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

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 11 C/ 7 Be, we obtained an effective "single shot" temperature of the TNSA plasma.We used this value to evaluate the yield of  particles from the reaction p+ 11 B → 3 which may reach 1.6±0.510 9 in 2.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.We stress that the KdV fit is phenomenological, not a claim about the plasma satisfying KdV conditions.Further experimental and theoretical efforts are needed to clarify the nature of the deviation from the ideal case.