  A theoretical study of laser and plasma based electron acceleration is
presented. An effective model has been used, in which the presence of an
underdense plasma has been taken account via its index of refraction $n_{m}$.
In the confines of this model, the basic phenomena can be studied by
numerically solving the classical relativistic equations of motion. The key
idea of this paper is the application of chirped, bichromatic laser fields. We
investigated the advantages and disadvantages of mixing the second harmonic to
the original $\lambda = 800 \, \mathrm{nm}$ wavelength pulse. We performed
calculations both for plane wave and Gaussian pulses.
