  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
