The document describes an SR_LNLS computer code for calculating optical parameters of photon beams from undulators. The code accounts for effects of finite electron beam emittance and energy spread, which are important for low-emittance sources like Sirius in Brazil. Benchmarking showed SR_LNLS produces satisfactory results compared to other codes. It can calculate parameters like flux, brightness, and coherence to aid ray-tracing simulations of hard and soft X-ray beamlines for the new Sirius light source.

1. SR_LNLS: A COMPUTER CODE FOR CALCULATING OPTICAL PARAMETERS FROM
UNDULATORS FOR RAY-TRACING SIMULATION OF HARD AND TENDER X-RAY
BEAMLINES. R. Celestre¹ ², B. Meyer², E. Granado³
¹ Faculty of Electrical and Computer Engineering, University of Campinas, Campinas, SP, Brazil
² Brazilian Synchroton Light Laboratory, Brazilian Center for Research in Energy and Materials, Campinas, SP, Brazil
³ Department of Quantum Electronics, Physics Institute ‘Gleb Wataghin’, University of Campinas, Campinas, SP, Brazil
Optical characteristics, i.e. photon flux, brightness, brilliance, coherence, polarization, etc., as well as spatial and angular dimensions from the photon beam are
parameters of great importance regarding ray-tracing simulations as they determine the quality of the X-ray source for photon experiments. Accurate computation of
such parameters are of paramount importance for X-ray beamline projects of the new light source Sirius, Campinas, Brazil, where energy spread effects show great
influence on the photon beam, being able to cause discrepancies between observed and simulated results.
The observation and systematic study of the energy spread effect on photon beams are quite recent, given that it is relevant only in low emittance (high brilliance)
sources or at free electron lasers (FEL’s) facilities. Aiming to address correctly to this effect at undulator insertion devices, a computer code that handles finite
emittance effects and energy spread was proposed in order to aid the calculation of optical characteristics, spatial and angular profiles of the photon beam.
Comparisons between the proposed code and already-stablished-codes that handle the energy spread effect were held for benchmarking.
ENERGY SPREAD EFFECT ON THE PHOTON BEAM
CONCLUSION REFERENCES
OPTICAL PARAMETERS CALCULATION FOR THE IVU19
Figure 2 – Effects owing to the energy spread of the electron beam
on the source size and angular divergence and its relative influence
on the IVU19’s characteristics (generated with SR_LNLS).
Figure 3 – Graphical user interface as a pre-
processor of SR_LNLS.
Contact: rafael.celestre@lnls.br
Figure 4 – Optical parameters of the IVU19 generated using the computer code SR_LNLS. The graphs presented above take into account
emittance and energy spread effects. The calculations were performed using the parameters shown in Figure 3.
The energy spread of the electron beam has a
influence on both source size and divergence of
the photon beam generated at undulators. Those
effects are stronger on diffraction limited sources,
like the forthcoming Sirius, in Campinas, Brazil.
The energy spread effect grows with the number of
magnetic periods 𝑁 of the undulator, the harmonic
number 𝑛 and the energy spread of the storage
ring 𝜎 𝐸. This effect introduces two growth factors
(shown in Figure 2 – upper graphs): one for the
natural undulator size and one for the natural
divergence.
Figure 2 (lower graphs) makes it clear that the
energy spread effect is stronger for lower energies,
although it is strongly dependent on the harmonic
number.
The undulator IVU19 is a planar insertion device
proposed to be used at the low 𝛽 straight sections.
Its parameters are shown in Figure 3.
Benchmarking of the SR_LNLS was done in three ways: through direct
comparisons between the SR_LNLS and two other widely used softwares - SRW
and SPECTRA; backpropagation through a imaging system of 1:1 magnification;
and through the computation of the Wigner function. Since it only uses
equations found at the most relevant literature (see References), the SR_LNLS
code has shown satisfactory results and can be used to calculate and generate
optical parameters from planar undulators for ray-tracing simulation of hard and
tender X-ray beamlines. Although minor bugs still exist, it is possible to exclude
implementation and codification errors, since the code has been through
extensive revision.
SR_LNLS was written in MATLAB and could be implemented in Python to provide
input parameters to be used by the ray-tracing program Shadow.
KIM, K.-J. (1995). Optical Engineering. 34, 342–352.
LIU, L., et al. (2014). “Parameters Sirius v500: AC10 6.”
TANAKA, T. & KITAMURA, H. (2009). Journal of Synchrotron Radiation. 16, 380–
386.
Figure 1 – Schematic drawing of a periodic magnet
structure of period 𝜆 𝑢 and with a number 𝑁 of periods.
The deflection parameter of a planar undulator is
given by:
K =
𝑒𝐵0 𝜆 𝑢
2𝜋 𝑚𝑐
And the wavelength of the radiation generated can
be calculated as follows:
𝜆 𝑛 =
𝜆 𝑢
2𝑛𝛾2
1 +
K2
2
+ 𝛾2
𝜃2
ACKNOWLEDGMENTS
The authors would like to thank Dr. Harry Westfahl Jr., Dr. Antonio Ricardo
Droher Rodrigues, Eng. James Francisco Citadini, Dr. Liu Lin and Dr. Natália Milas
from the Brazilian Synchrotron Light Source for the support given to this work.