We develop the physical model and the system of equations for the impulse neutron source (INS) of high-energy neutrons ($sim$14 MeV) emitted by fusion reactions during compression of D-T gas by cumulative detonation waves. The system of INS equations includes a system of gas dynamic equations that takes into account the energy transfer by radiation, equations for the radiation flux, the equation of the shock adiabat (the Hugoniot adiabat) for a compressed gas, and the equation for the neutron yield. We perform the INS dynamics simulation for the spherical and cylindrical geometries, and calculate maximum temperatures of D-T plasma, its density and neutron yield in the pulse. The obtained temperature estimates and simulation results show that the thermonuclear fusion temperatures are reached within this approach, and the fusion reactions proceed. Their yield determines the yield of neutrons.
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