Series solution for the image charge fields in arbitrary cylindrically symmetric Penning traps

This paper presents a series solution to the image charge fields of a single ion in a Penning trap. The calculation of these fields and resulting frequency shifts will be important for advances in a variety of high precision Penning trap studies, particularly for work with highly charged ions. The simple technique is applicable to cylindrically symmetric traps of otherwise arbitrary geometry and provides an efficient alternative to finite grid relaxation techniques. The present calculation is in agreement with previous measurements in a hyperbolic trap, and systematic frequency shifts for recent atomic mass measurements using multiply charged ions are given.