Patent Publication Number: US-6983610-B1

Title: Cold inertance tube for multi-stage pulse tube cryocooler

Description:
CROSS-REFERENCES TO RELATED APPLICATIONS 
   This is a continuation application of application Ser. No. 10/388,187, filed Mar. 12, 2003, now U.S. Pat. No. 6,865,894, which in turn claims the benefit of U.S. Provisional Application No. 60/367,782, filed Mar. 28, 2002, which is incorporated by reference herein for all purposes. 

   BACKGROUND OF THE INVENTION 
   Cooling structures find use in a variety of applications. One class of cooling structures utilizes the compression, translation, and subsequent expansion of a gas to provide cooling effects. 
     FIGS. 1–1D  show simplified cross-sectional views of a conventional Stirling cryocooler apparatus.  FIG. 1  shows the basic Stirling cooler structure  1 , wherein tube  2  contains a compressible gas  4  positioned between two moveable pistons  6  and  8 . A first heat exchanger structure  10  is positioned in contact with the gas proximate to first piston  6 . A second heat exchanger structure  12  is positioned in contact with the gas proximate to second piston  8 . A thermal regenerator  14  in contact with the gas is positioned between the first and second heat exchangers  10  and  12 . 
   Operation of the Stirling cooler shown in  FIG. 1  is now described in connection with  FIGS. 1A–1D . Generally, first piston  6  serves as a source of a pressure oscillation, and second piston  8  offers resistance to the pressure oscillation created by the first piston. 
   Specifically, in  FIG. 1A , work is applied from an external source to move first piston  6 . As shown in  FIG. 1B , compressible gas  4  within tube  2  responds to movement of piston  6  first by being compressed, and then by being translated in the direction of the second piston  8 . Some energy applied to the system at this time is absorbed and dissipated at first (hot) heat exchanger  10 . 
   Translation of the gas compressed by the first piston is opposed by the mass of the second piston. As shown in  FIG. 1C , because of the flow resistance posed by the second piston, translation of the gas ultimately halts and the gas expands.  FIG. 1D  shows that as a consequence of this gas expansion, the gas cools and second heat exchanger  12  in contact with the expanding gas absorbs thermal energy from the surrounding environment, imparting a cooling effect. 
   Regenerator  14  may comprise a porous solid matrix (such as parallel plates or holes, screens, felts or packed sphere beds) which intercepts heat from the gas, insulating the warm end from the cold end. As the gas flows from the warm end to the cold end, it deposits heat in the regenerator matrix, and as it flows back from cold to hot, it extracts the same amount of heat. Thus, the regenerator acts as a passive thermal insulation device. 
   The efficiency and effectiveness of the Stirling cooler is highly dependent upon the phase relationship between the velocity and pressure of gas within the tube. This is because the cooling mechanism requires that the gas be in the warm end during compression, and in the cold end during expansion. 
   The conventional Stirling cryocooler design shown and illustrated in connection with  FIGS. 1–1D  has been successful in providing cooling under a variety of conditions. However, the Stirling cryocooler design includes two separate moving parts: the first piston  6  and the second piston  8 . The complexity offered by these moving parts can offer a disadvantage in extraterrestrial applications such as satellites or space craft, where repair or replacement of worn moving parts is not possible. 
   Accordingly, efforts have been made to simplify the Stirling cryocooler design shown in  FIGS. 1–1D . One such design is the orifice pulse tube cryocooler shown in simplified cross-sectional view in  FIG. 2 . 
   Like the Stirling cryocooler shown in  FIGS. 1–1D , orifice pulse tube cryocooler  200  includes tube  202  enclosing compressible gas  204  in contact with a moveable piston  206  and first heat exchanger  208  proximate to the compressible gas. Also like the Stirling cryocooler shown in  FIGS. 1–1D , orifice pulse tube cryocooler  200  of  FIG. 2  includes thermal regenerator  214  in contact with the compressible gas at a point between first heat exchanger  208  and second heat exchanger  212  in contact with the compressible gas at a point distal from first heat exchanger  208 . 
   Unlike the Stirling cryocooler structure shown in  FIGS. 1–1D , however, the orifice pulse tube cryocooler  200  has no second moveable piston. Instead, this element has been replaced by pulse tube  220  in fluid communication with tube  202  at the location of the second heat exchanger  212 . Pulse tube  220  is in turn in fluid communication with a gas reservoir  222  through an orifice  224 . A third, pulse tube heat exchanger  226  is positioned in contact with the gas at the junction between pulse tube  220  and orifice  224 . 
