Generalised model of a sheath of a plasma bubble excited by a short laser pulse or by a relativistic electron bunch in transversely inhomogeneous plasma

An analytical model of a plasma bubble (a wake wave in the strongly nonlinear regime) in transversely inhomogeneous plasma is generalised to an arbitrary profile of an electron sheath at its boundary. Within the framework of this generalisation we have found the potential within the bubble and shown that its envelope is described by a second-order equation, similar to the equation of a less general theory. We have also determined the domain of parameters at which this equation is considerably simplified and no longer depends on the profile of the electron sheath.