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Non-Dissipative Decay of Linear Quasimodes in a Pure Electron Plasma


Pillai, N. Sateesh (1995) Non-Dissipative Decay of Linear Quasimodes in a Pure Electron Plasma. Dissertation (Ph.D.), California Institute of Technology. doi:10.7907/GHGX-Z547.


This thesis describes the first experimental observations of linear collisionless damping of perturbations in a pure electron plasma and provides the theoretical proof for collisionless damping in two dimensional inviscid incompressible fluids. Observations in the non-linear regime provide evidence for fluid trapping in the potential well of the perturbation.

The perturbations are in the form of diocotron waves which possess azimuthal symmetries described by the eigen number m = 2. The plasma is a cylindrical column of electrons confined in a Penning trap. Diocotron waves are excited by applying azimuthally propagating electric fields to the electrode structures forming the wall of the Penning trap.

Experiment shows that the damping of diocotron waves is not caused by dissipation at the electrode wall, and that the presence of such a dissipation decreases the decay rate of these waves, confirming that the m = 2 diocotron wave is a negative energy wave.

A self consistent set of equations for the perturbed potential is derived using the cold two dimensional fluid model. This results in the diocotron equation, which is the cylindrical plasma analog of Rayleigh's equation for shear flow of an inviscid incompressible fluid between parallel sheets. The complex form of the diocotron equation is solved, with homogeneous boundary conditions, for a particularly simple radial density profile showing that the diocotron resonances are quasimodes of the 2-D fluid. The solution reveals a complex eigenvalue which is consistent with the observed collisionless exponential damping of the diocotron wave in the linear regime.

Solution of the diocotron equation with more complicated density profiles is carried out numerically using the Runge-Kutta method on a computer.

Item Type:Thesis (Dissertation (Ph.D.))
Subject Keywords:(Electrical Engineering) ; Diocotron, quasimode, pure electron plasma
Degree Grantor:California Institute of Technology
Division:Engineering and Applied Science
Major Option:Electrical Engineering
Thesis Availability:Public (worldwide access)
Research Advisor(s):
  • Gould, Roy Walter
Thesis Committee:
  • Gould, Roy Walter (chair)
  • Martel, Hardy Cross
  • Corngold, Noel Robert
Defense Date:12 April 1995
Non-Caltech Author Email:sateeshpillai (AT)
Record Number:CaltechETD:etd-10122007-090003
Persistent URL:
Default Usage Policy:No commercial reproduction, distribution, display or performance rights in this work are provided.
ID Code:4051
Deposited By: Imported from ETD-db
Deposited On:25 Oct 2007
Last Modified:17 Jul 2023 23:38

Thesis Files

PDF (Pillai_ns_1995.pdf) - Final Version
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