1. Synrad3D Photon propagation and scattering simulation G. Dugan, D. Sagan CLASSE Cornell University Ithaca, NY USA

2. SYNRAD3D Features As part of the Bmad software library, a program called Synrad3d has been written to track synchrotron radiation photons generated in storage rings and beamlines. The purpose of the program is primarily to estimate the intensity and distribution of photon absorption sites, which are critical inputs to codes which model the growth of electron clouds. It can also be used to estimate radiation heat loads. Synrad3d can handle any planar lattice and a wide variety of vacuum chamber profiles. Synrad3d uses Monte Carlo techniques to generate photons based on the standard synchrotron radiation formulas for dipoles, quadrupoles and wigglers. Photons are generated with respect to the particle beam’s closed orbit, so the effect of variations in the orbit can be studied. The particle beam size is also taken into account when generating the photon starting positions. Photons are tracked to the vacuum chamber wall, where the probability of being scattered is determined by the angle of incidence, the energy of the photon, and the properties of the wall’s surface.

3. Vacuum chamber model The vacuum chamber wall is characterized at a number of longitudinal positions by its cross-section. A vacuum chamber wall cross-section may also be characterized using a piecewise linear outline. In between the cross-sections, linear interpolation or triangular meshing can be used. Linear interpolation is faster but is best suited for convex chamber shapes. Vacuum chamber cross- section for an elliptical chamber with an antechamber on the +x side of the chamber and an aperture on the -x side.

4. Scattering model: specular reflection SYNRAD3D includes scattering from the vacuum chamber walls, based on X-ray data from an LBNL database for the smooth-surface reflectivity, and an analytical model for diffuse scattering from a surface with finite roughness. B. L. Henke, E. M. Gullikson & J. C. Davis, \X-Ray Interactions: Photoabsorption, Scattering, Transmission, and Reection at E = 50{30,000 eV, Z = 1{92," At. Data Nucl. Data Tables 54, p. 181{342 (Jul. 1993). CesrTA smooth-surface reflectivity model:

5. Simple example (1) Photon emission only in CESR dipole B12W, 2.1 GeV positron beam, simple elliptical chamber throughout the ring, pure specular reflection Red dots: photon sources Blue dots: photon absorption points B12W B13W Straight section 3D photon trajectories Transverse geometry distorted from ellipse to circle. Longitudinal distance divided by 10. Geometry distorted for presentation

6. Photon reflection number distribution Distribution of photon absorption sites around the vacuum chamber perimeter Photon energy distribution Avg. number of reflections=5.4 Simple example (2)

7. Photon emission throughout the ring, averaged over different magnetic environments. Actual Cesr vacuum chamber, specular reflection only, beam energy 2.1 GeV SYNRAD3D predictions for photon absorption site distributions polar angle chamber wall

8. Scattering model: diffuse scattering (1) SYNRAD3D uses an analytical model for diffuse scattering from a surface with finite roughness, based on scalar Kirchoff theory, as described in P. Beckmann & A. Spizzichino, The Scattering of Electromagnetic Waves from Rough Surfaces, Pergamon Press, New York (1963) and J. A. Ogilvy, Theory of Wave Scattering from Random Rough Surfaces, Hilger, Bristol (1993) In this theory, the probability of specular reflection depends on the rms surface roughness  the photon wavelength, and the incident grazing angle.

9. Scattering model: diffuse scattering (2) The full expression for the diffusely scattered power depends on  the transverse correlation length T, the photon wavelength, and the incident grazing angle. In general, the result is given as an infinite series, but for  >> 1, which is the regime of “very rough” diffuse scattering, the formulae for the diffusely scattered power (using Kirchoff theory as developed by Beckmann) becomes (relatively) simple. In terms of P 0 (incident power), (smooth-surface reflectivity), y=cos (incident polar angle), x=cos (scattered polar angle),  = out-of-plane angle, the differential scattered power is T=rms distance scale for a Gaussian autocorrelation function (1)

10. Scattered power vs. polar scattering angle, evaluated at out-of-plane angle = 0. Small- wavelength limit (Eq. 1) Long- wavelength result for 30 eV photons

11. Scattered power vs. out-of-plane angle, evaluated at polar scattering angle = incident angle Small- wavelength limit (Eq. 1) Long- wavelength result for 30 eV photons

12. Comparison of scattering model predictions with results from measurements at DAPHNE Daphne data from N. Mahne, A. Giglia, S. Nannarone, R. Cimino, C. Vaccarezza, EUROTEV-REPORT-2005-013 Measurement quoted rms surface roughness as 200 nm. Transverse correlation length T and surface film layer adjusted to obtain best fit with data.

13. polar angle SYNRAD3D predictions for photon absorption site distributions chamber wall Black: specular only Cyan:  = 4 nm, T = 200 nm Blue:  = 100 nm, T = 5500 nm Red:  = 200 nm, T = 5500 nm Photon emission throughout the ring, averaged over different magnetic environments. Actual Cesr vacuum chamber, beam energy 2.1 GeV

14. DR Vacuum System Conceptual Design June 6, 2012ECLOUD'1214 ILCDR vacuum chamber Same profile in quads and drifts in wiggler cells Arc quads and drifts Fully- absorbing photon stops

15. polar angle SYNRAD3D predictions ILCDR (dtc03 lattice) chamber wall Photon emission throughout the ring, averaged over different magnetic environments. ILCDR design vacuum chamber shape, 5 GeV beam energy Arc 1, Arc 2: the two arcs of the racetrack ring Wiggler: wiggler cells Surface parameters: 10 nm C film on Al substrate; Roughness:  = 100 nm, T = 5000 nm

16. Conclusions As part of the Bmad software library, a program called SYNRAD3D has been written to track synchrotron radiation photons generated in storage rings. It can handle any planar lattice and a wide variety of vacuum chamber profiles. The program includes scattering from the vacuum chamber walls, based on X- ray data from an LBNL database for the smooth-surface reflectivity, and an analytical model for diffuse scattering from a surface with finite roughness. The predictions of the scattering model have been benchmarked against measurements at DAPHNE. Additional benchmarking against recent X-ray scattering measurements are planned. Results from the program have given photon absorption site distributions for the CesrTA ring, which have been used as input to electron cloud buildup simulations, whose results can be compared with tune shift, RFA, and shielded pickup measurements (talk by J. Crittenden). The program has also been used to model the radiation environment in the ILC damping ring and the APS (talk by L.Boon).