Kinetic theory of ion ring compression

A general kinetic theory is developed for the adiabatic compression of ion rings, and associated plasma, in an external magnetic mirror field Be(t). The single particle distribution function is shown to be given by f (ℋ,𝒫ϑ,t) =F (I,𝒫ϑ) during axisymmetric compression in the absence of instabilities and under conditions where the particle motion is ergodic in the poloidal (r,z) plane. Here, ℋ and 𝒫ϑ are the energy and canonical momentum of a ring ion; I (ℋ,𝒫ϑ) is an adiabatic invariant involving an average over the region of the poloidal plane accessible to a particle with constants ℋ and 𝒫ϑ; and F is an invariant function. A complete description of ring compression is obtained from F, which gives the ring current density Jbϑ, from an appropriate constitutive relation for the plasma response, which gives the plasma current density Jpϑ, and from Ampère’s law. The theory is valid for rings of arbitrary aspect ratio, the particle orbits are essentially unrestricted, and account is taken of ring particle evaporation. A general analysis is made of energy and angular momentum conservation during compression. In particular, the total power input and the power absorbed are derived in terms of the magnetic moment of the ring-plasma system, M (Be).