A Deep Dive into the Distribution Function: Understanding Phase Space Dynamics with Continuum Vlasov-Maxwell Simulations. (arXiv:2005.13539v1 [physics.plasm-ph])

<a href="http://arxiv.org/find/physics/1/au:+Juno_J/0/1/0/all/0/1">James Juno</a>

In collisionless and weakly collisional plasmas, the particle distribution

function is a rich tapestry of the underlying physics. However, actually

leveraging the particle distribution function to understand the dynamics of a

weakly collisional plasma is challenging. The equation system of relevance, the

Vlasov-Maxwell-Fokker-Planck (VM-FP) system of equations, is difficult to

numerically integrate, and traditional methods such as the particle-in-cell

method introduce counting noise into the distribution function.

In this thesis, we present a new algorithm for the discretization of VM-FP

system of equations for the study of plasmas in the kinetic regime. Using the

discontinuous Galerkin (DG) finite element method for the spatial

discretization and a third order strong-stability preserving Runge-Kutta for

the time discretization, we obtain an accurate solution for the plasma’s

distribution function in space and time.

We both prove the numerical method retains key physical properties of the

VM-FP system, such as the conservation of energy and the second law of

thermodynamics, and demonstrate these properties numerically. These results are

contextualized in the history of the DG method. We discuss the importance of

the algorithm being alias-free, a necessary condition for deriving stable DG

schemes of kinetic equations so as to retain the implicit conservation

relations embedded in the particle distribution function, and the computational

favorable implementation using a modal, orthonormal basis in comparison to

traditional DG methods applied in computational fluid dynamics. Finally, we

demonstrate how the high fidelity representation of the distribution function,

combined with novel diagnostics, permits detailed analysis of the energization

mechanisms in fundamental plasma processes such as collisionless shocks.

In collisionless and weakly collisional plasmas, the particle distribution

function is a rich tapestry of the underlying physics. However, actually

leveraging the particle distribution function to understand the dynamics of a

weakly collisional plasma is challenging. The equation system of relevance, the

Vlasov-Maxwell-Fokker-Planck (VM-FP) system of equations, is difficult to

numerically integrate, and traditional methods such as the particle-in-cell

method introduce counting noise into the distribution function.

In this thesis, we present a new algorithm for the discretization of VM-FP

system of equations for the study of plasmas in the kinetic regime. Using the

discontinuous Galerkin (DG) finite element method for the spatial

discretization and a third order strong-stability preserving Runge-Kutta for

the time discretization, we obtain an accurate solution for the plasma’s

distribution function in space and time.

We both prove the numerical method retains key physical properties of the

VM-FP system, such as the conservation of energy and the second law of

thermodynamics, and demonstrate these properties numerically. These results are

contextualized in the history of the DG method. We discuss the importance of

the algorithm being alias-free, a necessary condition for deriving stable DG

schemes of kinetic equations so as to retain the implicit conservation

relations embedded in the particle distribution function, and the computational

favorable implementation using a modal, orthonormal basis in comparison to

traditional DG methods applied in computational fluid dynamics. Finally, we

demonstrate how the high fidelity representation of the distribution function,

combined with novel diagnostics, permits detailed analysis of the energization

mechanisms in fundamental plasma processes such as collisionless shocks.

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