Electron acceleration in a relativistic electron plasma wave

Abstract
The acceleration of electrons in a relativistic electron plasma wave is computed analytically and numerically. The electron acceleration is first computed as an expansion in powers of the electric field amplitude. A relation between the first- and second-order terms is derived, which corresponds to the relativistic Landau damping effect. Energy conservation in the wave frame enables one to obtain the maximum energy gain for a given injection energy. Optimum lengths are similarly calculated.