Ponderomotive acceleration and the supra-bubble regime for electrons in tenuous plasmas

In the present work, we study electron acceleration via interaction with ultraintense laser pulses in tenuous plasma. For electrons injected inside a pulse with arbitrary momenta, we demonstrate different regimes of ponderomotive acceleration and show that plasma dispersion affects this process at densities $n/n_c>a_0^{-4}$, where $n_c$ is the critical plasma density, and $a_0=eA/mc^2$ is the normalized laser amplitude, which we assume much larger than one. For a cold electron beam, the so-called \textit{supra-bubble} acceleration is studied, when electrons are pushed by a moving ponderomotive potential \textit{ahead} of the wakefield potential. In this case, the maximum energy gain, $\gamma\propto a_0\gamma_g$, is attained when the particle Lorentz factor $\gamma$ is initially about $\gamma_g/a_0$, where $\gamma_g$ is the pulse group speed Lorentz factor. The supra-bubble acceleration scheme operates at $\gamma_g\geq a_0$ and yields energies comparable to those attained through conventional wakefield acceleration for the same plasma and laser parameters.