In this paper the generation of electrostatic wake field and electron acceleration in this field by intense laser pulse propagating in plasma in the presence of external magnetic field is investigated. It is shown that if the change in the laser pulse wave amplitude (approximation of the constant laser pulse wave field) is not taken into account, it is possible by switching to Lagrangian variables to reduce the system of equations describing excitation of the wake field and electron acceleration to a simplified system of ordinary differential equations (ODE), which can be easily integrated. This makes it possible to find the energy, transferred to electron oscillations in the wake field for different angles between the direction of laser pulse propagation and magnetic field. Stability of the laser pulse propagating with arbitrary angle to external magnetic field towards excitation of parametric and decay instabilities with involvement of upper hybrid and lower hybrid waves is investigated, as well. Equations describing these instabilities are derived and growth rates are found analytically for a small amplitude wake field and with the help of numerical calculations in the case of the finite wake field amplitude.

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