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.

High heat-load x-ray optics development has progressed tremendously since the arrival of 3rd generation synchrotron radiation (SR) light sources (ESRF, APS, SPring-8, etc.) at the end of 1980 and the beginning of 1990. With the emerging free electron laser (FEL) and low emittance (or diffraction limited) SR light sources, wavefront preservation is a new challenge for x-ray optics. This is especially the case for high repetition rate hard x-ray FEL (XFEL) light sources such as Euro XFEL and LCLS-II, as the heat-load on x-ray optics can reach hundreds of watts of average power and gigawatt to petawatt levels of peak power.

Different methods have been proposed to minimize the thermal deformation of x-ray optics. Water cooling is the technique of choice for most white beam mirrors in third-generation synchrotron light sources and reflecting mirrors in high repetition rate FEL light sources. To minimize thermal deformation of a water-cooled mirror, one effective method is to cool the mirror along the “top-sides”1 of the substrate, fully illuminate or overfill the mirror length, shape the beam to the desired final size with downstream secondary slits, and optimize the mirror cross section with notches.2–4 The thermal slope error of such a mirror, with about 800 W of absorbed beam power, can be minimized to 0.018 μrad. A mirror cross section with notch structures was also proposed previously.5 This notch-based, fully illuminated water cooling technique is widely used for white or pink beam x-ray mirror in synchrotron light sources. For high repetition rate XFEL mirror, the beam footprint changes by a few factors with varying photon energy. A novel technique utilizing water cooling in combination with variable electric heaters, called REAL—Resistive Element Adjustable Length, was proposed in 2015,6 demonstrated recently,7 and will be implemented at SLAC. Electric heaters of variable lengths are used to actively correct the thermal deformation in the x-ray mirrors.

For a silicon crystal monochromator at synchrotron light sources, liquid nitrogen (LN2) cooling has been widely investigated8–16 and subsequently used in many beam lines. The motivation to use LN2 cooling for the monochromator crystal is based on the following points: (1) The thermal deformation of the x-ray optics is proportional to the ratio of α/k, where α and k are the thermal expansion coefficient and the thermal conductivity of the crystal material, respectively. The ratio α/k of silicon at LN2 temperature (77 K at 1 atm) is much lower than that at room temperature. Therefore, LN2 cooling can significantly reduce the thermal deformation of the silicon crystal, compared to water cooling at near room temperature. (2) The beam footprint (x-ray beam illuminated area) on the monochromator crystal is variable and typically 1 mm–2 mm wide and 2 mm–10 mm long, much smaller than the crystal size (about 50 mm size in three directions), due to the large and variable Bragg angle. This is very different from the x-ray white beam mirror where the beam footprint is as long as the mirror with a typical length of 500 mm. The water cooling technique with notch structure in the mirror is not effective for the monochromator crystal.

There are many applications of silicon-based crystal optics in high rep-rate hard x-ray FEL, such as monochromator, four-bounce delay line, and x-ray cavity-based new FEL sources (regenerative amplifier FEL, x-ray free-electron laser oscillator, etc.). For LCLS-II and LCLS-II-HE (High Energy), the power load on the silicon crystal optics is typically less than 40 W. The high resolution monochromator for the LCLS-II-HE beamline is targeting a few eV energy resolution for photon energy above 12 keV, namely, a resolving power of 106–107. The mechanical stability of this monochromator is one of the key requirements. Cryocoolers based on the compression + heat exchanger + regenerator with helium gas can provide cooling capability of 100 W at liquid nitrogen temperature. However, this type of cryocoolers generates vibrations on the monochromator crystal and leads to large beam intensity fluctuation. The pulse tube cryocoolers and Gifford–McMahon cryo-refrigerator has not been used to cool x-ray crystal optics since the past two decades due to the vibration issues. Cryocooling systems with close-loop active recirculation of liquid nitrogen are currently most widely utilized for x-ray crystal optics. A heat exchanger with the secondary liquid nitrogen cooling circuit can extract about 500 W of power on the silicon crystal optics. The active pumping of coolant allows high cooling power, but mechanical work heating and long length of plumbing typically leads to high liquid nitrogen consumption and reduced operation efficiency. In addition, to achieve high heat transfer efficiency, the coolant runs under the turbulent flow condition and can therefore introduce mechanical excitation to the system.

