Analysis of beam loading in electrostatic columns

A lumped element circuit model is derived which accounts for both electric and magnetic coupling of the beam to the electrodes and drive circuitry of an electrostatic column. A modified one dimensional Poisson equation which incorporates two dimensional effects is discussed. An effective capacitance between the beam and the column electrodes which affects the electric coupling is estimated. Simple analytic cases which treat electric and magnetic coupling separately are solved and compared against a numerical simulation. Scaling laws are given for the magnitude of the beam loading. >