Electron Acceleration in Underdense Plasmas Described with a Classical Effective Theory

An effective theory of laser--plasma based particle acceleration is presented. Here we treated the plasma as a continuous medium with an index of refraction $n_{m}$ in which a single electron propagates. Because of the simplicity of this model, we did not need to perform PIC simulations in order to study the properties of the electron acceleration. We studied the properties of the electron motion due to the Lorentz force and the relativistic equations of motion were numerically solved and analysed. We compared our results to PIC simulations and experimental data. Keywords: Underdense plasma; Electron acceleration; Classical electrodynamics; Relativistic equation of motion; Ultrashort laser pulses