Reinhard Klatt

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. >

The 3-D MAFIA group of electromagnetic codes

The MAFIA group of fully three-dimensional computer codes for solving Maxwells equations for a wide range of applications is discussed. The MAFIA family consists of a number of independent programs that interact through a common file base. A single preprocessor acts as the input program, which defines the geometry of the problem, the mesh, and the different materials of the various bodies. Extensive comparisons with measurements have demonstrated the accuracy of the computations. The authors describe the mathematical approach taken by the MAFIA codes for the solution of Maxwells equations in the time and frequency domains in three dimensions. >

Recent advances and applications of the MAFIA codes

Over the last years MAFIA has grown to a more and more universal design tool for a vast range of applications not only in the field of accelerator physics. The currently distributed version 3.1 now includes a new solver module for time harmonic fields that enables the computation of eddy current distributions as well as the fields in driven rf systems. MAFIA 3.1 also includes static modules for electric and magnetic fields, 2D and 3D resonator solvers, 2D and 3D time domain solvers as well as 2.5D and 3D PIC modules. Thus MAFIA 3.1 now virtually covers the entire range of electromagnetic field problems. The fully menu driven user interface has been enhanced by implementation of macros, symbolic variables, and language structures that makes MAFIA fully programmable. On the application side there are numerous highlights such as extremely fast and accurate computations of S‐parameters, calculation of antennas including farfield patterns, non‐destructive testing analysis for carbon fiber reinforced plastic as...

Theoretical Prediction of Head Tail Tune Shift in PETRA

The shift in frequency of the fundamental m = 0 head tail mode in a storage ring can be calculated from the optics and the wake potentials. Such calculations have been performed for various beam pipe components in PETRA and are summarized here. Comparison with measurements shows good agreement for long bunches and that the theoretical description of the impedance is incomplete for short bunches (high frequencies).

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.