Theory of Raman sidescattering for a laser-produced plasma with an exponential density profile

Equations for the stimulated Raman sidescattering from a laser-produced plasma with an exponential density profile have been derived. They have been solved by using the WKB method, and the resulting Bohr--Sommerfeld condition has been solved numerically for the growth rates of the absolute instability and the frequency shifts as a function of the laser intensity, the density gradient scale length, and the plasma frequency. The results have been discussed and compared with the previously reported work on the plasma with linear density profile. Instability growth rates are found to be nearly the same for both cases, except for very steep density profiles, for which the difference can become appreciable. The two theories, one of which considers a hot plasma, lead to significantly different frequency shifts. It is found that, for high laser powers, the instability persists even for very steep profiles. Furthermore, for such profiles the maximum of the growth rate occurs far away from the quarter critical layer, for moderately high power lasers