EP4515157A1

EP4515157A1 - Dynamic acoustic impedance matching for cryocoolers

Info

Publication number: EP4515157A1
Application number: EP23796981.1A
Authority: EP
Inventors: Scott Backhaus; Ryan Snodgrass; Vincent Kotsubo
Original assignee: University of Colorado System; University of Colorado Colorado Springs; University of Colorado Denver
Current assignee: University of Colorado System; University of Colorado Colorado Springs; University of Colorado Denver
Priority date: 2022-04-25
Filing date: 2023-02-28
Publication date: 2025-03-05
Also published as: WO2023211563A1; US20250207824A1; US20240271834A1; EP4515157A4

Abstract

This disclosure describes systems, methods, and apparatus for improving the cooldown time, or efficiency of cooling systems, for a low-frequency one or multi-stage pulse-tube refrigerator. More specifically, actuation is performed on the driving frequency of the oscillating pressure and flow, on flow resistance of valves in the acoustic network that terminate the LF-OPTR or LF-DIPTR, and/or on the asymmetric flow resistance of the bypass valves in a LF-DIPTR's flow network. The actuation of these parameters is informed by measurements of the output pressure or output-input differential pressure at the steady flow compressor, the temperature of each stage of the refrigerator, and the temperature difference between the final stage and upper stages of the refrigerator, to name a few non-limiting examples.

Description

TITLE: DYNAMIC ACOUSTIC IMPEDANCE MATCHING FOR CRYOCOOLERS

CLAIM OF PRIORITY UNDER 35 U.S.C. §119

[0001] The present Application for Patent claims priority to Provisional Application Nos. 63/334,463 entitled “DYNAMIC ACOUSTIC IMPEDANCE MATCHING FOR CRYOCOOLERS” filed April 25, 2022, and 63/335,112 entitled “DYNAMIC ACOUSTIC IMPEDANCE MATCHING FOR CRYOCOOLERS” and filed April 26, 2022, both of which are assigned to the assignee hereof and hereby expressly incorporated by reference herein.

FIELD OF THE DISCLOSURE

[0002] The present disclosure relates generally to cryogenic refrigeration. In particular, but not by way of limitation, the present disclosure relates to systems, methods and apparatuses for decreasing cooldown time and electrical power consumption of cryocoolers by active acoustic impedance matching.

DESCRIPTION OF RELATED ART

[0003] In some cases, cryogenic refrigerators (or cryocoolers), such as, orifice pulse tube refrigerators (OPTRs) or dual-inlet pulse tube refrigerators (DIPTRs), comprise a single stage or multiple stages of refrigeration. In some low frequency OPTRs (LF-OPTRs), LF-DIPTRs, and other variants, the driving mechanism includes a continuous flow compressor that supplies both high-pressure and low-pressure working gas sources to a set of valves that alternately connect these sources to the cryocooler to generate oscillating pressure and flow in the cryocooler. In high frequency OPTRs (HF-OPTRs), HF-DIPTRs, or other variants, the driving mechanism includes one or more oscillating pistons that are directly connected to the cryo-refrigerator to generate oscillating pressure and flow in the working gas in the cryo-refrigerator. [0004] In some circumstances, the quality of the fluid coupling, and thus fluid flow, between the driving mechanism and the refrigerators changes as the temperature of the refrigerator changes. Generally, the refrigerator and the fluid coupling to the driving mechanism are optimized to achieve performance targets at the nominal operating temperature of the refrigerator, which is usually near the lowest obtainable temperature. This fixed design approach results in poor coupling (and poor fluid flow) between the driving mechanism and the cryo-refrigerator at higher temperatures, which results in lower cooling power at these higher temperatures and longer times to reach the cryo- refrigerator’ s desired operating temperature. In addition, the fixed design approach does not allow for adjustment and real-time performance optimization of the cryo- refrigerator at its final operating temperature, which may differ between end-users. Given the lack of flexibility in these systems, they are often oversized for steady-state operation and thus inefficient during most of their useful operating periods (i.e., other than during cooldown).

[0005] To achieve better fluid flow to the refrigerator, various efforts have been made to vary acoustic impedance in a pulse tube refrigerator (PTRs). For instance, Kim discusses the addition of an adjustable orifice valve followed by a reservoir at the warm end of a pulse tube. Kim, Hyo-Bong & Park, Jong-Ho. (2010). Research on fast cool-down of orifice pulse tube refrigerator by controlling orifice valve opening. Progress in Superconductivity and Cryogenics. In this single-stage low-frequency pulse tube refrigerator, Kim adjusted the orifice valve to modify the acoustic impedance between the driving mechanism and the regenerator (i.e., fluid coupling between the driving mechanism (steady-flow compressor and rotary valve)) leading to increased cooling power at temperatures above the nominal operating temperature. Adjustments to the orifice valve were predetermined and not based on feedback from the system (e.g., see FIG. 7 of Kim). Despite these attempts to impedance match the driving mechanism to the refrigerator, Kim concedes that the reduction in cooldown time was “small” and in at least one instance, actually caused a slowing of cooldown time as compared to the reference where no varying of the orifice valve occurred (compare Case 1 and 3 in FIG.

8 of Kim). Further, Kim addresses a single-stage system, and provides no evidence or insights that Kim’s system would be operable with or helpful in a two-stage pulse tube refrigerator, nor provides any enabling disclosure as to how it would be implemented in a two-stage pulse tube refrigerator. Further, there is no disclosure as to how Kim’s methods would work, or if they would be operable, in high frequency pulse tube refrigerators (e.g., above 10Hz).

[0006] Similarly, Radebaugh added an inertance tube, valve, and reservoir to the hot end of a high frequency pulse tube, and gradually opened the valve between the inertance tube and the reservoir as the refrigerator cooled. Radebaugh, Ray, et al. (2007). Proposed Rapid Cooldown Technique for Pulse Tube Cryocoolers, Cryocoolers 14, International Cryocooler Conference. The result was a significant reduction in cooling time for this single-stage system, but again without any disclosure as to how to apply this system and whether it would be operable with a two-stage system or low frequency pulse tube refrigerators.

[0007] As another example Koh adjusts drive frequency of a two-stage Gifford McMahon cryocooler at low frequency to optimize steady state operation. D.Y. Koh, S.J. Park, C.J. Yoo, H.O. Choi, An Experimental Study of Two-Stage Gifford-McMahon Cryorefrigerator, Editor(s): M.D. Kelleher, K.R. Sreenivasan, R.K. Shah, Y. Joshi, In Elsevier Series in Thermal and Fluid Sciences, Experimental Heat Transfer, Fluid Mechanics and Thermodynamics 1993, Elsevier, 1993, Pages 511-515, ISBN 9780444816191. However, Koh does not disclose use of or application to a pulse tube refrigerator nor how such would be implemented. Koh also fails to discuss application to a cooldown procedure or varying the drive frequency during cooldown.

[0008] Pfotenhauer adjust an inertance of a two-stage, high frequency pulse tube refrigerator, but again, only during steady state and in an arbitrary control scheme. Continuously Variable Inertance Tubes for Pulse Tube Refrigerators. J.M Pfotenhauer, T. Steiner, and L.M. Qiu. Cryocooler 16. 2011.

[0009] The description provided in the Description of Related Art section should not be assumed to be prior art merely because it is mentioned in or associated with this section. The Description of Related Art section may include information that describes one or more aspects of the subject technology.

SUMMARY OF THE DISCLOSURE

[0010] The following presents a simplified summary relating to one or more aspects and/or embodiments disclosed herein. As such, the following summary should not be considered an extensive overview relating to all contemplated aspects and/or embodiments, nor should the following summary be regarded to identify key or critical elements relating to all contemplated aspects and/or embodiments or to delineate the scope associated with any particular aspect and/or embodiment. Accordingly, the following summary has the sole purpose to present certain concepts relating to one or more aspects and/or embodiments relating to the mechanisms disclosed herein in a simplified form to precede the detailed description presented below.

[0011] Broadly, the present disclosure relates to the actuation and control of valves and/or compressor frequency within cryo-refrigerators that employ oscillating pressure and flow in working gas to provide cooling at cryogenic temperatures. More particularly, the present invention relates to the actuation and control of valves and/or compressor frequency within cryo-refrigerators, such as, but not limited to, orifice pulse tube refrigerators (OPTR) and dual-inlet pulse tube refrigerators (DIPTR). In some cases, these cryo-refrigerators comprise a single cooling stage, or alternatively, two or more coupled cooling stages. The use of two or more coupled cooling stages may help reduce the time required for these refrigerators to reach their operating temperatures, optimize performance after the cryo-refrigerator has reached the base operating temperature, or both.

[0012] To minimize cool down time in single-stage and multi-stage LF-OPTRs and LF- DIPTRs, the present disclosure includes actuation of several components and operating parameters that maximize the compressor- to-refrigerator oscillating fluid flow coupling and hence the refrigerator’s cooling power at temperatures between room temperature (e.g., 20-25 degrees Celsius or 293-298 Kelvin) and the final operating temperature (e.g., 3-4 Kelvin). Actuation of these components (e.g., orifice valves, asymmetric bypass valves, and or a drive frequency of the compressor) may facilitate in optimizing steady- state performance at the final operating temperature as well as cooldown operation and thereby allow reduced size systems and lower power requirements. In one embodiment, the actuation is performed on one or more of the driving frequency of the oscillating pressure and flow, on flow resistance of valves in the acoustic network that terminate the LF-OPTR or LF-DIPTR, and on the asymmetric flow resistance of the bypass valves in a LF-DIPTR’ s flow network. The actuation of these parameters is informed by measurements of the output pressure or output-input differential pressure at the compressor, the temperature of each stage of the refrigerator, and the temperature difference between the final stage and upper stages of the refrigerator, to name a few non-limiting examples. [0013] Some aspects of the disclosure can be described as a multi-stage cryocooling system.

The system can include a compressor, a refrigerator, and a controller. The compressor can be configured to be driven at a drive frequency and the refrigerator can be coupled the compressor and receiving an oscillatory fluid flow therefrom. The refrigerator can include a first stage, a second stage, a first fluid path, a second fluid path, and a third fluid path. The first stage can have an input coupled to the compressor via the first fluid path. The first stage can further can a first regenerator, a first cold heat exchanger, a first thermal buffer tube, and an output. The second stage can have an input coupled to the first cold heat exchanger, a second regenerator, a second cold heat exchanger, a second thermal buffer tube, and an output. The second fluid path can run between the first-stage output and the first-stage reservoir. A first-stage orifice valve can control fluid flow along the second fluid path. The third fluid path can be arranged between the second-stage output and a second-stage reservoir. A second-stage orifice valve can control fluid flow along the third fluid path. The controller can be configured to adjust the first-stage orifice valve and the second-stage orifice valves in order to optimize a cooling characteristic of the second stage (for instance, based on real time feedback from the second and optionally the first stage and optionally the compressor, during cooling).

