Showing papers by "John R. Cary published in 1994"
TL;DR: The Hamiltonian provides a simple model for the fundamental physics of narrow-spectrum plasma turbulence, for strong rf current drive in a tokamak, and for electron dynamics in a recirculating free-electron laser.
Abstract: Particles interacting resonantly with large-amplitude coherent one-dimensional wave packets can trap and subsequently detrap or even reflect. Many resonant particles are strongly scattered in the process, and the long-time dynamics of such particles is stochastic throughout a large region of phase space when repeated wave-particle interactions occur. We apply adiabatic invariance theory and separatrix crossing theory to this Hamiltonian system, which is beyond the realm of quasilinear theory. We calculate the adiabatic invariant through first order in the (small) slowness parameter [var epsilon] for all particle trajectories. Because the trajectories of resonant particles cross a separatrix, the adiabatic invariant is broken and separatrix-crossing theory must be used. Our Hamiltonian provides a simple model for the fundamental physics of narrow-spectrum plasma turbulence, for strong rf current drive in a tokamak, and for electron dynamics in a recirculating free-electron laser.
11 citations
TL;DR: For a particle moving in the electric field of many, randomly phase waves, numerical measurements show that the Lyapunov exponent asymptotes to a value of 0.4 times the resonance broadening frequency, in contrast with previous calculations as discussed by the authors.
Abstract: For a particle moving in the electric field of many, randomly phase waves, numerical measurements show that the Lyapunov exponent (1) asymptotes to a value of 0.4 times the resonance broadening frequency, in contrast with previous calculations, and (2) has a peak at intermediate values of the overlap parameter. This latter result indicates that the previously observed enhancement of the diffusion coefficient is not due to coherence effects near stable regions of phase space. These results provide further evidence that the standard model is an inadequate description of the turbulent electric field.
5 citations
TL;DR: A method for creating integrable nonlinear accelerator lattices by minimizing the residues of fixed points by varying lattice parameters eliminates large islands and regions of chaos.
Abstract: A method for creating integrable nonlinear accelerator lattices is presented. Fixed points for the two-dimensional return map corresponding to the lattice are found. Minimizing the residues (an indicator of the size of the associated island) of these fixed points by varying lattice parameters eliminates large islands and regions of chaos. The resulting nonlinear systems have larger dynamical apertures and are more stable to perturbations induced by, for example, error fields.
4 citations
TL;DR: In this article, it was shown that for nearly integrable nonsymmetric magnetic fields, the current closure condition need not hold and that ∮dl/B is a flux surface quantity.
Abstract: Magnetic fields with translational symmetry, axisymmetry, and helical symmetry are integrable. That is, they have good flux surfaces. The current closure condition, that ∮dl/B is a flux surface quantity, also holds. It is possible to construct magnetic fields with broken symmetry, which have nearly integrable magnetic fields. It is shown that for nearly integrable nonsymmetric fields, the current closure condition need not hold.
2 citations