Showing papers by "John R. Cary published in 1998"

Increasing the dynamic aperture of accelerator lattices

Abstract: A method for reducing chaotic dynamics in four-dimensional symplectic maps is presented. The method is to reduce certain chaos measures related to the invariants of the tangent map of fixed points. This method is applied to circular accelerators, where chaotic dynamics determines the dynamic aperture, the region of long-time stable orbits. A factor of 3{endash}4 increase in the phase-space volume of confined trajectories is obtained. {copyright} {ital 1998} {ital The American Physical Society }

Enhanced velocity diffusion in slow-growing 1-D langmuir turbulence

Abstract: Numerical simulations show an enhancement of the 1-D velocity diffusion coefficient over the quasilinear value in the regime where the autocorrelation time is much smaller than the linear growth time or resonance broadening time. The diffusion enhancement occurs when the resonance broadening time is small compared with the linear growth time. These simulations are self consistent, use a hybrid PIC/spectral symplectic integration method, and have enough modes to be in the continuous spectrum limit. That is, even at the initial amplitudes the intermode spacing is sufficiently small that the resonance overlap parameter is large. A possible mechanism for the enhanced diffusion (spontaneous spectrum discretization) is discussed.

General linear theory of damped, beam-driven oscillations of a single mode

Abstract: A single wave model of beam-cavity interactions is developed. The single wave model makes use of the spatial periodicity of a circular accelerator to Fourier expand the on-axis cavity vector potential. Combined with a harmonic time dependence, this Fourier expansion expresses the cavity vector potential as a sum of traveling waves. The single wave model keeps only the wave most resonant with the particles. The linearized dispersion relation is examined as a function of three parameters, damping rate, detuning, and beam temperature, and the analysis here is shown to span that parameter space (previous work has not given such a general treatment). The regions of validity within the parameter space for some familiar results, including a negative mass-like instability of accelerator physics, the cold-beam plasma result, the Keil-Schnell criterion, and Landau damping are discussed. A further result of this analysis is a clarification of the differences between Landau damping in plasma physics and Landau dampin...

Expression templates for truncated p

Abstract: Truncated Power Series technique (Differential Algebra or DA) is a powerful tool for non-linear map analysis of accelerators. The most natural language for numerical DA’s is C++, since it is object oriented and has operator overloading. Traditional C++, though, can be inefficient for scientific programming due to creation of many temporaries and extra loops in overloaded operators. Recent Expression Templates technique allows a user to combine the elegance of object oriented approach with the speed of procedural languages. The way it was created, it is not directly applicable for DA. We created a set of classes whose structure will be suitable for implementing DA vectors and maps. Classes realizing the Expression Templates technique are separated from the client classes, which allows their reuse for different mathematical concepts. Speed tests on KCC compiler showed that new C++ classes for DA have the same speed as hand-coded C.

Finding four dimensional symplectic maps with reduced chaos: Preliminary results

Abstract: A method for finding integrable four-dimensional symplectic maps is outlined. The method relies on solving for parameter values at which the linear stability factors of the fixed points of the map have the values corresponding to integrability. This method is applied to accelerator lattices in order to increase dynamic aperture. Results show a increase of the dynamic aperture after correction, which implies the validity of the method.