Moment-Based Accelerators for Kinetic Problems with Application to Inertial Confinement Fusion

In inertial confinement fusion (ICF), the kinetic ion and charge separation field effects may play a significant role in the difference between the measured neutron yield in experiments and the predicted yield from fluid codes. Two distinct of approaches exists in modeling plasma physics phenomena: fluid and kinetic approaches. While the fluid approach is computationally less expensive, robust closures are difficult to obtain for a wide separation in temperature and density. While the kinetic approach is a closed system, it resolves the full 6D phase space and classic explicit numerical schemes restrict both the spatial and time-step size to a point where the method becomes intractable. Classic implicit system require the storage and inversion of a very large linear system which also becomes intractable. This dissertation will develop a new implicit method based on an emerging moment-based accelerator which allows one to step over stiff kinetic time-scales. The new method converges the solution per time-step stably and efficiently compared to a standard Picard iteration. This new algorithm will be used to investigate mixing in Omega ICF fuel-pusher interface at early time of the implosion process, fully kinetically

Kinetic Modeling of Magnetic Field Dynamics and Thermal Energy Transport in Inertial Fusion Energy Plasmas.

In indirect-drive inertial-fusion experiments, a hohlraum converts laser energy into X-rays that heat an ablator material on a fuel capsule. The expansion of the ablator leads to implosion of the fuel capsule and fusion conditions in a hot spot, where alpha particles are produced and propagate a burn wave through the fuel. Accurate determination of the balance of energy fluxes in the hohlraum not only requires consideration of X-ray transport, but also needs careful treatment of electron transport, because laser energy is coupled primarily to the electrons in the plasma. The steep electron-thermal-energy gradients in this environment can lead to breakdown of diffusive heat-transport and introduce non-local effects. Additionally, the plasmas produced in such laser-plasma experiments are subject to the influence of self-generated magnetic fields. A kinetic formulation enables detailed calculations of thermal-energy transport and magnetic-field dynamics in these plasmas due to self-consistent inclusion of effects in electron transport that depend not only on details of the particle energy distribution but also on the electromagnetic fields in the plasma. The dissertation describes novel comparisons between Braginskii transport and kinetic modeling that quantify the importance of kinetic effects. In addition to the theoretical contributions and modeling results, the author was also responsible for the development of a ray-tracing module to model laser propagation. Through kinetic modeling, the heat flow near the laser heating region retains non-local effects. In the case of an externally applied magnetic field, non-local contributions to the Nernst effect increase the rate of field transport by the Nernst mechanism. The Nernst effect leads to significantly faster transport of the magnetic field to the hohlraum axis in comparison to field transport through plasma hydrodynamic motion only. The self-generated magnetic fields are oppositely aligned with respect to each other and and are subject to reconnection. The magnetic reconnection mechanism is, in this case, governed by heat flow that transports the magnetic field. This mechanism is prevalent in plasmas where the thermal energy density is higher than the magnetic energy density. Such an environment is present in hohlraums near the critical surface, where reconnection results in redistribution of the thermal energy.PhDNuclear Engineering and Radiological SciencesUniversity of Michigan, Horace H. Rackham School of Graduate Studieshttp://deepblue.lib.umich.edu/bitstream/2027.42/120806/1/archisj_1.pd

High order resolution of the Maxwell-Fokker-Planck-Landau model intended for ICF applications

A high order, deterministic direct numerical method is proposed for the nonrelativistic $2D_{\bf x} \times 3D_{\bf v}$ Vlasov-Maxwell system, coupled with Fokker-Planck-Landau type operators. Such a system is devoted to the modelling of electronic transport and energy deposition in the general frame of Inertial Confinement Fusion applications. It describes the kinetics of plasma physics in the nonlocal thermodynamic equilibrium regime. Strong numerical constraints lead us to develop specific methods and approaches for validation, that might be used in other fields where couplings between equations, multiscale physics, and high dimensionality are involved. Parallelisation (MPI communication standard) and fast algorithms such as the multigrid method are employed, that make this direct approach be computationally affordable for simulations of hundreds of picoseconds, when dealing with configurations that present five dimensions in phase space

Studies of magnetised and non-local transport in laser-plasma interactions

The application of magnetic fields in inertial fusion experiments has led to renewed interest in fully understanding magnetised transport in laser-plasma regimes. This motivated the development of a new laser magnetohydrodynamic code PARAMAGNET, written to support investigations into classical magnetised transport phenomena and laser propagation in a plasma. This code was used to simulate laser-underdense plasma interactions such as the pre-heat stage of magneto-inertial fusion. Alongside these simulations, this thesis will present analytic focusing and filamentation models derived from magnetohydrodynamics extended with classical magnetised transport coefficients. These results showed the focal length and filamentation growth length shortened with magnetisation, a result of the magnetisation of the thermal conductivity. Further investigation of the transport properties using the diffusion approximation kinetic code IMPACT showed significant deviation of the growth rate at intermediate values of magnetisation and non-locality, inexplicable using fluid models. The kinetic code result motivated exploring the influence of the high-order anisotropies of the distribution function (in terms of spherical harmonics), ignored in conventional approximations. By using a recursive matrix inverse method, corrections to the transport coefficients including all orders of the electron distribution expansion were found. Analysis of the conductivity, resistivity and thermoelectric coefficients showed deviation by up to 50% from the classical form at intermediate magnetisation and nonlocality. The diffusive approximation of the IMPACT simulations was insufficient to capture the transport behaviour present in the theoretical high order calculation. Modern inertial fusion experiments work in regimes that are non-local and susceptible to significant focusing exacerbated by magnetisation. The resulting filamentation has detrimental implications to laser absorption and the modified non-local transport behaviour is a possible source of error in simulations. The complex interplay between non-locality and magnetisation in transport suggests using more terms of the spherical harmonic expansion in closures of plasma equations. Particular consideration is given to the implications to inertial fusion experiments. Together these results suggest the necessity of including non-local magnetised transport in the modelling of high-energy-density laser plasma experiments.Open Acces

Magnetic Fields and Non-Local Transport in Laser Plasmas

The first Vlasov-Fokker-Planck simulations of nanosecond laser-plasma interactions – including the effects of self-consistent magnetic fields and hydrodynamic plasma expansion – will be presented. The coupling between non-locality and magnetic field advection is elucidated. For the largest (initially uniform) magnetic fields externally imposed in recent long-pulse laser gas-jet plasma experiments (12T) a significant degree of cavitation of the B-field will be shown to occur (> 40%) in under 500ps. This is due to the Nernst effect and leads to the re-emergence of non-locality even if the initial value of the magnetic field strength is sufficient to localize transport. Classical transport theory may also break down in such interactions as a result of inverse bremsstrahlung heating. Although non-locality may be suppressed by a large B-field, inverse bremsstrahlung still leads to a highly distorted distribution. Indeed the best fit for a 12T applied field (after 440ps of laser heating) is found to be a super- Gaussian distribution – f0 α e−vm – with m = 3.4. The effects of such a distribution on the transport properties under the influence of magnetic fields are elucidated in the context of laser-plasmas for the first time. In long pulse laser-plasma interactions magnetic fields generated by the thermoelectric (‘∇ne × ∇Te’) mechanism are generally considered dominant. The strength of B-fields generated by this mechanism are affected, and new generation mechanisms are expected, when non-locality is important. Non-local B-field generation is found to be dominant in the interaction of an elliptical laser spot with a nitrogen gas-jet