Subignition fusion yields generated by fast heating of compressed deuterium–tritium and break-even scaling

A simple model is presented to calculate the fusion yield from the fast heating of compressed deuterium–tritium (DT). The model is applicable when the fusion yield is small enough to neglect self-heating. Since 80% of the fusion yield escapes as 14 MeV neutrons, self-heating is small as long as the fusion yield is less than the deposited energy, i.e., the fusion gain, Q⩽1. We show the model is in good agreement with detailed numerical simulations when this condition is satisfied, as will be the case for fast ignition experiments in the near future. The model is used to calculate the fast heating fusion yields as a function of the important parameters such as the fuel density, deposited energy, and pulse length. The model is also used to obtain the minimum energy, Eq1, and the fuel diameter, d, necessary to obtain Q=1, which is given approximately by the scaling laws Eq1=15.3(ρ/100)−1.5 kJ, and d=16.5(ρ/100)−0.84 μm, where ρ is the DT density. These scaling laws should help the design of Q=1 experiments.