Mathematical modeling of the heating of a fast ignition target by an ion beam

We develop a BIN computer code for simulating the interaction of a monochromatic ion beam with a plasma, which takes into account changes in the spatial distribution of the heated-plasma temperature. This enables us to calculate the heating of both homogeneous and inhomogeneous plasmas with parameters corresponding to their real spatial distributions at the time of maximum compression of the inertial confinement fusion (ICF) target. We present the results of a numerical simulation using the BIN code for the heating of a homogeneous deuterium-tritium plasma by a short pulse of monochromatic ions at various ion velocity and plasma-electron thermal velocity ratios. We also present the results of calculations for the heating of an inhomogeneous plasma of a non-cryogenic target formed as a beryllium deuteride-tritide shell by beams of light, medium, and heavy ions. As the initial distributions, we use the results of numerical simulations for such a target, precompressed by a laser pulse (carried out at the M. V. Keldysh Institute of Applied Mathematics using the DIANA code). We demonstrate the possibility of forming the central ignitor with the parameters sufficient for igniting the targets by beams of ions with energies E similar to 100 - 400 MeV/u and specific energy densities of the beam Q similar to 5-20 GJ/cm(2). The required specific energy density drops with increase in the ion energy; however, due to the increased path length, larger-charge ions have to be used.