Self-consistent profile modification in the underdense region of laser-produced plasmas

Profile modification in the underdense region of laser-plasmas with spatially uniform temperature T_e, is studied. A multiple scale method is used to describe self-consistently the plasma flow and the wave field, in (i) the scale of the field wavelength, and (ii) the overall expansion scale. For T_e t^aordinary differential equations with definite boundary conditions are obtained. For a = 0 and weak fields, we explicitly solve the equations and relate the field in the critical layer to the incident field.