The electron density distribution and field profile in underdense magnetized plasma

In this work propagation of a high frequency electromagnetic wave in underdense plasma in presence of an external magnetic field is investigated. When a constant magnetic field perpendicular to the motion of electrons is applied, then the electrons rotate around the magnetic field lines and generate electromagnetic part in the wake with a nonzero group velocity. By using of the Maxwell equations and nonlinear differential equation for the electric field a direct one-dimensional (1D) procedure for calculating hydrodynamic equations are developed and the electric and magnetic field profiles in the plasma are investigated. It is shown that by using the external (dc) magnetic field in constant laser intensity, the magnetic field profile in plasma deviates from the sinusoidal structure. It is found that the wavelength of electric and magnetic field oscillations increases by increasing the external magnetic field and the density distribution of electrons also increases in comparison to the unmagnetized underdense plasma. We noticed that by the increase in electron temperature in the unmagnetized and magnetized plasmas the electron density distribution ratio δn/n0e increases and the wavelength of electric and magnetic fields increase where in the magnetized system it becomes positive in some regions.