X-rays from Proton Bremsstrahlung: Evidence from Fusion Reactors and Its Implication in Astrophysics

TL;DR

This paper investigates proton bremsstrahlung in fusion reactors, revealing that low-energy nuclear reactions produce characteristic X-ray spectra, which could improve plasma diagnostics and explain certain astrophysical X-ray sources.

Contribution

It introduces a semiclassical calculation of X-ray spectra from low-energy proton-deuteron fusion, linking nuclear bremsstrahlung to plasma diagnostics and astrophysical X-ray emissions.

Findings

X-ray spectra peak near 1.1 keV for proton-deuteron fusion

Spectrum follows a power-law decay at high energies

Estimated X-ray luminosity matches observed astrophysical data

Abstract

In a fusion reactor, a proton and a neutron generated in previous reactions may again fuse with each other. Or they can in turn fuse with or be captured by an un-reacted deuteron. The average center-of-mass (COM) energy for such reaction is around 10 keV in a typical fusion reactor, but could be as low as 1 keV. At this low COM energy, the reacting nucleons are in an s-wave state in terms of their relative angular momentum. The single-gamma radiation process is thus strongly suppressed due to conservation laws. Instead the gamma ray released is likely to be accompanied by x-ray photons from a nuclear bremsstrahlung process. The x-ray thus generated has a continuous spectrum and peaks around a few hundred eV to a few keV. The average photon energy and spectrum properties of such a process are calculated with a semiclassical approach. The results give a peak near 1.1 keV for the proton-deuteron fusion and a power-to-the-minus-second law in the spectrum's high-energy limit. An analysis of some prior tokamak discharge data shows that this phenomenon might have been observed before and it may lead to new plasma diagnostics which are more sensitive to the ionic or nuclear degree of freedom. This phenomenon should also play a role in nuclear astrophysics as one of the sources for astrophysical x-rays. The process contributes particularly to stellar evolution in the early stage, where the temperature of proto-stars or the so called pre-main sequence stars (T Tauri stars, for example), is at a relatively low of several million degrees Kelvin. An order-of-magnitude calculation was made on the proton-deuteron fusion rate in young star objects. The estimated x-ray luminosity from this reaction is found enough in magnitude to account for experimental ones.