1. 1 BROOKHAVEN SCIENCE ASSOCIATES Lonny Berman EFAC May 10 th 2007 ID Beamline Optics and Damping Wigglers

2. 2 BROOKHAVEN SCIENCE ASSOCIATES Outline Hard x-ray undulator beamline monochromator thermal modelling (silicon and diamond) Hard x-ray undulator beamline mirror modelling Damping wiggler beamline monochromator thermal modelling (silicon) Damping wigglers: to cant or not to cant

3. 3 BROOKHAVEN SCIENCE ASSOCIATES Undulator Beamline Silicon Monochromator Simulation of “hockey- puck” liquid nitrogen cooled crystal design using 2σ beam size (1.2 mm wide x 0.75 mm high) from U14 superconducting undulator at maximum K, 30 m distance from source, 12.7º Bragg angle (corresponds to 8.9 keV for Si(111)). Total power = 109 W (unfiltered), 92 W (filtered) Maximum temperature = 98 K (unfiltered), 94 K (filtered) Maximum thermal slope error in beam footprint = ±5 µrad (unfiltered), ±4 µrad (filtered) Courtesy of Viswanath Ravindranath

4. 4 BROOKHAVEN SCIENCE ASSOCIATES Performance for Longer Undulators U14 Undulator Length (m) Filtered or UnfilteredTotal Power at Maximum K Maximum Temperature (K) Maximum Thermal Slope Error (µrad) 2unfiltered 109 98 ±5 2 filtered 92 94 ±4 4unfiltered 219 144 ±7.4 4 filtered 185 125 ±1 6unfiltered 326 232 ±100 6 filtered 275 180 ±32

5. 5 BROOKHAVEN SCIENCE ASSOCIATES 4 m Long Undulator Case with Filter Conclusion: for silicon, there is no better temperature for the illuminated area of the crystal to be at, than 125 K. Action Item: investigate the use of controls and diagnostics to make sure that this is the temperature of the illuminated area of the crystal.

6. 6 BROOKHAVEN SCIENCE ASSOCIATES Using a Water-Cooled Diamond The diamond wafer is 0.5 mm thick and the (111) Bragg reflection is used (Bragg angle is 19.7º at 8.9 keV). Beam size 2.4 mm wide x 1.5 mm high (4σ). Here, 60% of the incident power is transmitted through the crystal, and the depth dependence of the 40% absorbed power has to be taken into consideration. The transmitted power propagates through a hole in the copper substrate. There is 1 mm of overlap of the diamond wafer and copper substrate all around. A crucial consideration, in such a design, is the thermal contact between the diamond and the substrate. Courtesy of Paul Montanez

7. 7 BROOKHAVEN SCIENCE ASSOCIATES Diamond Crystal Peformance Means of Thermal Contact of Diamond with Copper (Presumed Heat Transfer Coefficient in W/mm 2 -°C) Power Absorbed by Diamond (W) Maximum Temperature of Diamond (°C) Maximum Thermal Slope Error (µrad) Ga-In Eutectic (0.04) 166 267 ±30 Brazing (0.4) 166 103 ±9 Conclusion: pathways to improvement involve better thermal contact, larger contact area, thinner diamond to absorb less power. Action Item: watch developments in the field, as the main challenge with diamonds is in obtaining an assured supply of large, good quality crystals.

8. 8 BROOKHAVEN SCIENCE ASSOCIATES NSLS X25 1 m Long Vertical Focusing Mirror X25 Vertical Mirror Parameters Source to Optic = 23 m Optic to Focus = 3.5 m Demag = 6.6:1 measured rms slope = 1.4 μrad NSLS-I perfect image size fwhm = 3.25 μm calc. image size incl. fig. err. fwhm = 23 μm NSLS-II perfect image size fwhm = 1.1 μm calc. image size incl. fig. err. fwhm = 23 μm 1 m long dynamically bent palladium coated mirror, fused silica substrate. electron source size, σ VFM ellipse demag. source, σ’ 23 m3.5 m X25 Mirror Bender System Courtesy of James Ablett

