# Field ionization rate for PIC codes

## TL;DR

This paper introduces an improved formula for calculating field ionization rates in PIC codes, accurately modeling the transition between tunnel and barrier suppression regimes for better simulation of intense laser-matter interactions.

## Contribution

The paper presents a new ionization rate formula that more precisely captures the transitional regime, enhancing the accuracy of PIC simulations in laser-matter interaction studies.

## Key findings

- More accurate transition modeling between ionization regimes.
- Formula depends mainly on ionization potentials and electric field.
- Suitable for implementation in PIC simulation codes.

## Abstract

An improved formula is proposed for field ionization rate covering tunnel and barrier suppression regime. In contrast to the previous formula obtained recently in [I. Yu. Kostyukov and A. A. Golovanov, Phys. Rev. A 98, 043407 (2018)], it more accurately describes the transitional regime (between the tunnel regime and the barrier suppression regime). In the proposed approximation, the rate is mainly governed by two parameters: by the atom ionization potentials and by the external electric field, which makes it perfectly suitable for particle-in-cell (PIC) codes dedicated to modeling of intense laser-matter interactions.