Description
In inertial confinement fusion, inverse bremsstrahlung (IB) is the primary mechanism by which laser energy is transferred to hot plasma. It is well known that IB’s preferential heating of slow moving electrons can drive the electron energy distribution function towards a super-Gaussian distribution through the Langdon effect. We demonstrate that while the industry standard Matte-Virmont-Epperlein (MVE) quasi-static fit for the super-Gaussian coefficient $m$ accurately predicts temperature evolution in 0D Vlasov-Fokker-Planck simulations, it overpredicts the inhibition of heat transport if used to calculate transport coefficients. The reason for this is two-fold: 1. The coefficient only correctly describes the distribution function at low velocities and 2. The MVE model has no sense of memory and does not correctly capture the lag in transitioning between super-Gaussian states, especially for non monotonic pulses such as pickets.
We directly address 2 by training a hidden state universal differential equation for temperature evolution over a large dataset of 0D VFP simulations using diverse pulse shapes. The model is formulated in a dimensionless manner to ensure it will generalise to various scales and is also constrained to recover behaviour in the Maxwellian limit. A second neural network is trained to map our hidden state to thermal conductivity (partially addressing 1), showing that we can estimate thermal conductivity with meaningfully greater accuracy than using the MVE model. We will present initial findings on coupling this to the SNB model for nonlocal transport in a 1D heating problem where both IB and nonlocality are expected to play an important role.