Accurate Transfer Maps for Realistic Beamline Elements: Part I, Straight Elements

The behavior of orbits in charged-particle beam transport systems, including both linear and circular accelerators as well as final focus sections and spectrometers, can depend sensitively on nonlinear fringe-field and high-order-multipole effects in the various beam-line elements. The inclusion of these effects requires a detailed and realistic model of the interior and fringe fields, including their high spatial derivatives. A collection of surface fitting methods has been developed for extracting this information accurately from 3-dimensional field data on a grid, as provided by various 3-dimensional finite-element field codes. Based on these realistic field models, Lie or other methods may be used to compute accurate design orbits and accurate transfer maps about these orbits. Part I of this work presents a treatment of straight-axis magnetic elements, while Part II will treat bending dipoles with large sagitta. An exactly-soluble but numerically challenging model field is used to provide a rigorous collection of performance benchmarks.Comment: Accepted to PRST-AB. Changes: minor figure modifications, reference added, typos corrected

Exact evolution of time-reversible symplectic integrators and their phase error for the harmonic oscillator

The evolution of any factorized time-reversible symplectic integrators, when applied to the harmonic oscillator, can be exactly solved in a closed form. The resulting modified Hamiltonians demonstrate the convergence of the Lie series expansions. They are also less distorted than modified Hamiltonian of non-reversible algorithms. The analytical form for the modified angular frequency can be used to assess the phase error of any time-reversible algorithm.Comment: Submitted to Phys. Lett. A, Six Pages two Column

Exploring Minimal Scenarios to Produce Transversely Bright Electron Beams Using the Eigen-Emittance Concept

Next generation hard X-ray free electron lasers require electron beams with low transverse emittance. One proposal to achieve these low emittances is to exploit the eigen-emittance values of the beam. The eigen-emittances are invariant under linear beam transport and equivalent to the emittances in an uncorrelated beam. If a correlated beam with two small eigen-emittances can be produced, removal of the correlations via appropriate optics will lead to two small emittance values, provided non-linear effects are not too large. We study how such a beam may be produced using minimal linear correlations. We find it is theoretically possible to produce such a beam, however it may be more difficult to realize in practice. We identify linear correlations that may lead to physically realizable emittance schemes and discuss promising future avenues.Comment: 7 pages, 2 figures, to appear in NIM

Solvable Map Representation Of A Nonlinear Symplectic Map

The evolution of a particle under the action of a beam transport system can be represented by a nonlinear symplectic map M. This map can be factorized into a product of Lie transformations. The evaluation of any given lie transformation in general requires the summation of an infinite number of terms. There are several ways of dealing with this difficulty: The summation can be truncated, thus producing a map that is nonsymplectic, but still useful for short term tracking. Alternatively, for long term tracking, the Lie transformation can be replaced by some symplectic map that agrees with it to some order and can be evaluated exactly. This paper shows how this may be done using solvable symplectic maps. A solvable map gives rise to a power series that either terminates or can be summed explicitly. This method appears to work quite well in the various examples that we have considered

The Moyal-Lie Theory of Phase Space Quantum Mechanics

A Lie algebraic approach to the unitary transformations in Weyl quantization is discussed. This approach, being formally equivalent to the $\star$-quantization, is an extension of the classical Poisson-Lie formalism which can be used as an efficient tool in the quantum phase space transformation theory.Comment: 15 pages, no figures, to appear in J. Phys. A (2001

Landgoed De Schaffelaar: natuur en verleden bij Barneveld

About 1700 a sober noble man's house called 'Hackfort' was built on the place of a ruinous castle surrounded by a canal in the province of Gelderland near Barneveld. The house and property probably owed this name to the scenery. In the 17th century the country seat was known as 'De Schaffelaar' by a supposed relationship with the hero Jan van Schaffelaar, who leapt from the tower in Barneveld during the so-called 'Hoekse and Kabeljauwse twisten' (quarrels) in 1482. In 1767 one started the building of a house in Louis-XVI style on the same location. Between 1767 and 1793 a garden was laid out in Anglo-Chinese style in the direct surroundings of the house. Also the rest of the estate was embellished at the time. The oldest laying-out of avenues at right angles probably dates from the second half of the 17th century. An extension in the form of a starred wood must have taken place between the twenties and sixties of the 18th century. The connection with the landscape played an important role at laying-out. This becomes evident from the integration of farming-land, orchards and farms. Representative and economic use herewith are united at this country seat. In the winter of 1799 the house burnt down. Baron van Zuylen van Nievelt bought the country seat in 1808 and took the English landscape style as starting point for renewal. Between 1808 and 1852 an already present watercourse was changed into a 'natural' landscape-element, a so-called 'winding pond' and the meanwhile unexplored field, where the former house was built, was taken up in the laying-out as an island. In addition a family grave, a 'flower hill' and duck-pipe were laid out and the starring wood was extended. The sober laying-out fits into the changing attitude around 1800 whereby exuberant elements - as at the Anglo-Chinese laying-out - were avoided and elements to be considered characteristic of Dutch agricultural nature were used at the laying-out of the park. This also perfectly fitted the extant laying-out of De Schaffelaar. From 1840 one started to design a new house on the estate. Here a clear development of thoughts can be distinguished, whereby acquaintance with the revival of the gothic style with belonging philosophies in England played an important role. As a consequence of this, in 1852 the building of a neo-gothic castle was started on the south-west part of the estate. Both the 'castellated character' and the changed site refer to the connection of the estate and his inhabitants with nature and Barneveld's past. In 1853 the Zochers were commissioned to design a garden in the castle's direct surroundings. The combination of neo-gothic 'castle' and laying-out of the landscape into a picturesque unit stresses the reference to nature and the past. The way an ideal image here has been created makes De Schaffelaar a unique monument in the Netherlands