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Considering the popularity of two-dimensional particle-in-cell simulations, a2D model of plasma wakefield in the strongly nonlinear (bubble) regime intransversely non-uniform plasma is developed. A differential equation for theboundary of the bubble in the 2D geometry is obtained, its analytic solution isderived. 2D particle-in-cell simulations are used to confirm the validity ofour 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 hasstronger focusing forces, while the structure of the accelerating field remainscompletely unchanged. A method of generating a quasi-2D bubble in the realisticthree-dimensional geometry is proposed.

Bubble regime of plasma wakefield in 2D and 3D geometries