E. Forest

Fourth-order symplectic integration

Abstract In this paper we present an explicit fourth-order method for the integration of Hamiltons equations. This method preserves the property that the time evolution of such a system yields a canonical transformation from the initial conditions to the final state. That is, the integration step is an explicit symplectic map. Although the result is first derived for a specific type of Hamiltonian, it is shown to be quite general. In particular, the results can be applied to any Lie group.

Foundations of a Lie algebraic theory of geometrical optics

We present the foundations of a new Lie algebraic method of characterizing optical systems and computing their aberrations. This method represents the action of each separate element of a compound optical system —including all departures from paraxial optics— by a certain operator. The operators can then be concatenated in the same order as the optical elements and, following well-defined rules, we obtain a resultant operator that characterizes the entire system. These include standard aligned optical systems with spherical or aspherical lenses, models of fibers with polynomial z-dependent index profile, and also sharp interfaces between such elements. They are given explicitly to third aberration order.

An x-ray photoemission electron microscope using an electron mirror aberration corrector for the study of complex materials

A new ultrahigh-resolution photoemission electron microscope called PEEM3 is being developed at the advanced light source (ALS). An electron mirror combined with a sophisticated magnetic beam separator is used to provide simultaneous correction of spherical and chromatic aberrations. Installed on an elliptically polarized undulator beamline, PEEM3 will be operated with very high spatial resolution and high flux to study the composition, structure, electric and magnetic properties of complex materials.

Geometric integration for particle accelerators

This paper is a very personal view of the field of geometric integration in accelerator physics—a field where often work of the highest quality is buried in lost technical notes or even not published; one has only to think of Simon van der Meer Nobel prize work on stochastic cooling—unpublished in any refereed journal. So I reconstructed the relevant history of geometrical integration in accelerator physics as much as I could by talking to collaborators and using my own understanding of the field. The reader should not be too surprised if this account is somewhere between history, science and perhaps even fiction.

Marylie 3.0 - A Program for Nonlineapr Analysis of Accelerator and Beamline Lattices

MARYLIE 3.0 is a Fortran-language beam transport and tracking code developed at the University of Maryland. It employs algorithms based on a Lie algebraic formalism for charged particle trajectory calculations/sup 1/, and is designed to compute transfer maps for and trace rays through single or multiple beam-line elements. This is done without the use of numerical integration or traditional matrix methods; all nonlinearities (including chromatic effects) through third (octupole) order are included. Thus MARYLIE 3.0 includes effects one order higher than those usually handled by existing matrix-based programs. In addition MARYLIE is exactly symplectic (Canonical) through all orders. The Lie algebraic treatment of higher order multipoles is under study. MARYLIE 4.0, a MARYLIE version that includes decapole effects, is currently being tested. All versions of MARYLIE have provisions for user written subroutines that permit the treatment of any multipole element by the usual approximations or numerical integration.

Sixth-order Lie group integrators

LBL-28684 ESG Note-93 SIXTH-ORDER LIE GROUP INTEGRATORS * Etienne Forest Exploratory Studies Group Lawrence Berkeley Laboratory University of California Berkeley, CA 94720 March 1990 Purpose: Submitted to the Journal of Computational Physics This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, High Energy Physics Division, of the U.S. Department of Energy under Contract No. DE-AC03-76SF00098.

A Hamiltonian - free description of single particle dynamics for hopelessly complex periodic systems

LBL-28471 Preprint Submitted to Journal of Mathematical Physics A Hamiltonian-Free Description of Single Particle Dynamics for Hopelessly Complex Periodic Systems E. Forest January 1990 Prepared for the U.S. Department of Energy under Contract Number DE·AC03·76SF00098.

A Contemporary Guide To Beam Dynamics

A methodological discussion is given for single particle beam dynamics in circular machines. The discussions are introductory, but (or, even therefore) we avoid to rely on too much simplified concepts. We treat things from a very general and fundamental point of view, because this is the easiest and rightest way to teach how to simulate particle motion and how to analyze its results. We give some principles of particle tracking free from theoretical prejudices. We also introduce some transparent methods to deduce the necessary information from the tracking: many of the traditional beam-dynamics concepts can be abstracted from them as approximate quantities which are valid in certain limiting cases.

Dynamic aperture study for the Duke FEL storage ring

Abstract The new lattice design of the Duke free electron laser (FEL) storage ring is described. The results of the 6-dimensional dynamic aperture study using single particle tracking codes are presented. The influence of 8-m FEL undulator on the dynamic aperture is studied.

Correction and alignment strategies for the beam separator of the photoemission electron microscope 3 (PEEM3)

A high-resolution aberration-corrected photoemission electron microscope (PEEM3) will be installed on an undulator beamline at the Advanced Light Source at the Lawrence Berkeley National Laboratory. The aim of this instrument is to provide a substantial flux and resolution improvement by employing an electron mirror for correcting both the third-order spherical aberration and the primary chromatic aberration. In order to utilize this concept of correction, a beam separator is a prerequisite. Crucial to achieving a resolution of 5nm for the high-resolution mode, and a 16-fold increase in throughput at the same resolution as its predecessor, PEEM2, specified as 20nm at 2% transmission, for the high flux mode is the double-symmetric design of the beam separator, which eliminates all the second-order geometric aberrations. Nonetheless, substantial tuning capabilities must be incorporated into the PEEM3 design to compensate for both systematic and random errors. In this article, we investigate how to correct f...