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To cite this version:
L. Zhang, M. Sanchez del Rio, G. Monaco. Liquid nitrogen cooled Si crystal monochromator: X-ray focusing by controlled heat load. 11th International Conference on Synchrotron Radiation Instrumen- tation (SRI), Jul 2012, Lyon, France. 4 p., �10.1088/1742-6596/425/5/052008�. �hal-01572941�
Liquid nitrogen cooled Si crystal monochromator: X-ray focusing by controlled heat load
L. Zhang, M. Sanchez del Rio, G. Monaco
European Synchrotron Radiation Facility, 6 rue Jules Horowitz, F-38000 Grenoble, France
E-mail: zhang@esrf.fr
Abstract. The thermal deformation of a liquid nitrogen cooled silicon crystal under increasing absorbed power undergoes five phases: i) no deformation at zero power, ii) concave shape of the crystal, iii) appearance of a central bump, iv) minimum of the slope error averaged over the beam footprint on the crystal due to the balance between the initial concave shape and the growing central bump, and v) rapid growth of the thermal bump. In general, a liquid nitrogen cooled silicon crystal is designed to operate before the appearance of phase v), and mostly in phase ii) (concave shape). This concave shape of the crystal leads to a focusing effect on the beam, which should be considered in combination with other optical elements in the design and optimization of the beamline optical layout.
1. Introduction
In applications at 3rd generation light sources, the incoming beam power density on the monochromator crystal is usually very high (typically 10 to 100 W/mm2), and liquid nitrogen cooling [1-6] is the most effective way to limit thermal deformations in the monochromator, thus keeping to a minimum the degradation of the beam characteristics (size and divergence). The thermal deformation of the liquid nitrogen cooled silicon crystal goes through different phases on increasing the absorbed power: i) no deformation at zero power, ii) concave shape of the crystal, iii) appearance of a central bump, iv) minimum of the slope error averaged over the beam footprint on the crystal due to the balance between the initial concave shape and the growing central bump, and v) rapid growth of the thermal bump. The transition from one phase to the following one is highly non-linear in the absorbed power and depends on both crystal parameters (dimensions and cooling) and beam parameters (total power and beam footprint size). The relation between the thermal deformation and absorbed power is well known [7-8, 5], but the effects of these deformed crystal shapes on the beam are not well identified. In general, a liquid nitrogen cooled silicon crystal is designed to operate before the appearance of phase v), and mostly in phase ii) (concave shape). The concave shape of the crystal leads to a focusing effect on the beam and observed in some beamlines. This effect can be very relevant in connection with the use of further optical elements downstream (e.g. mirrors or lenses) or upstream (e,g, white beam mirror) of the monochromator.
2. Thermal deformation
Thermal deformation of the silicon crystal depends on the thermal expansion coefficient α and thermal conductivity k. These material properties of the silicon are highly non-linear from room temperature to liquid nitrogen temperature. Both theoretical prediction and experimental measurements [5-8] showed
Figure 1. RMS thermal slope error of a liquid nitrogen cooled silicon crystal under variable heat load at different Bragg angles
that the thermal deformation of a liquid nitrogen cooled silicon crystal increases linearly with absorbed power, then decreases to local minimum, and finally increases very strongly. Finite Element Analysis (FEA) has been used to calculate the thermal deformation of the liquid nitrogen cooled silicon crystal.
From FEA results, we can plot the RMS thermal slope error of the crystal versus absorbed power at different Bragg angles as shown in Figure 1 for the ESRF UPBL6 beamline (an upgrade beamline under construction on port ID20). It is easy to identify where are the working points of the silicon crystal at the actual e-beam current of 200 mA and at the possible future current of 300 mA. These results are convenient to guide the design and optimisation of the silicon crystal monochromator, and similar curves have been used at the ESRF for many years. The idea is to avoid working on the right side of the local minimum of each curve.
However, the increasing requirements on beam quality, such as those necessary to achieve micro- and nano-meter focused beam sizes, or exceptionally low and stable values of beam collimation before high resolution monochromators, place great importance on the consideration of the focusing- defocusing effects of the crystal monochromator. The thermal slope error expressed in terms of RMS does not provide sufficient information for modern monochromator design. The crystal shape variation
(a) (b) (c) (d) (e)
Figure 2. RMS thermal slope error and maximum temperature of the ID06 liquid nitrogen cooled silicon crystal (deformed shape) at different e-beam current
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with thermal deformation should be considered in the beamline optical layout design. This deformed crystal shape is generally calculated by FEA which should be accurate and reliable. To validate predictions by FEA, heat load tests have been conducted at the ESRF beamline ID06 and others in 2010. In order to linearly increase heat load on the liquid nitrogen cooled monochromator crystal by keeping all the other parameters unchanged, the e-beam current in the storage ring has been ramped from 0 to 300 mA, although the maximum operational beam current is 200 mA for the ESRF storage ring. In the test beamline ID06, an in-vacuum undulator U18 and a normal undulator (in-air) U32 were simultaneously used in order to have as high as possible power on the monochromator crystal. The total absorbed power by the silicon crystal was 381 W at 200 mA and with primary slits opening of 2 mm horizontally and 1 mm vertically. The Bragg angle was set to 25.4 degrees. We measured crystal profiles and calculated crystal deformed shapes by FEA at various conditions (e-beam current, beam size). The obtained results show an excellent agreement between the measurements and FEA calculations and validate our finite element method [9].
