Deceleration phase of inertial confinement fusion implosions

A model for the deceleration phase and marginal ignition of imploding capsules is derived by solving a set of ordinary differential equations describing the hot-spot energy balance and the shell dynamics including the return shock propagation. It is found that heat flux leaving the hot spot goes back in the form of internal energy and PdV work of the material ablated off the inner-shell surface. Though the hot-spot temperature is reduced by the heat conduction losses, the hot-spot density increases due to the ablated material in such a way that the hot-spot pressure is approximately independent of heat conduction. For hot-spot temperatures exceeding approximately 7 keV, the ignition conditions are not affected by heat conduction losses that are recycled into the hot spot by ablation. Instead, the only significant internal energy loss is due to the hot-spot expansion tamped by the surrounding shell. The change of adiabat induced by the shock is also calculated for marginally igniting shells, and the relation between the in-flight and stagnation adiabats is in general agreement with the numerical fit of LASNEX simulations by Herrmann et al. [Nucl. Fusion 41, 99 (2001)] and the self-similar solution of Kemp et al. [Phys. Rev. Lett. 15, 3336 (2001)]. The minimum kinetic energy required for ignition is also calculated from the same model and shown to be in good agreement with the numerical fit of LASNEX simulations. It is also found that mass ablation leads to a significant reduction of the deceleration phase Rayleigh-Taylor instability growth rates and to the suppression of short wavelength modes