  In the shock-ignition inertial confinement fusion scheme, high-intensity
lasers propagate through an inhomogeneous coronal plasma, driving a shock
designed to cause fuel ignition. During the high-intensity ignitor laser pulse,
SRS backscatter in the long scale-length coronal plasma is likely to be in the
kinetic regime. In this work, we use one-dimensional particle-in-cell
simulations to show that there is a non-linear frequency shift caused by
kinetic effects, resulting in the growth of Stimulated Raman Scattering (SRS)
in an inhomogeneous plasma far exceeding the predictions of the fluid theory,
so-called inflationary SRS or iSRS. We find that iSRS occurs over a wide range
of density scale-lengths relevant to shock-ignition and other directly-driven
inertial confinement fusion schemes. The presence of iSRS in shock-ignition
plasmas has implications for the theoretical gains from shock-ignition inertial
confinement fusion. Here we quantify the intensity threshold for the onset of
iSRS for shock-ignition relevant parameters.