[0014] Some aspects of the disclosure can be described as a method of increasing time- averaged flow of fluid power due to oscillatory fluid flow in a multi-stage cryocooler. The method can include driving an oscillatory fluid flow between a compressor and a multi-stage cryocooler at a drive frequency. The multi-stage cryocooler can include a first-stage pulse tube refrigerator, a second-stage pulse tube refrigerator, a first-stage orifice valve, and a second-stage orifice valve. The first-stage pulse tube refrigerator can be coupled to the compressor. The second-stage pulse tube refrigerator can be coupled toa cold heat exchanger of the first-stage pulse tube refrigerator. The first- stage orifice valve can be coupled between the first-stage pulse tube refrigerator and a first-stage reservoir and can be configured to control fluid flow between the first-stage pulse tube refrigerator and the first-stage reservoir. The second-stage orifice valve can be coupled between the second-stage pulse tube refrigerator and a second-stage reservoir. This valve can be configured to control fluid flow between the second-stage pulse tube refrigerator and the second-stage reservoir. The method can further include adjusting a magnitude of an acoustic impedance seen by the compressor by adjusting the first-stage orifice valve and the second-stage orifice valve (e.g., based on real time feedback from the second and optionally the first stage and optionally the compressor, during cooling).

[0015] Yet further aspects of the disclosure can be described as a cryocooling system including a compressor, a refrigerator, and a controller. The compressor is configured to be driven at a drive frequency. The refrigerator is coupled to the compressor and receiving an oscillatory fluid flow therefrom. The refrigerator can include an input coupled to the compressor via a first fluid path, a regenerator, a cold heat exchanger, a thermal buffer tube, and an output. The second fluid path is between the output and a reservoir and an orifice valve can control fluid flow along the second fluid path. The controller is configured to adjust the orifice valve based on optimizing a cooling characteristic of the refrigerator.

BRIEF DESCRIPTION OF THE DRAWINGS

[0016] Various objects and advantages and a more complete understanding of the present disclosure are apparent and more readily appreciated by referring to the following detailed description and to the appended claims when taken in conjunction with the accompanying drawings:

[0017] FIG. 1 illustrates an embodiment of a single-stage orifice pulse tube refrigerator coupled to a compressor;

[0018] FIG. 2 illustrates an embodiment of a single-stage, optionally dual inlet pulse tube refrigerator coupled to a compressor;

[0019] FIG. 3 illustrates a more detailed diagram of the single-stage, optionally dual inlet, pulse tube refrigerator of FIG. 2;

[0020] FIG. 4 illustrates an embodiment of a two-stage orifice pulse tube refrigerator coupled to a compressor;

[0021] FIG. 5 illustrates an embodiment of a two-stage, optionally dual-inlet, pulse tube refrigerator coupled to a compressor;

[0022] FIG. 6 illustrates a more detailed diagram of the two-stage, optionally dual-inlet, pulse tube refrigerator of FIG. 5

[0023] FIG. 7 illustrates details of an embodiment of a compressor that can be implemented in any of FIGs. 1-7;

[0024] FIG. 8 illustrates an embodiment of a method of increasing time- averaged flow of fluid power due to oscillatory fluid flow in a two-stage cryocooler;

[0025] FIGs. 9 A and 9B show measured cooldown rates for a manufacturer- tuned cryocooler (e.g., pulse-tube refrigerator) and the same cryocooler tuned via various aspects of the present disclosure.

[0026] FIG. 10 shows measured cooling power as a function of drive frequency, refrigerator temperature, and/or orifice tuning, via various aspects of the present disclosure; and [0027] FIG. 11 is a block diagram depicting physical components that may be utilized to realize a device running the controller in FIGs. 1-7, in accordance with various aspects of the disclosure.

DETAILED DESCRIPTION

[0028] The word “for example” is used herein to mean “serving as an example, instant, or illustration.” Any embodiment described herein as “for example” or any related term is not necessarily to be construed as preferred or advantageous over other embodiments. Additionally, a reference to a “device” is not meant to be limiting to a single such device. It is contemplated that numerous devices may comprise a single “device” as described herein.

[0029] The word “exemplary” is used herein to mean “serving as an example, instance, or illustration.” Any embodiment described herein as “exemplary” is not necessarily to be construed as preferred or advantageous over other embodiments.

[0030] For the purposes of this disclosure, the terms pulse tube refrigerator, cryocooler and cryo-refrigerator may be used interchangeably.

[0031] For the purposes of this disclosure, cooling power is a function of pressure and flow in a cryocooler such as a pulse tube refrigerator.

[0032] For the purposes of this disclosure a compressor will be implemented as a steady flow compressor, for instance a timed dual-valve style steady flow compressor, a linear piston style resonant compressor, or a compressor with a rotary valve to generate pulsating pressure. [0033] For the purposes of this disclosure, acoustic impedance refers to resistance to oscillatory fluid flow in a system, where a drive frequency of a compressor along with a resistance of certain valves are controlled to alter this acoustic impedance and thus control a flow of fluids in a cryocooler and hence control acoustic power transfer in the system.

[0034] Preliminary note: the flowcharts and block diagrams in the following Figures illustrate the architecture, functionality, and operation of possible implementations of systems, methods and computer program products according to various embodiments of the present invention. In this regard, some blocks in these flowcharts or block diagrams may represent a module, segment, or portion of code, which comprises one or more executable instructions for implementing the specified logical function(s). It should also be noted that, in some alternative implementations, the functions noted in the block may occur out of the order noted in the figures. For example, two blocks shown in succession may, in fact, be executed substantially concurrently, or the blocks may sometimes be executed in the reverse order, depending upon the functionality involved. It will also be noted that each block of the block diagrams and/or flowchart illustrations, and combinations of blocks in the block diagrams and/or flowchart illustrations, can be implemented by special purpose hardware-based systems that perform the specified functions or acts, or combinations of special purpose hardware and computer instructions.

[0035] The present disclosure relates generally to cryogenic refrigeration. In particular, but not by way of limitation, the present disclosure relates to systems, methods and apparatuses for decreasing cooldown time and electrical power consumption of cryocoolers by active acoustic impedance matching. [0036] The present disclosure leverages aspects of low frequency orifice pulse tube refrigerators (LF-OPTRs) and low frequency dual-inlet pulse tube refrigerators (LF- DIPTRs) and the driving mechanisms that provide them with oscillating pressure and flow. Further, the present disclosure optimizes power consumption of multi-stage cryocoolers, as compared to the prior art. Currently used techniques often “oversize” the cryo-refrigerator to increase cooldown rates. However, these compressors are unnecessarily large for the steady state cooling requirement at the low temperature target (e.g., 3-4 K) and consume an excessive amount of power. In some circumstances, three-phase 208V electrical power is used to power such cryocoolers, which is significantly more infrastructure and/or power than needed for some refrigerators in steady state (e.g., maintaining 3-4 K after cooldown). Aspects of the present disclosure enable cryocooler stages to be appropriately sized (e.g., compact), as compared to the prior art, for instance enabling common and less costly 120V operation. Additionally, or alternatively, the present disclosure helps decrease the cooldown time for the coldest stage of a multi-stage cryocooler.

[0037] FIG. 1 illustrates an embodiment of a single-stage orifice pulse tube refrigerator coupled to a compressor, according to various aspects of the disclosure. The cooling system 100 includes a compressor 102, a refrigerator 104, and a controller 106. The compressor 102 provides oscillating fluid flow to the refrigerator 104, and in particular to a pulse-tube refrigerator 108. The pulse-tube refrigerator 108 can have an input 110 and an output 112. The input 110 can be coupled to the compressor 102 via a first fluid path 152. The compressor 102 can provide high-pressure room-temperature fluid to the input 1 10 of the pulse-tube refrigerator 108 and receive low-pressure roomtemperature fluid back from the pulse-tube refrigerator 108 in a cyclic manner. The period or frequency of this oscillating fluid flow is governed by a drive frequency 114 of the compressor 102. The high-pressure and low-pressure extremes of the cycle are normally proportional to the fluid power input to the refrigerator 104. The time phasing between the oscillating pressure and flow in a regenerator of the pulse-tube refrigerator 108 serves to create an oscillating heat transfer between the working gas and the regenerator. The time phasing of this oscillating heat transfer creates a time-averaged transport of heat from a cold heat exchanger in the pulse-tube refrigerator 108 at temperature Ti back up to the input 110 at ambient temperature To. This heat is ultimately rejected to ambient temperature through a heat exchanger in the compressor 102.

[0038] At an opposing end of the cold heat exchanger the flow path enters a thermal buffer tube (sometimes referred to as a pulse tube) allowing fluid (acoustic) power to flow away from the cold heat exchanger, which creates cooling power capacity at the cold heat exchanger. In some examples, the fluid (acoustic) power flows into a terminating acoustic network comprising a flow resistance 128 (e.g., an orifice valve) and a volume 130 (also known as a reservoir or compliance), where it is dissipated. The dissipated acoustic power is converted to heat and, in some circumstances, is rejected to ambient temperature by a warm heat exchanger at the output 112 end of the thermal buffer tube. The volume of the volume 130 and/or the value of the resistance 128 primarily control an acoustic impedance of the refrigerator 104 seen by the compressor 102. In other words, control of the volume 130 and/or the resistance 128 is primary in setting a time phasing between the oscillating pressure and flow and a magnitude of oscillating flow in the pulse-tube refrigerator 108. As seen in FIG. 1, the working fluid follows the first- stage oscillating flow path between the compressor 102 and the volume 130. The pulsetube refrigerator 108 can be coupled to the reservoir 130 via a second fluid path 156 and fluid flow along the second fluid path 156 is controlled via the resistance 128. [0039] At a given temperature of the pulse-tube refrigerator 108 (and in particular at a cold heat exchanger thereof), the controller 106 seeks to optimize a fluid (acoustic) power flow from the compressor 102 to the refrigerator 104 by adjusting an acoustic impedance of the refrigerator 104 seen by the compressor 102. This may involve an increase or decrease in the acoustic impedance of the refrigerator 104 and thus may involve a decrease or increase in the volume of the volume 130 and/or a value of the resistance 128. For instance, where a volume of the volume 130 is adjustable, the volume of the volume 130 can be increased to reduce an impedance of the refrigerator 104. As another example, where the resistance 128 is implemented as an orifice valve, opening the orifice valve 128 decreases an acoustic impedance of the refrigerator 104. Thus, opening or closing the orifice valve (e.g., 128) to an extent can tailor the refrigerator 104 acoustic impedance to that seen by the compressor 102 and in this way maximize fluid (acoustic) power transfer from the compressor 102 to the refrigerator 104.

[0040] At the same time, or alternatively, the compressor 102 can adjust the drive frequency 114 to adjust an acoustic impedance seen by the compressor 102. In other words, the controller 106 can (1) adjust the drive frequency 114 and not adjust the volume 130 or resistance 128, (2) adjust the drive frequency 114 and the volume 130 and the resistance 128, (3) adjust the drive frequency 114 and the resistance 128, but not the volume 130, (4) and other variations of the above. An increase in drive frequency 114 typically results in a decrease in an acoustic impedance of the terminating network (i.e., 128 and 130) and hence of the refrigerator 104 (i.e., the acoustic impedance seen by the compressor 102).

