Self-generated magnetic field in plasma reconstructed by using inverse Abel transformation in proton radiography

Abstract

The magnetic fields generated in plasmas have inclusive influences on many processes of the inertial confinement fusion and the astrophysics. Therefore, the quantitative diagnosis of the magnetic field is quite essential. Proton radiography is a widely used experimental technique to diagnose the electric field or magnetic field in high-energy-density plasma physics. The effective interpretation of the results of proton radiography depends on the reliability and availability of the inversion method. Traditional inversion methods can only provide 1D or 2D structures of the self-generated magnetic field. In this study, it was found that there was an Abel transformation relationship between the deflection velocity and the magnetic field with column symmetry, which allowed us to reconstruct the 3D structure of the magnetic field for the first time. We theoretically deduce the process of reconstructing the cylindrical magnetic field through proton radiography with the Abel inversion algorithm. The feasibility of this method is verified by numerical simulation as well. Based on this inversion method, we reanalyzed the proton radiography experimental results of C.K. Li et al. [Nat. Commun. 7 13081(2016)] on the self-generated magnetic field of plasma jets. The inversion results show that the maximum magnetic field intensity is about 1.9 times of the traditional inversion results. We discuss a new proton radiography inversion method for the existence of magnetic fields with cylindrical symmetry in this paper, which will contribute to an intensive understanding of the self-generated electromagnetic field and its spatial-temporal evolution related to the laser fusion and the laboratory astrophysics.