Finding the radial parallel temperature profile in a non-neutral plasma using equilibrium calculations on experimental data

In 1992, Eggleston et al. ͓D. L. Eggleston et al., Phys. Fluids B 4, 3432 ͑1992͔͒ reported on a technique for measuring the radial temperature profile in a pure-electron plasma confined in a Malmberg-Penning trap by partially dumping the plasma onto a charge collector at the end of the trap. For short plasmas and short confining rings, the assumptions in their paper are violated and a more general calculation is needed. This paper presents a variation of the standard equilibrium calculation to find the temperature profile of a pure-electron plasma. Eggleston's shortcut " evaporation " temperature method is found to require a correction factor that can be calculated using methods described in this paper. For typical conditions, the evaporation method overstates the actual temperature by a factor ranging from 1.1 to 1.5 or more, depending on the plasma's total charge and temperature and the geometry of the trap.