For an application that requires high mechanical stability but not high sustained power dissipation, a simpler setup may be devised with low mechanical excitation (in both broad and narrow frequency range) and high efficiency. In this manuscript, we describe a prototype system designed and built at SLAC National Accelerator Laboratory with the objective of providing a design basis for a high performance and cost effective cryocooling system for LCLS x-ray crystal optics. The principle is based on the phase change in liquid nitrogen and natural convection. Neither active circulation nor the pumping system is needed. The performance requirement of such a cryocooling system is as follows: cooling power up to 100 W, temperature of the crystal kept around 100 K, and no significant vibration contribution by the cryocooling system. First experimental results are presented and analyzed.

The prototype system generates cooling power by natural convection and boiling evaporation of liquid nitrogen (LN2) under atmospheric pressure. At the current stage, the complete system is designed to be passive and the supply of liquid nitrogen is by action of gravity only. As shown in Fig. 1, LN2 is tapped from the bottom of the reservoir via a 6 mm nominal diameter bellow and flows downwards into the lower port of the exchanger block. LN2 then fills the internal cooling channels of the exchanger, while natural convection and boiling action take place on the channel surfaces. The evaporated nitrogen gas travels upward and is collected on the top horizontal channel of the exchanger and guided through a 13 mm diameter bellow to a venting port directly above the main chamber. Note that the exhaust port is positioned higher than the maximum liquid height of reservoir (just below the external neck of the reservoir) to prevent spillage. A gas flow meter (to be described later) is connected to the end of the venting port. The headspace of LN2 is always vented directly to the atmosphere, while the exhaust port can be closed to stop the flow of LN2 into the exchanger.

FIG. 1.

Model of the liquid nitrogen cooling system as rendered by the computer. All liquid lines and cold sections are in vacuum, with exhaust bellow leading directly up. The exhaust port is higher in elevation than the reservoir to facilitate gravity feed without the risk of overflow. The liquid nitrogen system operates under 1 atm.

FIG. 1.

Model of the liquid nitrogen cooling system as rendered by the computer. All liquid lines and cold sections are in vacuum, with exhaust bellow leading directly up. The exhaust port is higher in elevation than the reservoir to facilitate gravity feed without the risk of overflow. The liquid nitrogen system operates under 1 atm.

Close modal

Given the enthalpy of vaporization of nitrogen to be 5.6 kJ/mol at 77 K and its liquid density of 0.807 g/cm3, one can estimate the liquid volume consumption rate to be 5.3 l/day for a sustained power of 10 W. For our prototype reservoir of 38 l capacity, this translates to a life of about 6 days between refills.

The wall of the LN2 reservoir forms an integral part of the vacuum system. The CAD (Computer Aided Design) rendition of the overall system is shown in Fig. 1. The chamber is constructed from standard 10 in. conflat components, except for the integrated reservoir, which is custom designed and fabricated. All cooling lines are routed in vacuum with VCR fittings for in-vacuum connections to reduce any unnecessary heat loss. A more detailed view of the main heat exchanger is shown in Fig. 2. The main exchanger block is made from OFE (oxygen free electrical) copper with internal channels cut vertically for better boiling characteristics. There are six vertical channels 9.5 mm in diameter, 76 mm in length, and 15 mm in separation. The vertical channels are joint both at the top and bottom by exhaust (11 mm) and inlet (5 mm) channels with brazed VCR fittings for external connections. The dimensional envelop of the exchanger block is approximately (W × D × H) 100 × 90 × 114 mm3, with a total mass of 3.5 kg. The dummy silicon block (50 × 50 × 30 mm3) is held down with clamps and over a piece of 0.1 mm thick indium foil to the exchanger. The indium foil ensures good thermal contact between the heater and silicon block. To simulate thermal loading on the silicon crystal, heat is deposited directly onto the top surface of the silicon block from an in-vacuum electrical heater encased in Al2O3. Both the heater voltage and current are measured to calculate the power accurately. Voltage measurement is made very close to the connection to ceramic heater in vacuum to reject voltage drop through copper wire, and current is measured through a 0.0339 Ω in the shunt resistor in the air. Note the heater is vertically loaded via a leaf spring made from 0.4 mm thick 301 stainless steel to ensure reliable contact.

FIG. 2.

