Plasma Wall Potentials with Secondary Electron Emissions up to the Stable Space-Charge-Limited Condition

Numerical solutions to floating plasma potentials for walls emitting secondary elec- trons are obtained for various surface materials. The calculations are made with plasma moment equations and the secondary electron emission coefficients, which were determined from recent lab- oratory experiments. The results estimate the wall potentials up to the physical conditions that allow stable plasma sheaths under the space-charge-limited condition. The materials often used in the laboratory, such as aluminum, silicon, boron, molybdenum, silicon dioxide, and alumina, are considered. The minimum wall potential before the onset of space-charge-limited emission is determined by the electron temperatures at which the effective secondary electron emission coefficient integrated over the velocity distributions is about 0.62. The corresponding potential is given by −eφ 0 ∼ 1.87k B T. The condition for space-charge-limited emission is newly found by numerically searching for all the stable sheaths. The new condition is −eφ 0 ∼ 0.95k B T, and this predicts a wall potential that is less negative than the previously found one. Calculation of the power dissipated to the wall for hydrogen plasmas shows that there is a large difference in terms of power dissipation among the considered materials in the temperature range 20∼50 eV.