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