Abstract
A new recursive technique is used for the solution of the equations of motion for charged particles, taking into account the effect of space charge. The paraxial equations are solved for an infinitely long beam with an elliptical cross-section in a static electric field. An effective computer code, based on the method of a continuous generalized analogue of the Gauss brackets and on the method of the envelope matrix, has been written. The code has been used to study the beam dynamics in the injection system of the Pelletron electrostatic accelerator in Lund.
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