The range of charged particles in a degenerate electron gas (applied to fusion reactors)

Using the quantum-mechanical form of the Boltzmann equation, a general expression has been deduced for the rate of energy transfer between two species of particles in different velocity distributions. The special case of a charged test particle in a degenerate electron gas is considered in the cold limit. The two-body Rutherford collision cross section is employed, and it is shown that the energy transfer differs little from that obtained when the electrons are treated in the many-body approximation characterized by a dielectric. A rigorous calculation of the Debye shielding distance is given using Fermi-Dirac statistics. The calculations are applied to a compressed deuterium-tritium plasma typical of laser fusion thermonuclear devices and the range of alpha particles is obtained.