[0041] Often, effective impedance matching involves adjusting the drive frequency 114 by a factor of 1.5:1 or 3:1 or more (where the “1” indicates the drive frequency when the refrigerator is at its nominal operating temperature). For instance, given a starting frequency of 1.5 Hz, the drive frequency can be adjusted up to 2.25 Hz or 4.5 Hz. In some cases, a linear compressor may not be able to achieve such large swings / adjustments in drive frequency, and thus other compressor types, such as a timed dualvalve compressor (e.g., see FIG. 7) may be used.

[0042] The Applicants discovered that an optimal acoustic impedance of the terminating network (i.e., 128 and 130) does not remain constant during cooldown. The thermodynamic and fluid mechanical processes in the pulse tube refrigerator 108 transform the terminating network impedance into the impedance seen by compressor 102, which determines the fluid (acoustic) power flowing into the pulse tube refrigerator 108 and the cooling power available at its cold end. The lower the temperature of the cold end of the pulse tube refrigerator 108 below the nominally room- temperature fluid supplied by compressor 102, this transformation creates a lower acoustic impedance seen by compressor 102.

[0043] In a typical design where the drive frequency 114, volume 130, and resistance 128 are all fixed, these are chosen to match the impedance seen by the compressor 102 to the maximum pressure and flow capabilities of compressor when the pulse tube refrigerator 108 is at its nominal cold end operating temperature (e.g. 4-6 K). This matching seeks to create maximum fluid (acoustic) power flow from the compressor to the pulse tube refrigerator and maximum cooling power at its cold end.

[0044] During a cooldown to the nominal operating temperature, the impedance transformation at the higher cold end temperature of the pulse tube refrigerator 108 results in a higher impedance seen by the compressor 102, which lowers the fluid (acoustic) power flow from the compressor to the pulse tube refrigerator and lowers the cooling power available at its cold end. [0045] To improve the impedance matching between the compressor 102 and pulse tube refrigerator, increase cooling power, and decrease cooldown times, the controller 106 not only adjusts one or more of drive frequency 114, resistance 128, and volume 130 to optimize acoustic impedance matching between compressor 102 and refrigerator 104 at a given temperature, but further adjusts these ‘knobs’ over time during cooldown since every change in cold heat exchanger temperature is associated with a different optimum acoustic impedance. On average, the controller 106 adjusts one or more of the drive frequency 114, the resistance 128, and the volume 130 to increase acoustic impedance as the cold heat exchanger temperature decreases. More specifically, the drive frequency 114 can be expected to be lowered on average and or a state of the resistance 128 can be expected to be closed on average, as the cold heat exchanger temperature decreases toward a steady state target (e.g., 3-4 K).

[0046] The controller 106 can be in communication with the compressor 102 and the refrigerator 104 and can receive feedback from one or both used to adjust the acoustic impedance (i.e., to adjust one or more of 114, 128, 130). More specifically, the controller 106 can monitor a cooling characteristic, which is the basis for adjusting the drive frequency 114, the resistance 128, and/or the volume 130. The cooling characteristic can be a temperature measured in the pulse-tube refrigerator 108. In an embodiment, the cooling characteristic is a pressure in the compressor 102 (many existing compressors have built-in pressure sensors) or a pressure in the pule-tube refrigerator 108. For instance, the cooling characteristic can be the compressor output pressure or output-input differential pressure. In another embodiment, the cooling characteristic is a rate of cooling in the pulse-tube refrigerator 108, for instance a rate of cooling at the cold heat exchanger. In yet another embodiment, the cooling characteristic is a combination of one or more of the above pressures and cooling rate. In another embodiment, the controller 106 can be programmed with a calibration that maps settings for one or more of the drive frequency 114, resistance 128, and volume 130 to cooling characteristics, where this calibration can be performed before the refrigerator 104 is put into operation.

[0047] FIG. 2 illustrates an embodiment of a single-stage, optionally dual-inlet, pulse tube refrigerator coupled to a compressor, according to various aspects of the disclosure. This embodiment is substantially the same as that of FIG. 1, but with the additional of an asymmetric bypass valve 146 between the first path 152 and the second path 156. With the addition of the fluid path 158 some fluid in the first-stage oscillating flow is able to circulate through the asymmetric bypass valve 146 rather than merely oscillate between the compressor 102 and the reservoir 130. Fluid making this complete loop degrades the cooling power of the pulse-tube refrigerator 108, and thus the asymmetric bypass valve 146 has an asymmetric resistance to fluid flow (i.e., more resistance in one direction than in the other). This asymmetry is adjusted until the time-averaged flow around the first-stage loop is suppressed or the steady-state thermodynamic performance of the overall pulse-tube refrigerator 108 is maximized, in accordance with various aspects of the disclosure.

[0048] FIG. 3 illustrates a more detailed diagram of the single-stage pulse tube refrigerator of FIG. 2. The compressor 102 provides an oscillating pressure and flow along first fluid path 152 and hence to an input to the refrigerator 104. The drive frequency 114 is often selected by the manufacturer to maximize cooling power at low temperature (e.g., 3-4 K), although it is not optimal during cooldown.

[0049] The first fluid path 152 provides high pressure , nominally room-temperature fluid to a regenerative heat exchanger (or “regenerator”) 332 of a pulse tube refrigerator 308. In some examples, the regenerator 332 is typically composed of a porous solid with a high heat capacity (e.g., compared to the heat capacity of the working gas). Further, a cold heat exchanger 322 at temperature Ti<To (e.g., Ti = 30-50 Kelvin and To = 298 K) is located at the distal end of the regenerator 332. Typically, most end users attach a thermal payload to the cold heat exchanger 332. The time phasing between the oscillating pressure and flow in the regenerator 332 serves to create an oscillating heat transfer between the working gas and the regenerator solid. The time phasing of this oscillating heat transfer creates a time- averaged transport of heat from the cold heat exchanger 322 at temperature Ti back up to the proximal end of the first stage regenerator 332 at ambient temperature To. This heat is ultimately rejected to ambient temperature through a heat exchanger in the compressor 102.

[0050] At the distal end of the cold heat exchanger 322, the flow path enters a thermal buffer tube 334, and this flow allows fluid (acoustic) power to flow away from the cold heat exchanger 322, which creates cooling power capacity at the cold heat exchanger 322. In some examples, this fluid (acoustic) power flows into a terminating acoustic network comprising a flow resistance 128 and reservoir 130 (i.e., compliance), where it is dissipated and converted to heat. In some circumstances, this heat is rejected to ambient temperature by a warm heat exchanger 326 at an end of the thermal buffer tube 334 opposite to the cold heat exchanger 322.

[0051] The combined flow impedance of the flow resistance 128 and reservoir 130 is primary in setting the time phasing of the oscillating pressure and flow and the magnitude of the oscillating flow in the regenerator 332. Optionally, an asymmetric bypass valve 146 can be arranged along a fluid path 158 between the first and second fluid paths 152, 156. In other words, the fluid path 158 can connect an inlet of the pulse-tube refrigerator 308 to the acoustic network. This optional asymmetric bypass valve 146 can be used to further optimize the time-phasing of the oscillating pressure and flow in the regenerator 332. This helps enhance the thermodynamic performance of the pulsetube refrigerator 308. However, this also creates a multi-connected flow path in the pulse-tube refrigerator 308. A nonlinear hydrodynamic process in the oscillating pressure and flow creates a time-average flow of working gas around this loop that degrades the thermodynamic performance of the pulse-tube refrigerator 308. To suppress this time-average flow, optional asymmetric bypass valve 146 is typically asymmetric with a flow resistance in one direction being higher than the resistance in the opposite direction. This asymmetry is adjusted until the time-averaged flow through the asymmetric bypass valve 146 is suppressed or the steady-state thermodynamic performance of the pulse-tube refrigerator 308 is maximized, in accordance with various aspects of the disclosure.

[0052] The controller 106 can base adjustments on feedback from the compressor 102 and/or the pulse-tube refrigerator 308. In some embodiments, a temperature or rate of cooling at the cold heat exchanger 322, monitored via sensor 352 can be used to adjust one or more of: drive frequency 114, resistance 128, reservoir 130, and valve 146. Alternatively, or in combination with temperature or cooling rate, the controller 106 can use a pressure measured in the compressor 102 and/or the regenerator 332 to determine how to adjust one or more of: drive frequency 114, resistance 128, reservoir 130, and valve 146. Although not explicitly shown, the I/O connection between the controller 106 and the refrigerator 104 can include a connection to the sensor 352.

[0053] FIG. 4 illustrates an embodiment of a multi-stage orifice pulse tube refrigerator coupled to a compressor, according to various aspects of the disclosure. The cooling system 400 includes a compressor 102, a refrigerator 404, and a controller 106. The compressor 102 provides oscillating fluid flow to the refrigerator 404, and in particular to a multi-stage pulse-tube refrigerator 416, shown as a two-stage refrigerator. The multi-stage pulse-tube refrigerator 416 can have an input 410 and a first-stage output 412 and a second-stage output 414. The first stage 408 can be coupled to an acoustic network comprising a resistance 128 and a reservoir 130 via a second fluid path 156. The input 410 can be coupled to the compressor 102 via a first fluid path 152. The first stage 408 can be coupled to the second stage 418, and the second stage can be coupled to a second acoustic network via a third fluid path 454. The second acoustic network can include a resistance 440 and a reservoir 442. Oscillating flow in the refrigerator 404 can take two paths: a first oscillating flow between the input 410 and the first reservoir 130 and a second oscillating flow between the input 410 and the second reservoir 442.

[0054] The compressor 102 can provide high-pressure room temperature fluid to the input 410 of the multi-stage pulse-tube refrigerator 416 and receive low-pressure room temperature fluid back from the multi-stage pulse-tube refrigerator 416 in a cyclic manner. The period or frequency of this oscillating fluid flow is governed by a drive frequency 114 of the compressor 102. Where the drive frequency 114 is adjustable, increasing the drive frequency 114 decreases an acoustic impedance of the refrigerator 404, or more specifically, decreases an acoustic impedance of the reservoirs 130 and 442. The high-pressure and low-pressure extremes of the cycle are normally proportional to the fluid power input to the multi-stage pulse-tube refrigerator 416. The time phasing between the oscillating pressure and flow in a regenerator of the multistage pulse-tube refrigerator 416 serves to create an oscillating heat transfer between the working gas and regenerators of the first stage 408 and second stage 418 of the multi-stage pulse-tube refrigerator 416. The time phasing of this oscillating heat transfer creates a time- averaged transport of heat from a cold heat exchanger in the second stage 418 at temperature T2 back up to the input 410 at ambient temperature To.

