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. Granado³¹ 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, Brazil³ 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 areparameters of great importance regarding ray-tracing simulations as they determine the quality of the X-ray source for photon experiments. Accurate computation ofsuch parameters are of paramount importance for X-ray beamline projects of the new light source Sirius, Campinas, Brazil, where energy spread effects show greatinfluence 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 finiteemittance 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 beamon the source size and angular divergence and its relative influenceon 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 accountemittance and energy spread effects. The calculations were performed using the parameters shown in Figure 3.

The energy spread of the electron beam has ainfluence on both source size and divergence ofthe photon beam generated at undulators. Thoseeffects are stronger on diffraction limited sources,like the forthcoming Sirius, in Campinas, Brazil.The energy spread effect grows with the number ofmagnetic periods 𝑁 of the undulator, the harmonicnumber 𝑛 and the energy spread of the storagering 𝜎𝐸. This effect introduces two growth factors(shown in Figure 2 – upper graphs): one for thenatural undulator size and one for the naturaldivergence.Figure 2 (lower graphs) makes it clear that theenergy spread effect is stronger for lower energies,although it is strongly dependent on the harmonicnumber.The undulator IVU19 is a planar insertion deviceproposed 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 directcomparisons between the SR_LNLS and two other widely used softwares - SRWand SPECTRA; backpropagation through a imaging system of 1:1 magnification;and through the computation of the Wigner function. Since it only usesequations found at the most relevant literature (see References), the SR_LNLScode has shown satisfactory results and can be used to calculate and generateoptical parameters from planar undulators for ray-tracing simulation of hard andtender X-ray beamlines. Although minor bugs still exist, it is possible to excludeimplementation and codification errors, since the code has been throughextensive revision.SR_LNLS was written in MATLAB and could be implemented in Python to provideinput 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 magnetstructure of period 𝜆𝑢 and with a number 𝑁 of periods.

The deflection parameter of a planar undulator isgiven by:

K =𝑒𝐵0𝜆𝑢2𝜋 𝑚𝑐

And the wavelength of the radiation generated canbe calculated as follows:

𝜆𝑛 =𝜆𝑢2𝑛𝛾2

1 +K2

2+ 𝛾2𝜃2

ACKNOWLEDGMENTS

The authors would like to thank Dr. Harry Westfahl Jr., Dr. Antonio RicardoDroher Rodrigues, Eng. James Francisco Citadini, Dr. Liu Lin and Dr. Natália Milasfrom the Brazilian Synchrotron Light Source for the support given to this work.