Numerical modeling of laser tunneling ionization in Particle in Cell Codes with a laser envelope model

TL;DR

This paper introduces an extended envelope ionization model for Particle in Cell simulations that accurately reproduces electron beam properties during laser wakefield acceleration, significantly reducing computational resources needed.

Contribution

An extension to the envelope ionization procedure is proposed, enabling accurate modeling of tunneling ionization in high-intensity laser pulses within Particle in Cell codes.

Findings

The extended model accurately reproduces phase space properties of ionized electron bunches.

It achieves comparable accuracy to full simulations while using fewer computational resources.

The method is effective even in complex nonlinear regimes and cylindrical geometries.

Abstract

The resources needed for Particle in Cell simulations of Laser Wakefield Acceleration can be greatly reduced in many cases of interest using an envelope model. However, the inclusion of tunneling ionization in this time averaged treatment of laser-plasma acceleration is not straightforward, since the statistical features of the electron beams obtained through ionization should ideally be reproduced without resolving the high frequency laser oscillations. In this context, an extension of an already known envelope ionization procedure is proposed, valid also for laser pulses with higher intensities, which consists in adding the initial longitudinal drift to the newly created electrons within the laser pulse ionizing the medium. The accuracy of the proposed procedure is shown with both linear and circular polarization in a simple benchmark where a nitrogen slab is ionized by a laser pulse, and in a more complex benchmark of laser plasma acceleration with ionization injection in the nonlinear regime. With this addition to the envelope ionization algorithm, the main phase space properties of the bunches injected in a plasma wakefield with ionization by a laser (charge, average energy, energy spread, rms sizes, normalized emittance) can be estimated with accuracy comparable to a non-envelope simulation with significantly reduced resources, even in cylindrical geometry. Through this extended algorithm, preliminary studies of ionization injection in Laser Wakefield Acceleration can be easily carried out even on a laptop.