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.