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Abstract:

Our understanding of physical systems often depends on our ability to match complex computational modeling with the measured experimental outcomes. However, simulations with large parameter spaces suffer from inverse problem instabilities, where similar simulated outputs can map back to very different sets of input parameters. While of fundamental importance, such instabilities are seldom resolved due to the intractably large number of simulations required to comprehensively explore parameter space. Here, we show how Bayesian inference can be used to address inverse problem instabilities in the interpretation of x-ray emission spectroscopy and inelastic x-ray scattering diagnostics. We find that the extraction of information from measurements on the basis of agreement with simulations alone is unreliable and leads to a significant underestimation of uncertainties. We describe how to statistically quantify the effect of unstable inverse models and describe an approach to experimental design that mitigates its impact.

Abstract:

Proton radiography is a technique in high energy density science to diagnose magnetic and/or electric fields in a plasma by firing a proton beam and detecting its modulated intensity profile on a screen. Current approaches to retrieve the integrated field from the modulated intensity profile require the unmodulated beam intensity profile before the interaction, which is rarely available experimentally due to shot-to-shot variability. In this paper, we present a statistical method to retrieve the integrated field without needing to know the exact source profile. We apply our method to experimental data, showing the robustness of our approach. Our proposed technique allows not only for the retrieval of the path-integrated fields, but also of the statistical properties of the fields.

Abstract:

Magnetic reconnection is a process that contributes significantly to plasma dynamics and energy transfer in a wide range of plasma and magnetic field regimes, including inertial confinement fusion experiments, stellar coronae, and compact, highly magnetized objects like neutron stars. Laboratory experiments in different regimes can help refine, expand, and test the applicability of theoretical models to describe reconnection. Laser-plasma experiments exploring magnetic reconnection at a moderate intensity (IL ∼1014 W cm-2) have been performed previously, where the Biermann battery effect self-generates magnetic fields and the field dynamics studied using proton radiography. At high laser intensities (ILλL2>1018 Wcm-2μm2), relativistic surface currents and the time-varying electric sheath fields generate the azimuthal magnetic fields. Numerical modeling of these intensities has shown the conditions that within the magnetic field region can reach the threshold where the magnetic energy can exceed the rest mass energy such that σcold = B2/(μ0nemec2) > 1 [A. E. Raymond et al., Phys. Rev. E 98, 043207 (2018)]. Presented here is the analysis of the proton radiography of a high-intensity (∼1018 W cm-2) laser driven magnetic reconnection geometry. The path integrated magnetic fields are recovered using a "field-reconstruction algorithm" to quantify the field strengths, geometry, and evolution.