High order calculation of the multipole content of three dimensional electrostatic geometries

An accurate and simple method is presented for 3-D multipole decomposition of the field of arbitrary electrode geometries. The induced charge on the surface is obtained by inverting the capacity matrix. The multipole moment decomposition of the resulting potential is readily accomplished using differential algebra methodology. The method is applied to the focusing lattice geometry of the MBE-4 accelerator at Lawrence Berkeley Laboratory. Multipole terms of up to the order 5 are computed, and a numerical accuracy of <1% is obtained. The effective quadrupole and dodecapole field strengths are in good agreement with previous results.<>