Probing In-Solid Proton Energy Distributions in Laser-Driven Fusion via Nuclear Activation Diagnostics

TL;DR

This paper introduces a nuclear activation diagnostic method to measure the in-solid proton energy distribution in laser-driven fusion, overcoming limitations of conventional particle diagnostics.

Contribution

It develops a quantitative internal probing technique using nuclear reactions within the target to reconstruct proton energy distributions in solid materials.

Findings

Reconstructed exponential-equivalent proton energy distributions from activation yields.

Quantified the number of specific nuclear reactions within the target.

Demonstrated the method's applicability to high-energy laser-driven fusion experiments.

Abstract

The energy distribution of energetic protons inside a solid target is a key quantity governing nuclear reaction yields and energy deposition in high-intensity laser-driven fusion, including nonthermal proton--boron (p--B) schemes and proton fast ignition. Yet it has remained inaccessible to conventional particle diagnostics, which detect only ions escaping the target and are perturbed by intense plasma electromagnetic fields. Here we establish a quantitative diagnostic that uses nuclear activation reactions occurring within the target itself as an internal probe of the in-solid proton energy distribution. Applied to laser-driven p--B fusion experiments on the kJ-class laser, the method reconstructs an exponential-equivalent in-solid proton energy distribution from the absolute yields of $^{11}\mathrm{C}$ and $^{7}\mathrm{Be}$ produced via $\mathrm{^{11}B(p,n)^{11}C}$ and $\mathrm{^{10}B(p,\alpha)^{7}Be}$, and yields the absolute number of $\mathrm{^{11}B(p,2\alpha)^{4}He}$ reactions through a side-channel analysis with propagated cross-section uncertainties. This work opens a quantitative window onto the in-solid proton dynamics that drive nuclear reactions in laser-driven fusion experiments.