On the importance of minimizing “coast-time” in x-ray driven inertially confined fusion implosions

Abstract

By the time an inertially confined fusion (ICF) implosion has converged a factor of 20, its surface area has shrunk 400×, making it an inefficient x-ray energy absorber. So, ICF implosions are traditionally designed to have the laser drive shut off at a time, toff, well before bang-time, tBT, for a coast-time of tcoast=tBT−toff>1 ns. High-foot implosions on NIF showed a strong dependence of many key ICF performance quantities on reduced coast-time (by extending the duration of laser power after the peak power is first reached), most notably stagnation pressure and fusion yield. Herein we show that the ablation pressure, pabl, which drives high-foot implosions, is essentially triangular in temporal shape, and that reducing tcoast boosts pabl by as much as ∼2× prior to stagnation thus increasing fuel and hot-spot compression and implosion speed. One-dimensional simulations are used to track hydrodynamic characteristics for implosions with various coast-times and various assumed rates of hohlraum cooling after toff to illustrate how the late-time conditions exterior to the implosion can impact the fusion performance. A simple rocket model-like analytic theory demonstrates that reducing coast-time can lead to a ∼15% higher implosion velocity because the reduction in x-ray absorption efficiency at late-time is somewhat compensated by small (∼5%−10%) ablator mass remaining. Together with the increased ablation pressure, the additional implosion speed for short coast-time implosions can boost the stagnation pressure by ∼2× as compared to a longer coast-time version of the same implosion. Four key dimensionless parameters are identified and we find that reducing coast-time to as little as 500 ps still provides some benefit. Finally, we show how the high-foot implosion data is consistent with the above mentioned picture.