A computational- simulation study was performed to assess the feasibility of laser-induced fusion of deuterium nuclei with tritium nuclei as a means of generating neutrons for use in neutron radiography. [D-T fusion reactions produce α particles (He nuclei) plus the desired neutrons.] As in prior studies of laser-induced D-T fusion, the basic idea is to irradiate a small deuterium-and- tritium-containing target with a brief, intense laser pulse that causes a shock wave to propagate into the target. The shock wave ionizes and accelerates a substantial portion of the D and/or T molecules, resulting in, among other phenomena, collisions between D and T nuclei. The question of feasibility is essentially the question of whether, by use of a realistic target and a realistic laser pulse, a sufficient number of ions could be accelerated to sufficient kinetic energy such that the number of resulting D-T fusion reactions would suffice to produce a radiographically usefully large number of neutrons.

Figure 1. The Target and Laser Model for a set of simulations included a deuterium-coated hemispherical cavity in a piece of tin foil and a tritium sphere suspended at the center of the hemisphere, with a laser beam impinging along the axis of symmetry and the hemispherical surface acting as a mirror.
The computational-simulation study was performed by use of an augmented version of a plasma-simulation computer program called "VORPAL." The program was originally designed for the investigation of laser-wake-field acceleration of electrons, but its design is general enough to enable extension of it to other applications, including modeling of radio-frequency phenomena in superconducting cavities, examining microwave breakdown phenomena in waveguides, and investigation of astrophysical plasmas.

Shortly before the beginning of the study reported here, the program was enhanced by incorporation of a variety of models. One of them is a kinetic impact-ionization model that is a hybrid between a classical particle in cell model and a direct simulation Monte Carlo model. In this hybrid model, particles are represented as being pushed in their self-consistent electromagnetic field. At every time step, particles within a cell are considered for possible collision (and therefore reaction) by use of Monte Carlo methods. The main parameters required in this model are energy-dependent cross sections for ionization. While the model was designed mainly for ionization processes, it can relatively easily be adapted to other reaction-type processes, including fusion: in this study, the adaptation to D-T fusion was effected by incorporating a parameterized submodel of the energy dependence of the cross section for a D-T fusion reaction.

Figure 2. The Neutron Flux Density vs. Time at a distance of 1 m from the target was computed for laser beams having peak power densities corresponding to peak electric-field strengths ranging from 1.5 to 6 TV/m. The flux density depends strongly on the peak electric-field strength and, hence, on the peak laser power density.
This study included simulations in test cases involving laser beams impinging on shaped D-T targets. Figure 1 shows the target setup for a set of test cases in which (1) the target included a 10-μmthick tin foil of density 2.5×1027 m-3 containing a 5-μm-radius hemispherical cavity, (2) the cavity surface was coated with a 2.5-μm-thick layer of deuterium at a density of 4.4×1026 m-3, (3) a 2-μm-diameter tritium ball was suspended at the center of the hemisphere, (4) a laser beam of 0.8-μm-wavelength and 2.5-μmspot radius impinged along the axis of symmetry of the cavity, and (5) the peak electric-field strength in the laser pulse ranged from 1.5 to 6 TV/m in the various test cases. Figure 2 shows the temporal evolution of the neutron flux density. On the basis of the results from these and other test cases, it was concluded that neutron fluxes large enough for radiography could be generated by use of laser pulses having moderate (approximately between 1017 and 1018 W/cm2) peak power densities.

This work was done by Jean Luc Cambier of the Air Force Research Laboratory, and Peter Messmer, Kevin Paul, and Peter Stoltz of Tech-X Corp.

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Kinetic Modeling of Laser-Induced D-T Fusion

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This article first appeared in the June, 2008 issue of Defense Tech Briefs Magazine.

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