Identifying the source of super-high energetic electrons in the presence of pre-plasma in laser-matter interaction at relativistic intensities

The generation of super-high energetic electrons influenced by pre-plasma at relativistic intensity laser-matter interaction is studied in a one-dimensional slab approximation with particle-in-cell simulations. Different pre-plasma scale-lengths of $1\mu \text{m}$, $5\mu \text{m}$, $10\mu \text{m}$ and $15
\mu$\text{m}$$ are considered, showing an increase in both particle number and cut-off kinetic energy of electrons with the increase of pre-plasma scale-length, and the cut-off kinetic energy greatly exceeding the corresponding laser ponderomotive energy. A two-stage electron acceleration model is proposed to explain the underlying physics. The first stage is attributed to the synergetic acceleration by longitudinal electric field and laser pulse, with its efficiency depending on the pre-plasma scale-length. These electrons pre-accelerated in the first stage could build up an intense electrostatic potential barrier with its maximal value several times as large of the initial electron kinetic energy. Part of energetic electrons could be further accelerated by the reflection off the electrostatic potential barrier, with their finial kinetic energies significantly higher than the values pre-accelerated in the first stage.