Non-neutral plasma equilibria 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. Analytical and semianalytical solutions for the potential variations inside the trap are found in a paraxial limit of the perturbations for various radial density profiles of the plasma, including the case of global thermal equilibrium. It is shown that a magnetic perturbation produces a potential variation with a sign which is changing along the plasma radius. The fraction of magnetically and electrostatically trapped particles thus created is calculated explicitly for the case of a Maxwellian distribution function, and it is shown to be independent from the sign of the magnetic field perturbation. The analysis of the potential perturbation is extended to the case of an anisotropic distribution function, with an arbitrary ratio between the parallel and the perpendicular plasma temperature. Two-dimensional thermal equilibrium simulations for parameters relevant to the CamV device [A. A. Kabantsev, J. H. Yu, R. B. Lynch, and C. F. Driscoll, Phys. Plasmas 10, 1628 (2003)] confirm the predictions of the analytical theory for smooth and weak perturbations of the magnetic field