Equilibrium of charged plasmas with weak axisymmetric magnetic perturbations

The effect of weak axisymmetric magnetic and/or electrostatic perturbations on the equilibrium of a non-neutral plasma in a Malmberg-Penning trap is analyzed. A semi-analytic solution for the potential variations inside the trap is found in a paraxial limit of the perturbations for the case of global thermal equilibrium. The fraction of magnetically and electrostatically trapped particles is calculated for a bi-Maxwellian distribution function.