Plasma electron fluid motion and wave breaking near a density transition

Recently, Suk, Barov, and Rosenzweig [Phys. Rev. Lett. 86, 1011 (2001)] proposed a scheme for trapping background electrons in a plasma wake field using a sudden downward transition in the background ion density, where the density transition length is small compared to the plasma skin depth. In the present paper we present a fluid dynamical description of this mechanism that is self-consistent up to the point of wave breaking. A one-dimensional nonlinear relativistic second-order differential equation is derived for the electron fluid velocity in Lagrangian coordinates. Numerical integrations of this equation are used to map out the regions of parameter space in which wave breaking occurs and to determine the extent of the downstream region of plasma involved in wave breaking. Comparisons with one-dimensional particle-in-cell (PIC) simulations show that the onset of trapping occurs at the parameter values where wave breaking begins in the fluid analysis, but that the downstream extent of plasma involved in wave breaking is not a reliable predictor of the number of trapped particles. The PIC simulations also reveal that particles initially located on the upstream side of the density transition may become trapped, although these particles do not participate in wave breaking in the fluid description.