The kinetic energy of hot (multi-keV) ions from the laser-driven Coulomb explosion of deuterium clusters and the resulting fusion yield in plasmas formed from these exploding clusters has been investigated under a variety of conditions using the Texas Petawatt laser. An optimum laser intensity was found for producing neutrons in these cluster fusion plasmas with corresponding average ion energies of 14 keV. The substantial volume (1-10 mm 3 ) of the laser-cluster interaction produced by the petawatt peak power laser pulse led to a fusion yield of 1.6 ×10 7 neutrons in a single shot with a 120 J, 170 fs laser pulse. Nuclear fusion from laser-heated deuterium clusters has been studied since 1999 [1]. Deuterium clusters are nanometerscale assemblies of atoms bound at liquid density by van der Waals forces, which can be produced by forcing cold deuterium gas under high pressure through a supersonic nozzle into vacuum. In these experiments, the deuterium clusters are irradiated by an intense ultrashort laser pulse. The clusters absorb the pulse energy very efficiently [2] and the process by which the ions attain their high kinetic energies has been well explained by the Coulomb explosion model [3,4]. In this model, the electrons in the atomic cluster first absorb the laser pulse energy as the atoms are ionized. The electrons further gain energy through other absorption mechanisms such as above-threshold ionization [5], inverse bremsstrahlung heating [6], resonant heating [6][7][8], and escape from the space-charge forces of the cluster, on the time scale of tens of fs. At high enough laser intensity, almost all of the electrons are removed from the cluster on a time scale short relative to the ion motion. What remains is a highly charged cluster of ions at liquid density, which promptly explodes by Coulomb repulsion.In experiments with peak laser intensities of 10 16 -10 18 W/cm 2 , deuterium ions with average kinetic energies up to about 10 keV have been observed, which were energetic enough to drive DD fusion events in a plasma with an average ion density near 10 19 cm −3 [9][10][11][12]. DD fusion can also occur when energetic ions collide with cold atoms in the background gas jet [13]. As a result of both of these fusion reactions, quasimonoenergetic 2.45 MeV neutrons are produced from the localized fusion plasma in a subnanosecond burst until the plasma disassembles in about 100 ps.Neutron yields greater than 10 8 n/shot would yield neutron fluences near the cluster jet greater than 10 10 n/cm 2 enabling subnanosecond time-resolved pump-probe experiments of neutron damage studies [14]. The petawatt lasers currently operating and being built with pulse durations below 200 fs have the potential to drive such sources. Therefore, the laser-cluster-generated fusion plasma is attractive as a bright, * Author to whom correspondence should be addressed: dws223@physics.utexas.edu short, and localized neutron source that is potentially useful for material damage studies.In this paper, we describe the scaling of cluster pl...