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

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

Parallelizing the Kolmogorov-Fokker-Planck Equation

We design two parallel schemes, based on Schwarz Waveform Relaxation (SWR) procedures, for the numerical solution of the Kolmogorov equation. The latter is a simplified version of the Fokker-Planck equation describing the time evolution of the probability density of the velocity of a particle. SWR procedures decompose the spatio- temporal computational domain into subdomains and solve (in parallel) subproblems, that are coupled through suitable conditions at the interfaces to recover the solution of the global problem. We consider coupling conditions of both Dirichlet (Classical SWR) and Robin (Optimized SWR) types. We prove well-posedeness of the schemes subproblems and convergence for the proposed algorithms. We corroborate our findings with some numerical tests

Modélisation et méthodes numériques pour l'étude du transport de particules dans un plasma chaud

Angular moments models represent alternative descriptions situated in between the kinetic and the fluid models. In this work, angular moments models based on an entropy minimisation principle are considered for plasma physics applications. This manuscript is organised in three parts. The first one is a contribution to plasma physics modelling within the formalism of angular moments models. The validity domain of angular moments models in collisionless regimes is studied. It is also shown that the collisional operators proposed for the M1 angular moments model enable to recover accurate plasma transport coefficients. The second part of this document deals with the derivation of numerical methods for the long timescales particle transport. Appropriate asymptotic-preserving numerical schemes are designed for the M1 angular moments model and numerical validations are performed. The third part represents a first important step toward multi-species modelling. The M1 angular moments model in a moving frame is introduced and applied to rarefied gas dynamics. The model properties are highlighted, a numerical scheme is proposed and a numerical validation is carried out.Les modèles aux moments angulaires constituent des descriptions intermédiaires entre les modèles cinétiques et les modèles fluides. Dans ce manuscrit, les modèles aux moments angulaires basés sur un principe de minimisation d'entropie sont étudiés pour des applications en physique des plasmas. Ce mémoire se découpe en trois parties. La première est une contribution à la modélisation en physique des plasmas à travers le formalisme des modèles aux moments angulaires. Dans celle-ci, le domaine de validité de ces modèles est étudié en régimes non-collisionels. Il est également montré que les opérateurs de collisions proposés pour le modèle M1 permettent de retrouver des coefficients de transport plasma précis. La deuxième partie de ce document concerne la dérivation de méthodes numériques pour l'étude du transport de particules en temps long. Dans ce cadre, des schémas numériques appropriés pour le modèle M1, préservant l'asymptotique, sont construits et validés numériquement. La troisième partie représente un premier pas significatif vers la modélisation multi-espèces. Ici, le modèle aux moments angulaire M1, construit dans un référentiel mobile, est appliqué à la dynamique des gaz raréfiés. Les propriétés de ce modèle sont détaillées, un schéma numérique est proposé et une validation numérique est menée

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

Short-pulse laser interactions with high density plasma

The constraints on particle-in-cell (PIC) simulations of short-pulse laser interactions with solid density targets severely limit the spatial and temporal scales which can be modelled routinely. Although recent advances in high performance computing (HPC) capabilities have rendered collisionless simulations at a scale and density directly applicable to experiments tractable, detailed modelling of the fast electron transport resulting from the laser interaction is often only possible by sampling the fast electron populations and passing this information to a separate, dedicated transport code. However, this approach potentially neglects phenomena which take place or are seeded near the transition between the two codes. Consequently there is a need to develop techniques capable of efficiently modelling fast electron transport in high density plasma without being subject to the usual grid-scale and time-step constraints. The approach employed must also be compatible with retaining the standard PIC model in the laser interaction regions in order to model laser absorption and charged particle acceleration processes. Such an approach, proposed by Cohen, Kemp and Divol [J. Comput. Phys., 229:4591, 2010], has been identified, adapted and implemented in EPOCH. The final algorithm, as implemented, is presented here. To demonstrate the ability of the adapted code to model high intensity laser-plasma interactions with peak densities at, and above, solid density, the results of simulations investigating filamentation of the fast electron population and heating of the bulk target, at high densities, are presented and compared with the results of recent experiments as well as other, similar codes

Vlasov Simulations of Kinetic Enhancement of Raman Backscatter in Laser Fusion Plasmas

PhD Thesis at MIT