   Operation of the pulse tube orifice cryocooler of  FIG. 2  is similar to that of the Stirling cryocooler of  FIGS. 1–1D . Specifically, external work is initially applied to piston  206  from an external source. Compressible gas  204  within tube  202  responds to movement of piston  206  first by being compressed, and then by being translated in the direction of the pulse tube  220 . Some energy applied to the system at this time is absorbed and dissipated at first (hot) heat exchanger  210 . 
   Translation of the gas compressed by piston  206  is opposed by the constriction offered by orifice  224 . Because of the flow resistance posed by the orifice  224 , translation of the gas ultimately halts and the gas expands. As a consequence of this gas expansion, the gas cools and second (cold) heat exchanger  212  absorbs thermal energy from the surrounding environment, thereby imparting a cooling effect. Energy is dissipated in the orifice  224  and removed at the (third) pulse tube heat exchanger  226 . The pulse tube  220  is an open tube filled with gas that transmits work from the cold end to the orifice, while thermally insulating the cold end from the warm end. 
   In sum, the cooling cycle of the orifice pulse tube cryocooler shown in  FIG. 2  is the same as that of a Stirling cooler, but with the cold piston replaced by passive acoustic component having no moving parts. The pulse tube acts like gas piston, insulating the cold (second) heat exchanger from the warm (third) heat exchanger. The orifice dissipates power at the third, pulse tube heat exchanger, and this dissipated power represents the gross cooling power of the orifice pulse tube cooler. 
   If the volume of the reservoir is sufficiently large (that is, if it has a large enough compliance, a gas analogy to electrical capacitance), the velocity of gas at the warm end of the pulse tube and the pressure oscillations will be in phase, and the orifice will perform as a gas equivalent to a simple resistor of an analogous electrical system. If, however, the volume of the reservoir is small, the velocity of the gas will lead the pressure of the gas by some phase angle. Optimum cooler performance usually has the gas pressure leading the velocity by about 45° at the second (cold) heat exchanger. 
   The orifice pulse tube design shown in  FIG. 2  offers the advantage of fewer moving parts and reduced complexity over the Stirling cooler. However, the orifice pulse tube cryocooler of  FIG. 2  does suffer from certain disadvantages relative to operation of the Stirling cryocooler. Specifically, the gas pressure and velocity are in-phase at the orifice, whereas the optimum condition has the pressure leading the velocity by about 45° at the second (cold) heat exchanger. 
   Therefore, there is a need in the art for improved cooling structures having simplified designs. 
   BRIEF SUMMARY OF THE INVENTION 
   In accordance with an embodiment of the present invention, performance of a multi-stage inertance pulse tube cryocooler may be enhanced by cooling the inertance tube of a later stage by placing it into thermal contact with the heat exchanger of a preceding stage. Cooling at least one inertance tube of a multi-stage cryocooler in accordance with an embodiment of the present invention lowers the viscosity and sound speed of gas in the inertance tube, thereby improving the cooling power for that cooling stage and for the entire device. 
   An embodiment of a cooling structure in accordance with the present invention comprises a moveable piston or heat engine in fluid communication with a compressible gas located within a tube. A first cooling stage is in fluid communication with the tube and including a cold heat exchanger in thermal communication with the tube. A second cooling stage is in fluid communication with the first cooling stage, the second cooling stage including an inertance tube in thermal communication with the cold heat exchanger of the first cooling stage through a thermal link. 
   An embodiment of a method in accordance with the present invention for improving the efficiency of a multi-stage inertance tube cooling structure, comprises placing a cold heat exchanger of a preceding stage in thermal communication with an inertance tube of a subsequent stage in order to reduce a viscosity of gas within the inertance tube. 
   A cooling method comprising creating at a first point an oscillation in pressure of a compressible gas disposed within a tube, and translating the compressed gas to a second point of the tube proximate to a heat exchanger. The translated gas is allowed to expand, and the heat exchanger is placed in thermal communication with an inertance tube of a subsequent cooling stage in fluid communication with the tube, thereby reducing a viscosity and sound speed of gas within the inertance tube. 
   A further understanding of embodiments in accordance with the present invention can be made by way of reference to the ensuing detailed description taken in conjunction with the accompanying drawings. 

