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