Frank Ebeling

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

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. >

A proposed superconducting photoemission source of high brightness

Abstract We describe the design of an electron injector for the production of a bunched cw electron beam of high brightness, low energy spread, and potentially high beam power. Electron beams of this kind are required for high efficiency and short wavelength free electron lasers. The injector consists of a superconducting reentrant cavity housing a photoemission cathode evaporated on a superconducting substrate. The cathode is illuminated with short light pulses of a mode-locked frequency doubled Nd: YAG laser. The experimental layout of the “superconducting photoemission source” is described together with its components: the photocathode preparation chamber, the cavity, the cryogenic setup, and the beam analysis system. The conceptual beam parameters are discussed and first results of calculations on beam dynamics using a particle-in-cell computer code are given.

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. >

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.

Hollow beam dynamics in the DESY wake field accelerator

The characteristic requirements for studies of an intense hollow electron beam do not permit the use of simulation codes usually used for linac or storage ring design. At DESY, two special codes have been developed for this purpose: WAKTRACK, a tracking code which includes arbitrarily shaped external fields and collective effects and TBCI‐SF, a 2‐1/2 dimensional, fully relativistic particle‐in‐cell code used for studies of the ring shaping and bunching process. TBCI‐SF also includes arbitrarily shaped static or dynamic fields. Both computer codes will be discussed and applications for the Wake Field Transformation Linac will be indicated.