Evolution of equilibrium particle beams in plasma under external wakefields

A beam of ultrarelativistic charged particles in a plasma can reach equilibrium with its own radial wakefield and then propagate little change shape. If some co-moving perturbation appears ahead the beam, it may or not destroy wakefield, depending on phase amplitude wakefield. We numerically study which perturbations single short bunch train many bunches at parameters interest for acceleration an axysimmetric configuration, how fast. find that there are particularly dangerous phases be destroyed by very low amplitude. also larger than always destructive.