Neutron yield scaling law in laser-cluster fusion experiments

We present a scaling law (Y similar to E-beta) of fusion neutron yields (Y) for laser pulse energy (E) in laser-cluster fusion experiments. We compare the available neutron yield data from previous deuterium cluster fusion experiments with those calculated using the cylindrical fusion plasma model. The calculated neutron yields are shown as functions of the incident laser pulse energy, average number density, and ion temperature. Although the deuterium-deuterium fusion reactivity is known to increase rapidly with ion temperature, the neutron yield shows a modest increase above similar to 10 keV for a given laser pulse energy. We find the scaling exponent beta approaching 1.0 as the ion temperature increases from 1 keV to 100 keV. We explain the observed temperature dependence of beta by examining the temperature dependence of the beam-beam and beam-target fusion neutron yields separately. Our scaling law differs from previously reported scaling laws from individual experiments, but it shows an excellent agreement with the scaling law determined by the maximum neutron yields of individual experiments.