Laser wakefield acceleration of electrons holds great promise for producing ultracompact stages of GeV scale, high-quality electron beams for applications such as x-ray free electron lasers and high-energy colliders. Ultrahigh intensity laser pulses can be self-guided by relativistic plasma waves (the wake) over tens of vacuum diffraction lengths, to give >1  GeV energy in centimeter-scale low density plasmas using ionization-induced injection to inject charge into the wake even at low densities. By restricting electron injection to a distinct short region, the injector stage, energetic electron beams (of the order of 100 MeV) with a relatively large energy spread are generated. Some of these electrons are then further accelerated by a second, longer accelerator stage, which increases their energy to ∼0.5  GeV while reducing the relative energy spread to <5% FWHM.

A nonlocal quantum model is presented for calculating the atomic dielectric response to a strong laser electric field. By replacing the Coulomb potential with a nonlocal potential in the Schrodinger equation, a 3+1D calculation of the time-dependent electric dipole moment can be replaced with a 0+1D integral equation, offering significant computational savings. The model is benchmarked against an established ionization model and ab initio simulation of the time-dependent Schrodinger equation. The reduced computational overhead makes the model a promising candidate to incorporate full quantum mechanical time dynamics in laser pulse propagation simulations.

Nonlocal potential models have been used in place of the Coulomb potential in the Schrodinger equation as an efficient means of exploring high field laser-atom interaction in previous works. Although these models have found use in modeling phenomena including photo-ionization and ejected electron momentum spectra, they are known to break electromagnetic gauge invariance. This paper examines if there is a preferred gauge for the linear field response and photoionization characteristics of nonlocal atomic binding potentials in the length and velocity gauges. It is found that the length gauge is preferable for a wide range of parameters.

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