Doppler shift of laser light reflected from expanding plasmas

The Doppler shift of light reflected from a plane stratified expanding plasma is analyzed. Nonlinear effects are not considered and oblique incidence is restricted to the case of s polarization. The frequency shift is shown to consist of two components, one due to the motion of the reflecting surface, and another due to plasma flow through that surface. The shifts have a different dependence on the angle of incidence. Typically, the two contributions are comparable in laser fusion applications, being of order dw/w∼cs/c∼10−3, where cs = (Z Te/M)1/2 is the ion sound speed in the underdense plasma. In general, the Doppler shift has a time variation which induces a bandwidth in the reflected wave.