Detailed view of the heat exchanger assembly with markings for sensor locations. The top plate of the exchanger has been removed to show arrangement of cooling channels. Two T-type thermocouples (Cu1 and Cu2) are located directly on the exchange body (Cu), while another (Si) is clamped onto the silicon block. An embedded K-type thermocouple is located inside the ceramic heater (Ht). Also shown is the pick-up location for vibration measurements.

FIG. 2.

Detailed view of the heat exchanger assembly with markings for sensor locations. The top plate of the exchanger has been removed to show arrangement of cooling channels. Two T-type thermocouples (Cu1 and Cu2) are located directly on the exchange body (Cu), while another (Si) is clamped onto the silicon block. An embedded K-type thermocouple is located inside the ceramic heater (Ht). Also shown is the pick-up location for vibration measurements.

Close modal

Finally, the main exchanger assembly is connected to the base flange via a hollow box support constructed from a pair of half sections also made from 0.4 mm thick 301 stainless steel spot welded together. It is important to have a rigid support structure so that the natural frequency is sufficiently high (500 Hz) for better stability. Additionally, the support should have a low thermal conductivity to minimize the quiescent consumption of liquid nitrogen. We estimated an overall heat conduction loss of about 5 W when the exchanger is at 77 K and the base flange is at ambient temperature.

The vacuum system consists of a turbo pump installed on the rear flange near the integrated reservoir and can be isolated from the system with a manual gate valve. Vibration measurement on the dummy silicon is performed using a dual beam laser vibrometer (OFV-552, Polytec, Inc.) through a 6 in. view port looking directly at the front face of the silicon. As we are interested in measuring the excitation induced by the phase change of liquid nitrogen, it will be necessary to isolate and stop all vacuum pumps when making vibration measurements. The inner tank of the reservoir acts as an adsorption pump under LN2 temperature. Typical vacuum level without liquid nitrogen was in the range of 10−5 Torr to 10−6 Torr and in the range of 10−9 Torr after being cooled down.

To directly monitor the consumption of liquid nitrogen, a liquid level sensor (Cryomagnetics, Inc.) was installed in the reservoir. The sensor operates by measuring the capacitance between two long coaxial electrodes using liquid nitrogen as dielectric. Knowing the inner tank diameter of the reservoir to be 406 mm, the volumetric liquid consumption rate can be determined. To complement liquid level measurement, total N2 flow from the exchanger block is measured with a home-built orifice meter with a 4 mm diameter aperture plate. Flow-induced pressure differential is measured with the MKS 120 Baratron gauge (10 Torr full range). The temperature of exhaust gas is also measured to allow calculation of mass flow. This flow meter is calibrated under ambient temperature with the MKS mass flow controller, with special attention paid to characterize the region where gas flow transitions from laminar to turbulent. T-type thermocouples were used for point measurements at various locations on the dummy silicon and the copper exchanger, as marked in Fig. 2. Fine gauge wires (No. 30) were used with the length of embedment of at least 5 mm from the thermocouple junction to ensure reading accuracy. Internal temperature of ceramic heater is obtained via an embedded K-type thermocouple.

Several tests were performed to characterize the system under various thermal loads. Here, we present the results in Secs. III A–III C, starting with the thermal budget (cooling power loss due to heat transfer from ambient) of the system when no additional heat load is applied, followed by application of additional heating power to the dummy silicon block up to 83 W, and finalize with the vibration characterization of the system.

The thermal budget can be deduced both dynamically and under steady state condition by observing temperature differences in various parts of the system. Figure 3 shows the system undergoing a “fill” operation, with steps marked as “a” to “d.” Prior to point “a,” the reservoir was empty and the system sits at ambient temperature. At point “a,” the exhaust port was closed while LN2 was being transferred into the reservoir. Subsequently the liquid level increased to point “b,” the point at which the liquid transfer was stopped. At point “c,” the exhaust port was opened and LN2 started cooling the exchanger efficiently. At the same time, an increase in exhaust flow was observed. The exchanger temperature reached near 77 K at point “d” and the boiling evaporation slowed down.

FIG. 3.

Thermal behavior of the system under liquid nitrogen transfer (“a”–“b”) and cooling down from ambient temperature (“c”–“d”). LN2 level in the reservoir was measured by using a capacitive probe. Flow rate for nitrogen boil off gas at the exhaust port is shown as red trace scaled by a factor of 10.

FIG. 3.

