Fig. 1. (a) Geometrical basis of the fixed exit bender. Actual bending mechanism (b) when the crystal is flattened and (c) when the crystal is bent. S a g i t t a l f o c u s i n g i s a n e f f i c i e n t m e t h o d f o r focus ing synch rotro n X-ray s. Usual ly, the secon d cry sta l of a dou ble -cr yst al mon och rom ato r is ben t into a cylindrical shape, ideally without introducing a n y d e f o r m a t i o n o f t h e c r y s t a l i n t h e s c a t t e r i n g p l a n e . A c c o r d i n g l y , b o t h e n e r g y a n d m o m e n t u m resolutions are kept as high as those achieved by flat-flat double-crystal monochromators. The radius of the bend that will provide optimal focussing is a f u n c t i o n o f t h e B r a g g a n g l e ; a s t h e B r a g g a n g l e b e c o m e s s m a l l e r , s o d o e s t h e r a d i u s . V a r i o u s b e n d i n g m e c h a n i s m s f o r s a g i t t a l f o c u s i n g h a v e been developed. However, most applications have been restricted to relatively low energy X-rays due t o t h e d i f f i c u l t y o f g e n e r a t i n g a n i d e a l b e n d w i t h sm al l ra di us . In ad di ti on , si mu lt an eo us ac hi ev em en t FIXED HEIGHT EXIT BENDER OF SYNCHROTRON X-RAY ABOVE 40 keV Alth oug h the rho mbo hed ral or dou ble tria ngl e ribb ed crys tals bent with a cam driv er mech anis m f u l f i l l t h e f i x e d - e x i t c o n d i t i o n , t h e y a r e a p t t o introduce non-uniform bend due to cramping at the crystal center. We developed a new sagittal focus b e n d e r [ 1 ] t h a t i s c o m p a t i b l e w i t h t h e S P r i n g - 8 standard monochromator [2,3] for bending-magnet b e a m l i n e s . I n p r i n c i p l e , t h e b e n d e r u s e s a conventional four-point bending mechanism, but the r o l l e r s f o r f o u r - p o i n t b e n d i n g a r e a t t a c h e d t o r o t a t i o n a r m s , m a k i n g t h e c e n t r a l p o s i t i o n o f t h e crystal fixed regardless of the bending radius. This pr oc ed ur e is ba se d on a si mp le ge om et ri ca l the or em il lu st ra te d in Fi g. 1( a) . Tw o ci rc le s, A an d B, ar e al wa ys ac ro ss at th e ri gh t an gl es to th e ci rc le s C and D, the centers, O C and O D , of which lie on the A C L B F E D O C O D O A O B (a) E F crystal O A O B O A O B crystal E E F F (b) (c) of optimal focus and fixed-exit height d e s p i t e c h a n g i n g o u t p u t e n e r g y i s preferable for most applications, and r e q u i r e s a n e v e n m o r e c o m p l e x bending mechanism. Fig. 2. Schematic diagram for a series of crystal slabs joined by thin hinges, cut parallel to the bending rods. perpe ndicu lar bisec tor L of the cente rs of circl e A a n d B . T h i s s h o w s t h a t t h e c r y s t a l , w h i c h corresponds to either circle C or D in Fig. 1 , is bent c y l i n d r i c a l l y w i t h o u t c h a n g i n g t h e h e i g h t o f t h e middle point of its arc, when pure torque is applied at th e cr os s po in ts E an d F. Th e ac tu al be nd in g mechanism when the crystal is flattened is shown i n F i g . 1 ( b ) . T h e c r y s t a l w a s c r a m p e d w i t h f o u r cylindrical rollers of the cradle (gray region in Figs. 1(b) and 1(c) ). The bending is performed without c h a n g i n g t h e p o s i t i o n o f t h e c r y s t a l c e n t e r b y rotating the cradle around O A and O C , as shown in Fig. 1(c) . Since the SPring-8 standard monochromator is d e s i g n e d t o k e e p t h e e x i t - b e a m h e i g h t c o n s t a n t , ev en wi th in ch an gi ng en er gy , co mb in at io n of th e bend ing mech anis m with the mono chro mato r also p r e s e r v e s e x i t - b e a m h e i g h t c o n s t a n c y w i t h a n optimized bending radius for each energy. We used a row of grouped crystals joined by thin hinges of a Si (3 1 1) plate with a rectangular s h a p e o f 9 0 m m ( a l o n g t h e b e a m ) × 1 0 0 m m (across the beam) × 2 mm (thickness), as shown in F i g . 2 , i n o r d e r t o a v o i d a n t i c l a s t i c b e n d i n g t h a t would degrades the total throughput. The focusing test was carried out at BL14B1 , which is a bending m a g n e t b e a m l i n e d e d i c a t e d t o J A E R I a n d e q u i p p e d wi th a SP ri ng -8 st an da rd do ub le -c ry st al m o n o c h r o m a t o r . T h e f i x e d - e x i t b e n d e r w a s m o u n t e d on the second crystal stage of the monochromator a s s h o w n i n F i g . 