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Collimation and acceleration of mono-energetic electron beams in Laser Plasma accelerators

Motivated by rapid advances in plasma based accelerators, we propose a simple mechanism for the production of highly collimated quasi monochromatic electrons beams. By considering Compton scattering of electrons (in the plasma) with virtual photons -- through an effective interaction --- we demonstrate angular collimation with a divergence less than 3 mrad quasi mono-energetic nature of the beam and an energy gain of O (1 GeV/cm), in laser induced accelerators.