Global dynamics of the advanced light source revealed through experimental frequency map analysis

Mapping Solar System chaos with the Geological Orrery

The Geological Orrery is a network of geological records of orbitally paced climate designed to address the inherent limitations of solutions for planetary orbits beyond 60 million years ago due to the chaotic nature of Solar System motion. We use results from two scientific coring experiments in Early Mesozoic continental strata: the Newark Basin Coring Project and the Colorado Plateau Coring Project. We precisely and accurately resolve the secular fundamental frequencies of precession of perihelion of the inner planets and Jupiter for the Late Triassic and Early Jurassic epochs (223-199 million years ago) using the lacustrine record of orbital pacing tuned only to one frequency (1/405,000 years) as a geological interferometer. Excepting Jupiter's, these frequencies differ significantly from present values as determined using three independent techniques yielding practically the same results. Estimates for the precession of perihelion of the inner planets are robust, reflecting a zircon U-Pb-based age model and internal checks based on the overdetermined origins of the geologically measured frequencies. Furthermore, although not indicative of a correct solution, one numerical solution closely matches the Geological Orrery, with a very low probability of being due to chance. To determine the secular fundamental frequencies of the precession of the nodes of the planets and the important secular resonances with the precession of perihelion, a contemporaneous high-latitude geological archive recording obliquity pacing of climate is needed. These results form a proof of concept of the Geological Orrery and lay out an empirical framework to map the chaotic evolution of the Solar System.

The MAX IV storage ring project

The MAX IV facility, currently under construction in Lund, Sweden, features two electron storage rings operated at 3 GeV and 1.5 GeV and optimized for the hard X-ray and soft X-ray/VUV spectral ranges, respectively. A 3 GeV linear accelerator serves as a full-energy injector into both rings as well as a driver for a short-pulse facility, in which undulators produce X-ray pulses as short as 100 fs. The 3 GeV ring employs a multibend achromat (MBA) lattice to achieve, in a relatively short circumference of 528 m, a bare lattice emittance of 0.33 nm rad, which reduces to 0.2 nm rad as insertion devices are added. The engineering implementation of the MBA lattice raises several technological problems. The large number of strong magnets per achromat calls for a compact design featuring small-gap combined-function magnets grouped into cells and sharing a common iron yoke. The small apertures lead to a low-conductance vacuum chamber design that relies on the chamber itself as a distributed copper absorber for the heat deposited by synchrotron radiation, while non-evaporable getter (NEG) coating provides for reduced photodesorption yields and distributed pumping. Finally, a low main frequency (100 MHz) is chosen for the RF system yielding long bunches, which are further elongated by passively operated third-harmonic Landau cavities, thus alleviating collective effects, both coherent (e.g. resistive wall instabilities) and incoherent (intrabeam scattering). In this paper, we focus on the MAX IV 3 GeV ring and present the lattice design as well as the engineering solutions to the challenges inherent to such a design. As the first realisation of a light source based on the MBA concept, the MAX IV 3 GeV ring offers an opportunity for validation of concepts that are likely to be essential ingredients of future diffraction-limited light sources.

Detecting chaos in particle accelerators through the frequency map analysis method

The motion of beams in particle accelerators is dominated by a plethora of non-linear effects, which can enhance chaotic motion and limit their performance. The application of advanced non-linear dynamics methods for detecting and correcting these effects and thereby increasing the region of beam stability plays an essential role during the accelerator design phase but also their operation. After describing the nature of non-linear effects and their impact on performance parameters of different particle accelerator categories, the theory of non-linear particle motion is outlined. The recent developments on the methods employed for the analysis of chaotic beam motion are detailed. In particular, the ability of the frequency map analysis method to detect chaotic motion and guide the correction of non-linear effects is demonstrated in particle tracking simulations but also experimental data.

