the discussion of equilibrium and stability of low-pressure plasma in arbitrary mirror fields. One specifies by α and β the line of force on which a particle is moving and also specifies its adiabatic invariants μ, J; the energy of the particle is then determined as a function K(μ, J, α, β) which plays the role of a Hamiltonian. Any equilibrium distribution can then be written in the form F {μ, J, K(α, β, μ, J)} and it is shown that a sufficient criterion for such distributions to be stable against interchanges is (∂F/∂K)μJ < 0. Necessary and sufficient criteria are also derived. When approached in this way, the exact form of the field configuration only enters the problem through the determination of the function K, which may be easily calculated. In general a comprehensive view of plasma behavior, convenient for the discussions of equilibrium, confinement and stability, can be obtained from the structure of the K(α, β, μ, J) = constant contours. An example of the application of this approach to a Ioffe stabilized mirror is described. This confirms the existence of stable plasma equilibria in this field configuration.