Inferring Morphology and Strength of Magnetic Fields From Proton Radiographs

TL;DR

This paper develops a theoretical framework for analyzing proton radiographs to infer the morphology and strength of magnetic fields in plasmas, enabling more detailed magnetic field reconstructions from experimental data.

Contribution

It introduces a linear-order theory linking proton radiographs to magnetic field structures and provides an inversion method to reconstruct magnetic fields from radiograph data.

Findings

Reconstruction of magnetic field structure via solving a diffusion equation.

Analysis of limitations due to noise, discretization, and edge effects.

Extension potential to nonlinear contrast regimes.

Abstract

Proton radiography is an important diagnostic method for laser plasma experiments, and is particularly important in the analysis of magnetized plasmas. The theory of radiographic image analysis has heretofore only permitted somewhat limited analysis of the radiographs of such plasmas. We furnish here a theory that remedies this deficiency. We show that to linear order in magnetic field gradients, proton radiographs are projection images of the MHD current along the proton trajectories. We demonstrate that in the linear approximation, the full structure of the perpedicular magnetic field can be reconstructed by solving a steady-state inhomogeneous 2-dimensional diffusion equation sourced by the radiograph fluence contrast data. We explore limitations of the inversion method due to Poisson noise, to discretization errors, to radiograph edge effects, and to obstruction by laser target structures. We also provide a separate analysis that is well-suited to the inference of isotropic-homogeneous magnetic turbulence spectra. We discuss extension of these results to the nonlinear contrast regime.