Density steepening formation in the interaction of microwave field with a plasma

A modification of the electron density distribution of an unmagnetized plasma by the ponderomotive force of high-power microwave propagating into the plasma is studied. Using the Maxwell and fluid equations, nonlinear differential and integral equations for the electric field are obtained. The solution of these nonlinear equations shows that the profiles of the electric and magnetic field depart slightly from a sinusoidal shape, the amplitude of oscillations decreases in the plasma, and these oscillations become lengthened. Also, the period of oscillations decreases by increasing the microwave energy flux and the electron density becomes highly steepened for high microwave energy flux. Furthermore, the axial density profile shows a stationary density modulation that is phase-shifted with respect to the wave amplitude. This density modulation increases with the microwave energy flux