  In the past, calculation of wakefields generated by an electron bunch
propagating in a plasma has been carried out in linear approximation, where the
plasma perturbation can be assumed small and plasma equations of motion
linearized. This approximation breaks down in the blowout regime where a
high-density electron driver expels plasma electrons from its path and creates
a cavity void of electrons in its wake. In this paper, we develop a technique
that allows to calculate short-range longitudinal and transverse wakes
generated by a witness bunch being accelerated inside the cavity. Our results
can be used for studies of the beam loading and the hosing instability of the
witness bunch in PWFA and LWFA.