A preliminary design of a knot undulator

The magnetic field configuration of the previously proposed knot undulator [Qiao et al. (2009). Rev. Sci. Instrum. 80, 085108] is realised in the design of a hybridized elliptically polarized undulator, which is presented. Although the details of the field distribution are not the same as those in the theoretical proposal, it is demonstrated that the practical knot undulator could work perfectly. In order to understand the minor discrepancies of the two, mathematical formulae of the synchrotron radiation are derived based on the Fourier transform of the magnetic field. From the results of calculations by simulation program, the discrepancies could be well interpreted by the corresponding formulae. The results show the importance of optimization of the end sections of the knot undulator to suppress the on-axis heat load. Furthermore, a study of the impact of the undulator on beam dynamics of the storage ring was conducted using the Shanghai Synchrotron Radiation Facility as an example and the results show that the knot undulator has little effect on the beam.

Extracting photon periodic orbits from spontaneous emission spectra in laterally confined vertically emitted cavities

We report our observation of the signature of photon periodic orbits in the spontaneous emission spectra of large-aperture vertical-cavity surface-emitting lasers (VCSELs). The high-resolution measurement clearly demonstrates that over a thousand cavity modes with a narrow linewidth can be perfectly exhibited in the spontaneous emission spectrum just below the lasing threshold. The Fourier-transformed spectrum is analyzed to confirm that the spontaneous emission spectra of large-aperture VCSELs can be exploited to analogously investigate the energy spectra of the 2D quantum billiards.

Multiple components in narrow planetary rings

The phase-space volume of regions of regular or trapped motion, for bounded or scattering systems with 2 degrees of freedom, respectively, displays universal properties. In particular, drastic reductions in the volume (gaps) are observed at specific values of a control parameter. Using the stability resonances we show that they, and not the mean-motion resonances, account for the position of these gaps. For more degrees of freedom, exciting these resonances divides the regions of trapped motion. For planetary rings, we demonstrate that this mechanism yields rings with multiple components.

Extracting multidimensional phase space topology from periodic orbits

We establish a hierarchical ordering of periodic orbits in a strongly coupled multidimensional Hamiltonian system. Phase space structures can be reconstructed quantitatively from the knowledge of periodic orbits alone. We illustrate our findings for the hydrogen atom in crossed electric and magnetic fields.

Analyzing intramolecular dynamics by fast Lyapunov indicators

We report an analysis of intramolecular dynamics of the highly excited planar carbonyl sulfide below and at the dissociation threshold by the fast Lyapunov indicator method. By mapping out the variety of dynamical regimes in the phase space of this molecule, we obtain the degree of regularity of the system versus its energy. We combine this stability analysis with a periodic orbit search, which yields a family of elliptic periodic orbits in the regular part of phase space and a family of in-phase collinear hyperbolic orbits associated with the chaotic regime.

Explicit symplectic integrator fors-dependent static magnetic field

This paper reports our recent work on explicit symplectic integration techniques for the charged particle motion in an s-dependent static magnetic field. Using the extended phase space, symplectic integrators can be developed for Hamiltonians with or without the paraxial approximation using either the space or time as an independent variable. This work extends the successful element-by-element tracking method for studying single-particle nonlinear dynamics to a set of s-dependent magnetic elements. Important applications of this work include the studies of the charged particle dynamics in a storage ring with various insertion devices, superconducting magnets, large aperture magnets with significant fringe fields, and solenoid magnets in the interaction region. Consequently, this work is expected to make an impact on design and optimal operation of existing and future light source rings and high energy physics accelerators.

Measuring and optimizing the momentum aperture in a particle accelerator

Particle motion in storage rings is confined by various aperture limits, the size of which restricts the performance of the ring in terms of injection efficiency, lifetime, etc. Intrabeam scattering makes particles sweep a large portion of the phase space, where their motion may eventually be resonantly or chaotically excited to large amplitudes leading to collision with the vacuum chamber. We report here the studies performed at the Advanced Light Source (ALS) on the on- and off-momentum particle motion that provides a good understanding of these limitations. Using off-momentum simulations and experiments together with frequency map analysis, we could precisely correlate beam loss areas with resonance locations. The very good agreement between simulations and experiments allowed us to provide guidance for avoiding these dangerous areas. This analysis results in predictive improvements of the momentum aperture, which actually led to a lifetime increase of 25% at the ALS for very high bunch charge.