Number 19

Abstract

ma interaction, our simuIation parameters scale as follows. For a CO, laser, the power is 3&10" W/cm', the density scale length is L=2&10 ' cm, the time duration of the simulation is 6 psec, the interaction is at a density of one seventh the critical density, and the electron temperature is 1 keV. On the other hand, for a neodymium-glass laser the power is 2&& 10" W/cm', the density scale length is 2&10 cm, the time duration of the simulation is 0.6 psec, the interaction is at one seventh the critical density, and the temperature is still 1 keV. We solve exactly the temporal evolution and spatial dependence of a three-wave para-metric instability in an inhomogeneous plasma. An initial fluctuation develops into a pulse and grows initially with the same growth rate as it would in a homogeneous plasma, Growth continues until convection saturation occurs. The pulse broadens as it grows and eventually assumes the form of a totally amplified region flanked by two shock fronts. Effects of damping are also discussed. The basic equations governing the growth of a parametric three-wave instability in an inhomogeneous medium, as discussed (1) where y, is the growth rate for the instability in a homogeneous medium and ~ = (d/dx)[k, (x)+ k, (x) + k, (x)j, assumed to be a constant, determines the phase mismatch between the decay waves. In deriving (1) the amplitudes of the waves propagating (oppositely directed) in the plasma have been written A,. = a, (x, t) e px(iv,. t-ik, x-if bk; dx), and it is assumed that a,. (x, t) varies slowly in space compared to exp(-ik,. x). This assumption is clearly inconsistent with (1) for z Ixl&k, ", and thus this equation is limited to this range of x. In the following analysis we will assume Ixl «k, "/w, and also less than the characteristic size of the system. Taking a Laplace transform in time and letting a; =a,e "" ', we find (p+ v,)a, + ~iK'v, xa, +v, Ba, /Bx=yoa, +a, (0), (p+ v,)a, +-, ia'v2xa,-v, Ba,/Bx=yoa, +a, (0). (2) We choose initial values as a, (0) = 0, a, (0) = (-a/Wic)5(x-x,), where a represents the thermal level of the wave amplitude, normalization chosen such that fa, d xa/vg', noting that (K') '~' is the region of