   
     BRIEF DESCRIPTION OF THE DRAWINGS 
       FIG. 1  is a simplified cross-sectional view of a conventional Stirling-type cryocooler. 
       FIGS. 1A–1D  are simplified cross-sectional views illustrating operation of the Stirling-type cryocooler shown in  FIG. 1 . 
       FIG. 2  is a simplified cross-sectional view of a conventional orifice pulse tube cryocooler. 
       FIG. 3  is a simplified cross-sectional view of a conventional inertance pulse tube cryocooler. 
       FIG. 4  is a simplified cross-sectional view of a conventional multi-stage inertance pulse tube cryocooler. 
       FIG. 5  is a simplified cross-sectional view of a multi-stage cold inertance pulse tube cryocooler in accordance with an embodiment of the present invention. 
       FIG. 6  shows a simplified cross-sectional view of an alternative embodiment of a multi-stage inertance tube cryocooler structure in accordance with the present invention. 
   

   DETAILED DESCRIPTION OF THE INVENTION 
     FIG. 3  shows a simplified cross-sectional view of a conventional inertance tube cryocooler structure. The inertance tube cryocooler structure  300  of  FIG. 3  combines the desirable phase relationship between gas velocity and gas pressure exhibited by the Stirling cryocooler design of  FIGS. 1–1D , with the reduced number of moving parts characteristic of the pulse tube cryocooler design of  FIG. 2 . 
   Specifically, like the pulse tube cryocooler shown in  FIG. 2 , inertance pulse tube cryocooler  300  of  FIG. 3  includes tube  302  enclosing compressible gas  304  in contact with a moveable piston  306  and first heat exchanger  308  proximate to the compressible gas. Also like the pulse tube cryocooler shown in  FIG. 2 , the inertance tube cryocooler of  FIG. 3  includes thermal regenerator  314  in contact with the compressible gas at a point between first heat exchanger  308  and second heat exchanger  312  that is in contact with the compressible gas at a point distal from first heat exchanger  308 . 
   Unlike the pulse tube cryocooler shown in  FIG. 2  however, the orifice has been replaced by an inertance tube  330  that is in fluid communication with the pulse tube  320  at a point distal from the second heat exchanger  312 . The inertance tube  330  is also in fluid communication with gas reservoir  322 , and pulse tube heat exchanger  326  remains positioned in contact with gas of pulse tube  320  proximate to the inlet to inertance tube  330 . 
   Operation of the inertance pulse tube cryocooler of  FIG. 3  is similar to that of the orifice pulse tube cryocooler of  FIG. 2 . Specifically, work from an external source is applied to move piston  306  into compressible gas  304 . Compressible gas  304  within tube  302  responds to movement of piston  306  first by being compressed, and then by being translated in the direction of the pulse tube and inertance tube. Some energy applied to the system at this time is absorbed and dissipated at first (hot) heat exchanger  308 . 
   Translation of the gas compressed by the piston is opposed by resistance offered as the gas flows through the narrow and elongated inertance tube. As a result of the flow resistance offered by the inertance tube, the translated gas ultimately halts and expands. As a consequence of this gas expansion, the gas cools and second heat exchanger  312  in contact with the expanding gas absorbs thermal energy from the surrounding environment thereby imparting a cooling effect. 
   The inertance tube  330  improves performance of the cooling structure by providing a phase shift between the pressure and the velocity of the translated gas. Specifically, inertance tube  330  functions as the gas equivalent of an inductor in series with a resistor in an analogous electrical system. The simple orifice configuration cannot provide the optimum phase reductions between pressure and velocity. The long thin capillary of the inertance tube  330  can shift the phase relationship between velocity and pressure of the moving gas at the cold heat exchanger to the optimum value of forty-five degrees. 
   Multiple inertance tube cryocoolers can be arranged in series to provide a cumulative cooling effect.  FIG. 4  shows a simplified plan view of such a conventional multi-stage cooling structure. Cooler  400  comprises first stage  401  in series with second stage  450 . 
   First stage  401  comprises first tube  402  containing compressible gas  404  and in fluid communication with a moveable piston  406 . First heat exchanger  408  is positioned in contact with the compressible gas at a point proximate to the piston  406 . Second heat exchanger  412  is positioned in contact with the compressible gas  404  at a point distal from the first heat exchanger  408 . Regenerator  414  is positioned in contact with the compressible gas between first heat exchanger  408  and second heat exchanger  412 . 