3 . A p a i r o f ( 3 1 1 ) S i c r y s t a l s w e r e u s e d b o t h f o r t h e f i r s t a n d s e c o n d c r y s t a l s . Fo r th e fi rs t cr ys ta l, an in di re ct ly co ol ed fl at pl at e was used instead of the standard direct fin-cooled crystal. Figure 4 shows the observed beam profiles at 4 0 k e V w i t h d i f f e r e n t b e n d i n g r a d i i , R . T h e h o r i z o n t a l b e a m s i z e w a s 6 5 m m a t t h e s c r e e n position for the unbent crystal. The beam reflected from the slot parts of the crystal appeared like the tee th of a com b. We can qua nti fy the num ber of s l o t s r e f l e c t i n g t h e X - r a y b e a m b y c o u n t i n g t h e sharp lines. From the image, all slots were found to r e f l e c t t h e X - r a y b e a m e v e n w h e n t h e b e n d i n g r a d i u s w a s 4 m . T h e g a i n o f t h e p h o t o n d e n s i t y w a s m e a s u r e d b y h o r i z o n t a l s l i t s c a n s , a n d w a s f o u n d t o b e 1 2 t i m e s l a r g e r t h a n t h e f l a t t e n e d crystal, when the bending radius of 4 m was used ( Fig. 4 ). Dy na mi c sa gi tt al fo cu si ng te st es we re pe rf or me d 2.8 mm 2 mm 120 mm 90 mm 0.2 mm 2.8 mm 2 mm 120 mm 90 mm 0.2 mm Fig. 4. Beam profiles using the sagittally focusing cr ys ta l mo no ch ro ma to r at 40 ke V. Th e pe ri od of the slo tte d cry sta l is 3 mm. The X-r ay bea m was more effectively focused at smaller bending radii R. between 40 keV ( R = 4 m) and 60 keV ( R = 2 m). The beam height at the sample position was measured after optimizing of the bending radius and the parallel alignment the first and second crystals. The deviation of the beam height in the above energy range was within 0.15 mm. Preliminary setup was carried out wi th fl at -f la t do ub le cr ys ta ls be fo re in st al li ng t h e b e n d e r . T h e d e v i a t i o n o f b e a m h e i g h t w i t h f l a t - f l a t d o u b l e c r y s t a l s w a s 0 . 1 m m i n th e 40 ke V to 60 ke V ra ng e. Th e pr ac ti ca l deviation of beam height with the bender was s o m e w h a t l a r g e r t h a n e x p e c t e d . W h e n bending is performed, the fixed points are not on the surface of the bent crystal, but only in t h e c e n t e r o f t h e c r y s t a l . B e c a u s e o f t h e t h i c k n e s s a n d p o l y g o n a l n a t u r e o f t h e b e n t c r y s t a l , t h e p r a c t i c a l b e a m h e i g h t w a s changed slight in the 40 keV to 60 keV range. H o w e v e r , t h e b e a m d e v i a t i o n s h o u l d b e negligible in most experiments. This sagittal focus bender is designed for a n i n c l i n e d d o u b l e c r y s t a l m o n o c h r o m a t o r . The properties of sagittal focusing of inclined g e o m e t r y w i t h a S i ( 1 1 1 ) r e f l e c t i o n w e r e t e s t e d . I n F i g . 5 w e c o m p a r e a n e a r - e d g e s p e c t r u m o f a C u f o i l r e g i s t e r e d i n a d y n a m i c a l l y f o c u s i n g m o d e w i t h t h a t o f a normal flat crystal. Because the two spectra a r e i d e n t i c a l , w e c o n c l u d e t h a t e n e r g y resolution is not affected by sagittal focusing, nor is any distortions introduced. D y n a m i c a l s a g i t t a l f o c u s i n g i n a w i d e e n e r g y r a n g e , f r o m 8 . 5 k e V t o 1 5 0 k e V , pe rf or me d wi th ou t ex ch an gi ng m on oc hr om at or c r y s t a l s w i l l b e c o m e f e a s i b l e b y u s i n g t h e p r e s e n t b e n d i n g m e c h a n i s m i n t h e i n c l i n e d geometry. F i g . 3 . S a g i t t a l f o c u s b e n d e r w i t h a r o w o f grouped crystals joined by thin hinges installed in standard monochromator as the second crystal. flat R = 8 m R = 6 m R = 4 m F i g . 5 . N e a r - e d g e a b s o r p t i o n s p e c t r a o f C u f o i l , r e g i s t e r e d i n t h e dynamical focusing mode and in the flat crystal mode. Energy resolution is not affected, as all edge structures are reproduced without distortion. Yasuhiro Yoneda SPring-8 / JAERI E-mail: yoneda @ spring8.or.jp References [1] Y. Yoneda, N. Matsumoto, Y Furukawa, and T. Ishikawa, J. Synchrotron Rad. 8 (2001) 18. [2] T. Uru ga et al. , Rev . Sci . Ins tru m. 66 (19 95) 2254. [3] M. Yabashi et al. , SPIE Proc. 3773 (1999) 2. 8.94 8.96 8.98 9.00 9.02 9.04 9.06 1.0 Photon Energy ( keV ) μ μ D flat crystal dynamical focusing mode
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