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

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.