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Modelling Nonlocal Thermal Transport in Realistic ICF Plasmas – Plasma Strand Project

Supervisors: Christopher Ridgers (University of York) and Jack Goodman (AWE).

Thermal transport is critically important in high energy density plasmas, particularly those found in inertial confinement fusion (ICF) schemes. Our models of thermal transport, predominantly by electrons, typically assume that the plasma is in local thermodynamic equilibrium, but it is known that this is not the case. In particular, the heat-carrying electrons can have a mean free path which is comparable to the temperature scale-length. In this case the electrons can carry heat to distant regions of the plasma, the thermal transport no longer depends solely on the local temperature gradient and therefore becomes non-local [1]. Accurately modelling non-local transport is important as, for example, it controls the flow of energy in direct drive ICF between the critical surface (where the laser energy is absorbed) and the ablating surface of the fusion capsule.

Given its importance, there have been many attempts to include non-local electron transport in radiation hydrodynamics codes. Many codes still use a flux-limiter, where the heat flux is capped at a particular value. This value is highly problem-specific, limiting predictive capability. Indeed a major issue with initial simulations of the National Ignition Campaign (NIC) on the National Ignition Facility (NIF) was with the flux-limiter. The NIC was plagued by discrepancy between experiment and simulations [2], the latter having been calibrated against smaller scale experiments on the Nova facility. One way to improve the agreement was to move to the high-flux model in the LASNEX radiation-hydrodynamics code, with flux liter of 0.15 instead of the previously used 0.03-0.05 [2]. Flux-limited heat flow also completely neglects pre-heat by the hot electrons that stream long distances.

More recently a more sophisticated model for non-local transport has been included in LASNEX, HYDRA and other codes. This Schutz-Nicolai-Busquet (SNB) model [3] is based on the kinetic equation for the electrons (the Vlasov-Fokker-Planck – VFP – equation). We have shown that, while this model can work well in very simplified test problems, it does not work well in the presence of large density gradients, as commonly found in ICF plasmas [4]. In addition, it is known from HYDRA simulations that self-generated magnetic fields should play a role in ICF and these are not well included in current SNB [5].

In collaboration with Lawrence Livermore National Laboratory we have developed the first code that can accurately model non-local transport in ICF simulations by directly solving the VFP equation (including the effect of magnetic fields). In this project we will explore the effect of non-local transport on thermal transport in the conduction zone, in particular investigating the effect of self generated magnetic fields [5] and the resulting anisotropies they create. We will use the knowledge gained here to determine whether computationally less intensive, simplified models (such as SNB) are accurate in realistic ICF simulations.

As a PhD student, you will:
• Work at the cutting edge of computational modelling for fusion plasmas.
• Collaborate closely with major international laboratories such as LLNL.
• Gain skills in plasma simulation and interface with leading0edge ICF experiments at NIF.

This is a unique opportunity for a passionate graduate in physics, engineering, or applied mathematics to contribute to the advancement of fusion energy, working with the largest fusion experiment in the world – an area of profound scientific complexity and significant real-world relevance.

[1] A.R. Bell, R.G. Evans & D.J. Nicholas, Phys. Rev. Lett. 46, 243 (1981)
[2] M.D. Rosen et al. HEDP 7, 180 (2011)
[3] G.P, Schurtz, P.D. Nicolai & M. Busquet, Phys. Plasmas 7, 4238–4249 (2000)
[4] J.P. Brodrick et al., Phys. Plasmas 24, 092309 (2017)
[5] D.W. Hill et al., Phys. Plasmas 28, 092708 (2021)

The project will be mainly based in York, but there is the opportunity for travel to conferences and collaborations with other groups, particularly at LLNL and AWE.

During the first six months of the PhD, students will typically travel to undertake taught modules at all of the Fusion CDT partner universities.

This project is offered by University of York. For further information please contact: Christopher Ridgers (christopher.ridgers@york.ac.uk).

This project may be compatible with part time study, please contact the project supervisors if you are interested in exploring this.

For details on how to apply, please visit: Apply

Image above: K2/Gorgon simulation of a laser heated plasma shows the development of anomalous magnetic fields driven by heat flow.  This magnetic turbulence is not predicted by standard rad-hydro codes.