Detailed study of non-equilibrium characteristics of quasi-neutral TNSA plasmas

TL;DR

This study analyzes non-equilibrium features of TNSA plasmas through experimental proton distributions, deriving plasma temperature, fusion yields, and a novel TNSA-Equation of State that aligns with soliton solutions of the KdV equation.

Contribution

It introduces a method to determine TNSA plasma temperature and derives a new TNSA-Equation of State based on experimental data and soliton theory.

Findings

Effective single-shot plasma temperature derived from yield ratios.

Predicted alpha particle yield of approximately 1.6 x 10^9 in 2pi.

TNSA-Equation of State deviates from ideal gas law and matches KdV soliton solutions.

Abstract

In an experiment performed in November 2022 at the petawatt (PW) laser facility at Vega III located in Salamanca-Spain, we have studied the successful production of several radioisotopes using protons accelerated by the Target Normal Sheath Acceleration (TNSA) mechanism (Rodrigues et al. [1]). The experimental proton energy distribution recorded on a shot-to-shot basis and confirmed in a follow up experiment (K. Batani et al. [2]), allowed us to derive the number of nuclear reactions taking place in different targets on a single shot. From this analysis, using the ratio of the yields 11C/7Be, we obtained an effective "single shot" temperature of the TNSA plasma. We used this value to evaluate the yield of alpha particles from the reaction p + 11B -> 3 alpha which may reach (1.6 +/- 0.5) x 10^9 alpha particles in 2pi. From the fluctuations of the protons and the fusion yields, we derived a "TNSA-Equation of State" (EoS), The deviation of such "EoS" from the classical ideal gas limit is well reproduced by the soliton solution of the Korteweg-de Vries (KdV) equation for each shot.