Transport induced by symmetry breaking in a nonneutral plasma

Small asymmetries of the confining electric and magnetic fields pose an upper limit on the lifetime of nonneutral plasmas trapped in Malmberg-Penning traps. The present paper reviews the effect of magnetic and electric field errors on the equilibrium of nonneutral plasma based on a suitable parallel current constraint. Together with Poisson's equation, this constraint provides a full set of equations for determining self-consistent asymmetric equilibria of non-neutral plasmas in a Malmberg-Penning trap. Using this approach, the effect on the plasma equilibrium of weak magnetic and electric squeezes (field errors with azimuthal number m=0), tilt (m=1) and quadrupole (m=2) distortions is investigated. Analytical and semi-analytical solutions for the electric potential variation inside the trap are found in a paraxial limit for various radial density profiles of the plasma, including the case of global thermal equilibrium. A direct analog of the Pfirsch-Schlüter and Stupakov currents is also derived. The presented theory of the plasma equilibrium distorted by field errors provides the basis for elaborating a self-consistent theory of the asymmetry induced transport in a Malmberg-Penning trap.