Structure of two-dimensional plasma crystals in anharmonic Penning traps

Abstract

This paper derives an analytic expression for the density per unit area of charges confined in a two-dimensional configuration in a Penning trap with an anharmonic applied trap potential that is expressed as a multipole expansion. This expression is used to find the optimum potential, with a given number of multipoles, for trapping a plasma with the most uniform possible density per unit area. Minimum energy states in such an optimized trap potential are evaluated numerically and the resulting crystal structures are shown to be defect-free over the central region of the plasma where the density is most nearly uniform. The paper also briefly considers the possibility of using an $\ensuremath{\ell}=3$ rotating wall trap potential in order to confine minimum energy states with triangular symmetry and no defects.