Petra Schütt

Solution of Maxwell's equations

Abstract A numerical approach for the solution of Maxwells equations is presented. Based on a finite difference Yee lattice the method transforms each of the four Maxwell equations into an equivalent matrix expression that can be subsequently treated by matrix mathematics and suitable numerical methods for solving matrix problems. The algorithm, although derived from integral equations, can be considered to be a special case of finite difference formalisms. A large variety of two- and three-dimensional field problems can be solved by computer programs based on this approach: electrostatics and magnetostatics, low-frequency eddy currents in solid and laminated iron cores, high-frequency modes in resonators, waves on dielectric or metallic waveguides, transient fields of antennas and waveguide transitions, transient fields of free-moving bunches of charged particles etc.

Maxwell's grid equations

A numerical approach for the solution of Maxwells equation is presented. Based on a finite difference Yee lattice the method transforms each of the four Maxwell equations into an equivalent matrix expression that can be subsequently treated by matrix mathematics and suitable numerical methods for solving matrix problems. The algorithm, although derived from integral equations, can be considered to be a special case of finite difference formalisms

MAFIA version 4

MAFIA Version 4.0 is an almost completely new version of the general purpose electromagnetic simulator known since 13 years. The major improvements concern the new graphical user interface based on state of the art technology as well as a series of new solvers for new physics problems. MAFIA now covers heat distribution, electro-quasistatics, S-parameters in frequency domain, particle beam tracking in linear accelerators, acoustics and even elastodynamics. The solvers that were available in earlier versions have also been improved and/or extended, as for example the complex eigenmode solver, the 2D–3D coupled PIC solvers. Time domain solvers have new waveguide boundary conditions with an extremely low reflection even near cutoff frequency, concentrated elements are available as well as a variety of signal processing options. Probably the most valuable addition are recursive sub-grid capabilities that enable modeling of very small details in large structures.

Status and future of the 3D MAFIA group of codes

An overview is presented of the MAFIA group of fully three-dimensional computer codes for solving Maxwells equations by the finite integration algorithm. The codes are well established. Extensive comparisons with measurements have demonstrated the accuracy of the computations. The latest additions include a static solver that calculates 3-D magnetostatic and electrostatic field and a self-consistent version of TBCI that solves the field equations and the equations of motion in parallel. Work on new eddy-current modules has started, which will allow treatment of laminated and/or solid iron cores by low-frequency current. Based on experience with the present releases 1 and 2, a complete revision of the whole user interface and data structure has begun that will be included in release 3. >

Status and future developments of the wake field transformer experiment

Abstract Future e + e − linear colliders with center-of-mass energies of 2 TeV need high average accelerating gradients to be built within a reasonable length. The gradients required by colliders at this energy range can be economically provided by resonant wake field transformers. At the wake field experiment at DESY a 20 cm long transformer section was investigated. The basic ideas are reviewed and the most recent results are presented in this paper. Furthermore an overview of the present status of research concerning the proposed next stage of a multibunch driver linac with superconducting cavities and long wake field transformer sections is presented.

New simulation results for the S-DALINAC electron source

For the operation of its mid-infrared FEL the superconducting electron accelerator S-DALINAC has to produce bunches with a charge of 6 pC and a duration of 2 ps FWHM. In order to achieve these figures a subharmonic injection scheme was added to the 3 GHz cw accelerator. The electron gun consists of a grid controlled thermionic cathode on a 250 kV terminal. It produces electron pulses with a charge of 20 pC and a width of 800 ps FWHM at a repetition rate of 10 MHz. For a reliable simulation of the subsequent parts of the injector (600 MHz chopper/prebuncher section and a superconducting linac consisting of 2- and 5-cell capture cavities and two 20-cell accelerating structures) the beam parameters at its input have to be known as exactly as possible. Since we expect that due to the pulsed operation of the gun, longitudinal space charge effects might be important, the electron gun and the 250 kV electrostatic acceleration have been studied using the 2 1/2 dimensional PIC code MAFIA-TS2 and the tracking code GPT. This calculation takes into account the time structure of the beam and yields results like bunch shape at the gun exit, correlated and uncorrelated energy spread, as well as the transverse emittance. The results of the simulation as well as a comparison with measurements of the transverse emittance and the electron pulse length at the exit of the electrostatic acceleration will be presented in this paper.

Mafia in Practice: the Capabilities of the Mafia Cad System

The program group MAFIA which solves Maxwells equations has been further improved by the inclusion of new programs, by the integration of both two and three dimensional modules under a unified user interface and by the extension of pre- and post-processor capabilities. In the present release, 3.1, a module for the calculation of eddy currents in solid or laminated iron cores is the latest addition to the family of codes, two and three dimensional particle-in-cell codes, which solve the equations of motion in parallel with the electromagnetic field equations, are also included and the time domain solver has been extended to calculate the transient fields of antennae and waveguide transitions. The programs are described and a series of large (up to a million mesh points), realistic examples are presented to indicate the range and complexity of the problems which MAFIA can solve.

Wake Field Acceleration, a Way to TeV e+ e- Collisions

Future e + e -- accelerators in the energy range above 1 TeV will be linear colliders with a high accelerating gradient. For creating the high gradient, new concepts are investigated, such as wake field acceleration, which need driver beams with high current and short bunches. At DESY an experiment with a Wake Field Transformer has been set up, where electromagnetic wake fields of a highly charged hollow driver beam are spatially focussed, and the resulting high longitudinal electric field is used for the acceleration of a second beam. The basic idea, the layout of the experiment and the results are presented. In a stage-1 experiment several bunches, each of 50 to 100 nC charge, have been produced and accelerated to an energy of 6.5 MeV and bunched down to a length of 3–4 mm. Using longer bunches of 1 cm, a gradient of 8 MeV/m has already been measured in a short Wake Field Transformer section.