Role of laser-pulse duration in the neutron yield of deuterium cluster targets

We present an experimental and computational study of the ion and fusion neutron yields from explosions of deuterium clusters irradiated with 100-TW laser pulses. We find that the cluster explosion energy and resultant fusion yield are sensitive to the laser pulse rise time as determined by the pulse duration for a fixed envelope shape. Our experimental observations are consistent with the results of particle simulations of the laser-cluster interaction which show that the explosion energies of the clusters are determined by a single parameter: the ratio of the cluster ionization time to its intrinsic expansion time. This competition of time scales sets a fundamental constraint on the ion emission and resultant neutron yield performance of these targets as a function of laser-pulse duration.

Figure 1

Time-of-flight (TOF) ion current captured on Faraday cup A from a supersonic cluster plasma irradiated by a $100\text{−}\mathrm{fs}$ pulse of energy $5.4\mathrm{J}$. The part of this current corresponding to the energetic deuterium ions generated in the cluster explosions is fitted to a Maxwellian distribution (thin solid line) providing the number and average energy in this group.

Figure 2

Fusion neutron yield from exploding deuterium cluster plasmas as a function of pulse energy for two different pulse durations: $1\mathrm{ps}$ (squares) and $100\mathrm{fs}$ (circles). The solid lines are the least mean squares fit to a power law dependence of the yield on pulse energy.

Figure 3

Ion yield (a), average ion energy (b), and fusion neutron yield (c) as a function of laser energy for a $100\mathrm{fs}$ pulse duration. The ion yield and energies as well as the expected fusion neutron yield were determined from the two Faraday cup signals: cup A (open circles) and cup B (open squares). The measured fusion neutron yield at each energy is also shown (filled circles) and fitted to a power law dependence (dotted line) with $Y=Q{E}^{\alpha }$, where $Q=7.1\times {10}^4$ and $\alpha =1.6$.

Figure 4

Average ion energy from a cluster explosion plotted against the ratio $g=t_{\exp }∕t_{\text{ion}}$. The cluster expansion time $t_{\exp }\sim 10.7\mathrm{fs}$, and the cluster ionization time was calculated at various pulse durations between 25 and $3200\mathrm{fs}$ (doubling between each data set—the results at $100\mathrm{fs}$ and $800\mathrm{fs}$ are marked) for clusters of sizes $N=100$ (empty circles and squares) and $N=1000$ (filled squares). The peak laser intensities were $2.8\times {10}^{17}$ (circles) and $1.12\times {10}^{18}\mathrm{W}∕{\mathrm{cm}}^2$ (squares). The inset shows a calculation of the final explosion energy for a cluster of size $N=100$, a pulse duration of $100\mathrm{fs}$, and various peak laser intensities.

Figure 5

Schematic of cluster ionization and expansion dynamics during the laser pulse. The ionization time $t_{\text{ion}}$ is determined by the time required for the laser intensity to rise from the first threshold, at which atomic ionization begins, to the second threshold, at which the electric field of the laser exceeds the threshold for complete ion charge uncovering (approximately when the laser electric field exceeds the space charge electric field of the fully stripped cluster) [18]. The second threshold, which is shown for a cluster of radius $a=5\mathrm{nm}$, depends on the size and density of the cluster and will fall from its initial value as the cluster expands. Because of the finite duration of the cluster ionization time, the cluster will explode more slowly than its characteristic expansion time $t_{\exp }$ resulting in a final kinetic energy below the characteristic energy $E_{\exp }$ by the factor $1∕F\left(g\right)$.