Monoenergetic electron acceleration in plasmas by an ultrashort petawatt laser pulse

Focusing an ultra-short (tens of fs) petawatt laser pulse in a wide focal spot ($\sim100$~$\mu$m) in rarefied plasma ($\sim10^ {17}$~cm$^{-3}$) enables accelerating electrons up to 1 GeV by a laser wake-field without a channel. An ultrashort laser pulse with an overcritical power for relativistic self- focusing propagates in plasmas as in vacuum. The nonlinear quasi-plane plasma wake effectively traps and accelerates injected electrons with a wide range of initial energies. The accelerating and focusing phases of the nonlinear three- dimensional axi-symmetric laser wake can almost entirely overlap starting from a certain distance behind the laser pulse in homogeneous plasma. Such a field structure results from the curvature of phase fronts due to the transversely inhomogeneous relativistic plasma frequency shift. Consequently, the number of trapped low-energy electrons can be much greater than that predicted by the linear wake theory. This effect is favorable for quasi-monoenergetic acceleration of several hundreds of pC to about 1 GeV per electron. External electron injection into the plasma wake (RF-based, colliding laser pulses etc.) is discussed.