Temporal and spatial expansion of a multidimensional model for electron acceleration in the bubble regime

TL;DR

This paper extends an analytical model for electron acceleration in plasma wake fields by including time-dependent bubble radius and full field solutions, improving the accuracy of particle trapping and spectrum predictions.

Contribution

It generalizes a previous piecewise model to incorporate cavity dynamics and full field solutions, enabling better simulation of electron trapping and spectral features.

Findings

Inclusion of cavity dynamics is essential for accurate trapping simulation.

Full longitudinal field gradient is necessary to reproduce mono energetic electron peaks.

The extended model improves agreement with observed electron spectra.

Abstract

An extended analytical model for particle dynamics in fields of a highly-nonlinear plasma wake field (the bubble or blow out regime) is derived. A recently proposed piecewise model (Kostyukov et al., New J. Phys., {\bf 12}, 045009 (2010)) is generalized to include a time dependent bubble radius and full field solution in the acceleration direction. Incorporation of the cavity dynamics in the model is required to simulate the particle trapping properly. On the other hand, it is shown that the previously reported piecewise model does not reproduce the formation of a mono energetic peak in the particle spectrum. The mono energetic electron beams are recovered only when the full longitudinal field gradient is included in the model.