Performance limits of indirectly cryogenically cooled silicon monochromators--experimental results at the APS

Modelling the power threshold and optimum thermal deformation of indirectly liquid-nitrogen cryo-cooled Si monochromators

Maximizing the performance of crystal monochromators is a key aspect in the design of beamline optics for diffraction-limited synchrotron sources. Temperature and deformation of cryo-cooled crystals, illuminated by high-power beams of X-rays, can be estimated with a purely analytical model. The analysis is based on the thermal properties of cryo-cooled silicon crystals and the cooling geometry. Deformation amplitudes can be obtained, quickly and reliably. In this article the concept of threshold power conditions is introduced and defined analytically. The contribution of parameters such as liquid-nitrogen cooling efficiency, thermal contact conductance and interface contact area of the crystal with the cooling base is evaluated. The optimal crystal illumination and the base temperature are inferred, which help minimize the optics deformation. The model has been examined using finite-element analysis studies performed for several beamlines of the Diamond-II upgrade.

A thermal deformation optimization method for cryogenically cooled silicon crystal monochromators under high heat load

A method to optimize the thermal deformation of an indirectly cryo-cooled silicon crystal monochromator exposed to intense X-rays at a low-emittance diffraction-limited synchrotron radiation source is presented. The thermal-induced slope error of the monochromator crystal has been studied as a function of heat transfer efficiency, crystal temperature distribution and beam footprint size. A partial cooling method is proposed, which flattens the crystal surface profile within the beam footprint by modifying the cooling contact area to optimize the crystal peak temperature. The optimal temperature varies with different photon energies, which is investigated, and a proper cooling strategy is obtained to fulfil the thermal distortion requirements over the entire photon energy range. At an absorbed power up to 300 W with a maximum power density of 44.8 W mm-2 normal incidence beam from an in-vacuum undulator, the crystal thermal distortion does not exceed 0.3 µrad at 8.33 keV. This method will provide references for the monochromator design on diffraction-limited synchrotron radiation or free-electron laser light sources.

Highly efficient thermal deformation optimization method for smart-cut mirrors over the entire photon energy range

A method to optimize the notches of water-cooled white-beam mirrors over the entire photon energy range is proposed. A theoretical method is used to quantitatively evaluate the influence of the thermal load on the thermal deformation of a mirror. The result of theoretical calculations and finite-element analysis are consistent, which proves the feasibility of the method. The root mean square of the curvatures of the thermal deformation of the white-beam mirror over the entire photon energy range can be minimized. This method greatly simplifies the design work of water-cooled white-beam mirrors.

New mounting mechanism for cryogenically cooled thin crystal x-ray optics in high brightness high repetition rate free-electron laser applications

We present a new mounting design for thin crystal optics with cryogenic cooling compatibility. We design a crystal geometry with two symmetric strain-relief cuts to mitigate the distortion from mounting. We propose to sputter gold onto the crystal and the holder to ensure excellent thermal contact and sufficient mechanical bonding. The system is analyzed and verified by finite element analysis to have an acceptable level of strain due to mounting. The thermal performance of this mounting scheme is validated in an example cryogenic cooling system and the results indicate a tolerance of power density up to ∼1 kW/mm².

Design simulations of a horizontally deflecting high-heat-load monochromator

The performance of a liquid-nitrogen-cooled high-heat-load monochromator with a horizontal scattering plane has been analysed, aiming to preserve the high quality of the X-ray beam in the vertical plane for downstream optics. Using finite-element analysis, height profiles of the crystal surface for various heat loads and the corresponding slope errors in the meridional and sagittal planes were calculated. Then the angular distortions of the reflected beam in both meridional and sagittal planes were calculated analytically and also modelled by ray tracing, revealing a good agreement of the two approaches. The results show that with increasing heat load in the crystal the slope errors of the crystal surface reach their smallest values first in the sagittal and then in the meridional plane. For the considered case of interest at a photon energy of 14.412 keV and the Si(111) reflection with a Bragg angle of 7.88°, the angular distortions of the reflected beam in the sagittal plane are an order of magnitude smaller than in the meridional one. Furthermore, they are smaller than the typical angular size of the beam source at the monochromator position. For a high-heat-load monochromator operating in the horizontal scattering plane, the sagittal angular distortions of the reflected beam appear in the vertical plane. Thus, such an instrument perfectly preserves the high quality of the X-ray beam in the vertical plane for downstream optics. Compared with vertical scattering, the throughput of the monochromatic beam with the horizontal scattering plane is reduced by only 3.3% for the new EBS source, instead of 34.3% for the old ESRF-1 machine. This identifies the horizontal-scattering high-heat-load monochromator as a device essentially free of the heat-load effects in the vertical plane and without significant loss in terms of throughput.

A high efficiency and low vibration liquid nitrogen cooling system for silicon crystal based x-ray optics

A compact low-cost cryocooling system has been designed, constructed, and tested at SLAC National Accelerator Laboratory. The cooling power is provided by natural convection and phase change of the liquid nitrogen. The initial application was to cool silicon crystal optics to the sub-100 K range. A silicon crystal of dimension (width × depth × height) 50 × 50 × 30 mm³ has been used with an electric heater on the top surface in this prototyping test. This system can effectively provide more than 80 W of cooling power to the optics with a consumption of liquid nitrogen less than 2.1 l/h. The vibration of the silicon crystal was monitored during the tests with added electric heater power on the crystal. The vibration of the silicon crystal due to liquid nitrogen boiling is negligible.