Thermal behavior of the system under liquid nitrogen transfer (“a”–“b”) and cooling down from ambient temperature (“c”–“d”). LN2 level in the reservoir was measured by using a capacitive probe. Flow rate for nitrogen boil off gas at the exhaust port is shown as red trace scaled by a factor of 10.

Close modal

Let us examine the behavior of the system at each stage. From “a” to “b,” the exhaust port was capped, while LN2 was transferred into the reservoir from an external Dewar via a vacuum transfer line. We found it to be beneficiary to cap the exhaust during filling operation as vigorous boiling at this stage can spew liquid nitrogen out of the exhaust. The liquid level steadily rose to about 60% capacity. The exhaust flow meter measured zero net flow but showed higher fluctuations because of pressure pulses during this transfer in Fig. 3 (red line between “a” and “b”). We note that liquid level sensor did not indicate zero while empty (prior to point “a”) because the probe was larger in size when at room temperature than at LN2 temperature and interpreted this apparent increase in capacitance as a liquid signal. The temperature of the silicon block remained largely constant during this period as trapped air in the exhaust system prevented liquid nitrogen from entering the exchanger directly. There was some mild cooling still as a result of heat conduction by the connecting bellow. Between mark “b” and “c,” the system stabilized as the level sensor and other sections of the reservoir continued cooling down.

The exhaust port was opened on mark “c” and the increase in exhaust gas flow and the decrease in silicon temperature were immediately observed. The boiling evaporation settled down rapidly once the temperature of silicon block reached around 80 K, at mark “d.” The cooling curve of silicon (gold trace) shows regions of different slopes or cooling rates. Between room temperature and about 110 K, the slope corresponds to about 104 W of cooling power drawn from the copper exchanger with a heat capacity of ∼1.16 × 103 J/K (at 293 K). The cooling rate accelerated once the temperature dropped below 110 K to about 160 W. This change is likely a manifestation of transition in boiling behavior, as illustrated in Fig. 4(a) for forced convective flow, from the work of Collier.17 Note that the data shown is for water under 1 atm. Liquid nitrogen is expected to have different values due to difference in boiling point, viscosity, and surface tension as well as the fact that the boiling was taking place in a confined channel without forced flow in this work. A similar curve generated from this work is shown in Fig. 4(b). In general, the boiling behavior is quite similar up to point “E” in Fig. 4(a) but tends to depart at higher temperatures. The two cooling rates indicate the limitation of cooling power that can be supplied by the current system. If we assume that the higher power value coincides with the region near critical heat flux (CHF) while the lower power with the film boiling region (EF), the limitation for nucleate boiling should be around 160 W or 0.9 W/cm2 with an internal surface area of 180 cm2. We further note that the limit shown in our system is expected to be lower due to confinement in the liquid space. This is particularly pronounced in the region “E” to “F” when boiling in forced flow liquid phase shows a continuous increase in power dissipation [Fig. 4(a)], whereas in Fig. 4(b), the cooling power decreases when the exchanger temperature exceeds about 150 K. We believe that this is simply because the back pressure generated from gas flow pushed the liquid section in the cooling channels in exchanger back toward the LN2 reservoir.

FIG. 4.

(a) Convective boiling heat flux vs heater surface temperature diagram for water under 1 atm. From Collier and Thome, Convective Boiling and Condensation. Copyright 1994 Clarendon Press. Reproduced with permission from Oxford Publishing Limited through PLSclear. (b) Heat flux vs temperature of the copper exchanger for LN2 boiling in vertical channels as measured in this experiment. Similar features in (a) are marked with the corresponding lowercase letter. The temperature in horizontal axis is the outside temperature of the copper exchanger, not the interfacial temperature as shown in (a). The absence of further increase from “e” to “f” is likely the result of liquid displacement by the back pressure of gas, specific to the geometry of the internal channels. Since the extent of the liquid level in the channels, hence surface coverage, is uncertain during intensive boiling, we cannot convert total cooling power to surface heat flux directly, especially after point “d.”

FIG. 4.

