  Based on a model of plasma wakefield in the strongly nonlinear (bubble)
regime, we develop a lowest-order perturbation theory for the components of
electromagnetic fields inside and outside the bubble using the assumption of
small thickness of the electron sheath on the boundary of the bubble. Unlike
previous models, we derive simple explicit expressions for the components of
electromagnetic fields not only in the vicinity of the center of the bubble,
but in the whole volume of the bubble (including areas of driving or
accelerated bunches) as well as outside it. Moreover, we apply the results to
the case of radially non-uniform plasma and, in particular, to plasma with a
hollow channel. The obtained results are verified with 3D particle-in-cell
(PIC) simulations which show good correspondence to our model.
