2015-2016 AMOP Seminar Abstracts

Wednesday, Sept. 23, 2015

Collisions of Positronium with Atoms and Molecules

Experimental measurements of the total scattering cross section of Positronium (Ps) from various atomic and molecular targets are very similar to electron scattering cross sections above the Ps ionization threshold. This phenomenon has been explained theoretically using the impulse approximation. Below the ionization threshold the impulse approximation breaks down, and pseudopotential calculations have given good results for rare gas atoms. We apply the impulse approximation and the pseudopotential method to elastic scattering of Ps by H₂ by assuming that H₂ is spherically symmetric. We have supplemented the elastic cross sections by calculation of the Ps ionization cross section using a binary encounter approach. The ionization cross sections are in good agreement with other calculations and the total cross section is in good agreement with experimental measurements for rare gas atoms and H₂. We also discuss the extension of our methods to include the non-spherical nature of the electron-molecule interaction.

Wednesday, Nov. 11, 2015

Variational Formulation of Macro-Particle Algorithms for Studying Electromagnetic Plasmas

The interaction of an intense laser pulse with a plasma can be well described by the Vlasov-Maxwell system of equations. However, due to the immense number of particles involved, only approximate solutions can be attained for problems of interest. Currently, the most common method for solving these equations is known as particle-in-cell (PIC). It is a macro-particle method, where an individual macro-particle represents a large quantity of electrons or ions characterized by a single momentum. While the traditional PIC code has been used successfully in many instances to model important physics, its inadequacies have long been understood. One example of this is the phenomenon known as grid-heating, which amounts to a failure of the code to conserve energy. Another important issue, identified more recently, is unphysical trapping that occurs due to inaccuracies in the representation of phase space.

To address these issues, we have developed a rigorous variational formulation for deriving a set of discrete, self-consistent, macro-particle kinetic plasma equations from a discretized Lagrangian. The primary advantage of the variational technique is the well-known connection between the symmetries of a system and conservation laws. This inherent structure allows for the optimization of computational resources for a given physical problem.

In my dissertation, I discuss the development of the variational approach, an illustration of how to utilize its flexibility with regard to coordinate transformations, the implementation of symplectic time integrators, and the application of this technique to examples drawn from important problems in laser-plasma interactions. I emphasize throughout the advantages over the traditional PIC method including proper energy conservation, improved smoothness of the density profile, and a more physical representation of the phase space for a similar, and often reduced, computational cost.

Wednesday, Apr. 6, 2016

Hamiltonian fluid reductions of kinetic equations in plasma physics

A wide variety of plasmas can be considered as weakly collisional. Such plasmas are accurately described by kinetic equations, which give the dynamics of the distribution function of particles in phase space. Due to the high dimensionality of the problem, solving these equations for realistic values of the physical parameters is impossible with nowadays computing power and storage capabilities.

Fluid reductions of kinetic equations aim at replacing the distribution function defined in phase space with more tangible fluid quantities such as the plasma density and temperature which are defined in configuration space solely. This allows one to gain physical insight into the phenomenon under investigation and reduce the amount of data that is being handled.

I will present a reduction procedure which preserves the Hamiltonian structure of the parent kinetic model. This is important in order to ensure that no non-physical dissipation is introduced in the resulting fluid model. I will focus on the framework and main concepts of the method and finally apply it to build a Hamiltonian fluid model for the first three fluid moments of the Vlasov distribution.