Dynamics of Cuspy Triaxial Galaxies with a Supermassive Black Hole

This talk provides a progress report on an extended collaboration which has aimed to address two basic questions, namely: Should one expect to see cuspy, triaxial galaxies in nature? And can one construct realistic cuspy, triaxial equilibrium models that are robust? Three technical results are described: (1) Unperturbed chaotic orbits in cuspy triaxial potentials can be extraordinarily sticky, much more so than orbits in many other three-dimensional potentials. (2) Even very weak perturbations can be important by drastically reducing, albeit not completely eliminating, this stickiness. (3) A simple toy model facilitates a simple understanding of why black holes and cusps can serve as an effective source of chaos. These results suggest that, when constructing models of galaxies using Schwarzschild's method or any analogue thereof, astronomers would be well advised to use orbital building blocks that have been perturbed by `noise' or other weak irregularities, since such building blocks are likely to be more nearly time-independent than orbits evolved in the absence of all perturbations.Comment: a contributed talk at The International Conference on Stellar Dynamics: From Classical to Modern, Sobolev Astronomical Institute, St. Petersburg State University, August 200

Propagation of a Gaussian Wigner Function Through a Matrix-Aperture Beamline

A Gaussian Wigner function may be defined in terms of its covariance matrix and centroid. In the framework of statistical optics, a Wigner function represents partially coherent radiation. A Gaussian Wigner function is an equivalent representation to the more commonly used Gaussian Schell model cross spectral density. Starting from the relationship between Gaussian Wigner functions and the Gaussian Schell model, we derive coherence properties of the Gaussian Wigner function including coherence length and degree of coherence. We define a simplified beamline called a matrix-aperture beamline composed of linear transport sections separated by physical apertures. This is an idealized form for a transport beamline in a synchrotron light source or X-ray free electron laser. An envelope model provides a basic foundation to understand the optics of a given beamline in an analogous manner with which linear optics are treated in particle beam dynamics, with corresponding definitions of emittance and Twiss parameters. One major challenge to such an envelope model lies in the hard edge apertures which break the Gaussian condition raising the question as to the adequacy of a Gaussian model. We present a consistent way to construct a Gaussian approximation of the far-field Wigner function following the hard edge aperture. To this end, we introduce the concept of a Gaussian aperture and analyze its effects on the radiation Wigner function. A software implementation of this model is described

Parallel beam dynamics simulation tools for future light source linac modeling

Large-scale modeling on parallel computers is playing an increasingly important role in the design of future light sources. Such modeling provides a means to accurately and efficiently explore issues such as limits to beam brightness, emittance preservation, the growth of instabilities, etc. Recently the IMPACT codes suite was enhanced to be applicable to future light source design. Simulations with IMPACT-Z were performed using up to one billion simulation particles for the main linac of a future light source to study the microbunching instability. Combined with the time domain code IMPACT-T, it is now possible to perform large-scale start-to-end linac simulations for future light sources, including the injector, main linac, chicanes, and transfer lines. In this paper we provide an overview of the IMPACT code suite, its key capabilities, and recent enhancements pertinent to accelerator modeling for future linac-based light sources

Nonlinear response of electrons to a positive ion

Electric field dynamics at a positive ion imbedded in an electron gas is considered using a semiclassical description. The dependence of the field autocorrelation function on charge number is studied for strong ion-electron coupling via MD simulation. The qualitative features for larger charge numbers are a decreasing correlation time followed by an increasing anticorrelation. Stopping power and related transport coefficients determined by the time integral of this correlation function result from the competing effects of increasing initial correlations and decreasing dynamical correlations. An interpretation of the MD results is obtained from an effective single particle model showing good agreement with the simulation results.Comment: To be published in the proceedings of the International Workshop on Strongly Coupled Coulomb Systems, Journal of Physics

Noise-Induced Phase Space Transport in Two-Dimensional Hamiltonian Systems

First passage time experiments were used to explore the effects of low amplitude noise as a source of accelerated phase space diffusion in two-dimensional Hamiltonian systems, and these effects were then compared with the effects of periodic driving. The objective was to quantify and understand the manner in which ``sticky'' chaotic orbits that, in the absence of perturbations, are confined near regular islands for very long times, can become ``unstuck'' much more quickly when subjected to even very weak perturbations. For both noise and periodic driving, the typical escape time scales logarithmically with the amplitude of the perturbation. For white noise, the details seem unimportant: Additive and multiplicative noise typically have very similar effects, and the presence or absence of a friction related to the noise by a Fluctuation-Dissipation Theorem is also largely irrelevant. Allowing for colored noise can significantly decrease the efficacy of the perturbation, but only when the autocorrelation time becomes so large that there is little power at frequencies comparable to the natural frequencies of the unperturbed orbit. Similarly, periodic driving is relatively inefficient when the driving frequency is not comparable to these natural frequencies. This suggests strongly that noise-induced extrinsic diffusion, like modulational diffusion associated with periodic driving, is a resonance phenomenon. The logarithmic dependence of the escape time on amplitude reflects the fact that the time required for perturbed and unperturbed orbits to diverge a given distance scales logarithmically in the amplitude of the perturbation.Comment: 15 pages, including 13 Figures and 1 Table, uses Phys. Rev. macro

Particle-in-cell beam dynamics simulations with a wavelet-based Poisson solver

We report on a successful implementation of a three-dimensional wavelet-based solver for the Poisson equation with Dirichlet boundary conditions, optimized for use in particle-in-cell (PIC) simulations. The solver is based on the operator formulation of the conjugate gradient algorithm, for which effectively diagonal preconditioners are available in wavelet bases. Because of the recursive nature of PIC simulations, a good initial approximation to the iterative solution is always readily available, which we demonstrate to be a key advantage in terms of overall computational speed. While the Laplacian remains sparse in a wavelet representation, the wavelet-decomposed potential and density can be rendered sparse through a procedure that amounts to simultaneous compression and denoising of the data. We explain how this procedure can be carried out in a controlled and near-optimal way, and show the effect it has on the overall solver performance. After testing the solver in a stand-alone mode, we integrated it into the IMPACT-T beam dynamics particle-in-cell code and extensively benchmarked it against the IMPACT-T with the native FFT-based Poisson solver. We present and discuss these benchmarking results, as well as the results of modeling the Fermi/NICADD photoinjector using IMPACT-T with the wavelet-based solver

Electron Dynamics at a Positive Ion

Submitted to Phys. Rev. EInternational audienceThe dynamics of electrons in the presence of a positive ion is considered for conditions of weak electron-electron couping but strong electron-ion coupling. The equilibrium electron density and electric field time correlation functions are evaluated for semi-classical conditions using a classical statistical mechanics with a regularized electron-ion interaction for MD simulation. The theoretical analysis for the equilibrium state is obtained from the corresponding nonlinear Vlasov equation. Time correlation functions for the electrons are determined from the linearized Vlasov equation. The resulting electron dynamics is described in terms of a distribution of single electron-ion trajectories screened by an inhomogeneous electron gas dielectric function. The results are applied to calculation of the autocorrelation function for the electron electric field at the ion for $0\leq Z\leq 40$, including conditions of strong electron-ion coupling. The electron stopping power and self-diffusion coefficient are determined from these results, and all properties calculated are compared with those obtained from semi-classical molecular dynamics simulation. The agreement with semi-classical MD simulation is found to be reasonable. The theoretical description provides an instructive interpretation for the strong electron-ion results