   Pulse tube  420  in fluid communication with inertance tube  430  and reservoir  422 , is positioned in fluid contact with tube  402  at the second heat exchanger  412 . A third heat exchanger  426  is positioned in contact with the compressible gas where the inertance tube connects with the pulse tube. 
   Cooling structure  400  also includes second stage  450 . Second stage  450  comprises first heat exchanger  458  in fluid communication with compressible gas  404  at second heat exchanger  412  of first stage  401 . Second heat exchanger  462  is positioned in contact with the compressible gas  404  at a point distal from the first heat exchanger  458 . Regenerator  464  is positioned in contact with the compressible gas between first heat exchanger  458  and second heat exchanger  462 . 
   Pulse tube  470  in fluid communication with inertance tube  480  and reservoir  472 , is positioned in fluid contact with regenerator  464  at the second heat exchanger  462 . A third heat exchanger  476  is positioned in contact with the compressible gas where the inertance tube connects with the pulse tube. 
   Operation of the conventional multi-stage cooling apparatus shown in  FIG. 4  is cumulative. Specifically, compressed gas translated from the first stage may in turn compress gas located at first heat exchanger  458  of the second stage  450 , in turn giving rise to translation and subsequent expansion of the gas of the second stage. As the translated gas has already been cooled by the first stage, further compression and cooling is possible by operation of the second stage. 
   Gardner and Swift, “Use of Inertance in Orifice Pulse Tube Refrigerators,” CRYOGENICS, Vol. 37, No. 2, (1997) (“the Gardner and Swift paper”) presents an insightful analysis of the performance of pulse tube cryocooler designs, including inertance tube cryocooler designs. The Gardner and Swift paper is hereby incorporated by reference for all purposes. 
   The Gardner and Swift paper makes a number of simplifying assumptions. First, the inertance tube is treated as a lumped element, with a single gas velocity and pressure throughout. In reality however, the length of the inertance tube is typically a quarter of the gas wavelength. The pressure amplitude thus goes from a maximum at the warm (first) heat exchanger, to zero at the reservoir volume. The gas velocity is smallest at the warm (first) heat exchanger and larger at the reservoir end of the inertance tube. 
   A second assumption of the Gardner and Swift paper is to ignore thermal dissipation at the tube wall. In reality however, gas undergoing oscillations in pressure also experiences a corresponding oscillation in temperature, and the temperature relaxation of gas near the tube walls causes dissipation. 
   A third assumption of the Gardner and Swift paper is a simplistic treatment of gas turbulence. This implications of this third assumption are complex, but ultimately it serves to underestimate the cooling power of an given inertance tube cooler design. 
   The Gardner and Swift paper concludes that for large-size coolers exhibiting a gross cooling power of about 50 W or greater, a single inertance tube can provide the proper inertance and dissipation. For smaller coolers, however, it becomes more difficult for the inertance tube to provide the desired phase shift while simultaneously providing sufficient inertance for a given dissipation. 
   In accordance with embodiments of the present invention, performance of a multi-stage inertance pulse tube cryocooler may be enhanced by cooling the inertance tube of a latter stage placing it into contact with the second (cold) heat exchanger of a preceding stage. Cooling at least one inertance tube of a multi-stage cooler in accordance with the present invention lowers the viscosity and sound speed of the gas in the inertance tube, thereby improving the cooling power for that subsequent cooling stage, and for the entire device. 
   The Gardner and Swift article just described summarizes performance of inertance pulse tube coolers in Equation (I) below: 
                     E   ⁢     &gt;   ∼       .     ⁢       π   ⁢           ⁢     p   m     ⁢   a   ⁢           ⁢     δ   v   2         4   ⁢   γ       ⁢              p     E   ⁢   .1         p   m            2       ,   where     ⁢     
     ⁢               E   .     =       ⁢     power   ⁢           ⁢   dissipated       ;                   p   m     =       ⁢     mean   ⁢           ⁢   gas   ⁢           ⁢   pressure       ;                 a   =       ⁢     sound   ⁢           ⁢   speed       ;                   δ   v     =       ⁢     viscous   ⁢           ⁢   penetration   ⁢           ⁢   depth       ;                   p     E   ⁢   .1       =       ⁢     pressure   ⁢           ⁢   amplitude       ;   and               γ   =       ⁢     ratio   ⁢           ⁢   of   ⁢           ⁢   isobaric   ⁢           ⁢   to   ⁢           ⁢   isochoric   ⁢           ⁢   specific   ⁢           ⁢   heats                     (   I   )             
 
