Ray-based calculations of backscatter in laser fusion targets

A one-dimensional, steady-state model for Brillouin and Raman backscatter from an inhomogeneous plasma is presented. The daughter plasma waves are treated in the strong damping limit, and have amplitudes given by the (linear) kinetic response to the ponderomotive drive. Pump depletion, inverse-bremsstrahlung damping, bremsstrahlung emission, Thomson scattering off density fluctuations, and whole-beam focusing are included. The numerical code DEPLETE, which implements this model, is described. The model is compared with traditional linear gain calculations, as well as “plane-wave” simulations with the paraxial propagation code PF3D. Comparisons with Brillouin-scattering experiments at the OMEGA Laser Facility [T. R. Boehly et al., Opt. Commun. 133, 495 (1997)] show that laser speckles greatly enhance the reflectivity over the DEPLETE results. An approximate upper bound on this enhancement, motivated by phase conjugation, is given by doubling the DEPLETE coupling coefficient. Analysis with DEPLETE of an ignition design for the National Ignition Facility (NIF) [J. A. Paisner, E. M. Campbell, and W. J. Hogan, Fusion Technol. 26, 755 (1994)], with a peak radiation temperature of $285\mathrm{eV}$ , shows encouragingly low reflectivity. Re-absorption of Raman light is seen to be significant in this design.