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 (ReMPI), 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 ${\mathrm{Kr}}^{8^{+}\to {10}^{+}}$ and ${\mathrm{Ar}}^{8^{+}\to {10}^{+}}$ , 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)/fluid 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 ReMPI configuration is discussed.

Ionization-induced electron injection in laser wakefield accelerators, which was recently proposed to lower the laser intensity threshold for electron trapping into the wake wave, has the drawback of generating electron beams with large and continuous energy spreads, severely limiting their future applications. Complex target designs based on separating the electron trapping and acceleration stages were proposed as the only way for getting small energy-spread electron beams. Here, based on the self-truncated ionization-injection concept which requires the use of unmatched laser–plasma parameters and by using tens of TW laser pulses focused onto a gas jet of helium mixed with low concentrations of nitrogen, we demonstrate single-stage laser wakefield acceleration of multi-hundred MeV electron bunches with energy spreads of a few percent. The experimental results are verified by PIC simulations.