93-34 Tennyson , J.L., Meiss , J.D., Morrison , P.J.

Selfconsistent Chaos in the Beam-Plasam Instability (64K, LaTeX, no figures included) Feb 15, 93

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Abstract. 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 ($10^4$) 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 {\sl reduce} the number of degrees-of-freedom. A simple low degree-of-freedom model is derived that treats the clump as a single {\it 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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