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For slowly evolving, discrete-time-dependent systems of difference equations (iterated maps), we believe the simplest means of demonstrating the validity of the averaging method at first order is by way of a lemma that we call Besjes’ inequality. In this paper, we develop the Besjes inequality for identity maps with perturbations that are (i) at low-order… (More)

- H. Scott Dumas, James A. Ellison, Mathias Vogt
- SIAM J. Applied Dynamical Systems
- 2004

After the design luminosity of the electron-proton collider HERA had been exceeded [1,2], the interaction regions were rebuilt to obtain smaller b* at the two interaction points (IPs) [3,4,5]. Spin rotators on both sides of the IPs were installed to achieve collisions with longitudinal electron or positron polarization. Since the new interaction regions… (More)

We present a mathematical analysis of planar motion of energetic electrons moving through a planar dipole undulator, excited by a fixed planar polarized plane wave Maxwell field in the x-ray free electron laser (FEL) regime. Our starting point is the 6D Lorentz system, which allows planar motions, and we examine this dynamical system as the wavelength of… (More)

- Mathias Vogt
- 1997

In this paper, a hybrid FEM/BEM approach for solving Maxwell's equations in the frequency domain is presented. The method can be applied to uniform transmission lines and waveguides containing anisotropic and lossy media. Based on a rigorous full-wave analysis, frequency-dependent propagation constants and electromagnetic elds can be obtained. Spurious… (More)

- Georg Hoffstätter, Mathias Vogt
- Physical review. E, Statistical, nonlinear, and…
- 2004

When polarized particles are accelerated in a synchrotron, the spin precession can be periodically driven by Fourier components of the electromagnetic fields through which the particles travel. This leads to resonant perturbations when the spin-precession frequency is close to a linear combination of the orbital frequencies. When such resonance conditions… (More)

- Tim Plath, Philipp Amstutz, +13 authors Tim Laarmann
- Journal of synchrotron radiation
- 2016

Free-electron lasers (FELs) generate femtosecond XUV and X-ray pulses at peak powers in the gigawatt range. The FEL user facility FLASH at DESY (Hamburg, Germany) is driven by a superconducting linear accelerator with up to 8000 pulses per second. Since 2014, two parallel undulator beamlines, FLASH1 and FLASH2, have been in operation. In addition to the… (More)

There is some ambiguity in the definitions and use of the concepts of spin tune and spin-orbit resonance on synchrobetatron orbits. We clarify these issues and provide a numerical illustration of the internal consistency of our definitions using the computer code SPRINT for HERA with a standard Siberian Snake arrangement. Furthermore, we demonstrate the… (More)

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