Harmonic generation of radiation in a steep density profile

It has been observed experimentally that the CO2-laser Gemini and Helios systems generate very high harmonics with nearly constant efficiency over several harmonics with a cutoff near the local plasma frequency at the upper density shelf. To understand the experimental results, the strongly nonlinear electron response to a time-dependent inhomogeneous force is studied. The equation of the electron motion in Lagrangian variables is derived and the conditions on the density scale length and power intensities for wavebreaking are found. By transforming the solution back to Eulerian variables, it is shown that the source of a given high harmonic frequency is localized around the density region where the local plasma wave is at that frequency. Using the numerically obtained nonlinear current density we evaluate the intensity of the radiation coming out of the plasma and verify the nearly constant harmonic production efficiency with a sharp decrease at the local plasma wave frequency at the upper shelf density