| Paper |
Title |
Page |
| MPPE036 |
Characterization of the Chaotic or Regular Nature of Dynamical Orbits: A New, Fast Method
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2449 |
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- I.V. Sideris
Northern Illinois University, DeKalb, Illinois
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A new method of characterization of the regular or chaotic nature of dynamical orbits is introduced. It takes advantage of both morphological and dynamical properties of orbits, and can be applied to systems of all degrees of freedom. The new technique has been designed to analyze time-independent, time-dependent and N-body systems. It can provide straightforward information about the transition of orbits from regular to chaotic and vice versa, which can be found in time-dependent regimes. Equally important is the distinction it can make in time-independent regimes between sticky and wildly chaotic epochs during the evolution of chaotic orbits. Its most important advantage over the existing methods is, that it characterizes an orbit using information from a very small number of orbital periods. For these reasons the new method is extremely promising to be useful and effective in a broad spectrum of disciplines.
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| TPAT038 |
Chaos in Time-Dependent Space-Charge Potentials
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2515 |
| |
- G.T. Betzel, C.L. Bohn, I.V. Sideris
Northern Illinois University, DeKalb, Illinois
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We consider a spherically symmetric, homologously breathing, space-charge-dominated beam bunch in the spirit of the particle-core model. The question we ask is: How does the time dependence influence the population of chaotic orbits? The static beam has zero chaotic orbits; the equation of particle motion is integrable up to quadrature. This is generally not true once the bunch is set into oscillation. We quantify the population of chaotic orbits as a function of space charge and oscillation amplitude (mismatch). We also apply a newly developed measure of chaos, one that distinguishes between regular, sticky, and wildly chaotic orbits, to characterize the phase space in detail. We then introduce colored noise into the system and show how its presence modifies the dynamics. One finding is that, despite the presence of a sizeable population of chaotic orbits, halo formation in the homologously breathing beam is much less prevalent than in an envelope-matched counterpart wherein an internal collective mode is excited.
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