Fast Ignition by a Proton Beam and Burning of a DT Cylindrical Shell Target

Abstract

Edge ignition of a cylindrical shell target by a proton beam with a small mass heating depth of about 0.5 g/cm² is analyzed for two values of the initial mass density of the DT fuel, \({{\rho }_{0}} \approx 110\) and 22 g/cm³, and given beam parameters (the intensity \(J \propto {{\rho }_{0}}\) and impact time \(\Delta {{t}_{{{\text{pr}}}}} \propto \rho _{0}^{{ - 1}}\)). By comparing results obtained using different models of heat transfer through the fuel–shell interface, it is shown that application of a strong magnetic field that suppresses heat transfer but does not affect the trajectories of the α-particles produced in the DT reaction reduces the ignition energy by only about 10%. The unsteady detonation wave generated in the course of ignition transforms into a steady-state fast shockless burning wave, in which the cold fuel is heated by α-particles. The wave parameters depend on the deposited energy. As the wave propagates through the fuel, the α-particles escaping from the fuel volume carry away about one-half of their initial power. For one of the simulation versions, the target length H is determined (\({{\rho }_{0}}H \approx 10\) g/cm²) at which the gain reaches a value of \(G = 1250\). An approximate formula is derived that relates the slope of the pressure profile in a steady-state wave to the wave velocity and the heating power per unit mass of the fuel near the wave front. The applicability of the formulas relating the pressure and velocity at the Chapman–Jouguet point to the propagation velocity of a strong detonation wave is demonstrated.