Slowing down of ion rings

A study is made of the slowing down of self-consistent, large-orbit ion rings due to small-angle Coulomb scattering in a dense, low-temperature plasma. A kinetic equation is derived for the ion-ring distribution function f(P,I,t), where P is the canonical angular momentum, and I is an adiabatic invariant which is an implicit function of P and the particle energy. The ratio of the time scale for the perpendicular momentum change (diffusion) to that for the parallel momentum change (drag) is m/M, with M the ion mass and m the electron mass. Therefore, drag is the dominant collisional effect, and the slowing down corresponds to incompressible flow in the (P,I) plane. This flow is calculated numerically by computing sequences of equilibria. Initially well-trapped distribution functions are found to have essentially no particle loss during the first slowing-down time tau, which is defined as the time it would take a single ring particle to slow down to zero energy. In most of the cases studied, the rings shrink in both radius and in axial length, with the field reversal increasing by approx. =10% within one tau. The rate of loss of toroidal kinetic energy exceeds the loss of poloidal energy by a factor of typically 1.5--2.0. The self-consistent toroidal electric field opposes the slowing down, increasing the ring life time by 20%--50% over the single-particle slowing-down time