Chaotic collisionless evolution in galaxies and charged-particle beams.

Both galaxies and charged particle beams can exhibit collisionless evolution on surprisingly short time scales. This can be attributed to the dynamics of chaotic orbits. The chaos is often triggered by resonance caused by time dependence in the bulk potential, which acts almost identically for attractive gravitational forces and repulsive electrostatic forces. The similarity suggests that many physical processes at work in galaxies, although inaccessible to direct controlled experiments, can be tested indirectly via controlled experiments with charged particle beams, such as those envisioned for the University of Maryland electron ring currently nearing completion.

Chaotic dynamics in charged-particle beams: possible analogs of galactic evolution.

During the last couple of years of his life, Henry Kandrup became intensely interested in using charged-particle beams as a tool for exploring the dynamics of evolving galaxies. He and I recognized that both galaxies and charged-particle beams can exhibit collisionless relaxation on surprisingly short time scales, and that this circumstance can be attributed to phase mixing of chaotic orbits. The chaos is often triggered by resonances caused by time dependence in the bulk potential, which acts almost identically for attractive gravitational forces as for repulsive electrostatic forces superposed on external focusing forces. Together we published several papers concerning evolving beams and galaxies, papers that relate to diverse topics such as the physics of chaotic mixing, the applicability of the Vlasov-Poisson formalism, and the production of diffuse halos. We also teamed with people from the University of Maryland to begin designing controlled experiments to be done at the University of Maryland electron ring. This paper highlights our collaborative findings as well as plans for future investigations that the findings have motivated.

Fluctuations do matter: large noise-enhanced halos in charged-particle beams.

The formation of beam halos has customarily been described in terms of a particle-core model in which the space-charge field of the oscillating core drives particles to large amplitudes. This model involves parametric resonance and predicts a hard upper bound to the orbital amplitude of the halo particles. We show that the presence of colored noise due to space-charge fluctuations and/or machine imperfections can eject particles to much larger amplitudes than would be inferred from parametric resonance alone.

Chaos, ergodicity, and the thermodynamics of lower-dimensional time-independent Hamiltonian systems.

This paper uses the assumptions of ergodicity and a microcanonical distribution to compute estimates of the largest Lyapunov exponents in lower-dimensional Hamiltonian systems. That the resulting estimates are in reasonable agreement with the actual values computed numerically corroborates the intuition that chaos in such systems can be understood as arising generically from a parametric instability and that this instability may be modeled by a stochastic-oscillator equation [cf. Casetti, Clementi, and Pettini, Phys. Rev. E 54, 5969 (1996)], linearized perturbations of a chaotic orbit satisfying a harmonic-oscillator equation with a randomly varying frequency.