Thermonuclear ignition and the onset of propagating burn in inertial fusion implosions

Separating ignition of the central hot spot from propagating burn in the surrounding dense fuel is crucial to conclusively assess the achievement of ignition in inertial confinement fusion (ICF). We show that the transition from hot spot ignition to the onset of propagating burn occurs when the alpha heating within the hot spot has amplified the fusion yield by $15\times$ to $25\times$ with respect to the compression-only case without alpha energy deposition. This yield amplification corresponds to a value of the fractional alpha energy $f_{\alpha }\approx 1.4$ ($f_{\alpha }=0.5$ alpha energy/hot spot energy). The parameter $f_{\alpha }$ can be inferred in ICF experiments by measuring the neutron yield, hot spot size, temperature, and burn width. This ignition threshold is measurable and applicable to all ICF implosions of deuterium and tritium targets both direct and indirect drive. The results of this Rapid Communication can be used to set the goals of the ICF effort with respect to the first demonstration of thermonuclear ignition.

Figure 1

The yield amplification is plotted as a function of $f_{\alpha }$ for the ensemble of 1D lilac [18] simulations (turquoise points). In the alpha-heating regime ($f_{\alpha }<1.4$), the yield amplification depends uniquely on $f_{\alpha }$ regardless of the target mass, areal density, and temperature. After $f_{\alpha }=1.4$, shell mass and burnup fraction determine the maximum fusion yield. The yellow, red, green, and dark-blue points respectively represent 2D draco [19] single-mode simulations of modes 2, 4, 6, and 10. The purple points are multimode simulations perturbed by modes 2 and 4.

Figure 2

In the burn propagation phase, the fuel burnup fraction $\mathrm{\Phi }$ depends uniquely on the parameter $\rho R/H_B$ and follows the same scaling as predicted by theory [Eq. (2)]. Here, the burnup fraction is defined as $\mathrm{\Phi }=\text{Yield}/N_{\text{DT}}$, where $N_{\text{DT}}$ is the initial number of DT ions in the unablated mass. The dark violet points correspond to implosions with yield amplifications larger than 25 and the black line is the analytic curve from Eq. (2).

Figure 3

The metric $f_{\alpha }$ is plotted against the intrinsic parameter $P_0\tau /S_{\alpha ,0}$. At $f_{\alpha }\sim 1.4$, this profile factor changes dramatically and the tight correlation observed between $f_{\alpha }$ and $P_0\tau /S_{\alpha ,0}$ breaks down. Toward the right, example profiles of the neutron production rate per unit volume are shown to illustrate that the neutron production rate is maximized near the hot spot edge.

Figure 4

The metric $f_{\alpha }$ computed using the pressure from Eq. (6) compares well with exact calculations from lilac (turquoise dots) as well as 2D single-mode and multimode simulations.