Time dependent analysis of short-range monopole wake fields driven by accelerated electron beams

Combinations of integral transforms and Greenʹs function are employed in order to obtain the distribution of the short-range monopole wake fields driven by accelerated electron beams in a cylindrical cavity. This constituted an alternative but simpler and more versatile method to the normal mode expansion which we used earlier to solve for such a distribution (Salah and Dolique, Nucl. Instr. and Meth. A 431 (1999) 27). Whereas direct comparisons of the resulting analytical expressions are found difficult to directly compare, numerical illustration of results obtained from both approaches show excellent agreements and hence confirm the fact that both approaches are equivalent.