The phenomenology of thermonuclear burn in deuterium-tritium microspheres at high densities is described, and numerical results characterizing the burn for a broad range of initial conditions are given. The fractional burnup, bootstrap-heating, and depletion of the DT fuel, its expansive disassembly, and thermonuclear ignition by propagating burn from central hot spots in the microspheres are discussed. Extensive numerical results from a 3 T Lagrangian simulation code are presented. The yields Y0 from uniform 10, 1, and 0.1 μg microspheres with densities ρ = 1 to 4 × 104 g/cm3 and temperatures Te = Ti = 1.8 to 100 keV are given. It is shown that Y0 ∼ ρR, ρR < 0.3 (R is the microsphere radius) or, equivalently, Y0 ∼ ρ2/3 for spheres of fixed mass m. The gain-factor G0 ≡ Y0/mI0 (I0 is the internal energy) is shown to measure burn efficiency in uniform microspheres. More than a four-fold increment in the gain factor is shown to derive from apportionment of the internal energy in a central hot spot. The limiting effects of electron degeneracy on the gain factor are outlined. As a guideline, the experimental observation of 1013 neutrons/kJ of input laser energy is established as proof of good absorption; 1015/kJ will imply yields exceeding break even.

The solution for the perturbation growth of a shock wave striking a density discontinuity at a material interface is developed. The Laplace transformation of the perturbation results in an equation which has a simple solution for weak shock waves. The solution for strong shock waves may be given by a power series. It is assumed that the equation of state is that of an ideal gas. The four independent parameters of the solution are the ratio of specific heat for each material, the density ratio at the interface, and the incoming shock strength. Properties of the solution which are investigated include the asymptotic behavior at large times of the perturbation velocity at the interface, the vorticity near the interface, and the rate of decay of the solution at large distances from the interface. The last is much weaker than the exponential decay in an incompressible fluid. The asymptotic solution near the interface, in addition to a constant term, consists of a number of slowly decaying discrete frequencies. The number is roughly proportional to the logarithm of the density ratio at the surface for strong shocks, and decreases with shock strength. For weak shocks the solution is compared with results for an incompressible fluid. Only interface perturbation velocities which tend to zero at large times lead to a limited deformation of the interface. It is found that these are possible only for density ratios less than about 1.5.

Stars with a core mass greater than about 30 M 0 become dynamically unstable due to electron-positron pair production when their central temperature reaches 1.5-2.G x 10 9 °K. The collapse and subsequent explosion of stars with core masses of 45, 52, and 60 Me is calculated.Tiie range of the final velocity of expansion (3,400-8, 500 km/sec ) and of the mass ejected ( 1-40 Me ) is comparable to that observed for type II supernovae.An implicit scheme of hydrodynamic difference equations (stable for large time steps) used for the calculation of the evolution is described.For fast evolution the turbulence caused by convective instability does not produce the zero entropy gradient and perfect mixing found for slower evolution.A dynamical model of the convection is derived from the equ a tions of motion and then incorporated into the difference equations.

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