This heat is ultimately rejected to ambient temperature through a heat exchanger in the compressor 102.

[0055] In some examples, the fluid (acoustic) power exits the first stage 408 at first-stage output 412 and into a terminating acoustic network comprising a flow resistance 128 (e.g., an orifice valve) and a volume 130 (also known as a reservoir or compliance), where it is dissipated and converted to heat. In some circumstances, the heat is rejected to ambient temperature by a warm heat exchanger at the first-stage output 412. The volume of the reservoir 130 and/or the resistance 128 along with the volume of the reservoir 442 and/or the resistance 440 control an acoustic impedance of the refrigerator 404 seen by the compressor 102. In other words, control of one or more of the reservoir 130, the resistance 128, the reservoir 442, and the resistance 440 is responsible for setting a time phasing of oscillating pressure and flow and a magnitude of oscillating flow in the first stage 408 and the second stage 418. The first stage 408 can be coupled to the reservoir 130 via a second fluid path 156 and fluid flow along the second fluid path 156 is controlled via the resistance 128. The second stage 418 can be coupled to the reservoir 442 via a third fluid path 454 and fluid flow along the third fluid path 454 is controlled via the resistance 440.

[0056] At a given temperature of the multi-stage pulse-tube refrigerator 416 (and in particular at a cold heat exchanger of the second stage 418), the controller 106 seeks to optimize a fluid (acoustic) power flow from the compressor 102 to the refrigerator 404 by adjusting an acoustic impedance of the refrigerator 404 seen by the compressor 102. This may involve an increase or decrease in the acoustic impedance of the refrigerator 404 and thus may involve a decrease or increase in the volume of the volumes 130 and/or 442 and/or a change in the value of the resistance 128 and/or 440. For instance, where a volume of the volume 130 is adjustable, the volume of the volume 130 can be increased to reduce an impedance of the refrigerator 404. As another example, where the resistance 440 is implemented as a second-stage orifice valve, opening the second- stage orifice valve 440 decreases an acoustic impedance of the refrigerator 404. Thus, opening or closing the orifice valves (e.g., 128 and 440) to an extent can tailor the refrigerator 404 acoustic impedance seen by the compressor 102 and in this way maximize fluid (acoustic) power transfer from the compressor 102 to the refrigerator 404 and maximize the cooling powers available at the cold ends of the first stage and second stage.

[0057] At the same time, or alternatively, the compressor 102 can adjust the drive frequency 114 to adjust an acoustic impedance seen by the compressor 102. In other words, the controller 106 can (1) adjust the drive frequency 114 and not adjust the volumes 130 and 442 or resistances 128 and 440, (2) adjust the drive frequency 114 and the volumes 130 and 442 and the resistances 128 and 440, (3) adjust the drive frequency 1 14 and the resistances 128 and 440, but not the volumes 130 and 442, (4) and other variations of the above. An increase in drive frequency 114 typically results in a decrease in an acoustic impedance of the terminating networks (i.e., 128 and 130 and 440 and 442) and hence of the refrigerator 404 (i.e., the acoustic impedance seen by the compressor 102).

[0058] Often, effective impedance matching involves adjusting the drive frequency 114 by a factor of 1.5:1 or 3:1 or more. For instance, given a starting frequency of 1.5 Hz, the drive frequency can be adjusted up to 2.25 Hz or 4.5 Hz. In some cases, a linear compressor may not be able to achieve such large swings / adjustments in drive frequency, and thus other compressor types, such as a timed dual-valve compressor

(e.g., see FIG. 7) may be used. [0059] The Applicants discovered that an optimal acoustic impedance of the terminating networks (i.e., 128 and 130 for the first stage and 440 and 442 for the second stage_ do not remain constant during cooldown. The thermodynamic and fluid mechanical processes in the pulse tube refrigerator 416 transform the terminating networks’ impedances into the impedance seen by the compressor 102, which determines the fluid (acoustic) power flowing into the pulse tube refrigerator 416 and the cooling power available at the second-stage cold end. The lower the temperature of the cold end of the second stage below the nominally room-temperature fluid supplied by compressor 102, the higher the acoustic impedance seen by the compressor 102. Matching this increased impedance as temperature decreases involves decreasing resistance 128, 440 and/or decreasing drive frequency 114.

[0060] In a typical design where the drive frequency 114, volumes 130, 442, and resistances 128, 440 are all fixed, these are chosen to match the impedance seen by the compressor to the maximum pressure and flow capabilities of a compressor when the multi-stage pulse tube refrigerator is at its nominal cold end operating temperature (e.g. 4-6 K). This matching seeks to create maximum fluid (acoustic) power flow from the compressor to the pulse tube refrigerator and maximum cooling power at its cold end. Example data points of this fixed tuning can be seen as the 4 square data points in FIGs. 10A-10D.

[0061] During a cooldown to the nominal operating temperature, the impedance transformation at the higher cold end temperature of the multi-stage pulse tube refrigerator results in a higher impedance seen by the compressor, which lowers the fluid (acoustic) power flow from the compressor to the multi-stage pulse tube refrigerator and lowers the cooling power available at its second-stage cold end. [0062] To improve the impedance matching between the compressor 102 and multi-stage pulse tube refrigerator 416, increase cooling power, and decrease cooldown times, the controller 106 not only adjusts one or more of drive frequency 114, resistance 128, volume 130, resistance 440, and volume 442 to optimize acoustic impedance matching between compressor 102 and refrigerator 404 at a given temperature, but further adjusts these ‘knobs’ over time during cooldown since every change in second-stage cold heat exchanger temperature is associated with a different optimum acoustic impedance. On average, the controller 106 adjusts one or more of drive frequency 114, resistance 128, volume 130, resistance 440, and volume 442 to increase acoustic impedance as the second-stage cold heat exchanger temperature decreases. More specifically, the drive frequency 114 can be lowered on average and/or a state of the resistances 128 and 440 can be gradually closed on average (i.e., greater resistance), as the second-stage cold heat exchanger temperature decreases toward a steady state target (e.g., 4-6 K).

[0063] The controller 106 can be in communication with the compressor 102 and the refrigerator 404 and can receive feedback from one or both used to adjust the acoustic impedance (i.e., to adjust one or more of 114, 128, 130, 440, 442). More specifically, the controller 106 can monitor a cooling characteristic, which is the basis for adjusting the drive frequency 114, the resistance 128, the volume 130, the resistance 440, and/or the volume 442. In an embodiment, the cooling characteristic is a pressure in the compressor 102 (many existing compressors have built-in pressure sensors) or a pressure in the multi-stage pule-tube refrigerator 408. For instance, the cooling characteristic can be the compressor output pressure or output-input differential pressure. As another example, pressure can be monitored in a regenerator of the first stage 408, a regenerator of the second stage 418, or both regenerators. In another embodiment, the cooling characteristic is a rate of cooling in the multi-stage pulse-tube refrigerator 416, for instance a rate of cooling at the second- stage cold heat exchanger and/or the first-stage cold heat exchanger. In another embodiment, the cooling characteristic is a temperature in any one or more of the multiple stages, or a temperature difference between the stages. In yet another embodiment, the cooling characteristic is a combination of one or more of the above pressures and cooling rates. In another embodiment, the controller 106 can be programmed with a calibration that maps settings for one or more of the drive frequency 114, resistance 128, volume 130, resistance 440, and volume 442 to cooling characteristics, where this calibration can be performed before the refrigerator 404 is put into operation.

[0064] FIG. 5 illustrates an embodiment of an optionally dual-inlet multi-stage pulse tube refrigerator coupled to a compressor, according to various aspects of the disclosure. This embodiment is substantially the same as that of FIG. 4, but with the additional of two asymmetric bypass valves 146 and 444. The first-stage asymmetric bypass valve 146 is coupled between the first fluid path 152 and the second fluid path 156, while the second-stage asymmetric bypass vale 444 is coupled between the first fluid path 152 and the third fluid path 454. With the addition of the fluid paths 158 and 460 some fluid in the first and second-stage oscillating flows is able to circulate through the asymmetric bypass valves 146 and 444 rather than merely oscillate between the compressor 102 and the reservoirs 130 and 442. Fluid making these complete loops degrades the cooling power of the multi-stage pulse-tube refrigerator 408, and thus the asymmetric bypass valves 146 and 444 have asymmetric resistance to fluid flow (i.e., more resistance in one direction than in the other). This asymmetry is adjusted in both 146 and 444 until the time-averaged flows around the first-stage loop and the second- stage loop are suppressed or the steady- state thermodynamic performance of the overall multi-stage pulse- tube refrigerator 416 is maximized, in accordance with various aspects of the disclosure.

[0065] FIG. 6 illustrates a more detailed diagram of the optionally dual-inlet multi-stage pulse tube refrigerator of FIG. 5. The compressor 102 provides an oscillating pressure and flow along first fluid path 152 and hence to an input to the refrigerator 404. The drive frequency 114 is often selected by the manufacturer to maximize cooling power at low temperature (e.g., 3-4 K), although it is not optimal during cooldown.

[0066] The first fluid path 152 provides high pressure warm fluid to a regenerative heat exchanger (or “regenerator”) 632 of a first stage. In some examples, the regenerator 632 is typically composed of a porous solid with a high heat capacity (e.g., compared to the heat capacity of the working gas). Further, a cold heat exchanger 622 at temperature Ti<To (e.g., Ti = 30-50 Kelvin and To = 298 K) is located at the distal end 604 of the regenerator 632. Typically, most end users attach a thermal payload to the cold heat exchanger 622. The time phasing between the oscillating pressure and flow in the regenerator 632 serves to create an oscillating heat transfer between the working gas and the regenerator solid. The time phasing of this oscillating heat transfer creates a time- averaged transport of heat from the cold heat exchanger 622 at temperature Ti back up to the proximal end of the first stage regenerator 632 at ambient temperature To. This heat is ultimately rejected to ambient temperature through a heat exchanger in the compressor 102.

[0067] At the distal end 610 of the first-stage cold heat exchanger 622, the flow path enters splits off to a first-stage thermal buffer tube 634, and this flow allows fluid (acoustic) power to flow away from the first-stage cold heat exchanger 622, which creates cooling power capacity at the first-stage cold heat exchanger 622. In some examples, this fluid (acoustic) power flows into a first terminating acoustic network comprising a flow resistance 128 and reservoir 130 (i.e., compliance), where it is dissipated and converted to heat. In some circumstances, the heat is rejected to ambient temperature by a first- stage warm heat exchanger 626 at an end of the first-stage thermal buffer tube 634 opposite to the first-stage cold heat exchanger 622.

