Bremsstrahlung constraints on proton-Boron 11 inertial fusion

TL;DR

This work analyzes the bremsstrahlung losses in proton-boron-11 inertial confinement fusion and whether radiative energy can be trapped to achieve breakeven. A simplified burn-model framework shows that, without reabsorption, maximum $Q_ ext{sci}$ is limited to about 2 and requires unrealistically large stagnation areal densities. Introducing a model for inverse bremsstrahlung absorption and incorporating radiative reabsorption into the burn dynamics raises $Q_ ext{sci}$ to roughly $15$–$20$, but only under very dense, high-$n_e$ regimes with $n_e \gtrsim 6\times10^{27}$ cm$^{-3}$ and areal densities around 100 g cm$^{-2}$; yields at these conditions remain far beyond current capabilities. The results imply that achieving power-plant-scale pB11 fusion would require next-generation lasers and substantial advances in dense-plasma physics, while also motivating exploration of nonuniform or fast-ignition approaches and more complete EOS/collision models in future work.

Abstract

Proton-Boron 11 (pB11) fusion is relatively safe and clean, but difficult to use for net power production, since bremsstrahlung radiation tends to radiate away power more quickly than it can be generated by fusion power, particularly once poisoning by alpha particles is taken into account. While in magnetic confinement fusion (MCF), this problem can be addressed by deconfining the alphas, in inertial confinement fusion (ICF) the alphas that heat the plasma linger for the duration of the reaction. Thus, it becomes essential to trap the bremsstrahlung radiation in the hotspot. Through burn simulations incorporating bremsstrahlung emission and reabsorption, we infer the necessary conditions to capture enough radiation to produce scientific breakeven in a pB11 ICF plasma. We find that breakeven requires a stagnation areal density roughly two orders of magnitude higher than the current state-of-the-art, at pressures three orders of magnitude higher.

Figures (14)

• Figure 1: Steady-state electron temperature from Eq. (\ref{['eq:ElectronQuasiSteadyState']}) as a function of ion temperature (top), and the resulting ratio between fusion power and bremsstrahlung power given those electron and ion temperatures (bottom), for several values of the boron fraction $f_b \equiv n_b/n_i$. With too high a boron fraction, the fusion power cannot exceed the bremsstrahlung power; thus, a boron fraction less than 50% is necessary to achieve sustained burn, with lower $f_b$ allowing burn at lower ion temperatures.
• Figure 2: $Q_\text{sci}$ as a function of $T_i$ for a plasma transparent to bremsstrahlung, for equal initial electron and ion temperatures ($\bar{T}_e = 1$), and for several values of the ion density $n_i$ and electron areal density $n_e R$. Dots indicate simulations where the burn completed ($P_{F,\text{final} }< P_{F,\text{max}}/10$), and diamonds indicate simulations where the burn was still ongoing when the simulation ended at the disassembly time.
• Figure 3: Optimal boron fraction $f_b \equiv n_{b0} / n_{i0}$ for the simulations without bremsstrahlung reabsorption [Figs. \ref{['fig:QSci_Transparent']}-\ref{['fig:QSci_Transparent_LowTe']}]. In line with the discussion in Sec. \ref{['sec:heuristics']}, $f_b \sim 0.25$ seems to represent the optimal tradeoff between limiting bremsstrahlung radiation and burning as much fuel as possible. As before, dots indicate completed burn, while diamonds indicate incomplete burn.
• Figure 4: Boron burn fraction $\Phi_b \equiv n_{b,\text{burn}}/n_{b0}$ for the simulations without bremsstrahlung reabsorption [Figs. \ref{['fig:QSci_Transparent']}-\ref{['fig:QSci_Transparent_LowTe']}]. As before, dots indicate completed burn, while diamonds indicate incomplete burn. The burn fraction hovers between 60-70% for the optimal cases.
• Figure 5: $Q_\text{sci}$ as a function of $T_i$ for a plasma transparent to bremsstrahlung, as in Fig. \ref{['fig:QSci_Transparent']}, but now with an initial electron temperature equal to 1/5 the initial ion temperature ($\bar{T}_e = 0.2$). As before, dots indicate completed burn, while diamonds indicate incomplete burn.