Model-independent determination of the astrophysicalSfactor in laser-induced fusion plasmas

Abstract

In this work, we present a new and general method for measuring the astrophysical S-factor of nuclear reactions in laser-induced plasmas and we apply it to 2 H(d,n) 3 He. The experiment was performed with the Texas Petawatt laser, which delivered 150-270 fs pulses of energy ranging from 90 to 180 J to D2 or CD4 molecular clusters. After removing the background noise, we used the measured time-of-flight data of energetic deuterium ions to obtain their energy distribution. We derive the S-factor using the measured energy distribution of the ions, the measured volume of the fusion plasma and the measured fusion yields. This method is model-independent in the sense that no assumption on the state of the system is required, but it requires an accurate measurement of the ion energy distribution especially at high energies and of the relevant fusion yields. In the 2 H(d,n) 3 He and 3 He(d,p) 4 He cases discussed here, it is very important to apply the background subtraction for the energetic ions and to measure the fusion yields with high precision. While the available data on both ion distribution and fusion yields allow us to determine with good precision the S-factor in the d+d case (lower Gamow energies), for the d+ 3 He case the data are not precise enough to obtain the S-factor using this method. Our results agree with other experiments within the experimental error, even though smaller values of the S-factor were obtained. This might be due to the plasma environment differing from the beam target conditions in a conventional accelerator experiment.

Nuclear probes of an out-of-equilibrium plasma at the highest compression

“…New methods to measure these quantities directly in the plasma have been recently investigated using a petawatt laser impinging on a cluster target. Fusion cross sections for d+ 3 He [16], dd [17] and the range [18] have been measured also in the cases where the system is prepared near the critical point for a liquid gas phase transition [19]. While the fusion cross sections have been found in reasonable agreement with accelerator experiments, the range showed some dependence on the cluster distribution, which in turn depends on the equation of state of the system [18,19].…”

How do charged environments affect low-energy fusion rates? Screening effects in laser-induced non-neutral plasmas

“…This scenario approximately describes secondary reactions and, in Coulomb explosion systems, beam-target reactions (as defined e.g. in [2,3]). It is then found that U = 0: an accurate evaluation of the average screened cross-section, via eq.…”

“…In the future, the model here discussed could be improved to include Debye-like screening and, possibly, to allow a comparison of its predictions with existing experimental data and simulations. For instance, [2] reports a reduction of the d + d cross-section extracted from Coulomb explosion measurements, with respect to conventional fixed-target experiments and Trojan Horse Method [7] measurements. The mechanism here described may be sufficient to explain that result, although further studies are needed to deduce the amount of net charge required to this end.…”

“…In this work, the fusion rate modifications provoked by a positively charged environment are discussed, from the theoretical point of view, for inertial confinement fusion (ICF) [1] and cluster Coulomb explosion [2,3] plasmas, both important in the field of terrestrial nuclear fusion energy production. The model here presented is discussed in greater detail in [4,5].…”

Fusion hindrance effects in laser-induced non-neutral plasmas

“…In the Coulomb explosion (CE) concept (see e.g. [2,3,4]), instead, the fuel is allowed through a nozzle to rapidly expand to average densities of ∼ 10 18 atoms/cm 3 [2] (to be compared with ICF hotspot densities, e.g. ∼ 10 25 atoms/cm 3 in the measurements in [13] at the NIF facility), forming molecular clusters.…”