Department Undulators

Simulation of insertion device performance: WAVE

WAVE [1,2] has been developed at BESSY over the years to calculate synchrotron radiation for almost arbitrary magnetic fields with high precision. The program also offers a variety of subroutines to calculate and manipulate magnetic fields as well as generating functions for symplectic tracking calculations.  The main features and options are given in the following list:

Magnetic fields

• Simulation of helical and planar wigglers and undulators as analytical models or permanent magnet structure as well as dipoles, quadrupoles, and sextupoles with fringe fields
• Simulation of magnetic field errors of insertion devices
• In- and output of  magnetic fields via field maps or tables
• Maxwell-conform parametrization and interpolation of magnetic fields

Synchrotron radiation

• Calculation of amplitude, polarization (Stokes-vectors) and phase of the irradiated field (acceleration and velocity terms) of a set of  electrons traveling through an arbitrary magnetic field. The calculations can be performed numerically (e.g. for undulators or for edge radiation) or by application of Schwinger's formula.
• Spatial and spectral distributions of synchrotron radiation and irradiated power and integration of the spatial distributions over an rectangular or circular aperture.
• Taking beam emittance, energy spread, and coherence effects for arbitrary phase-space distrbutions into account
• Propagation of the radiation field (Huygens' principle) e.g. to calculate the size of the source
• Brightness calculations
• Application of filters
• Taking into account the spectral efficiency of detectors
• Calculation of absorbed dose rate

Accelerator physics

• Trajectories of electrons for arbitrary magnetic fields
• Generating functions for symplectic tracking routines and linear transfer matrices
• Effects of insertion devices on beam emittance, energy spread, and on time and degree of  beam polarization
• Integrated quadrupole and sextupole  terms of magnetic fields
• Representation of insertion device as a sequence of dipoles with edge focusing

Interfaces

• User routines for data I/O, external magnetic field and treatment of tracking steps
• Output of data files of the calculated radiation for the ray-tracing codes RAY [3] and PHASE [4]
• Output of data files of generating functions and representation of insertion devices as a sequence of dipoles for tracking codes

WAVE has been used for the design of all insertion devices and the investigation of the insertion device – electron beam interaction, in particular of the superconducting wave-length shifters and  wigglers at the storage ring BESSY II.

^{[1] M. Scheer, Beschleunigerphysik und radiometrische Eigenschaften supraleitender Wellen-längenschieber, Humboldt-Universität zu Berlin, Dissertation 2008.
[2] M. Scheer, WAVE - A Computer Code for the Tracking of Electrons through Magnetic Fields and the Calculation of Spontaneous Synchrotron Radiation, ICAP 2012.
[3] F. Schäfers, RAY - THE BESSY RAYTRACE PROGRAM F. Schäfers, In: Springer Series in Modern Optical Sciences: Modern Developments in X-Ray and Neutron Optics, eds. A. Erko, M. Idir, Th. Krist, A.G. Michette, Springer Berlin/Heidelberg, Vol. 137, 9-41 (2008) PDF
[4] J. Bahrdt, Wave Front Propagation: Design Code for Synchrotron Radiation Beamlines, Applied Optics 36 (1997), Vol. 19, p. 4367-4381}