(a) Convective boiling heat flux vs heater surface temperature diagram for water under 1 atm. From Collier and Thome, Convective Boiling and Condensation. Copyright 1994 Clarendon Press. Reproduced with permission from Oxford Publishing Limited through PLSclear. (b) Heat flux vs temperature of the copper exchanger for LN2 boiling in vertical channels as measured in this experiment. Similar features in (a) are marked with the corresponding lowercase letter. The temperature in horizontal axis is the outside temperature of the copper exchanger, not the interfacial temperature as shown in (a). The absence of further increase from “e” to “f” is likely the result of liquid displacement by the back pressure of gas, specific to the geometry of the internal channels. Since the extent of the liquid level in the channels, hence surface coverage, is uncertain during intensive boiling, we cannot convert total cooling power to surface heat flux directly, especially after point “d.”

Close modal

Once the exchanger is cooled down (beyond “d” in Fig. 3), the liquid nitrogen consumption rate settles to a nearly constant 0.25 l/h, equivalent to 11.4 W from the LN2 phase change alone. We can also calculate cooling power from mass flow of the exhaust nitrogen in order to exclude contribution from the reservoir itself. The net consumption by the exchanger is 0.148 kg/h or 8.2 W. This suggests that the power requirement to maintain LN2 in the reservoir is 3.2 W. There is an additional 7.2 W dissipated as the cold gas travels upward to the exhaust port into the environment. The heating of cold exhaust gas counters heat flow down the exhaust bellow and typically gives an exhaust temperature of 246 K without any additional power input into the silicon. Of course, this power varies with the flow rate of exhaust but is not a significant factor in quiescent power consumption because it only acts to suppress heat transfer from ambient through the exhaust bellow, which already have low thermal conductance from thin wall construction. For this reason, we do not include this power as part of the cooling budget at the silicon crystal. Overall, of the 8.2 W power dissipation in the exchanger section, we estimated about 5 W contribution from thermal conduction through the vertical support using finite element analysis and the remainder ∼3 W to be dominated by thermal radiation from the chamber wall and through the view port. Heat conduction through thermal couple wires and heater wires are estimated to be negligible.

The primary goal of this prototype is to test the behavior of the cooling system under power load on the silicon crystal. In this manuscript, we demonstrate that the system is capable of absorbing up to 83 W of heat load, as limited by the power supply in use, on the silicon block.

The input power correlates directly with liquid nitrogen consumption rate, as shown in Fig. 5 where total power consumed via phase change is plotted against the heater input power. Each data point is an average over 20 s near the end of each voltage step when the system has reached equilibrium. Note that the power evacuated by phase change in liquid nitrogen is essentially proportional to the power from the heater, with a slope of 1.06. This indicates that essentially all heat deposited on the silicon block is absorbed by phase change. The y-axis-intercept of the blue data corresponds to the quiescent power consumption of 8.2 W from the exchanger. We define the efficiency of the device as the ratio of added power to the total cooling power due to phase change. This accounts for the quiescent consumption and allows simple estimation of LN2 consumption at the input power on the silicon crystal. The result is shown as golden trace in Fig. 5. Also shown is the power absorbed by the exhaust gas (red circle) in the exhaust system. Although this power cannot be used directly to improve efficiency of the exchange block, it may be used to provide pre-cooling of components around the exchanger, such as thermal shield to reduce the cooling power loss.

FIG. 5.

Total phase change power vs input heater power is shown as blue data. Each data point corresponds to one voltage step. At zero input power, the system requires about 8 W of maintenance power. Efficiency is calculated as the ratio of heater power over total cooling power. Also shown is gas heating that is the power abstracted by the cold gas prior to exiting the exhaust port.

FIG. 5.

Total phase change power vs input heater power is shown as blue data. Each data point corresponds to one voltage step. At zero input power, the system requires about 8 W of maintenance power. Efficiency is calculated as the ratio of heater power over total cooling power. Also shown is gas heating that is the power abstracted by the cold gas prior to exiting the exhaust port.

Close modal

Temperature measurement results are summarized in Fig. 6 (see Fig. 2 for notations). Note that the ceramic heater (Ht) temperature scale is on the secondary axis. As shown, the temperature increases with input power for both silicon and heater itself. However, the opposite trend is observed for both temperatures on the main exchanger. This is not an artifact as we have tested the thermocouples by direct immersion in liquid nitrogen bath while maintaining all wiring connections. Instead, such behavior is likely a phenomenon due to the boiling characteristics in the internal channels. It is well known that nucleus formation is energetically unfavorable due to existence of surface energy. A direct consequence is the need for superheating to initiate boiling action from a submerged heating surface. The same principle applies to homogeneous nucleation, which requires supercooling in the gas phase. We argue that when the power input is low, the boiling action in the exchanger is limited by the availability (or formation rate) of nucleus (or seed bubbles). Once the nucleus of a critical size is formed, it expands rapidly as the growth becomes barrierless. This nucleus-limited boiling is unstable and can be observed as strong pulses of exhaust gas flow, as shown in Fig. 7. We also note that the increase in boiling point due to the static pressure of liquid nitrogen column (40 cm) is only 0.8 K for a nearly full reservoir and is insufficient to account for the observed variation.