[0068] The distal end 610 of the first-stage cold heat exchanger 622 is also coupled to a proximal end of a second-stage regenerator 636. The distal end thereof is coupled to a second-stage cold heat exchanger 638. At the distal end of the second-stage cold heat exchanger 622, the flow path enters a second-stage thermal buffer tube 640, and this flow allows fluid (acoustic) power to flow away from the second-stage cold heat exchanger 638, which creates cooling power capacity at the second-stage cold heat exchanger 638. In some examples, this fluid (acoustic) power flows into a second terminating acoustic network comprising a flow resistance 440 and reservoir 442 (i.e., compliance), where it is dissipated and converted to heat. In some circumstances, this heat is rejected to ambient temperature by the second-stage warm heat exchanger 642 at an end of the second-stage thermal buffer tube 640 opposite to the second-stage cold heat exchanger 638.

[0069] The combined flow impedance of the (1) flow resistance 128 and reservoir 130 and the (2) flow resistance 440 and reservoir 442 is primary in setting the time phasing of the oscillating pressure and flow and the magnitude of the oscillating flow in the regenerators 632 and 636. Optionally, a first-stage asymmetric bypass valve 146 can be arranged along a fluid path 158 between the first and second fluid paths 152, 156, and a second-stage asymmetric bypass valve 444 can be arranged along a fluid path 460 between the first and third fluid paths 152, 454. In other words, the fluid path 158 can connect an inlet of the multi-stage pulse-tube refrigerator 616 to the first-stage acoustic network and the fluid path 454 can connect the inlet of the multi-stage pulse-tube refrigerator 616 to the second- stage acoustic network. These optional asymmetric bypass valves 146 and 444 can be used to further optimize the time-phasing of the oscillating pressure and flow in the regenerators 632 and 636. This helps enhance the thermodynamic performance of the multi-stage pulse- tube refrigerator 616. However, this also creates multi-connected flow paths in the multi-stage pulse-tube refrigerator 616. A nonlinear hydrodynamic process in the oscillating pressure and flow creates a time-average flow of working gas around these loops through the asymmetric bypass valves 146, 444 that degrades the thermodynamic performance of the multi-stage pulsetube refrigerator 616. To suppress these time-averaged flows, optional asymmetric bypass valves 146, 444 are typically asymmetric with a flow resistance in one direction being higher than the resistance in the opposite direction. This asymmetry is adjusted in both valves 146, 444 until the time-averaged flow through the asymmetric bypass valves 146, 444 is suppressed or the steady-state thermodynamic performance of the multi-stage pulse- tube refrigerator 616 is maximized, in accordance with various aspects of the disclosure.

[0070] The controller 106 can base adjustments on feedback from the compressor 102 and/or the first and second stages of the multi-stage pulse-tube refrigerator 616. In some embodiments, a temperature or rate of cooling at the first-stage cold heat exchanger 622, monitored via sensor 608, and/or a temperature at the second-stage cold heat exchanger 638, monitored via second 618, can be used to adjust one or more of: drive frequency 114, resistance 128, reservoir 130, valve 146, resistance 440, reservoir 442, and valve 444. Alternatively, or in combination with temperature or cooling rate, the controller 106 can utilize a pressure measured in the compressor 102 and/or the regenerators 632, 636, to determine how to adjust one or more of: drive frequency 114, resistance 128, reservoir 130, valve 146, resistance 440, reservoir 442, and valve 444. Although not explicitly shown, the I/O connection between the controller 106 and the refrigerator 404 can include a connection to one or both sensors 608 and 618.

[0071] Although this disclosure focuses on thermal transport between the first and second stage via fluid flow between a first-stage cold heat exchanger and a second-stage regenerator, in other embodiments, this thermal transport can be supplemented by or replaced by external thermal transport mechanisms such as, but not limited to, gravity driven heat pipes and thermosiphons (using two-phase fluids and the latent heat of vaporization/condensation to transfer heat). As yet another non-limiting example, forced convection using some portion of the helium being used in the main portion of the refrigerator can be implemented.

[0072] FIG. 7 illustrates an embodiment of a timed dual-valve compressor that can be implemented as the compressor 102 seen in FIGs. 1-6. This compressor is especially applicable to low-frequency pulse-tube refrigerators, though limited applications to high-frequency scenarios are also possible. The compressor 702 includes a heat exchanger 710, a compressor unit 708, and a valve 712. A timed-valve unit 714 (also referred to as oscillating valves), can be part of the compressor 702, part of the refrigerator 104/404, or arranged between these two. The timed-valve unit 714 includes a first valve 716 (e.g., high pressure valve) and a second valve 718 (e.g., low pressure valve). In embodiments of FIGs. 1-6 where adjustments to drive frequency are noted, a frequency of opening and closing the valves 716 and 718 can be one way to implement and adjust the drive frequency, and in this way adjusting the frequency of alternately opening and closing valves 716, 718 can be implemented to match an acoustic impedance between the compressor 702 and the refrigerator 104/404. Additionally, a frequency of alternately opening and closing valves 716, 718 can be used in combination with adjusting one or more of the resistances 128, 440, reservoirs, 130, 442, and bypass valves 146, 444 mentioned in FIGs. 1-6, to optimize acoustic impedance matching between the compressor 702 and the refrigerator 104/404.

[0073] The compressor 702 compresses low pressure gas to high pressure gas via the compressor unit 708. The heat of compression is removed and the high-pressure working gas is cooled back to near ambient temperature, To, by the heat exchanger 710, which may be an example of an air-cooled or water-cooled heat exchanger. In some cases, the valve 712 (e.g., a safety check valve) limits the differential pressure across the compressor unit 708 below a maximum pressure threshold. In this way, the compressor 702, which may be a steady flow compressor, provides high-pressure and low-pressure working fluid (e.g., working gas) to the timed-valve unit 714. The high- pressure line of the compressor 702 is connected to the high-pressure valve 716, and the low-pressure line of the compressor 702 is connected to the low-pressure valve 718. These two valves are typically combined into the timed- valve unit 714, which may be a stand-alone system or integrated into the structure of the compressor 702 as shown or into the structure of the refrigerator 104/404. The two valves 716, 718 are alternately opened and closed at a fixed frequency to create oscillating pressure and flow at the refrigerator 104/04 input (or at a first-stage regenerator input if the timed-valve unit 714 is part of the refrigerator 104/404. This frequency is chosen by the manufacturer to maximize cooling power at a low temperature (e.g., 3-4 K), although it is not optimal during cooldown. The squared difference between the high-pressure and low-pressure extremes of the cycle is nominally proportional to the fluid power input to the refrigerator 104/404. The check valve 712 serves to limit the pressure differential below a corresponding threshold value. This action also limits the input fluid power and may be one source of lost fluid power if the impedance matching between compressor and refrigerator is poor.

[0074] FIG. 7 will now be described in relation to FIGs. 1-6, to help explain implementation of single and multi-stage pulse-tube refrigerators. At the distal end of the timed-valve unit 714, the oscillating flow input to the refrigerator 104/404 passes into a regenerator (e.g., see FIGs. 3 and 6). In FIG. 2 and optionally FIG. 3, this oscillating flow splits two ways with one path into the regenerator and a second path into the asymmetric bypass valve. In FIG. 5 and optionally FIG. 6, this oscillating flow splits three ways with one path into the first-stage regenerator 632, a second path into the first-stage asymmetric bypass valve 146, and a third path into the second-stage asymmetric bypass valve 444. The regenerator(s), in some examples, is typically composed of a porous solid with a high heat capacity (e.g., compared to the heat capacity of the working fluid). Further, the first-stage cold heat exchanger 622 at temperature Ti<To (e.g., Ti = 30-50 Kelvin and To = 298 K) is located at the distal end of the first-stage regenerator 632, and the time phasing between the oscillating pressure and flow in the first-stage regenerator 632 serves to create an oscillating heat transfer between the working fluid and the first-stage regenerator 632 solid. The time phasing of this oscillating heat transfer creates a time-averaged transport of heat from the first- stage cold heat exchanger 622 at temperature Ti back up to the proximal end of the first stage regenerator 632 at ambient temperature To. This heat is ultimately rejected to ambient temperature through the heat exchanger 710 in the compressor 702.

[0075] At the distal end of the first-stage cold heat exchanger 622, the flow path splits again. The first path enters the first-stage thermal buffer tube 634. The second path enters the second-stage regenerator 636. The flow on the first path (i.e., into the first-stage thermal buffer tube 634) allows fluid (acoustic) power to flow away from the first-stage cold heat exchanger 622, which creates cooling power capacity at the first-stage cold heat exchanger 622. In some examples, this fluid (acoustic) power flows into a terminating acoustic network comprising a flow resistance 128 and volume 130 (i.e., compliance), where it is dissipated. In some circumstances, the dissipated acoustic power is converted to heat and is rejected to ambient temperature by the warm heat exchanger 626.

[0076] The combined flow impedance of the flow resistance 128 and volume 130 is primary in setting the time phasing of the oscillating pressure and flow and the magnitude of the oscillating flow in the first-stage regenerator 632. The flow resistance in the first-stage asymmetric bypass valve 146, which connects the multi-stage pulse-tube input 410 to the entrance of the acoustic network, is used to further optimize the time-phasing of the oscillating pressure and flow in the first-stage regenerator 632. This helps enhance the thermodynamic performance of the first stage of the refrigerator 404. However, this also creates a multi-connected flow path in the first stage of the refrigerator 404. A nonlinear hydrodynamic process in the oscillating pressure and flow creates a timeaverage flow of working fluid around this loop that degrades the thermodynamic performance of the first stage of the refrigerator 404. To suppress this time-average flow, the first-stage asymmetric bypass valve 146 is typically asymmetric with a flow resistance in one direction being higher than the resistance in the opposite direction. This asymmetry is adjusted until the time-averaged flow around the first-stage loop is suppressed or the steady-state thermodynamic performance of the overall refrigerator 404 is maximized, in accordance with various aspects of the disclosure. [0077] In some examples, the roles of the second-stage regenerator 636, second-stage cold heat exchanger 638, second-stage thermal buffer tube 640, warm heat exchanger 642, flow resistance 440, volume 442, and second-stage asymmetric bypass valve 444 are the same or substantially the same as their first-stage counterparts 632, 622, 634, 128, 130, and 146; respectively. Since the proximal end of the second-stage regenerator 636 starts at temperature Ti, the time-averaged transport of heat along its length creates T2<TI at the second-stage cold heat exchanger 638, where T2 - 3-4 K in some examples. The multi-stage flow loop created by bypass valve 446 encloses the first-stage regenerator 632, first-stage cold heat exchanger 622, second-stage regenerator 636, second-stage cold heat exchanger 638, second-stage thermal buffer tube 640 and second-stage warm heat exchanger 642. The asymmetry of the second-stage bypass valve 444 is adjusted to maximize the steady-state performance of the second-stage or the overall refrigerator 404. The single-stage flow loop created by asymmetric bypass valve 146 encloses the first-stage regenerator 632, first-stage cold heat exchanger 622, first-stage thermal buffer tube 634 and first- stage warm heat exchanger 626.

