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

Diffusion of energetic particles in turbulent MHD plasmas

In this paper we investigate the transport of energetic particles in turbulent plasmas. A numerical approach is used to simulate the effect of the background plasma on the motion of energetic protons. The background plasma is in a dynamically turbulent state found from numerical MHD simulations, where we use parameters typical for the heliosphere. The implications for the transport parameters (i.e. pitch-angle diffusion coefficients and mean free path) are calculated and deviations from the quasi-linear theory are discussed.Comment: Accepted for publication in Ap

Local and global Fokker-Planck neoclassical calculations showing flow and bootstrap current modification in a pedestal

In transport barriers, particularly H-mode edge pedestals, radial scale lengths can become comparable to the ion orbit width, causing neoclassical physics to become radially nonlocal. In this work, the resulting changes to neoclassical flow and current are examined both analytically and numerically. Steep density gradients are considered, with scale lengths comparable to the poloidal ion gyroradius, together with strong radial electric fields sufficient to electrostatically confine the ions. Attention is restricted to relatively weak ion temperature gradients (but permitting arbitrary electron temperature gradients), since in this limit a delta-f (small departures from a Maxwellian distribution) rather than full-f approach is justified. This assumption is in fact consistent with measured inter-ELM H-Mode edge pedestal density and ion temperature profiles in many present experiments, and is expected to be increasingly valid in future lower collisionality experiments. In the numerical analysis, the distribution function and Rosenbluth potentials are solved for simultaneously, allowing use of the exact field term in the linearized Fokker-Planck collision operator. In the pedestal, the parallel and poloidal flows are found to deviate strongly from the best available conventional neoclassical prediction, with large poloidal variation of a different form than in the local theory. These predicted effects may be observable experimentally. In the local limit, the Sauter bootstrap current formulae appear accurate at low collisionality, but they can overestimate the bootstrap current near the plateau regime. In the pedestal ordering, ion contributions to the bootstrap and Pfirsch-Schluter currents are also modified

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

Star clusters dynamics in a laboratory: electrons in an ultracold plasma

Electrons in a spherical ultracold quasineutral plasma at temperature in the Kelvin range can be created by laser excitation of an ultra-cold laser cooled atomic cloud. The dynamical behavior of the electrons is similar to the one described by conventional models of stars clusters dynamics. The single mass component, the spherical symmetry and no stars evolution are here accurate assumptions. The analog of binary stars formations in the cluster case is three-body recombination in Rydberg atoms in the plasma case with the same Heggie's law: soft binaries get softer and hard binaries get harder. We demonstrate that the evolution of such an ultracold plasma is dominated by Fokker-Planck kinetics equations formally identical to the ones controlling the evolution of a stars cluster. The Virial theorem leads to a link between the plasma temperature and the ions and electrons numbers. The Fokker-Planck equation is approximate using gaseous and fluid models. We found that the electrons are in a Kramers-Michie-King's type quasi-equilibrium distribution as stars in clusters. Knowing the electron distribution and using forced fast electron extraction we are able to determine the plasma temperature knowing the trapping potential depth.Comment: Submitted to MNRA

Trinity: A Unified Treatment of Turbulence, Transport, and Heating in Magnetized Plasmas

To faithfully simulate ITER and other modern fusion devices, one must resolve electron and ion fluctuation scales in a five-dimensional phase space and time. Simultaneously, one must account for the interaction of this turbulence with the slow evolution of the large-scale plasma profiles. Because of the enormous range of scales involved and the high dimensionality of the problem, resolved first-principles global simulations are very challenging using conventional (brute force) techniques. In this thesis, the problem of resolving turbulence is addressed by developing velocity space resolution diagnostics and an adaptive collisionality that allow for the confident simulation of velocity space dynamics using the approximate minimal necessary dissipation. With regard to the wide range of scales, a new approach has been developed in which turbulence calculations from multiple gyrokinetic flux tube simulations are coupled together using transport equations to obtain self-consistent, steady-state background profiles and corresponding turbulent fluxes and heating. This approach is embodied in a new code, Trinity, which is capable of evolving equilibrium profiles for multiple species, including electromagnetic effects and realistic magnetic geometry, at a fraction of the cost of conventional global simulations. Furthermore, an advanced model physical collision operator for gyrokinetics has been derived and implemented, allowing for the study of collisional turbulent heating, which has not been extensively studied. To demonstrate the utility of the coupled flux tube approach, preliminary results from Trinity simulations of the core of an ITER plasma are presented.Comment: 187 pages, 53 figures, Ph.D. thesis in physics at University of Maryland, single-space versio