Dynamics of a fast bunch of charged particles in a plasma

The dynamics of a one-dimensional bunch of charged particles injected into a cold plasma is analyzed in the hydrodynamic approximation. In contrast with the approximation of a specified bunch, the inverse effect of the electric field produced by the bunch in the plasma on the bunch itself is taken into account. An approximate solution is derived for this self-consistent problem, which describes the stage of the bunch dynamics before the onset of turbulence. Equations are derived which describe the evolution of the electric field, of the charge density in the bunch, and of the energy loss per unit time per unit path length traversed by the bunch. The two latter quantities are shown to be different when the inverse effect of the field on the bunch is taken into account. The energy loss of the bunch in this stage in the plasma is less than the loss of the same bunch in vacuum. Since the electrons of the bunch undergo a relativistic increase in mass, while the plasma electrons do not, a plasma nonlinearity contributes substantially to the expression for the bunch charge density and for the energy loss. If the bunch consists of ions, this contribution dominates in all the equations