Delta-layer model for the boundary of a bubble excited by an electron bunch or laser pulse in a plasma channel

We present an analytical model of a plasma bubble excited by a relativistic electron bunch or a high-power laser pulse moving in the plasma, with allowance for a surrounding thin electron layer (delta-layer). It is shown that in calculations of accelerating and focusing fields, the electron layer at the bubble boundary, provided the layer thickness is small enough, can be considered as two-dimensional and consisting of surface charges and currents. This model is compared with the bubble model having a finite thickness of the electron layer, and it is shown that the parameter region, within which our model is valid, is small compared to the region where the effect of finite thickness is significant. On the other hand, the proposed model, representing the simplest model of a bubble in a transversely inhomogeneous plasma, allows the transition to a model with a finite thickness of the electron layer by means of changing the scales of coordinates.