# Direct laser acceleration of electrons by tightly focused laser pulses

## TL;DR

This paper develops an analytical theory highlighting the role of the longitudinal electric field in laser-driven electron acceleration, showing it reduces energy gain, supported by particle-in-cell simulations.

## Contribution

It introduces a new analytical framework emphasizing the impact of the longitudinal electric field in direct laser acceleration, which was previously underappreciated.

## Key findings

- Longitudinal electric field counteracts transverse acceleration effects.
- Derived scalings match particle-in-cell simulation results.
- Longitudinal field reduces maximum electron energy gain.

## Abstract

We present an analytical theory that reveals the importance of the longitudinal laser electric field in the resonant acceleration of relativistic electrons by the tightly confined laser beam. It is shown that this field always counterworks to the laser transverse component and effectively decreases the final energy gain of electrons through direct laser acceleration mechanism. This effect is demonstrated by carrying out the particle-in-cell simulations in the setup where the wakefield in the plasma bubble is compensated by the longitudinal laser electric field experienced by the accelerated electrons. The derived scalings and estimates are in good agreement with numerical simulations.