   Equation (II) below sets forth a relationship between viscous penetration depth and viscosity: 
                   δ   v   2     =       2   ⁢   μ   ⁢           ⁢     a   2         ωγ   ⁢           ⁢     p   m           ,   where     ⁢     
     ⁢               δ   v     =       ⁢     viscous   ⁢           ⁢   penetration   ⁢           ⁢   depth       ;                 μ   =       ⁢     gas   ⁢           ⁢   viscosity       ;                 a   =       ⁢     sound   ⁢           ⁢   speed       ;                 ω   =       ⁢     angular   ⁢           ⁢   frequency   ⁢           ⁢   of   ⁢           ⁢   the   ⁢           ⁢   gas   ⁢           ⁢   oscillations       ;                 γ   =       ⁢     ratio   ⁢           ⁢   of   ⁢           ⁢   isobaric   ⁢           ⁢   to   ⁢           ⁢   isochoric   ⁢           ⁢   specific   ⁢           ⁢   heats       ;   and                   p   m     =       ⁢     mean   ⁢           ⁢   gas   ⁢           ⁢   pressure       ;                   (   II   )             
 
   Substituting Equation (II) into Equation (I) yields Equation (III): 
               E   .     ≥         π   ⁢           ⁢     a   3     ⁢   μ       2   ⁢     γ   2     ⁢   ω       ⁢              p     E   ⁢   .1         p   m            2               (   III   )             
 
