In the past, calculation of wakefields generated by an electron bunchpropagating in a plasma has been carried out in linear approximation, where theplasma perturbation can be assumed small and plasma equations of motionlinearized. This approximation breaks down in the blowout regime where ahigh-density electron driver expels plasma electrons from its path and createsa cavity void of electrons in its wake. In this paper, we develop a techniquethat allows to calculate short-range longitudinal and transverse wakesgenerated by a witness bunch being accelerated inside the cavity. Our resultscan be used for studies of the beam loading and the hosing instability of thewitness bunch in PWFA and LWFA.
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