  Considering the popularity of two-dimensional particle-in-cell simulations, a
2D model of plasma wakefield in the strongly nonlinear (bubble) regime in
transversely non-uniform plasma is developed. A differential equation for the
boundary of the bubble in the 2D geometry is obtained, its analytic solution is
derived. 2D particle-in-cell simulations are used to confirm the validity of
our model. The results are compared to the bubble in the realistic 3D geometry.
For uniform plasma, it is shown that the 2D bubble is elongated and has
stronger focusing forces, while the structure of the accelerating field remains
completely unchanged. A method of generating a quasi-2D bubble in the realistic
three-dimensional geometry is proposed.
