Fields, focusing, and aberration in electrostatic accelerator tubes

Electrostatic field distributions and particle trajectories have been computed using a standard software package for a number of geometries typical of the accelerator tubes used in modern electrostatic accelerators. The results have been used to confirm the validity of approximate formulae for the focusing action of the entrance and exit lens and to determine the effect of lens aberrations on the subsequent emittance and brightness of the beam. Nonuniform field distributions in the interior of the tube, due to finite electrode thickness, have been calculated for a range of parameters and the action of these fields on typical particle trajectories examined. Full three-dimensional finite-element calculations have been applied to the inclined-field geometries that are used to suppress secondary electrons in high-voltage systems. Particle trajectories through such tubes show the expected first-order deflections but higher order effects are shown to be small in typical designs.