Publication Date


Document Type


Committee Members

Amit Sharma, Ph.D. (Advisor); Ivan Medvedev, Ph.D. (Committee Member); Sarah Tebbens, Ph.D. (Committee Member)

Degree Name

Master of Science (MS)


A one-dimensional kinetic particle-in-cell (PIC) MATLAB simulation was created to demonstrate the time-evolution of various plasma distributions. Building on previous plasma PIC programs written in FORTRAN and Python, this work recreates the computational and diagnostic tools of these packages in a more user- and educational-friendly development environment. Plasma quantities such as plasma frequency and species charge-mass ratios are arbitrarily defined. A one-dimensional spatial environment is defined by total length and number and size of spatial grid points. In the first time-step, charged particles are given initial positions and velocities on a spatial grid. After initialization, the program solves for the electrostatic Poisson equation at each time step to compute the force acting on each particle. Using the calculated force on each particle and the “leap-frog” method, the particle positions and velocities are updated and the motion is tracked in phase-space. Modifying parameters such as spatial perturbation, number of particles, and charge-mass ratio of each species, the time-evolution for various distributions are examined. The simulated distributions examined are categorized as the following: Cold Electron Stream, Electron Plasma Waves, Two-Stream Electron Instability, Landau Damping, and Beam-Plasma. The time evolution of the plasma distributions was studied by several methods. Tracking the electric field, charge density and particle velocities through each time step yields insight into the oscillations and wave propagation associated with each distribution. One key diagnostic missing from the original FORTRAN code was the electric field dispersion relation. The numerical dispersion relation allows for further insight into modelling plasma oscillations/waves in addition to the kinetic/field energies and electric field tracking present in the original code. Simulated results show agreement with other kinetic simulations as well as plasma theory.

Page Count


Department or Program

Department of Physics

Year Degree Awarded


Included in

Physics Commons