On the importance of minimizing ``coast-time'' in x-ray driven inertial confinement fusion implosions

By the time an ICF implosion has converged a factor of 20, its surface area has shrunk 400x, making it an inefficient x-ray energy absorber. So traditionally, ICF implosions are designed to have the laser drive shut off at a time, $t_{off}$, well before bang-time, $t_{BT}$, for a coast-time of $t_{coast}=t_{BT}-t_{off}.$ Contrary to expectations, high-foot implosions on NIF show a strong dependence of many key ICF quantities on reduced coast-time (by extending the duration of laser peak power at constant power), most notably stagnation pressure. Herein we show that the ablation pressure, $p_{abl}$, which drives high-foot implosions, is essentially triangular in temporal shape, and that reducing $t_{coast}$ boosts $p_{abl}$ by \textasciitilde 2x. Analytic theory demonstrates that reducing coast-time can lead to a \textasciitilde 15{\%} higher implosion velocity, which together with the increased ablation pressure, can boost the stagnation pressure by \textasciitilde 2x as compared to a coasting version of the same implosion. Four dimensionless parameters are identified. We find that reducing coast-time to as little as 500 ps still provides some benefit.