New approach to the problem of Coulomb interaction in electron and ion bunches

The paper is devoted to numerical methods for space charge effects simulation. A fractal pre-ordering technique is proposed to essentially speed up the Coulomb field calculation without somewhat noticeable loss in calculation accuracy for a short enough bunch comprising a big number of charged particles The technique is combined with a special perturbation approach that allows extending the capabilities of the aberration theory in the form of the tau-variation method to efficient numerical evaluation of space charge effects. Some tests and examples illustrating the methods proposed are presented. (C) 2008 Elsevier B. V. All rights reserved