Collision of plane thermonuclear detonation waves in a preliminarily compressed DT mixture

The paper deals with a one-dimensional problem on symmetric irradiation of a plane DT fuel layer with a thickness 2H and density ρ0 ⩽ 100ρs (where ρs is the density of the DT fuel in the solid state at atmospheric pressure and a temperature of 4 K) by two identical monoenergetic proton beams with a kinetic energy of 1 MeV, an intensity of 1019 W/cm2, and a duration of 50 ps. The problem is solved in the framework of one-fluid two-temperature hydrodynamic model that takes into account the equation of state for hydrogen, electron and ion heat conductivities, kinetics of the DT reaction, plasma self-radiation, and plasma heating by α-particles. The irradiation of the fuel results in the appearance of two counterpropagating detonation waves to the fronts of which rarefaction waves are adjacent. The efficiency of the DT reaction after the collision (reflection from the plane of symmetry) of the detonation waves depends on the spatial homogeneity of thermodynamic functions between the fronts of the reflected detonation waves. At Hρ0 ≈ 1 g/cm2, the gain factor is G ≈ 200, whereas at Hρ0 ≈ 5 g/cm2, it is G > 2000. As applied to a cylindrical target that is ignited from ends and in which the cylinder with the fuel is surrounded by a heavy magnetized shell, the obtained values of the burn-up and gain factors are maximum possible. To estimate the ignition energy Eig of a cylindrical target by using solutions to the one-dimensional problem, a quasi-one-dimensional model is developed. The model assumes that the main mechanism of target ignition is fuel heating by α-particles. The trajectories of α-particles are limited by a cylindrical surface with a given radius, which is a parameter of the model and is identified with the fuel radius in the target and the radii of the irradiating proton beams. This model reproduces the well-known theoretical dependence Eig ∼ ρ0−2 and yields Eig = 160 kJ as a lower estimate of the ignition energy for ρ0 = 100ρs ≈ 22 g/cm3.