Plane thermonuclear detonation waves initiated by proton beams and quasi-one-dimensional model of fast ignition

Abstract

The one-dimensional problem on bilatiral irradiation by proton beams of the plane layer of condensed DT mixture with length 2H and density ρ 0 ≤ 100ρ s , where ρ s is the fuel solid-state density at atmospheric pressure and temperature of 4 K, is considered. The proton kinetic energy is 1 MeV, the beam intensity is 10 19 W/cm 2 and duration is 50 ps. A mathematical model is based on the one-fluid two-temperature hydrodynamics with a wide-range equation of state of the fuel, electron and ion heat conduction, DT fusion reaction kinetics, self-radiation of plasma and plasma heating by α-particles. If the ignition occurs, a plane detonation wave, which is adjacent to the front of the rarefaction wave, appears. Upon reflection of this detonation wave from the symmetry plane, the flow with the linear velocity profile along the spatial variable x and with a weak dependence of the thermodynamic functions of x occurs. An appropriate solution of the equations of hydrodynamics is found analytically up to an arbitrary constant, which can be chosen so that the analytical solution describes with good accuracy the numerical one. The gain with respect to the energy of neutrons G ≈ 200 at Hρ 0 ≈ 1 g/cm 2 , and G > 2000 at Hρ 0 ≈ 5 g/cm 2 . To evaluate the ignition energy E ig of cylindrical targets, the quasi-1D model, limiting trajectories of α-particles by a cylinder of a given radius, is suggested. The model reproduces the known theoretical dependence E ig ∼ ρ 0 −2 and gives E ig = 160 kJ for ρ 0 = 100ρ s ≈ 22 g/cm 3 .

Influence of shell effects on thermodynamic properties of matter at high pressures

“…Thermodynamic properties of matter at high pressure are of importance in many problems of high energy density physics, in particular, in astrophysics [1], in wide-range equations of state [2,3], in the problems of interaction of intense energy fluxes with matter [4][5][6], in perspective power generation facilities [7] and in some others. The finite-temperature Thomas-Fermi (TF) model [8] based upon semiclassical approximation is widely used to describe thermodynamic properties of matter, but there are many phenomena beyond this approach.…”