Let’s concentrate on the silicon crystal shape at different heat load conditions. Several FEA simulations have been performed for different heat load conditions on the crystal for different e-beam current and other experimental parameters (e.g., undulator gap, slit apertures). The power is absorbed in the crystal volume. Figure 2 shows FEA results for the RMS thermal slope error, the maximum temperature in the crystal versus e-beam current and crystal shapes (footprint region) at five values of e-beam current. :
(a) I=5mA, Pabs= 9.5 W, the crystal is slightly deformed in concave shape.
(b) I=100mA, Pabs= 190 W, the crystal is deformed in deepest concave shape.
(c) I=140mA, Pabs= 267 W, the crystal is close to the local minimum deformation, quite flat in shape.
(d) I=150mA, Pabs= 286 W, the crystal is just out of the local minimum deformation, with shape inversion from concave to convex.
(e) I=200mA, Pabs= 381 W, the crystal is very much deformed in convex shape.
In (c) and (d), one observes that the right side of the footprint changes from a concave to a convex shape at smaller e-beam current than the left side. This can be explained by the power absorption in the volume with beam incidence at Bragg angle θB=25.4° from left to right: the volume under the left half of the footprint absorbs less power than the volume under the right half of the footprint.
3. Focusing effects by crystal monochromator
The crystal deformation shown in Figure 2b approximately corresponds to a spherical shape with an average radius of 290 m. The focusing effects of this spherical shape are not negligible, and have to be taken into account in certain beamline optical configuration design and optimisation. It is the case for the ESRF UPBL6 beamline. In an intermediate version of the beamline optical configuration, the key optical elements were (from source to sample): a horizontal deflection white beam collimating mirror CM1 (toroidal shape), a double crystal monochromator (DCM), a high-resolution monochromator, focusing mirrors FM2, FM3, FM4. If the focusing or collimating effects of the liquid nitrogen cooled silicon crystal in the DCM under heat load were not considered, the radius of curvature of the CM1 should be in the range of 150 to 820 m. The deformed silicon crystal presents a spherical shape of average radius in this range. The possibility has been investigated of replacing the toroidal mirror CM1 with a flat mirror which is much easier to achieve, allowing beam collimation by the silicon crystal monochromator DCM.
The silicon crystal in the DCM is liquid-nitrogen cooled on both sides to obtain a maximum cooled surface area. The photon energy range is 5 to 20 keV, and the Bragg angle varies from 5.6° to 23.1°.
The DCM is p=31 m from the centre of the undulators (U26 or U32, mounted in a revolver setup). The opening of the primary slits at 27 m is set to 0.8 mm in the vertical direction, and variable in the horizontal direction. The required radius of curvature for the beam collimation varies with photon energy or Bragg angle as R=2p/sin(θB). The deformed shape of the silicon crystal was calculated for different Bragg angles with heat load corresponding to the undulator configuration at this Bragg angle.
The radius of curvature at the centre of the footprint on the crystal surface was calculated and then compared with the required radius. Tuning the horizontal slit opening in the range of 1.8 to 2.8mm allows heat load variation and consequently the variation of the thermal deformation of the silicon crystal. The best fit results are compared with the required radius in Figure 3. The liquid nitrogen cooled silicon crystal can acquire a good shape to achieve beam collimation, especially at a high Bragg angle. Ray-tracing has been performed with the deformed silicon crystal shapes under heat load.
Results confirm satisfactory beam collimation by the silicon crystal monochromator.
Figure 3. Required radius of curvature for the beam collimation and calculated radius of curvature at centre of the footprint on the crystal surface versus Bragg angle
4. Discussion and conclusion
The beamline UPBL6 should operate not only at 200 mA (74% of operation modes) but also at 90 mA (20% of operation modes: 16-bunch mode). The e-beam current decay at 16-bunch mode reaches 33%, compared to 9% decay at 200 mA operation modes. In the 90 mA operation mode, especially when the e-beam current decays to 60 mA, it is not possible to tune the radius of the concave crystal to a desired value by only changing the horizontal beam size. Therefore, using only the silicon crystal monochromator in the DCM at low e-beam current is not sufficient to achieve beam collimation. To obtain maximum flexibility and performance of the beamline, a bendable white beam mirror CM1 is finally adopted. This mirror allows good beam collimation in combination with the collimation effects of the liquid nitrogen cooled silicon crystal monochromator.
The thermal deformation shape of the liquid nitrogen cooled silicon crystal monochromator could have a significant impact on the beam collimation and focusing. The concave shape of the silicon crystal leads to a focusing effect on the beam, and should be considered in combination with other optical elements in the design and optimization of the beamline optical layout.
5. References
[1] Marot G et al. (1992) Rev. Sci. Instrum. 63(1), 477-480 [2] Rogers C S et al. (1995), Rev. Sci. Instrum. 66(6), 2494-2499
[3] Bilderback D H, Freund A K, Knapp G S and Mills D M (2001). J. Synchrotron Rad. 8, 22-25 [4] Mochizukia T et al. (2001), Nucl. Instr. Meth. Phys. Res. A 467–468, 647–649
[5] Zhang L, Lee W K, Wulff M & Eybert L (2003), J. Synchrotron Rad. 10, 313–319 [6] Chumakov A et al. (2004), J. Synchrotron Rad. 11, 132-141
[7] Zhang L (1993). Proc. SPIE, 1997, 223-235
[8] Lee W K, Fezzaa K, Fernandez P, Tajiri G & Mills D M (2001), J. Synchrotron Rad. 8, 22-25.
[9] Zhang L et al. (2012) to be submitted to J. Synchrotron Rad.
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