Prior-Art Cooldown Operation

[0078] The fluid coupling between the compressor 702 and the refrigerator 104, 404 (e.g., LF- DIPTR) is generally optimized for steady-state operation at the refrigerator's nominal base temperature, so that, at the operating frequency 114 of the timed- valve unit 714, the steady flow of high-pressure gas supplied by the compressor unit 708 is sufficient to maintain the pressure across check valve 712 close to (but lower than) its cracking pressure. In this configuration and at the nominal base temperature, almost all of the fluid flow supplied by the compressor unit 708 is utilized by the refrigerator 104, 404 (e.g., LF-DIPTR) near the maximum input pressure allowed by its design. [0079] During the initial steps in the cool down, the cold heat exchangers (e.g., 622 and 638) are at or near room temperature (e.g., 20-25 Celsius, or 293-298 Kelvin). When the refrigerator 104, 404 is operating at a temperature above its nominal base temperature of any of its stages, its input flow impedance is higher, and it may be unable to accept all the steady flow supplied by the compressor unit 708 at the high-pressure valve 716. In this case, the pressure on the high side of the check valve 712 rises, check valve 712 opens, and a fraction of the high-pressure gas is shunted to the low-pressure side of compressor unit 708. The fluid flow and fluid power input to the refrigerator 104, 404 is reduced and/or the cooling power available at the cold heat exchangers (e.g., 622 and 638) is reduced. In some circumstances, the reduction in cooling power can be quite large, approaching a factor of 5-10, resulting in extended cooldown times. This reduction is seen most readily where there is good heat exchange between stages, but where there is poorer heat exchange between stages, this factor may be lower, such as closer to 2 as seen in FIG. 10.

[0080] Typically, most end users attach a thermal payload to a cold heat exchanger of a final or coldest stage (e.g., 638 in FIG. 6) and are primarily concerned with the cool down time of this second or coldest stage. During the initial stages of the cooldown, the majority of the refrigerator cooling power is available at the first stage cold heat exchanger (e.g., 622), but there is relatively poor thermal coupling between the first stage cold heat exchanger and the lowest temperature cold heat exchanger. This poor thermal coupling between stages further increases the cooldown time for the refrigerator. Aspects of the present disclosure facilitate in enhancing (i.e., reducing) the cooldown time in multi-stage refrigerators, as further described below.

Enhanced Cooldown Operation [0081] In some cases, cooldown time of the second (or lowest temperature) stage of a multistage pulse-tube refrigerator may be reduced by improving one or more of the compressor-to-cryocooler fluid coupling and stage-to-stage thermal contact by actuation of one or more components. Actuation points may include the compressor drive frequency, the magnitude of the flow resistances 128 and 440, and the magnitude and/or direction of the asymmetry in flow resistances 146 and 444. In some cases, these improvements may be implemented via predetermined (time scheduled-based or condition-based) actuation. Alternatively, a control system (e.g., shown as controller 106 in FIGs. 1-7) may be used to continuously monitor the operation of refrigerator 104, 404 and compressor 102, 702 and automatically optimize one or more actuation points.

[0082] The improvement of the fluid coupling between compressor 102, 702, the timed-valve unit 714, and the refrigerator 104, 404 (e.g., LF-DIPTR) may be achieved by continuously modifying the input impedance of the refrigerator 104, 404 to reduce or eliminate shunting of high-pressure gas though the check valve 712. The elimination of this gas shunting helps maximize the fluid flow and/or fluid power input to the refrigerator 104, 404, which increases cooling power at the first and second-stage cold heat exchangers and helps to increase the cooldown rate for single and multi-stage implementations. In some examples, the input impedance of the refrigerator 104, 404 is modified/lowered during the initial stage of the cooldown (e.g., at or near room temperature) by actuating one or more of the first-stage flow resistance 128, the second- stage flow resistance 440, and the drive frequency of the compressor 702 (e.g., drive frequency supplied to the timed- valve unit 714). For example, in some embodiments, the frequency of the opening/closing of the valves 716 and 718 may be increased (e.g., to 3-4 Hz or higher), which helps lower the acoustic impedance of the terminating networks (for the first-stage regenerator 632, the terminating network is comprised of flow resistance 128 and volume 130; for the second-stage regenerator 636, the terminating network is comprised of flow resistance 440 and volume 442). The lowering of the acoustic impedance allows for more flow into regenerators 632 and 636, thereby increasing the cooling power at cold heat exchangers 622 and 638.

[0083] While the improvement to the compressor-to-cryocooler fluid coupling (described above) primarily results in a faster cooldown of the first-stage heat exchanger 622, it may or may not directly result in a faster cooldown of the end user’s pay load attached to the second-stage heat exchanger 638. In accordance with aspects of the present disclosure, the asymmetry of one or more of the optional first and second-stage asymmetric bypass valves 146 and 444, respectively, may be adjusted to improve the cooldown rate of the second-stage cold heat exchanger 638. For example, in some embodiments, the stage-to-stage thermal coupling may be enhanced by modifying (e.g., continuously) the asymmetry of the first-stage asymmetric bypass valve 146 and/or the second-stage asymmetric bypass valve 444. In some examples, the asymmetry of the second-stage bypass valve 444 is adjusted to induce a steady pressure drop across the valve 444. This steady pressure drop induces a steady flow of gas directed through a loop comprising the first-stage regenerator 632, the first stage cold heat exchanger 622, the second-stage regenerator 636, the second-stage cold heat exchanger 638, the second-stage thermal buffer tube 640, and the second-stage bypass valve 444. As the steady flow of gas transits this second-stage loop, it is cooled at the first-stage regenerator 632 and cold heat exchanger 622. This gas then cools one or more of the second-stage regenerator 636, the second-stage cold heat exchanger 638, and the end user’s thermal payload attached to 638. [0084] As the steady flow completes the second-stage loop, the heat absorbed at the second- stage cold heat exchanger 638 is eventually deposited at the first-stage cold heat exchanger 622, which serves to improve the stage-to-stage thermal coupling and increase the cooldown rate at the second-stage cold heat exchanger 638, as compared to the prior art. In some circumstances, a second closed loop that is comprised of components 632, 622, 634, 626, and 146 may siphon off some of the steady flow that is intended to flow through the second-stage loop, but the asymmetry of the first-stage asymmetric bypass valve 146 may be adjusted to minimize this effect.

[0085] In some circumstances, the set of actuations for maximizing cooldown rate/minimizing cooldown time may be different for specific cryocoolers and cryocooler types (e.g., LF- DIPTRs, LF-OPTRs) and for different thermal payloads attached to the cold heat exchangers of the different stages. In some examples, cooldown time may be reduced by determining a time-based or condition-based schedule of actuations using individual system characterization. Alternatively, a control system may be used (e.g., controller 106 in combination with feedback from sensors such as 608 and 618) that continuously monitors the compressor and refrigerator and adaptively determines the actuations that will reduce the cooldown time.

[0086] In one example, individual characterization of a specific cryocooler with a specific set of thermal payloads may be performed to determine a time-based schedule of actuations to reduce cooldown time. In this embodiment, individual characterization may be performed by monitoring the temperature of the lowest-temperature stage and varying the actuation point settings to increase the cooldown rate at each time point during the cooldown. The characterization process may be performed several times by making changes from the previous time-based actuation schedule to iteratively improve the cooldown rates.

[0087] In another example, individual characterization of a specific cryocooler may be performed to determine a condition-based schedule of actuations to reduce cooldown time for a range of thermal loads attached to that specific cryocooler. In this embodiment, the individual characterization measures net amount of heat that can be transferred from cold heat exchanger 622 to 638 for a range of temperatures at cold heat exchangers 622 to 638 as a function of the actuation point settings. From these data, the actuation point settings that generate the maximum cooling power at 622 to 638 may be determined for each set of temperatures at 622 to 638. During subsequent cooldowns, the temperature at heat exchangers 622 to 638 is monitored and the actuation point settings are adjusted to generate the maximum cooldown rates.

[0088] In another example, a control system (or controller 106) configured for automatically optimizing the cooldown rate may be utilized. In this example, the control system is able to increase cooldown rates for any combination of cryocooler and thermal pay load without requiring individual characterization. In one embodiment, the controller 106 monitors the gas pressure on the high-pressure side of check valve 712 and the temperatures of the first-stage cold heat exchanger 622 and second-stage heat exchanger 638. Further, a control algorithm may be employed. In a first step, the control algorithm may determine the actuation outputs for the operating frequency of the timed- valve unit 714 and the flow resistances 128 and 440 to (1) maintain the differential pressure across check valve 712 just below its cracking pressure, (2) to maximize the cooldown rate of the second-stage cold heat exchanger 638, and (3) to maximize the cooldown rate of the first-stage cold heat exchanger 622. In a second step, the control algorithm may determine the actuation settings for valves 146, 444 to minimize the temperature increase from 622 to 638 to enhance the thermal coupling between the first and second-stage cold heat exchangers during the initial portions of the cooldown. As the first-stage cold heat exchanger approaches its final operating temperature, the second step in the control algorithm may be modified to no longer minimize the temperature increase from 622 to 638 so that the second-stage may continue to cool to its final operating temperature.

[0089] FIG. 8 illustrates a method of increasing time-averaged flow of fluid power due to oscillatory fluid flow in a multi-stage cryocooler. The method 800 can include driving an oscillatory fluid flow between a compressor and a multi-stage cryocooler at a drive frequency (Block 802). The cryocooler can include a first-stage pulse tube refrigerator coupled to the compressor and a second-stage pulse tube refrigerator coupled to the first stage (e.g., via a cold heat exchanger of the first stage). The cryocooler can also include a first-stage orifice valve coupled between the first-stage pulse tube refrigerator and a first-stage reservoir and configured to control fluid flow between the first-stage pulse tube refrigerator and the first-stage reservoir. The cryocooler can further include a second-stage orifice valve coupled between the second-stage pulse tube refrigerator and a second-stage reservoir and configured to control fluid flow between the second-stage pulse tube refrigerator and the second-stage reservoir. The method 800 can include monitoring a cooling characteristic of the 2^nd stage (Block 804) such as a rate of cooling at the second cold heat exchanger and/or a pressure in a second-stage regenerator or the compressor, to name a few non-limiting examples. The method 800 can further include adjusting the acoustic impedance seen by the compressor by adjusting the first-stage orifice valve and the second-stage orifice valve (Block 808). Adjustment to these valves can include opening and/or closing them to different extents. For instance, in the plots shown in FIG. 10 one can compare the solid, dotted and dashed lines to see that different amounts of opening/closing of the orifice valves can have profound impacts on a rate of cooling.

[0090] In some embodiments, the method 800 can further include monitoring a cooling characteristic of the first stage (or a thermal difference between the first and second stages) (optional Block 806). In this case, the adjusting can further be based on this second cooling characteristic. For instance, adjustments can be based on cooling rates measured at a first and second stage cold heat exchanger as well as on compressor pressure.

[0091] In some embodiments, the method 800 can further include adjusting the acoustic impedance seen by the compressor by adjusting a drive frequency of the compressor (optional Block 810). The drive frequency can be adjusted in a linear compressor by adjusting a frequency of current passing through a drive coil while in a timed dual- valve compressor, a frequency of alternately opening and closing high and low-pressure valves can be the drive frequency. In a compressor with a rotary valve for providing pulsating pressure, the drive frequency can govern a number of rotations per second of the rotary valve.

