Scaling electron acceleration in the bubble regime for upcoming lasers

Electron acceleration in the laser-plasma bubble appeared to be the most successful regime of laser wake field acceleration in the last decade. The laser technology became mature enough to generate short and relativistically intense pulses required to reach the bubble regime naturally delivering quasi-monoenergetic bunches of relativistic electrons. The upcoming laser technology projects are promising short pulses with many times more energy than the existing ones. The natural question is how will the bubble regime scale with the available laser energy. We present here a parametric study of laser-plasma acceleration in the bubble regime using full three dimensional particle-in-cell simulations and compare numerical results with the analytical scalings from the relativistic laser-plasma similarity theory. Our simulations and the theory match almost perfectly for spot sizes above R = 2λ and laser amplitudes above a0 = 4. We also studied the emission of synchrotron radiation by the accelerated electrons. Both classical and a QED model were applied. We found borders, at which theory and simulations stopped matching. With small spot radii (R < 2λ) we almost never observed the formation of a bubble structure or any form of mono-energetic acceleration. Low laser amplitudes lead to higher energies than predicted by the theory