Accurate electron beam phase-space theory for ionization-injection schemes driven by laser pulses

After the introduction of the ionization-injection scheme in laser wake field acceleration and of related high-quality electron beam generation methods,such as two-color and resonant multi-pulse ionization injection(Re MPI),the theory of thermal emittance has been used to predict the beam normalized emittance obtainable with those schemes.We recast and extend such a theory,including both higher order terms in the polynomial laser field expansion and non-polynomial corrections due to the onset of saturation effects on a single cycle.Also,a very accurate model for predicting the cycle-averaged distribution of the extracted electrons,including saturation and multi-process events,is proposed and tested.We show that our theory is very accurate for the selected processes of Kr^(8+→10+) and Ar^(8+→10+),resulting in a maximum error below 1%,even in a deep-saturation regime.The accurate prediction of the beam phase-space can be implemented,for example,in laser-envelope or hybrid particle-in-cell(PIC)/fiuid codes,to correctly mimic the cycle-averaged momentum distribution without the need for resolving the intra-cycle dynamics.We introduce further spatial averaging,obtaining expressions for the whole-beam emittance fitting with simulations in a saturated regime,too.Finally,a PIC simulation for a laser wakefield acceleration injector in the Re MPI configuration is discussed.