Alpha Heating and Burning Plasmas in Inertial Confinement Fusion

Estimating the level of alpha heating and determining the onset of the burning plasma regime is essential to finding the path towards thermonuclear ignition. In a burning plasma, the alpha heating exceeds the external input energy to the plasma. Using a simple model of the implosion, it is shown that a general relation can be derived, connecting the burning plasma regime to the yield enhancement due to alpha heating and to experimentally measurable parameters such as the Lawson ignition parameter. A general alpha-heating curve is found, independent of the target and suitable to assess the performance of all laser fusion experiments whether direct or indirect drive. The onset of the burning plasma regime inside the hot spot of current implosions on the National Ignition Facility requires a fusion yield of about 50 kJ.

Figure 1

Trajectories from the model (1)–(5) using $\beta =0$, $\gamma =0$. The figure shows the time evolution of the hot spot radius, the return shock inside the shell and the shell outer surface.

Figure 2

Yield enhancement from alpha heating as a function of the alpha and no-alpha Lawson parameters using the model (1–5) (solid curve) and hydrodynamic simulations (dots). The measurable parameter ${\chi }_{\alpha }$ can be used to determine the yield amplification from Fig. 2. Fig. 2 can be used to infer the no-alpha parameter ${\chi }_{no\alpha }$ which is useful for assessing progress toward ignition. Points 1–3 represent simulations with mass, adiabat and velocity similar to NIF ID targets (see Fig. 3).

Figure 3

Plots of the yield amplification versus the hot-spot $Q_{\alpha }$ (a) and the total $Q_{\alpha }$ (b) from the model (1–5) (solid curve) and from 1D simulations (dots). The shaded areas identify the burning plasma regimes. Points (1–3) with yield amplification $\sim 2.5\times$ (like shot N140120 [19]), $3.3\times ,6.7\times$ have fuel kinetic energy of $\sim 12\mathrm{kJ}$, adiabat $\lesssim 2$ and DT mass $\approx 0.18\mathrm{mg}$ like current NIF ID experiments. Point 2 is at the hot-spot burning-plasma onset. Point 3 is in the full burning plasma regime.