Date of Award


Degree Type


Degree Name

Master of Science (MS)



Committee Chair(s)

Eric Held


Eric Held


A plasma, whether ”hot” or ”cold,” magnetized or unmagnetized, electrostatic or electromagnetic, exhibits normal modes of oscillation. Critical to understanding the stability of a plasma is the study of these normal modes. Waves originate from the long-range electric interactions between charged particles. This work will consider a class of waves known as Langmuir waves. These waves occur when a group of electrons are displaced with respect to the ions, with the electric Coulomb force playing the role of the restoring force of the oscillation [1]. Since the mass of ions is much greater than that of electrons, we can approximate the ions as stationary.

This work will begin by developing a set of equations based on our assumptions. We will derive the characteristic plasma frequency equation while ignoring pressure effects, an assumption used in studying cold plasmas. Using numerical methods with NIMROD [2], we will show how solutions converge in the spatial dimension. We then expand upon the plasma frequency equation by including the pressure gradient in the equation of motion. This results in a dispersion relation for electron plasma oscillations known as Langmuir waves. The work will conclude with numerical solutions for this dispersion relation being compared to the expected theoretical dispersion relation.

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