[0092] In yet other embodiments, the method 800 can further include adjusting acoustic impedance seen by the compressor by adjusting first and second-stage asymmetric bypass valves (optional Block 812).

[0093] The blocks 810 and 812 can be used in combination and at the same time as adjusting the first and second- stage orifice valves, or can be used as alternatives to each other. In other words, two or more of Blocks 808, 810, and 812 can be adjusted simultaneously to optimize fluid power flow from the compressor to the refrigerator. [0094] Additionally, while FIG. 8 discusses a two-stage refrigerator, in other cases a multistage refrigerator having three or more stages can be implemented using this same method 800 where the second stage can either be a stage adjacent to the first stage, or a last/coldest stage in the refrigerator. Similarly, the first stage can refer to a stage coupled to the compressor or any stage preceding the ‘second stage’.

[0095] FIGs. 9A and 9B illustrate example graphs 900-a and 900-b, respectively, showing measured cooldown rates for a manufacturer-tuned cryocooler (e.g., a LF-DIPTR) in the prior art (dashed lines) and the same cryocooler tuned for faster cooldown (solid lines), according to various aspects of the present disclosure.

[0096] FIG. 9A shows the temperature of the coldest stage of a pulse tube refrigerator during the first hour of cooldown for the cold heat exchanger (dashed line, optimized for performance near 4 K, as known in the art). FIG. 9A also shows the temperature of the coldest stage of the same pulse tube refrigerator during the first hour of cooldown for the cold heat exchanger using modified, but fixed, actuation parameters (e.g., asymmetry of the first and/or second-stage asymmetric bypass valves 146 and 444; drive frequency, to name a few non-limiting examples) in accordance with aspects of the present disclosure, as depicted by the solid line. Specifically, the drive frequency has been increased from 1.4 Hz to 2.3 Hz and one of the asymmetric bypass valves has been closed by 3 turns. At high temperatures (e.g., 295 K) it can be beneficial to close the asymmetric bypass valve(s) so that greater flow passes through the regenerator(s). As seen, the closing of the asymmetric bypass valve as well as increased drive frequency leads to much improved cooling rate between 295 K and 100 K.

[0097] FIG. 9B depicts a plot of the cooling rate for the data from FIG. 9A. As seen, the cooling rate near room temperature (~ 295 Kelvin) for the modified actuation parameters (i.e., corresponding to the solid line in FIG. 9A) is nearly twice as fast as the prior art. The faster cooldown rate of the known tuning at cold temperatures (i.e., near 50 K) demonstrates the advantage of dynamically and continuously optimizing actuation parameters (e.g., timed-valve frequency, asymmetric bypass valve settings, and orifice valve (resistance) settings) as temperature decreases.

[0098] It should be noted that the discussion in relation to FIGs. 9A and 9B is exemplary only and not intended to be limiting. For example, in some cases, the actuation parameters may be modified at all temperatures (i.e., dynamically changed during cooldown). Additionally, or alternatively, the frequency of the timed-valve unit and more than one resistance may be tuned/changed (versus only one resistance), which would facilitate a further optimization of the cooldown rate, as discussed in FIGs. 4-7 for instance.

[0099] FIGs. 10A, 10B, 10C, and 10D illustrate example graphs showing measured improvements in cooldown rates as compared to a manufacturer-tuned cryocooler (e.g., a LF-DIPTR). In particular, the square data point represents a known manufacturer tuning point (i.e., fixed frequency and orifice valve settings/positions). From that known tuning point, the inventors adjusted drive frequency without changing the orifice value (solid lines), and then opened the orifice slightly and again swept drive frequency (dotted lines), and finally opened the orifice even more and again swept drive frequency (dashed lines). It should be noted that the orifice value is the same for both the first and second-stage orifice valves. .

[00100] FIGs. 10 A and 10B show measurements early in a cooldown cycle, where temperatures are around ambient (e.g., 295 K). FIG. 10A shows measurements at the first-stage cold heat exchanger and FIG. 10B shows measurements at the second-stage cold heat exchanger. FIGs. 10C and 10D, respectively, also show measurements at the first and second-stage cold head heat exchangers, but later in a cooling cycle (e.g., at

95 K). One sees that in certain circumstances, adjusting one of (1) orifice value or (2) drive frequency leads to improvements in cooling power as compared to the known manufacturer tuning point. However, one also sees that when both orifice value and drive frequency are used in tuning, that the most optimal cooling powers can be achieved in different circumstances. For instance, early in cooling (FIGs. 10A and 10B) a more open orifice position tends to lead to more powerful cooling, especially for higher drive frequencies. However, as temperatures approach the steady-state target (FIGs. IOC and 10D), the widest orifice value doesn’t always correlate to the optimal cooling power. Instead, the cooling power at the first cold heat exchanger is optimized at the intermediate value of the orifice (dotted line) and drive frequencies between 1.7 and 2.7 Hz, and at the second cold heat exchanger is optimized for the intermediate value of the orifice for drive frequencies below around 2 Hz. It should be noted that drive frequency is the same for all stages in a multi-stage pulse tube refrigerator, and thus the optimal drive frequency for one stage may not be optimal for the system. Accordingly, feedback mechanisms that consider cooling characteristics at both the first and second stages are likely to achieve the greatest cooling power. Also recall that prior art systems are typically tuned for low temperature steady state operation (e.g., 4-6 K), and are thus less effective during cooldown. Further note that the known manufacturer tuning points all appear at the same drive frequency since known methods do not adjust drive frequency.

[00101] FIG. 10A shows that an increased orifice valve opening leads to greater cooling power for drive frequencies above around 2.2 Hz and that increased drive frequency paired with very open orifice valves leads to greatly improved cooling power over the prior art manufacturer tuning point. [00102] FIG. 10B shows improved cooling at the second-stage cold heat exchanger for most drive frequencies with a more open orifice valve.

[00103] FIG. 10C shows that at colder temperatures (i.e., later in a cooling cycle) certain combinations of orifice valve opening and drive frequency provide improvements to cooling rate as compared to the prior art manufacturer tuning point, while others may not.

[00104] FIG. 10D similarly shows that at the second-stage cold heat exchanger, a proper combination of orifice valve opening and drive frequency may be desired in order to see improved cooling rates as compared to the prior art manufacturer tuning point. For instance, for drive frequencies below 2.2 Hz, an intermediate value for the orifice valve provides the greatest benefit over the known manufacturer tuning point. However, at higher drive frequencies, a more open orifice valve (dashed line) provides the greatest gains.

[00105] It should be noted that cooling power of the system is best understood by combining the improvements at the first and second stages, and when this is done, the Applicants have demonstrated between 7-8x the cooling power of known tuning methods. Cooling power at the second stage may be increased by the amount available at the first stage using existing technology, e.g., gravity-driven heat pipes.

[00106] Although this disclosure has focused on examples where the orifice valves are opened and closed and the drive frequency increased and decreased, fundamentally the goal is to adjust an acoustic impedance seen by the compressor to best match its pressure and flow rate capabilities. To this end, other methods of adjusting acoustic impedance seen by the compressor can be employed instead of adjusting the orifice valves or the drive frequency. For instance, the reservoirs themselves can adjust volume and in such embodiments, the orifice valves may not be adjusted during operation (i.e., remain fixed).

[00107] The methods described in connection with the embodiments disclosed herein may be embodied directly in hardware, in processor-executable code encoded in a non- transitory tangible processor readable storage medium, or in a combination of the two. Referring to FIG. 11 for example, shown is a block diagram depicting physical components that may be utilized to realize the controller 106 in FIG. 1 according to an exemplary embodiment. As shown, in this embodiment a display portion 1112 and nonvolatile memory 1120 are coupled to a bus 1122 that is also coupled to random access memory ("RAM") 1124, a processing portion (which includes N processing components) 1126, an optional field programmable gate array (FPGA) 1127, and a transceiver component 1128 that includes N transceivers. Although the components depicted in FIG. 11 represent physical components, FIG. 11 is not intended to be a detailed hardware diagram; thus, many of the components depicted in FIG. 11 may be realized by common constructs or distributed among additional physical components. Moreover, it is contemplated that other existing and yet-to-be developed physical components and architectures may be utilized to implement the functional components described with reference to FIG. 11.

[00108] This display portion 1112 generally operates to provide a user interface for a user, and in several implementations, the display is realized by a touchscreen display. In general, the nonvolatile memory 1120 is non-transitory memory that functions to store (e.g., persistently store) data and processor-executable code (including executable code that is associated with effectuating the methods described herein). In some embodiments for example, the nonvolatile memory 1120 includes bootloader code, operating system code, file system code, and non-transitory processor-executable code to facilitate the execution of a method described with reference to FIG. 8 described further herein.

[00109] In many implementations, the nonvolatile memory 1120 is realized by flash memory (e.g., NAND or ONENAND memory), but it is contemplated that other memory types may be utilized as well. Although it may be possible to execute the code from the nonvolatile memory 1120, the executable code in the nonvolatile memory is typically loaded into RAM 1124 and executed by one or more of the N processing components in the processing portion 1126.

[00110] The N processing components in connection with RAM 1124 generally operate to execute the instructions stored in nonvolatile memory 1120 to enable acoustic impedance matching for cryocoolers. For example, non-transitory, processorexecutable code to effectuate the methods described with reference to FIG. 8 may be persistently stored in nonvolatile memory 1120 and executed by the N processing components in connection with RAM 1124. As one of ordinarily skill in the art will appreciate, the processing portion 1126 may include a video processor, digital signal processor (DSP), micro-controller, graphics processing unit (GPU), or other hardware processing components or combinations of hardware and software processing components (e.g., an FPGA or an FPGA including digital logic processing portions).

[00111] In addition, or in the alternative, the processing portion 1126 may be configured to effectuate one or more aspects of the methodologies described herein. For example, non-transitory processor-readable instructions may be stored in the nonvolatile memory 1120 or in RAM 1124 and when executed on the processing portion 1126, cause the processing portion 1126 to perform tuning of the frequency of operation of the timed- valve unit 714 and one or more of the valves 716, 718, 128, 146, 440, and 444, in FIGs. 1-7. Alternatively, non-transitory FPGA-configuration-instructions may be persistently stored in nonvolatile memory 1120 and accessed by the processing portion 1126 (e.g., during boot up) to configure the hardware-configurable portions of the processing portion 1126 to effectuate the functions of the controller 106.

