Design of experiments characterising heat conduction in magnetised, weakly collisional plasma

TL;DR

This work designs an Orion-laser-based platform to study heat conduction in weakly collisional, magnetised plasmas susceptible to the whistler heat-flux instability. It leverages FLASH radiation-MHD simulations to optimize a two-beam target that produces a planar, high-$\beta$ plasma with temperature gradients aligned to $\mathbf{B}$ and compares three conduction models ($q_{||}$ suppression scenarios) to predict observable differences in $T_e$ evolution and magnetic-field structure. The authors develop and test complementary synthetic diagnostics—GXD, X-ray spectroscopy, and proton imaging—to infer $T_e$, $n_e$, and $\mathbf{B}$, showing that the temperature evolution and field morphology are sensitive to the conduction model, with potential suppression factors up to $(q_{||\text{eff}}/q_S)^{-1} \approx 16.4$ at early times. The study demonstrates a viable route to constrain kinetic-regime heat transport in laboratory plasmas and links experimental observables to whistler-driven conduction models relevant to astrophysical and HED contexts.

Abstract

Heat conduction in weakly collisional, magnetised plasma is challenging to model accurately due to multifaceted physics governing heat-carrying electrons, including microinstabilities that scatter electrons and modify heat transport. Capturing these effects requires multidimensional kinetic theory simulations, which are computationally expensive. Experimental constraints overcome this issue, resulting in improved understanding of thermal transport in systems such as the intra-cluster medium of galaxy clusters, and the hot-spot in inertial confinement fusion. In this paper, we present a new experimental platform that produces a weakly collisional high-\b{eta} plasma expected to be susceptible to the whistler heat-flux instability. This platform, to be fielded on the Orion laser, enables characterisation of whistler-regulated thermal conductivity. The platform design is assessed using radiation-magnetohydrodynamics simulations with the code FLASH. Simulations using three thermal conduction models predict conductivity suppression by over an order of magnitude relative to the Spitzer value at whistler saturation, demonstrating the efficacy of the platform.

Figures (17)

• Figure 1: Simplified diagram of plasma generation in two phases: the driving of the target foil producing a front-side blow-off plasma. Then, the generation of a shocked plasma from the front-side blow off, threaded with self-generated magnetic fields parallel to the temperature gradients generated during the drive foil ablation.
• Figure 2: Evolution of the target design. (a) Original five beam proof of concept visualisation with all drive beams normal to target. The left shows all beams incident on the drive foil, and the resultant ablation plume on the right, with end of the shock foil ablating prior to contact with the jet plasma. (b) Updated four beam design visualisation using the Orion chamber beam alignment geometry, and shorter shock foil. The right top panel shows the target top-down, and the bottom right panel showing the target side-on matching the LoS seen in the top and bottom row, respectively, of (c). (c) 2D slices taken from the FLASH simulation data for $T_{e}$ (left), $B_{y}$ (centre), and $n_{e}$ (right), for $z = -0.114$ cm (top row), and $y = 0.00$ cm (bottom row) at $t = 1.5$ ns post the drive foils ablation. (d) Same as (b), but with the final two beam configuration (e) Comparison of 2D slices from FLASH simulation data for $T_{e}$ (top row), and $n_{e}$ (bottom row), as in (c) for the two beam and four beam design, indicating the more laminar nature of the temperature and density profiles for the two beam design.
• Figure 3: (a) VisRad visualisation of the experimental configuration within the Orion chamber. The drive and shock foils are placed in the centre of the chamber with the plane face of the shock foil facing out of the page, and the plane face of the drive foil facing northward. The LP drive beams are shown in blue targeting the drive foil, with the SP beams shown in red targeting the Au foils for proton production. The diagnostic detectors are off-screen with their radial position, relative to target chamber centre (TCC), and lines-of-sight (LoS) indicated by the orange arrows. The slit foil at the bottom of the image is to screen the X-rays for the spectrometer, which will be swapped out mid-way through the campaign to be replaced with a spatially resolved GXD. (b) Target configuration on Al mounting block. The orange chair will be 3D printed with with the drive and shock foils mounted on it. The cross-beam structure holding the chair will increase stability and ensure that the drive and shock foils' plane faces will remain orthogonal post ablation.
• Figure 4: 2D visualisations using FLASH simulation data, viewing front-on, into to the drive foil plane, for $T_{e}$ (left-most two columns), and $n_{e}$ (right-most two columns) for Spitzer (a) and (d), conduction-off (b) and (e), and Ryutov (c) and (f) simulations between $2.0~\text{ns}\leq t \leq 3.0$ ns. Slice taken at $x = 0.01$ cm from FLASH simulation domain.
• Figure 5: 2D visualisations using FLASH simulation data, viewing the side of the drive foil plane normal, for $T_{e}$ (left-most two columns), and $n_{e}$ (right-most two columns) for Spitzer (a) and (d), conduction-off (b) and (e), and Ryutov (c) and (f) simulations between $2.0~\text{ns}\leq t \leq 3.0$ ns. Slices taken at $y = 0.0$ cm from FLASH simulation domain.