9. 9 BROOKHAVEN SCIENCE ASSOCIATES X25 SHADOW Ray-Tracing Ideal Mirror X25 Mirror Source X25 Mirror, ‘width’ ~ 16 μm Ideal Mirror, fwhm = 1.03 μm x [mm] Normalized Intensity X25 Mirror at NSLS-II Source Ideal Mirror X25 Mirror X25 Mirror, fwhm = 16.6 μm Ideal Mirror, fwhm = 3.2 μm y [μm] X25 Mirror at NSLS-II x [mm]Normalized Intensity y [μm] rms slope=1.4 μrad distance along mirror [cm] vertical [microns] X25 Mirror at NSLS-I distance along mirror [cm]

10. 10 BROOKHAVEN SCIENCE ASSOCIATES Damping Wiggler Silicon Monochromator We looked at the same crystal design as we used for undulator beams, and studied its performance using different size wiggler beams. The case shown here is based on a beam size of 3.6 mm wide x 2.25 mm high at 30 m from the 7 m long damping wiggler source (original design), Si(111) at 8.9 keV (Bragg angle 12.7º). Total power = 475 W Maximum temperature = 125 K Maximum thermal slope error in beam footprint = ±6.6 µrad, not bad! Courtesy of Viswanath Ravindranath

11. 11 BROOKHAVEN SCIENCE ASSOCIATES Damping Wiggler Mono Using Bigger Beam We also looked at the case of a beam size twice as large in the horizontal and vertical directions, i.e. 7.2 mm wide x 4.5 mm high. Total power = 1.77 kW Maximum temperature = 355 K Maximum thermal slope error in beam footprint = ±300 µrad Notice that the temperature rise in this case is no longer concentrated right at the beam footprint. The crystal is too small in size to handle the power. Conclusion: bigger beams require bigger crystals with bigger cooling interfaces. Courtesy of Viswanath Ravindranath

12. 12 BROOKHAVEN SCIENCE ASSOCIATES Multiple yet independent damping wiggler beamlines may be accommodated in individual straight sections, either by viewing different off-axis portions of the same damping wiggler fan, or by viewing on-axis radiation emissions from separate wigglers which are canted by a few milliradians with respect to each other. The larger the canting angle, the larger the impact on the emittance of the ring. E.g. if two 3.5 m long wigglers canted by 2 mrad with respect to each other are installed in each of these 8 straight sections, then the emittance increases by 8%. 2 mrad Critical Energy Dependence Across Each Canted Wiggler Radiation Fan For each fan: E c = E c,max (1-[ө/ө max ] 2 ) 1/2 ө max = K/γ 10.8 keV E c (keV) ө (mrad) 10 5 0 0 5-5 Damping Wigglers: To Cant or Not to Cant

13. 13 BROOKHAVEN SCIENCE ASSOCIATES Flux Variation Across Wiggler Fan Flux Conclusion: canted damping wigglers offer no advantages for flux-dependent applications except at the highest photon energies, as compared with viewing the fan at even 1.5 mrad off-axis horizontally. Courtesy of Steve Hulbert

14. 14 BROOKHAVEN SCIENCE ASSOCIATES Brightness is a Different Matter Insertion device codes do not handle this effect correctly, but it has been empirically observed at the X25 wiggler: Lonny Berman and Zhijian Yin (1997) Brightness Conclusion: when viewed at 1 mrad off-axis horizontally, the horizontal source size of a 7 m long damping wiggler will appear to be 7 mm wide, diminishing the brightness by a factor of ~20, relative to on-axis viewing. If brightness is an important consideration for a damping wiggler source, it must be viewed on-axis. The only means to achieve this, for two completely independent beamlines, is to implement canted damping wigglers.

15. 15 BROOKHAVEN SCIENCE ASSOCIATES Conclusions Existing liquid nitrogen cooled silicon crystal design will handle NSLS-II undulator beams, with attention to temperature control For water-cooled diamond crystals to be effective in NSLS-II undulator beams, attention to crystal size and thermal contact is necessary Small mirror figure errors can introduce structure into an NSLS-II undulator focused beam as well as blur image Liquid nitrogen cooled silicon crystal designed for an NSLS-II undulator beam could handle a damping wiggler beam with dimensions of ~4-5 mm; larger size beams will need to be handled by larger size crystals Canted damping wigglers pose no advantage for flux-dependent applications (compared with off-axis views of a single wiggler), but will be necessary for brightness-dependent applications if more than one independent beamline per damping wiggler straight section is desired