   Equation (III) shows that the minimum gross cooling power (Ė) for an inertance tube scales with the viscosity (μ) and the cube of sound speed (a) of the gas. Embodiments of the present invention accordingly improve cooling performance by lowering the viscosity and sound speed by lowering the temperature of the gas within the inertance tube, reducing the minimum gross cooling power requirement. 
     FIG. 5  shows a simplified cross-sectional view of an embodiment of a cryocooler structure in accordance with the present invention. Specifically, cryocooler  500  comprises first stage  501  in series with second stage  550 . 
   First stage  501  comprises first tube  502  containing compressible gas  504  and in fluid communication with a moveable piston  506 . First heat exchanger  508  is positioned in contact with the compressible gas at a point proximate to the piston  506 . Second heat exchanger  512  is positioned in contact with the compressible gas  504  at a point distal from the first heat exchanger  508 . Regenerator  514  is positioned in contact with the compressible gas between first heat exchanger  508  and second heat exchanger  512 . 
   Pulse tube  520  in fluid communication with inertance tube  530  and reservoir  522 , is positioned in fluid contact with tube  502  at the second heat exchanger  512 . A third heat exchanger  526  is positioned in contact with the compressible gas where the inertance tube connects with the pulse tube. 
   Cooling structure  500  also includes second stage  550 . Second stage  550  comprises first heat exchanger  558  in fluid communication with compressible gas  504  at second heat exchanger  512  of first stage  501 . Second heat exchanger  562  is positioned in contact with the compressible gas  504  at a point distal from the first heat exchanger  558 . Regenerator  564  is positioned in contact with the compressible gas between first heat exchanger  558  and second heat exchanger  562 . 
   Pulse tube  570  in fluid communication with inertance tube  580  and reservoir  572 , is positioned in contact with regenerator  564  at the second heat exchanger  562 . A third heat exchanger  576  is positioned in contact with the compressible gas where the inertance tube  580  connects with the pulse tube  570 . 
   Operation of the conventional multi-stage cooling apparatus shown in  FIG. 4  is cumulative. Specifically, compressed gas translated from the first stage may in turn compress gas located at first heat exchanger  558  of the second stage  550 , in turn giving rise to translation and subsequent expansion of the gas of the second stage. As the translated gas has already been cooled at by the first stage, further compression and further cooling is possible by operation of the second stage. 
   The cryocooler embodiment of  FIG. 5  differs from the conventional multi-stage structure shown in  FIG. 4  in that inertance tube  580  of second stage  550  is in thermal communication with the second (cold) heat exchanger  512  of the first stage  501  through thermal link  590 . 
   As a result of the presence of thermal link  590 , the temperature of the compressible gas within the inertance tube is lowered, which in turn reduces its viscosity and improves the phase relationship between gas velocity and pressure. 
   The use of a cooled inertance tube cryocooler design in accordance with an embodiment of the present invention offers a number of advantages over conventional designs. For example, the cooled inertance tube of the subsequent stage may have a smaller pulse tube, thus requiring less gas to be moved through the regenerator. Moreover, as mentioned above, the inertance tube of the second stage will function more effectively because of the lowered temperature and viscosity of the gas present therein. 
   Cooling the inertance tube in accordance with an embodiment of the present invention increases the heat load on the warmer stages, because the energy dissipated in the tube is an extra heat load to the intermediate stage. However, cooling the inertance tube greatly enhances its performance. For example, the following TABLE lists the temperature at different points of a conventional two-stage cooler and a two-stage cooler having a cold inertance tube in accordance with an embodiment of the present invention. 
   
