Damping and Trapping in 2D Inviscid Fluids

We demonstrate collisionless decay due to phase mixing of a disturbance in an inviscid 2D fluid with sheared flow. Experiments performed on a cylindrical pure electron plasma, which behaves as a 2D inviscid fluid, show that a small amplitude quadrupole excitation (m=2, k=0 mode) decays exponentially. At larger amplitudes, the exponential decay is modulated by bounce motion of fluid elements trapped in the azimuthally traveling wave field, with the bounce frequency proportional to the square root of the excitation amplitude. We also show that the linear decay rate is decreased by the addition of external dissipation. We describe a calculation of the linearized response function

Non-dissipative decay of linear quasimodes in a pure electron plasma

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.</p