A study of fusion-neutron heating in laser-compressed deuterium-tritium spheres

On the role of the adjoint Boltzmann equation in the calculation of energy deposition

“…It appears therefore to be acceptable to use the isotropic scattering approximation for calculations of this type. Figure 2 compares our results with those of Beynon and Constantine (1977) which, considering the differences in scattering model, can be considered as satisfactory agreement. Energy deposition (MeV/source neutron) in a sphere of radius R, density p resulting from a uniformly distributed source of 14 MeV neutrons.…”

“…We shall present further evidence for this assertion below. Equations ( 52) and (54) enable us to write an expression for the rate of energy deposition from an isotropic point source in an infinite medium, viz: Now it is of considerable interest to calculate the fraction of energy given up in the sphere of radius R surrounding the source since this has some bearing on the neutron heating of laser-compressed deuterium-tritium spheres (Beynon and Constantine 1977). Thus we define the energy deposited per source neutron from equation ( 53) by…”

“…The number on each curve denotes the mass number of the moderator. 0 , results of Beynon and Constantine (1977) for deuterium-tritium spheres.…”

“…Moreover, in a graphite reactor, the neutrons lead to significant heating of the moderator and consequent effects on the kinetic behaviour of the system. More recently, from studies of the heating of laser-compressed deuterium-tritium spheres (Beynon and Constantine 1977) it has emerged that neutron heating can contribute significantly to the so-called 'bootstrap' effect. It is clear therefore that accurate methods for calculating the energy dissipation rate of neutrons as they slow down are desirable.…”

“…In the case of the finite sphere, we use a variational method which in itself contains some novel features. Extensive tables are given of the heating rates and these are compared graphically with the work of Beynon and Constantine (1977). Finally, to obtain some ideas on the effect of an energy-dependent cross-section we solve, for some special cases, the equations governing the mean square energy deposition length, i.e.…”