FIG. 6.

Temperature measured at various locations of the system when heater power is increased. For the heater itself and the silicon block, the trend is monotonic. However, the opposite trend is observed for temperatures on the exchanger block. This is characteristic of boiling behavior and is discussed in the main text.

FIG. 6.

Temperature measured at various locations of the system when heater power is increased. For the heater itself and the silicon block, the trend is monotonic. However, the opposite trend is observed for temperatures on the exchanger block. This is characteristic of boiling behavior and is discussed in the main text.

Close modal
FIG. 7.

Exhaust flow fluctuations as observed from the exhaust flow meter. Data shown are obtained without additional heat load on the system. Notice the out of phase relationship between pressure drop (flow rate) and exhaust temperature.

FIG. 7.

Exhaust flow fluctuations as observed from the exhaust flow meter. Data shown are obtained without additional heat load on the system. Notice the out of phase relationship between pressure drop (flow rate) and exhaust temperature.

Close modal

The thermal contact resistance (TCR) at the interfaces between various components can be derived by correlating the temperature difference between adjacent components to the heat load applied, as shown in Fig. 8. The relations are linear with the slope k = dT/dP proportional to the thermal contact resistance TCR = A × k, where A is the contact surface area at the interface. The value of k between ceramic heater and silicon block is 6.5 K/W, while that between the silicon block and the main exchanger (measured at Cu1) is 0.16 K/W. The thermal contact conductance (TCC = 1/TCR) of the interface between silicon block and copper block can be calculated with the k value and contact surface area A = 0.0023 m2–0.0025 m2. The result in TCC = 2713 W/(m2 K)–2500 W/(m2 K) is consistent with the numbers mentioned in Ref. 4. A small temperature difference is observed between location Cu1 and Cu2 consistent with the direction of heat flow (Cu2 being closer to the boiling surface). This apparent k value is 0.030 K/W. Deviation from the linear relationship is observed in Fig. 8 for a temperature difference between the heater and silicon block (blue data series) in the range above 70 W input power. This is due to the thermal radiation term becoming more important as the heater temperature approaches 300 °C.

FIG. 8.

Linear relationship of temperature difference between adjacent components and heater input power. The average slope of the curves are 6.5 K/W between the heater and silicon and 0.16 K/W between silicon and copper exchanger, respectively. These values can be used to calculate the thermal contact resistance of the interface.

FIG. 8.

Linear relationship of temperature difference between adjacent components and heater input power. The average slope of the curves are 6.5 K/W between the heater and silicon and 0.16 K/W between silicon and copper exchanger, respectively. These values can be used to calculate the thermal contact resistance of the interface.

Close modal

It is of interest to note that, due to the effect of nucleus-limited boiling, the system can operate in a self-regulated manner that maintains a rather constant temperature within a range of thermal load, specifically a standard deviation of only 0.2 K in the range of 0 W–50 W input power, as demonstrated in Fig. 6 at the location of Cu1. In this case, due to fortuitous match of thermal resistance, the downward slope of Cu2 temperature closest to the cooling channels is canceled out by the temperature difference driven by the thermal resistance. It is possible to optimize the system so that the temperature dependence of input power becomes near zero at different power level, but not over the full range due to the non-linearity of the temperature dependence (Cu2 curve).

Mechanical stability of the silicon crystal is a primary requirement of x-ray optics. The stability performance of silicon crystal cooled by the present cryo-cooling system was also investigated at various power loads on the silicon crystal. Vibration measurements were conducted on the front face of the exchanger block, as shown in Fig. 2 using a laser vibrometer, which is, in effect, a high bandwidth laser interferometer that measures the variation in differential path length between the sample beam and the reference beam. We have previously measured from the front face of the silicon and found the results to be similar to the copper exchanger block. The front face of the silicon was not polished and it was more difficult to align the laser with sufficient return beam intensity. The laser head was rigidly mounted on the same optical platform as the vacuum chamber and very close to the view port window to defocus any light reflected by the uncoated glass. The reference beam can either be capped (with a retro reflector) or aimed at exterior chamber wall. Both configurations show similar results and for data shown in the following paragraph the reference beam was capped.

