The effect of self-consistency on Hamiltonian systems with a large number of degrees-of-freedom is investigated for the beam-plasma instability using the single-wave model of O'Neil, Winfrey, and Malmberg.The single-wave model is reviewed and then rederived within the Hamiltonian context, which leads naturally to canonical action- angle variables. Simulations are performed with a large (10[sup 4]) number of beam particles interacting with the single wave. It is observed that the system relaxes into a time asymptotic periodic state where only a few collective degrees are active; namely, a clump of trapped particles oscillating in a modulated wave, within a uniform chaotic …
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The effect of self-consistency on Hamiltonian systems with a large number of degrees-of-freedom is investigated for the beam-plasma instability using the single-wave model of O'Neil, Winfrey, and Malmberg.The single-wave model is reviewed and then rederived within the Hamiltonian context, which leads naturally to canonical action- angle variables. Simulations are performed with a large (10[sup 4]) number of beam particles interacting with the single wave. It is observed that the system relaxes into a time asymptotic periodic state where only a few collective degrees are active; namely, a clump of trapped particles oscillating in a modulated wave, within a uniform chaotic sea with oscillating phase space boundaries. Thus self-consistency is seen to effectively reduce the number of degrees- of-freedom. A simple low degree-of-freedom model is derived that treats the clump as a single macroparticle, interacting with the wave and chaotic sea. The uniform chaotic sea is modeled by a fluid waterbag, where the waterbag boundaries correspond approximately to invariant tori. This low degree-of-freedom model is seen to compare well with the simulation.
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Tennyson, J.L. (Stanford Linear Accelerator Center, Menlo Park, CA (United States)); Meiss, J.D. (Colorado Univ., Boulder, CO (United States). Applied Mathematics Program) & Morrison, P.J. (Texas Univ., Austin, TX (United States)).Self-consistent chaos in the beam-plasma instability,
report,
February 8, 1993;
Austin, Texas.
(https://digital.library.unt.edu/ark:/67531/metadc1198655/:
accessed July 18, 2025),
University of North Texas Libraries, UNT Digital Library, https://digital.library.unt.edu;
crediting UNT Libraries Government Documents Department.