[00112] The input component 1130 operates to receive signals (e.g., corresponding to the temperature and/or cooling rate measurements at cold heat exchangers 622 and 638, or pressure measurements made in the compressor or in the regenerator(s)) that are indicative of one or more aspects of the acoustic impedance matching at the cryocooler. The signals received at the input component may include, for example, the temperature measurements at the cold heat exchangers 622 and 638, and/or the pressure readings at the compressor 102 and/or timed-valved unit 714, or in the regenerator(s), to name three non-limiting examples. The output component generally operates to provide one or more analog or digital signals to effectuate an operational aspect of the controller 106. For example, the output portion 1132 may provide the control output signal(s) described with reference to FIGs. 1-7. When the output component is realized by the controller 106, for example, the output signal may be a control output signal used for adjusting the resistance of valves 128 and 440, the operating frequency of timed-valve unit 714, tuning the asymmetry of the bypass valves 146 and 444, and adjusting the compliance/volume of the volumes 130, 442 to tune/match the acoustic impedance of the refrigerator and the compressor.

[00113] The depicted transceiver component 1128 includes N transceiver chains, which may be used for communicating with external devices via wireless or wireline networks. Each of the N transceiver chains may represent a transceiver associated with a particular communication scheme (e.g., WiFi, Ethernet, Profibus, etc.).

[00114] Some portions are presented in terms of algorithms or symbolic representations of operations on data bits or binary digital signals stored within a computing system memory, such as a computer memory. These algorithmic descriptions or representations are examples of techniques used by those of ordinary skill in the data processing arts to convey the substance of their work to others skilled in the art. An algorithm is a self-consistent sequence of operations or similar processing leading to a desired result. In this context, operations or processing involves physical manipulation of physical quantities. Typically, although not necessarily, such quantities may take the form of electrical or magnetic signals capable of being stored, transferred, combined, compared or otherwise manipulated. It has proven convenient at times, principally for reasons of common usage, to refer to such signals as bits, data, values, elements, symbols, characters, terms, numbers, numerals or the like. It should be understood, however, that all of these and similar terms are to be associated with appropriate physical quantities and are merely convenient labels. Unless specifically stated otherwise, it is appreciated that throughout this specification discussions utilizing terms such as “processing,” “computing,” “calculating,” “determining,” and “identifying” or the like refer to actions or processes of a computing device, such as one or more computers or a similar electronic computing device or devices, that manipulate or transform data represented as physical electronic or magnetic quantities within memories, registers, or other information storage devices, transmission devices, or display devices of the computing platform. [00115] As will be appreciated by one skilled in the art, aspects of the present invention may be embodied as a system, method or computer program product. Accordingly, aspects of the present invention may take the form of an entirely hardware embodiment, an entirely software embodiment (including firmware, resident software, micro-code, etc.) or an embodiment combining software and hardware aspects that may all generally be referred to herein as a "circuit," "module" or "system." Furthermore, aspects of the present invention may take the form of a computer program product embodied in one or more computer readable medium(s) having computer readable program code embodied thereon.

[00116] As used herein, the recitation of "at least one of A, B and C" is intended to mean "either A, B, C or any combination of A, B and C." The previous description of the disclosed embodiments is provided to enable any person skilled in the art to make or use the present disclosure. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the disclosure. Thus, the present disclosure is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

[00117] This invention was made with government support under grant number 70NANB18H006 awarded by NIST. The government has certain rights in the invention.

Claims

WHAT IS CLAIMED IS:

1. A multi-stage cryocooling system comprising: a compressor configured to be driven at a drive frequency; a refrigerator coupled to the compressor and receiving an oscillatory fluid flow therefrom, the refrigerator comprising: a first stage having an input coupled to the compressor via a first fluid path, and further having a first regenerator, a first cold heat exchanger, a first thermal buffer tube, and an output; a second stage having an input coupled to the first cold heat exchanger, and further having a second regenerator, a second cold heat exchanger, a second thermal buffer tube, and an output; a second fluid path between the first-stage output and a first- stage reservoir, a first-stage orifice valve controlling fluid flow along the second fluid path; a third fluid path between the second-stage output and a second-stage reservoir, a second-stage orifice valve controlling fluid flow along the third fluid path; and a controller configured to adjust the first-stage orifice valve and the second-stage orifice valve in order to optimize a cooling characteristic of the second stage.

2. The multi-stage cryocooling system of Claim 1, wherein the cooling characteristic is a rate of cooling at the cold heat exchanger of the second stage or a pressure in the compressor or the second stage.

3. The multi-stage cryocooling system of Claim 2, wherein the controller is configured to adjust the first-stage orifice valve and the second-stage orifice valve based on monitoring a cooling characteristic of the first stage.

4. The multi-stage cryocooling system of Claim 3, wherein the cooling characteristic of the first stage is a rate of cooling at the cold heat exchanger of the first stage or a pressure in the compressor or the second stage.

5. The multi-stage cryocooling system of Claim 4, wherein the compressor is a linear compressor.

6. The multi-stage cryocooling system of Claim 1, wherein the controller is further configured to adjust the first-stage orifice valve and the second-stage orifice valve based on monitoring a cooling characteristic of both the first and second stages.

7. The multi-stage cryocooling system of Claim 1, wherein the controller is further configured to adjust the drive frequency of the compressor based on the monitoring the cooling characteristic of the second stage.

8. The multi-stage cryocooling system of Claim 7, wherein the compressor is a dual valve compressor.

9. The multi-stage cryocooling system of Claim 8, wherein a ratio of the maximum to the minimum drive frequency is at least 1.5:1.

10. The multi-stage cryocooling system of Claim 7, wherein the controller is configured to adjust a first-stage asymmetric bypass valve and a second-stage asymmetric bypass valve based on the monitoring the cooling characteristic of the second stage.

11. The multi-stage cryocooling system of Claim 1, wherein the controller is configured to acoustically impedance match the compressor to the refrigerator at a first time with a first impedance, and to acoustically impedance match the compressor to the refrigerator at a second time later than the first time with a second impedance, the second impedance being larger than the first impedance.

12. The multi-stage cryocooling system of Claim 1, wherein the controller is configured to acoustically impedance match the compressor to the refrigerator with a variable impedance that increases on average as the temperature of the second-stage cold heat exchanger decreases.

13. A method of increasing time-averaged flow of fluid power due to oscillatory fluid flow in a multi-stage cryocooler, the method comprising: driving an oscillatory fluid flow between a compressor and a multistage cryocooler at a drive frequency, the multi-stage cryocooler comprising: a first-stage pulse tube refrigerator coupled to the compressor; a second-stage pulse tube refrigerator coupled to a cold heat exchanger of the first-stage pulse tube refrigerator; a first-stage orifice valve coupled between the first-stage pulse tube refrigerator and a first-stage reservoir and configured to control fluid flow between the first-stage pulse tube refrigerator and the first-stage reservoir; a second-stage orifice valve coupled between the second-stage pulse tube refrigerator and a second-stage reservoir and configured to control fluid flow between the second-stage pulse tube refrigerator and the second- stage reservoir; adjusting a magnitude of an acoustic impedance seen by the compressor by adjusting the first-stage orifice valve and the second-stage orifice valve.

14. The method of Claim 13, wherein the adjusting the first and second- stage orifice valves is based on optimizing a cooling characteristic of the second-stage pulse tube refrigerator.

15. The method of Claim 14, wherein the adjusting the first and second- stage orifice valves is based on optimizing a cooling characteristic of the first-stage pulse tube refrigerator.

16. The method of Claim 13, wherein the adjusting the first-stage orifice valve and the second-stage orifice valve is based on monitoring a cooling characteristic of both the first and second stages.

17. The method of Claim 13, wherein the cooling characteristic of the second-stage pulse tube refrigerator is a rate of cooling or a pressure in the compressor or the second stage.

18. The method of Claim 17, wherein the rate of cooling is monitored at a cold heat exchanger of the second-stage pulse tube refrigerator.

19. The method of Claim 13, further comprising adjusting the drive frequency based on optimizing a cooling characteristic of the second-stage pulse tube refrigerator.

20. The method of Claim 19, wherein the cooling characteristic of the second-stage pulse tube refrigerator is a rate of cooling or a pressure in the compressor or the second stage.

21. The method of Claim 19, further comprising adjusting: a first-stage asymmetric bypass valve coupled between an input of the first stage of the multi-stage cryocooler and an output of the first stage of the multistage cryocooler; and a second-stage asymmetric bypass valve coupled between an input of the first stage of the multi-stage cryocooler and an output of the second stage of the multi-stage cryocooler, wherein the adjusting is based on optimizing a cooling characteristic of the second- stage pulse tube refrigerator.

22. The method of Claim 13, further comprising adjusting: a first-stage asymmetric bypass valve coupled between an input of the first stage of the multi-stage cryocooler and an output of the first stage of the multi - stage cryocooler; and a second-stage asymmetric bypass valve coupled between an input of the first stage of the multi -stage cryocooler and an output of the second stage of the multi-stage cryocooler, wherein the adjusting is based on optimizing a cooling characteristic of the second- stage pulse tube refrigerator.

23. The method of Claim 13, wherein the adjusting the first and second- stage orifice valves optimizes a steady flow component of fluid flow between the first-stage pulse tube refrigerator and the second-stage pulse tube refrigerator, thereby minimizing a temperature difference between the cold heat exchanger of the first- stage pulse tube refrigerator and the second-stage pulse tube refrigerator by transferring heat from the second stage to the first stage.

24. The method of Claim 13, wherein the drive frequency determines the alternating opening and closing of a high pressure valve and a low pressure valve both having a common fluid connection to the first stage of the multi-stage cryocooler.

25. The method of Claim 13, wherein the adjusting a magnitude of an acoustic impedance comprises increasing an average acoustic impedance as a temperature of the second cold heat exchanger decreases.

26. A cryocooling system comprising: a compressor configured to be driven at a drive frequency; a refrigerator coupled to the compressor and receiving an oscillatory fluid flow therefrom, the refrigerator comprising: an input coupled to the compressor via a first fluid path, a regenerator, a cold heat exchanger, a thermal buffer tube, and an output; a second fluid path between the output and a reservoir, an orifice valve controlling fluid flow along the second fluid path; and a controller configured to adjust the orifice valve based on optimizing a cooling characteristic of the refrigerator.

27. The cryocooling system of Claim 26, wherein the cooling characteristic of the refrigerator is (1) a rate of cooling at the cold heat exchanger, (2) a pressure in the compressor, or (3) a pressure in the regenerator.

28. The cryocooling system of Claim 26, wherein the controller is further configured to adjust the drive frequency of the compressor based on the optimizing the cooling characteristic of the refrigerator.

29. The cryocooling system of Claim 28, wherein the compressor is a dualvalve compressor.

30. The cryocooling system of Claim 29, wherein a ratio of a maximum to a minimum drive frequency is at least 1.5:1.

31. The cryocooling system of Claim 26, wherein the compressor is a linear compressor.

32. The cryocooling system of Claim 26, wherein the cryocooling system is configured to adjust a bypass valve between the first and second fluid paths based on the optimizing the cooling characteristic of the refrigerator.

33. The cryocooling system of Claim 26, wherein the refrigerator comprises two or more cooling stages and wherein the cooling characteristic is optimized in one or more of the two or more cooling stages.