Thermal and log-normal distributions of plasma in laser driven Coulomb explosions of deuterium clusters

In this work, we explore the possibility that the motion of the deuterium ions emitted from Coulomb cluster explosions is highly disordered enough to resemble thermalization. We analyze the process of nuclear fusion reactions driven by laser-cluster interactions in experiments conducted at the Texas Petawatt laser facility using a mixture of D-2+He-3 and CD4+He-3 cluster targets. When clusters explode by Coulomb repulsion, the emission of the energetic ions is "nearly" isotropic. In the framework of cluster Coulomb explosions, we analyze the energy distributions of the ions using a Maxwell-Boltzmann (MB) distribution, a shifted MB distribution (sMB), and the energy distribution derived from a log-normal (LN) size distribution of clusters. We show that the first two distributions reproduce well the experimentally measured ion energy distributions and the number of fusions from d-d and d-He-3 reactions. The LN distribution is a good representation of the ion kinetic energy distribution well up to high momenta where the noise becomes dominant, but overestimates both the neutron and the proton yields. If the parameters of the LN distributions are chosen to reproduce the fusion yields correctly, the experimentally measured high energy ion spectrum is not well represented. We conclude that the ion kinetic energy distribution is highly disordered and practically not distinguishable from a thermalized one.