Power spectrum density (PSD) of the vibrational motion in the direction of the view port is shown in Fig. 9 at both maximum power (80 W) and standby case (0 W). Also shown is the contribution of the vibrometer mounting by blocking the measuring beam path with a reflective tape on the view port window. Most of the higher frequency modes can be attributed to the mounting or motion of the exterior of the chamber. The cumulative rms as an integration of the overall motion from about 250 Hz down to the indicated frequency is shown in Fig. 10 for power levels at 0 W, 30 W, 60 W, and 80 W. The specific rms values integrated down to 1 Hz are 23 nm, 30 nm, 30 nm, and 29 nm at the respective power levels. The most prominent contributor to the rms increase with input power can be observed in Fig. 10 around 200 Hz, although no significant increase beyond 30 W. Overall, the vibration spectrum has significant components by modes not strongly correlated with the input power and the additional contribution by 80 W input power is around 20 nm rms, likely driven by chamber modes excited by the exhaust flow. No significant broadband increase in motion was observed.

FIG. 9.

Power spectrum density of vibrational displacement measured at the idle and maximum power input. Displacement direction is perpendicular to the front face of the exchanger block. Baseline measurement was performed by blocking the measuring laser beam with a reflective tape on the view port. Most of the prominent modes are due to the environment, such as floor vibration.

FIG. 9.

Power spectrum density of vibrational displacement measured at the idle and maximum power input. Displacement direction is perpendicular to the front face of the exchanger block. Baseline measurement was performed by blocking the measuring laser beam with a reflective tape on the view port. Most of the prominent modes are due to the environment, such as floor vibration.

Close modal
FIG. 10.

Cumulative rms displacement on the exchanger block at four different heater power levels. Additional motion due to excitation from boiling action is not a strong function of the heater power beyond 30 W. Overall rms magnitude is 30 nm down to 1 Hz at 80 W input power.

FIG. 10.

Cumulative rms displacement on the exchanger block at four different heater power levels. Additional motion due to excitation from boiling action is not a strong function of the heater power beyond 30 W. Overall rms magnitude is 30 nm down to 1 Hz at 80 W input power.

Close modal

We have demonstrated the feasibility of a gravity-fed liquid nitrogen cooled optics system capable of more than 80 W of cooling power, as tested in this manuscript. Detailed power consumption is summarized in Table I. Study of the boiling curve shown in Fig. 4(b) suggests a maximum power approaching 200 W, corresponding to a surface heat flux in the range of 1 W/cm2 at the internal cooling surface. Temperature at the silicon crystal and regions of the exchanger was driven by nucleus-limited boiling behavior in the cooling channel and can potentially be utilized for temperature regulation. The vibration measurements did show contributions predominately around 200 Hz of 20 nm at 30 W–83 W input power but are likely specific to the design of the system and can be reduced.

TABLE I.

Summary of the system cooling power and LN2 consumption rate.

Power to maintain cold stateAdded power
LN2 reservoirExchanger assemblySi crystalTotal
Power (W) 3.2 8.2 0–83 11.4–94.4 
LN2 consumption rate (l/day) 1.7 4.3 0–44 6–50 
Power to maintain cold stateAdded power
LN2 reservoirExchanger assemblySi crystalTotal
Power (W) 3.2 8.2 0–83 11.4–94.4 
LN2 consumption rate (l/day) 1.7 4.3 0–44 6–50 

The data that support the findings of this study are available from the corresponding author upon reasonable request.

This work was supported by the U.S. Department of Energy, Office of Science, Office of Basic Energy Sciences under Contract No. DE-AC02-76SF00515.

1.

We use the term “top-up-sides” to indicate the location on the mirror substrate to which cooling is applied. Consider the mirror in an orientation with the polished surface facing up. The substrate edge sides, adjacent to the polished surface, are of two types, long sides, whose long edges are roughly parallel to the incident beam direction, and short sides, whose widths are perpendicular to the incident beam. Cooling is applied to the upper portions of the long sides, just adjacent to the polished top surface, i.e. “top-up-sides.”

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