Martin Dohlus

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.

Ultraviolet and Soft X-Ray Free-Electron Lasers

The main goal of the book is to provide a systematic and didactic approach to the physics and technology of free-electron lasers. Numerous figures are used for illustrating the underlying ideas and concepts, and many links to other fields of physics are provided. After an introduction to undulator radiation and the low-gain FEL, the one-dimensional theory of the high-gain FEL is developed in a systematic way. Particular emphasis is put on explaining and justifying the various assumptions and approximations that are needed to obtain the differential equations governing the FEL dynamics. The predictive power of the 1D FEL theory is demonstrated with numerous examples and figures, including exponential gain, saturation and FEL bandwidth. One of the most important features of a high-gain FEL, the formation of microbunches, is studied at length and illustrated with several figures. 3D corrections to the 1D theory are discussed. The process of self amplified spontaneous emission (SASE) is explained mathematically, and many experimental results are shown. The layout of the worlds first SASE FEL in the soft X-ray regime, FLASH, is described in some detail and the technological challenges of X-ray FELs are outlined. Important concepts of accelerator physics are explained while some of the more involved mathematical computations are put into the appendices.

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. >

Broadband calculation of scattering parameters in the time domain

By exciting a broadband pulse in the time domain and performing a fast Fourier transform on the sampled time domain data it is possible to obtain the scattering parameters for a broad frequency range with one single time domain calculation. This known technique, valid for non-dispersive waveguides, is extended to homogeneously loaded dispersive waveguides. In most cases this extended technique outperforms the frequency domain approach by orders of magnitude in terms of calculation time. We will give a short introduction to this method and present some examples. >

Comparison of CONDOR, FCI and MAFIA calculations for a 150 MW S-band klystron with measurements

To facilitate the design of high power klystrons an investigation into the reliability and accuracy of three modern particle-in-cell codes was performed. A 150 MW S-band klystron for which measurements were available was used for this comparison. The field calculations of the particle-in-cell codes are based on a finite difference time domain scheme, and use a port approximation to speed up the convergence to steady state. However they differ in many details (e.g. calculation of E, B or A, /spl phi/; space charge correction; 2D or 3D modelling of the output cavity).

Calculation of frequency domain parameters by time domain methods (for antennas)

By adequate postprocessing it is possible to extract many frequency-domain results out of sampled time-domain data. For the calculation of far-field patterns in the frequency domain one needs to determine the harmonic field amplitudes near the radiating structure. This is accomplished by a time-domain calculation with time harmonic excitation sources. As an example the far-field pattern of a corrugated horn is calculated and compared with results obtained by a mode matching method. Boundary conditions and mode amplitudes for the calculation of filter characteristics are computed by mode expansion and a convolution technique. These modes are calculated by solving the 2-D waveguide eigenvalue problem. Broadband characteristics of a commercially available hyperthermia treatment set are calculated by a pulse stimulation technique together with CW SAR patterns. >

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...

Spurious oscillations in high power klystrons

Spurious oscillations in high power klystrons are found to occur in the gun region, in the cavities in the main body of the tube, or in the drift tunnel. The criteria that determine whether a mode will oscillate is that its beam loading be negative, and that the power it extracts from the beam exceeds its losses to external loading and wall dissipation. Using the electromagnetic and particle-in-cell modules of MAFIA, we have devised numerical techniques with which the quality factors Q/sub b/, Q/sub e/, and Q/sub o/ can be evaluated and compared. Simulations involving a gun oscillation observed in the SLAC/DESY S-band klystron will be reported.