Magnet lattices for particle accelerators (the sequence of focusing and bending magnets and drift sections making up a beam line) are often designed numerically using computer codes like MAD that model each beam-line element using either a matrix description or numeric integration, or some other algorithm. The Lattice package for Maple—recently published in Maplesoft's Application Center—allows modelling such beam lines using the full algebraic power of Maple. In this way, analytic solutions to beam-optics problems can be found in order to establish feasibility of certain solutions or study parameter dependencies. Beam lines are constructed in an intuitive way from standard beam-optical elements (drifts, bends, quadrupoles etc.) using Maple's object-oriented features, in particular Records which represent individual elements or whole beam lines. These Records hold properties like the first-order transport matrices, element length and some other properties plus, for beam lines, the elements the line is composed of. Operations like finding matched Twiss (beam-envelope) functions and dispersion are implemented and the results can be plotted. The Lattice package knows about beam matrices and can track such matrices as well as particles in a beam. The tracking function (map) is implemented separately from the first-order matrices thus allowing nonlinear or even scattering simulations; at present sextupole elements, compensating-wire elements and scattering-foil elements take advantage of this feature. Standard textbook problems are programmed and solved easily, and more complicated ones are readily solved as well within the limits set by Maple's capabilities, memory and computing time. Many investigations are possible by using standard Maple operations on the relevant properties of the beam lines defined. An interesting possibility is, e.g., using Maple's mtaylor command to truncate the transfer map of a beam line to a desired order, making it a more manageable function.
The package can output a beam-line description in MAD8 format for further refinement of the solution, cross-checking the results and possibly more detailed tracking.
Developed initially for my own use I have found the package useful for a number of accelerator design problems, teaching at the US Particle Accelerator School as well as in modelling beam lines for experiments I have been involved in. Presently at Version 1.0 the package still has limits; esp. the higher-order descriptions are not yet as complete as desirable. Yet already many practical design problems can be tackled in great detail. The package is backwards compatible to Maple 15. It can be found in the Application center together with help database files (old and new style) and a Users Guide.
An example showing the flavor of working with the package is attached (FODO_example.mw). It analyzes a FODO cell, the basic cell used in many ring accelerators.
Uli Wienands, aka Mac Dude