Temperature Measurements of Fusion Plasmas Produced by Laser-Irradiated D$_{2}-^{3}$He or CD$_{4}-^{3}$He Clustering Gases

We report on experiments in which a mixture of D$_{2}$ or CD$_{4}$ clusters and $^{3}$He gas was irradiated by a petawatt-laser pulse, generating nuclear fusion reactions such as D($d$, $^{3}$He)$n$, D($d$, $t)p$, and $^{3}$He($d$, $p)^{4}$He. We measured the yields of fusion neutrons and protons from these reactions and found them to agree with yields based on a simple cylindrical plasma model. The plasma temperature was determined by two different methods. In the first, it was derived from time-of-flight data of deuterium ions ejected from exploding D$_{2}$ or CD$_{4}$ clusters. In the second, it was measured from the ratio of neutron yield to proton yield from D($d$, $^{3}$He)$n$ and $^{3}$He($d$, $p)^{4}$He reactions, respectively. The temperatures determined by these two methods agree well, indicating (i) the ion energy distribution is not significantly distorted when ions travel in the disassembling plasma; (ii) the kinetic energy of deuterium ions, especially the hottest part responsible for nuclear fusion, is well described by a near-Maxwellian distribution.