Tennyson , J.L., Meiss , J.D., Morrison , P.J.
Selfconsistent Chaos in the Beam-Plasam Instability
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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.