Calculation of finite-length hollow-beam equilibria [particle beams and plasma]

Finite-length equilibria occur in a number of intense-beam and plasma applications. Penning traps permit the study of intra-beam collective effects, as the additional freedom gained from having an internal conductor permits greater control over the plasma profile, so that monotonic, but not constant, plasma profiles can be obtained. On the basis that the thermal velocity of background neutrals and the drift velocity of the electrons are much lower than the thermal velocity of the electrons, and the rotation frequency is small compared to the gyrofrequency, the equilibrium equation can be reduced to a self-consistent Poisson equation where the source depends on the potential. We solve for these equilibria using a Gauss-Seidel relaxation method. Our results show the shape of the equilibria for various electrode configurations