Self-interacting, nonequilibrium, very-many-body systems such as elliptical galaxies and charged-particle beams seem generically to exhibit rapid evolution to a quasi-equilibrium state. Such systems comprise some 1010-12 particles. The associated collisional relaxation time of elliptical galaxies is ~1015-16 years, several orders of magnitude larger than the age of the universe. For a nonrelativistic charged-particle beam it is ~1-10 µs, i.e., "1-10 km", typically much longer than, e.g., the length of a linac. Yet, elliptical galaxies appear to be "relaxed" to a smooth density distribution, and charged-particle beams have likewise been seen to "relax" to a smooth density distribution, and also to equipartition in a few meters, depending on details of the space charge. How so? In this talk I will describe an "elementary" mechanism, one that is based on the behavior of the orbits comprising the system and how these orbits mix through their accessible phase space. I will then use it as the foundation for estimating time scales for relaxation to quasi-equilibria and show that they are in reasonable agreement with the true values computed in numerical simulations and seen in the (few) beam experiments done to date.


Talk Slides: PDF



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