Nuclear reaction rates and energy in stellar plasmas: The effect of highly damped modes

TLDR

Classical plasma analysis assumes de Broglie wavelengths are much smaller than the closest approach distance and that fluctuation energies ℏω≪kBT, leading to enhanced reaction rates through ion screening. The study discusses the impact of highly damped modes (ℏ≠0) on plasma energy and nuclear reaction rates. The authors incorporate ion screening via the Salpeter factor and examine the effects using sheet‑model particle simulations and a multiparticle quantum simulation code. Highly damped modes with k≫kD, even when weakly excited, significantly contribute to plasma energy and screening, but their fluctuation spectra are markedly reduced—especially at high frequencies (≈0.5–3 kBT)—according to the fluctuation‑dissipation theorem.

Abstract

The effects of the highly damped modes in the energy and reaction rates in a plasma are discussed. These modes, with wave numbers k≫kD, even being only weakly excited, with less than kBT per mode, make a significant contribution to the energy and screening in a plasma. When the de Broglie wavelength is much less than the distance of closest approach of thermal electrons, a classical analysis of the plasma can be made. It is assumed, in the classical analysis, with ℏ→0, that the energy of the fluctuations ℏω≪kBT. Using the fluctuation-dissipation theorem, the spectra of fluctuations with ℏ≠0 is appreciably decreased. The decrease is mainly for the highly damped modes at high frequencies (∼0.5–3kBT). Reaction rates are enhanced in a plasma due to the screening of the reacting ions. This is taken into account by the Salpeter factor, which assumes slow motion for the ions. The implication of including the highly damped modes (with ℏ≠0) in the nuclear reaction rates in a plasma is discussed. Finally, the investigations presently done on these effects in particle simulations with the sheet model and the multiparticle quantum simulation code are described.