Thermal bump removal by designing an optimised crystal shape

Transcription

1 Thermal bump removal by designing an optimised crystal shape J.-S. Micha 1, O. Geaymond 2, O. Ulrich 3, X. Biquard 3, F. Rieutord 3 French CRG-IF BM32 at ESRF 1 UMR SPrAM, CNRS/CEA-Grenoble/Univ. J. Fourier 2 Institut Néel, CNRS-Grenoble 3 CEA-Grenoble/ INAC CRG-IF BM32

2 Outline Motivations Modelling Results Conclusions

3 Motivations BM32 optics hutch at ESRF since 26 Bending Magnet at ESRF - heat power : 3W - acceptance: horiz. >1.5mrad, vert..1 mrad New Double Crystal Monochromator - Si(111) - from 5 to 3 kev keep cheap and simple cooling design - water (avoid LN2) - indirect cooling (simple + less vibrations) Cu ACCEL DCM Si InGa water Block crystal

4 Modelling : FEA - Heat Heat source: 2D domain incoming power ~ 1-15 W on 4x5 mm ~ 5-13 mw/mm 2 (on mono) Spatial distribution (uniform, gaussian-like) current in storage ring crystal inclination (working energy) Slits aperture (hxv), illuminated area X-ray XOP E=6.4 GeV R=25m B=.8T H accept= 2.9 mrad (mono. 26.9m Slits 23.9m).1 3keV Cooling power: - convective transfer: water/cu h = 5W/mm 2 /K - heat resistance Si/InGa/Cu.1 W/mm v keV 2keV

5 Modelling : FEA - deformation Get at (reflective) domain surface: uz vertical displacement along z => derivative of uz along y (// x-ray beam) => µ longitudinal slope errors FEA with COMSOL multiphysics (ex FEMLAB) Standard block Si crystal E =18keV ω = 16 µrad I = 2mA R int = 5% Less than to 25% with I = 35mA z max =.4 µm µ max = 15 µrad

6 Modelling : design of an optimised shape Previous works : side cooling better than bottom cooling General idea : decrease u z gradient by decreasing T gradient Reflective area z InGa Si y x Cu Water cooling First simulations : possibility to reverse the bump curvature! For a given heat load: possibility to remove longitudinal uz gradient (smooth profile) add deformation sources Constraints to the design: - several optics configurations - limited crystal size «cold» Uniformly «hot» & «flat» «cold» Strain and temperature gradient are outside the reflective domain

7 Reflectivity Model surface bump Simple Model: µ : Slope error at (x,y) on 1 rst crystal / flat 2 nd crystal ω : Darwin width Bragg reflectivity ~ gate function ω or E width ω θ or E DCM reflectivity per unit area: R(x,y) R(x,y) = 1- µ (x,y) / ω if µ (x,y) < ω = else θ B θ Β E B θ B +2µ(x,y) 2 nd nd Xtal Integrated reflectivity : R int = area R (x,y) dxdy 1 rst Xtal θ B Objective function to optimise two inputs: θ B +µ(x,y) µ - local slope error µ(x,y) from FEA - Darwin width ω (working energy)

8 Reflectivity Model thermal lattice expansion Two origins of lattice planes strain at illuminated surface: slope errors (longitudinal z-displacement gradient) thermal lattice spacing expansion θ B =α expansion.tanθ B T=µ kev, α Si = K -1 T=1 C θ B =1/4 µrad T=6 C θ B = ω If T1(x,y) uniform => perfect tuning with tilted 2 nd Xtal by θ B with T = T 2 -T 1 if T1(x,y) non uniform => best tuning with tilted 2 nd Xtal by θ B with T = T 2 -mean(t1) equivalent slope error ~ µ = α expansion.tanθ B T Max /2 For our heat load range, d-spacing variation can be omitted A more accurate computation can be done: µ th = (T 2 -T 1 (x,y)).α Si Si.tanθ B 2 µ (µrad) y // beam Gate function Xtal 1 with Gate function Xtal 2 with µ+µ th 2µ+offset => offset for highest R int

9 Results Optimised shape for 3 Energies X 3 horiz. acceptance 36K E =18keV ω = 16 µrad I = 2mA 34K Rint = 9% z max =.4 µm Gradient is along x! µ = -2 to 11 µrad µmean =2 µrad!

10 Results: comparison old-new crystal Old Xtal New Xtal 8 kev 4x5 mm ω = 4 µrad Total power W in rectangle h= 45.2 mm and v= mm on monochromator mean power density.127 W/mm 2 (mono),.5 W/mm 2 (HxV) 2 µrad 1 µrad 18 kev 5x3 mm ω = 16 µrad 11 µrad Total power W in rectangle h= mm and v= 3.36 mm on monochromator mean power density.72 W/mm 2,.1 W/mm 2 (HxV) 15 µrad -2 µrad 27 kev 5x3 mm ω = 1 µrad Total power W in rectangle h= 45.2 mm and v= mm on monochromator mean power density.48 W/mm 2 or.66 W/mm 2 (hxv) 1 µrad 4 µrad -2 µrad

11 Results: comparison Exp. - FEA Old Xtal New Xtal 8 kev 4x5 mm ω = 4 µrad 2 µrad R int =7% R int =85% ph/s/2ma.7 1 µrad 18 kev 5x3 mm ω = 16 µrad 11 µrad 15 µrad R int =56% R int =9% µrad 27 kev 5x3 mm ω = 1 µrad R int =56% R int =92% 1 µrad µrad -2 µrad

12 Conclusions Optimised crystals mounted on BM32 and BM2 at ESRF Photons flux at sample is very close to the theoretical flux FEA predicts high R int even for higher storage ring current Advantages Longitudinal bump removed Self-tuning crystal For one optics configuration => it should exist an optimised shape Cheap (indirect cooling + water) Simple to design & simple iterative converging methodology Standard manufacturing and tailoring Easy to mount & not sensitive to mounting defaults Drawbacks (?) Increase of temperature Weak sagittal bump (but whole setup might be cooled down anyway) (but could be compensated)

13 Outlook Automatic iterative method, use ray-tracing method Install on other BM ESRF, SOLEIL (DIFFABS, ), etc Apply on Ge/Si (Smart Cut) Apply on other reflective surfaces: - monochromator with higher power load (wiggler, ondulator) - mirror - other spectral range (laser)

14 Thank you for your attention T uz