     
       
         
             
             
             
           
             
               TABLE 
             
             
                 
             
             
                 
               CONVENTIONAL 
               TWO-STAGE CRYOCOOLER 
             
             
               LOCATION OF 
               TWO-STAGE 
               WITH COOLED SECOND 
             
             
               CRYOCOOLER 
               CRYOCOOLER 
               INERTANCE TUBE 
             
             
               STRUCTURE 
               (FIG. 4) 
               (FIG. 5) 
             
             
                 
             
           
          
             
               first (hot) heat 
               300° K 
               300° K 
             
             
               exchanger of 
             
             
               first stage 
             
             
               second (cold) heat 
               100° K 
               100° K 
             
             
               exchanger of 
             
             
               first stage 
             
             
               pulse tube heat 
               300° K 
               300° K 
             
             
               exchanger of 
             
             
               first stage 
             
             
               first (hot) heat 
               100° K 
               100° K 
             
             
               exchanger of 
             
             
               second stage 
             
             
               second (cold) heat 
                35° K 
                35° K 
             
             
               exchanger of 
             
             
               second stage 
             
             
               pulse tube heat 
               300° K 
               100° K 
             
             
               exchanger of 
             
             
               second stage 
             
             
                 
             
          
         
       
     
   
   The multi-stage inertance tube cryocoolers compared in the above TABLE exhibited the same cool temperature (35° K.) at the second heat exchanger of the second stage. However, the cryocooler structure in accordance with an embodiment of the present invention required 6% less input power to accomplish this result. 
   The foregoing description discloses only specific embodiments in accordance with the present invention, and modifications of the above disclosed apparatuses and methods falling within the scope of the invention will be apparent to those of ordinary skill in the art. Thus while the invention has been described so far in connection with the cooling of the second stage inertance tube of a two stage cryocooler, the invention is not limited either to a cryocooler having this number of stages, to this number of cooled inertance tubes, or to this particular thermal linkage of inertance tubes with cold heat exchangers of prior stages. 
   For example,  FIG. 6  shows a simplified cross-sectional view of an alternative embodiment of a multi-stage inertance tube cryocooler structure in accordance with the present invention. Cryocooler  600  of  FIG. 6  comprises three stages  602 ,  604 , and  606  arranged in series, with each stage including a respective first heat exchanger  608 , regenerator  614 , second heat exchanger  612 , pulse tube  620 , pulse tube heat exchanger  626 , inertance tube  630 , and reservoir  672 . Inertance tube  630   b  of second stage  604  is in thermal communication with second heat exchanger  612   a  of first stage  602  through first thermal link  690   a . Inertance tube  630   c  of third stage  606  is in thermal communication with second heat exchanger  612   b  of second stage  604  through second thermal link  690   b . Efficiency in operation of the coldest stage of the series shown in  FIG. 6  will benefit from this approach. 
   Again, while  FIG. 6  shows cooling of the inertance tube of a subsequent stage in a three-stage cooler, this is only one specific example and the present invention is not limited to a cryocooler having this or any particular number of stages. An inertance tube cooled by a heat exchanger of a prior stage of a cooler having four, five, six, or any number of stages, would also fall within the scope of the present invention. 
   And while the embodiment illustrated in  FIG. 6  shows the inertance tube of the second and third stages as being in thermal communication with the cold heat exchanger of the immediately preceding stage, this is not required by the present invention. In accordance with other additional alternative embodiments, the inertance tube of a subsequent stage could be in thermal communication with the cold heat exchanger of other than an immediately preceding stage. For example the inertance tube of the third stage of the cooler structure shown in  FIG. 6  could be in thermal communication with the cold heat exchanger of the first stage, rather than the cold heat exchanger of the second stage. 
   Moreover, while the embodiment illustrated in  FIG. 6  shows the gas proximate to the first heat exchanger of the first stage as being in fluid communication with a moveable piston, this is not required by the present invention. In accordance with alternative embodiments of the present invention, gas within the tube could be in fluid communication with a source of pressure oscillation other than a moveable piston. An example of such an alternative source of pressure oscillation is a heat engine. One particular type of heat engine is described in detail by G. W. Swift in “Thermoacoustic Engines”, J. Acous. Soc. of America, Vol. 84, pp. 1145–1180 (1988). 
   The scope of the invention should, therefore, be determined not with reference to the above description, but instead should be determined with reference to the appended claims along with their full scope of equivalents.