15.7 Assignments 459(c) Using the results from (a) express the instability threshold in a form where
ε 0 E^2 /nκTeis a function ofΓ 1 /ω 1 andΓ 2 /ω 2.
(d) Suppose a pump wave with frequencyω 3 propagates into a plasma with a monoton-
ically increasing density. Show the relative locations of stimulated Brillouin and
stimulated Raman backscattering in terms of a criterion for the local density.
Assume that the wavelengths of the waves are much shorter than the density
gradient scale length.
(e) The National Ignition Facility at the Lawrence Livermore National Lab in the
USA, nearing completion in 2004, has an array of 351 nm wavelength lasers
which are designed to apply 5 × 1014 watts over the surface of a target with
initial radius of 1 mm. If these lasers are considered the pump electromagnetic
wave with frequencyω 3 ,at what density doesω 3 =ωpeoccur. Assuming
Te=300eV, what is the value ofε 0 E^2 /nκTeat the location whereω 3 =ωpe?
IfΓ 1 /ω 1 =Γ 2 /ω 2 =0. 1 will this plasma be susceptible to the parametric decay
instability?