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We propose a new method for analytical self-consistent description of theexcitation of a strongly nonlinear wakefield (a bubble) excited by an electronbunch. This method makes it possible to calculate the shape of the bubble andthe distribution of the electric field in it based only on the properties ofthe driver, without relying on any additional parameters. The analyticalresults are verified by particle-in-cell simulations and show goodcorrespondence. A complete analytical solution for cylindrical drivers andscaling laws for the properties of the bubble and other plasma acceleratorparameters depending on the bunch charge and length are derived.

Excitation of strongly nonlinear plasma wakefield by electron bunches