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.

Fusion Energy Output Greater than the Kinetic Energy of an Imploding Shell at the National Ignition Facility

“…In addition to the power and pulse duration increase, the capsule drive was modified to reduce the time between the end of the laser and the peak neutron emission (coast time) (figure 1-c). A reduced coast time was demonstrated to increase stagnation pressure and yield for High Foot implosions [33]. These modifications led to record fusions yields and hot spot ρr shown on figure 4 (red dots).…”

Lawson Criterion for Ignition Exceeded in an Inertial Fusion Experiment

“…A key aspect shown is the laser typically turns off ≈1 ns before bang time (denoted "coast-time" duration), of order the hohlraum cooling time [17]. Increasing late-time x-ray drive results in reduced coast time which enhances the conversion of implosion kinetic energy to DT internal energy [18,19]. which are the 4 He nuclei).…”

“…The challenge of increasing initial capsule radius with fixed laser drive is the potential loss of energy density at the core of the implosion [71]. It is therefore essential to, while increasing the size, maintain the other implosion design parameters including the compressibility of the fuel ("adiabat"), v imp , and the late-time ablation pressure from the drive [18].…”

Design of inertial fusion implosions reaching the burning plasma regime

“…Both designs have worked to maintain the late-time ablation pressure but continued optimization is ongoing. A metric for this is the 'coast time' 36 or the time that the implosion has to decompress when the radiation drive is decreasing (Table 1 and Methods), which was order of magnitude lower than previously seen in high-gas-fill hohlraums using wavelength detuning. Reduced back-scatter and laserplasma-interaction instabilities in the presence of large amounts of transfer creates a stronger observed sensitivity of implosion symmetry to wavelength detuning, allowing for radiation-symmetry control throughout the drive history 11,22 .…”

“…10 These authors contributed equally: A. L. Kritcher, C. V. Young, H. F. Robey. ✉ e-mail: kritcher2@llnl.gov; young110@llnl.gov A short 'coast time'-nominally the time between the maximum radiation temperature and bang time (maximum compression)-is important for maintaining the ablation pressure and achieving high hot-spot pressures and fuel compression 36 , but is more challenging with a fixed laser energy and for maintaining symmetry. A ramped (or 'drooping') laser pulse 10,41 was used in HYBRID-E, which was designed to help maintain the late-time ablation pressure at the larger scale and enabling the full use of the NIF laser (Extended Data Fig.…”