Breakeven conditions for a deuterium-tritium mixture of prescribed temperature evolution in a spherical pinch configuration

In the present work, the authors examine in detail the complete system, i.e., source of energy and plasma sink, and consider various energy transfer efficiencies from the first to the second, as well as from the second to the first. The energy from the source is deposited in the plasma in a pulse of prescribed temporal power evolution. In order to ease the inclusion in the energy balance equation of conduction losses, the geometry considered here is the spherical one. More specifically, it is the spherical pinch geometry. However, the analysis can be extended to other geometries, including the toroidal one. They find that, contrary to Lawson's result, breakeven is independent of containment time, but it is a function of particle number density, temperature, dimension of the plasma, and temporal profile of the energy input. At or below ∼ 1015 cm-3 particle density there can be no breakeven, no matter the plasma temperature, unless the plasma size is extremely large. Likewise, there can be no breakeven at a temperature below ∼3 kV, no matter the particle density. The shape of the energy deposition pulse into the plasma has a bearing on the energy breakeven conditions