A cantilevered liquid-nitrogen-cooled silicon mirror for the Advanced Light Source Upgrade

This paper presents a novel cantilevered liquid-nitrogen-cooled silicon mirror design for the first optic in a new soft X-ray beamline that is being developed as part of the Advanced Light Source Upgrade (ALS-U) (Lawrence Berkeley National Laboratory, USA). The beamline is optimized for photon energies between 400 and 1400 eV with full polarization control. Calculations indicate that, without correction, this design will achieve a Strehl ratio greater than 0.85 for the entire energy and polarization ranges of the beamline. With a correction achieved by moving the focus 7.5 mm upstream, the minimum Strehl ratio is 0.99. This design is currently the baseline plan for all new ALS-U insertion device beamlines.

Soldering of silicon to Invar for double-crystal monochromators

At the Brazilian Synchrotron Light Laboratory (LNLS), new double-crystal monochromators are under development for use at the new Brazilian fourth-generation synchrotron, Sirius. The soldering technique used for the double-crystal monochromators ensures the union of monocrystalline silicon with FeNi alloy, Invar36 (64Fe-36Ni) from Grupo Metal and Invar39 (61Fe-39Fe) from Scientific Alloys, through SnSb (92.8Sn-7.2Sb), SnCu (Sn-0.3Cu) and SnBiCu (Sn-1.4Bi-0.7Cu) alloys from Nihon Superior. Following soldering tests and quantitative analysis, the Invar39/SnBiCu/Si samples were selected using base materials coated with different depositions - gold and copper. X-ray diffraction identified the formation of intermetallic compounds, such as AuSn₂ and AuSn₄ in base materials coated with gold and Cu₃Sn and Cu₆Sn₅ with copper. Before thermal cycling, the average force obtained in shear tests was 1131 N with copper deposition and 499 N with gold deposition. After five consecutive thermal cycles from room temperature down to cryogenic temperature (-196.15°C), specimens with gold deposition presented cracks in the interface region and those with copper deposition showed no defects. Based on this, qualitative and semi-quantitative analyses of specimens with copper deposition were carried out by scanning electron microscopy and energy-dispersive spectroscopy techniques to identify the composition, distribution and morphology of the elements.

Optimizing X-ray mirror thermal performance using matched profile cooling

To cover a large photon energy range, the length of an X-ray mirror is often longer than the beam footprint length for much of the applicable energy range. To limit thermal deformation of such a water-cooled X-ray mirror, a technique using side cooling with a cooled length shorter than the beam footprint length is proposed. This cooling length can be optimized by using finite-element analysis. For the Kirkpatrick-Baez (KB) mirrors at LCLS-II, the thermal deformation can be reduced by a factor of up to 30, compared with full-length cooling. Furthermore, a second, alternative technique, based on a similar principle is presented: using a long, single-length cooling block on each side of the mirror and adding electric heaters between the cooling blocks and the mirror substrate. The electric heaters consist of a number of cells, located along the mirror length. The total effective length of the electric heater can then be adjusted by choosing which cells to energize, using electric power supplies. The residual height error can be minimized to 0.02 nm RMS by using optimal heater parameters (length and power density). Compared with a case without heaters, this residual height error is reduced by a factor of up to 45. The residual height error in the LCLS-II KB mirrors, due to free-electron laser beam heat load, can be reduced by a factor of ∼11 below the requirement. The proposed techniques are also effective in reducing thermal slope errors and are, therefore, applicable to white beam mirrors in synchrotron radiation beamlines.

Performance of a silicon monochromator under high heat load

The performance of a cryogenically cooled double-crystal silicon monochromator was studied under high-heat-load conditions with total absorbed powers and power densities ranging from 8 to 780 W and from 8 to 240 W mm(-2), respectively. When the temperature of the first crystal is maintained close to the temperature of zero thermal expansion of silicon, the monochromator shows nearly ideal performance with a thermal slope error of 0.6 µrad. By tuning the size of the first slit, the regime of the ideal performance can be maintained over a wide range of heat loads, i.e. from power densities of 110 W mm(-2) (at total absorbed power of 510 W) to 240 W mm(-2) (at total absorbed power of 240 W).

Thermal deformation of cryogenically cooled silicon crystals under intense X-ray beams: measurement and finite-element predictions of the surface shape

X-ray crystal monochromators exposed to white-beam X-rays in third-generation synchrotron light sources are subject to thermal deformations that must be minimized using an adequate cooling system. A new approach was used to measure the crystal shape profile and slope of several cryogenically cooled (liquid nitrogen) silicon monochromators as a function of beam power in situ and under heat load. The method utilizes multiple angular scans across the Bragg peak (rocking curve) at various vertical positions of a narrow-gap slit downstream from the monochromator. When increasing the beam power, the surface of the liquid-nitrogen-cooled silicon crystal deforms from a concave shape at low heat load to a convex shape at high heat load, passing through an approximately flat shape at intermediate heat load. Finite-element analysis is used to calculate the crystal thermal deformations. The simulated crystal profiles and slopes are in excellent agreement with experiments. The parameters used in simulations, such as material properties, absorbed power distribution on the crystal and cooling boundary conditions, are described in detail as they are fundamental for obtaining accurate results.