Extended Biermann-Battery Fields via Proton Radiography with X-ray Fiducials*

Self-generated, Biermann-battery magnetic fields are ubiquitous in laser-heated plasmas and can affect heat transport in inertial confinement fusion. Despite nearly two decades of proton radiography experiments and extended magnetohydrodynamic (MHD) simulations, the field structure in laser-foil experiments remains uncertain due to measurement limitations and modelling challenges such as the Nernst effect. In this study, we present high fidelity measurements of Biermann-battery magnetic fields using a proton radiography scheme with in situ x-ray fiducials [1,2]. In this scheme, protons and x-rays are split into beamlets with a mesh and stream through the fields; protons are deflected whereas x-rays provide an undeflected reference image. In a single shot, the absolute path-integrated field is inferred from the shift between x-ray and proton beamlets. Experiments were conducted at the OMEGA laser system where Biermann-battery magnetic fields were generated by driving a plastic foil with a 3X10¹⁴ W/cm² laser pulse. The measured field extends more than twice as far as prior experimental results and yields significantly more energy deposition into the magnetic fields. The results are compared to Gorgon extended MHD simulations. The widely adopted reconstruction algorithm, PROBLEM, is compared to this technique. Good agreement is found only when nonzero magnetic boundary conditions are used from the x-ray mesh technique and the background proton fluence is assumed to be anisotropic.

[1] C. Johnson, S. Malko, W. Fox, D. Schaeffer et al., Review of Scientific Instruments 83 (2021).

[2] S. Malko, C. Johnson, W. Fox, D. Schaeffer et al., Applied Optics 61(6) (2021).