Abstract:
A cryocooler may comprise a first stage, a second stage and a phase control device. The first stage may define a first volume. The second stage may define a second volume. The phase control device may be positioned between the first stage and the second stage to receive a flow of working fluid between the first stage and the second stage. The phase control device may comprise a flange and a plunger. The flange may be positioned along a longitudinal axis parallel a direction of the working fluid flow. The plunger may be translatable along the longitudinal axis at least partially within the flange. The plunger and the flange may be sized such that the plunger and the flange define a gap there between and a dimension of the gap is determined by a position of the plunger along the longitudinal axis.

Description:
RELATED APPLICATIONS 
     This application is a continuation of U.S. patent application Ser. No. 12/611,784, filed on Nov. 3, 2009, now U.S. Pat. No. 8,474,272, which is incorporated herein by reference in its entirety. 
     This application is related to the following applications, which are incorporated herein by reference in their entirety: 
     (1) U.S. application Ser. No. 12/611,764, filed on Nov. 3, 2009, entitled, “PHASE SHIFT DEVICES FOR PULSE TUBE COOLERS,” and now issued as U.S. Pat. No. 8,397,520. 
     (2) U.S. application Ser. No. 12/611,774, filed on Nov. 3, 2009, entitled, “VARIABLE PHASE SHIFT DEVICES FOR PULSE TUBE COOLERS,” and now issued as U.S. Pat. No. 8,408,014. 
    
    
     BACKGROUND 
     Mechanical coolers are devices used for cooling, heating, and thermal transfer in various applications. For example, mechanical coolers are used to cool certain sensor elements, to cool materials during semiconductor fabrication, and to cool superconducting materials such as in Magnetic Resonance Imaging (MRI) systems. Mechanical coolers typically utilize a thermodynamic cycle (often involving the compression and expansion of a fluid) to shift heat and create cold portions that are useful for cooling. Cryocoolers are a class of mechanical coolers that can achieve cold temperatures in the cryogenic range (e.g., &lt;˜123 K). Different types of mechanical coolers may comprise various valves, thermal compressors, mechanical compressors, displacers, etc., to bring about expansion and compression of the working fluid. 
     A pulse tube cooler includes a stationary regenerator connected to a pulse tube. A reservoir or buffer volume may be connected to the opposite end of the pulse tube via a phase control device such as a sharp-edged orifice or an inertance tube. The reservoir, pulse tube, and regenerator may be filled with a working fluid (e.g., a gas such as helium). A compressor (e.g., a piston) compresses and warms a parcel of the working fluid. The compressed working fluid is forced through the regenerator, where part of the heat from the compression (Q o ) is removed at ambient temperature and stored at the regenerator. The working fluid is then expanded through the pulse tube and the phase control device into the reservoir. This expansion provides further cooling (Q c ) that takes place at a cold temperature (T c ). The cooling occurs at a cold end of the pulse tube nearest the regenerator. A hot end of the pulse tube farthest from the regenerator collects heat. 
     Pulse tube cryocoolers do not have moving parts at the cold end, such as displacer pistons or valves. To achieve the desired cooling, the combination of the phase control device and the reservoir cause a phase shift between mass waves and pressure waves generated by the compressor. By restricting or slowing the mass flow to the buffer volume, the phase control device may serve to shift the phase of the mass flow relative to the pressure wave generated by the compressor. 
     Multistage pulse tube coolers are used to achieve temperatures colder than can be achieved with a single cooler alone. Multistage coolers can be arranged in series, where the cold end of the first cooler is connected to the hot end of the second pulse tube, or in parallel, where the cold end of the first stage is connected to the cold end of the second stage. Some load shifting between stages can be brought about by varying the frequency, charge pressure and/or temperature of each stage. 
     SUMMARY 
     Various embodiments are directed to pulse tube coolers and components thereof. A pulse tube cooler may comprise a compressor, a regenerator, a pulse tube and a reservoir. A network of phase control devices may be placed in a fluid path between a hot end of the pulse tube and the reservoir. The network of phase control devices may have at least one flow resistance device and at least one inertance device. 
     Various embodiments are directed to multistage pulse tube coolers. In some embodiments, one or more stages of the pulse tube cooler may comprise a control valve positioned between the hot end of the pulse tube and the reservoir. Also, in various embodiments, one or more inter-stage control valves may be positioned between the pulse tubes of consecutive stages. 
    
    
     
       FIGURES 
       Various embodiments of the present invention are described here by way of example in conjunction with the following figures, wherein: 
         FIG. 1  illustrates one embodiment of a pulse tube cooler. 
         FIG. 2  illustrates one embodiment of the cooler of  FIG. 1  where the phase control device comprises an orifice. 
         FIG. 3  illustrates one embodiment of the cooler of  FIG. 1  where the phase control device comprises an inertance tube 
         FIG. 4  illustrates one embodiment of the cooler of  FIG. 1  where the phase control device comprises an inertance gap device. 
         FIG. 5  illustrates one example configuration of an inertance gap device comprising parallel plates. 
         FIG. 6  illustrates one example configuration of an inertance gap device comprising concentric tubes. 
         FIG. 7  illustrates one embodiment of the cooler of  FIG. 1  where the phase control device is a network comprising an orifice and an inertance device arranged in parallel. 
         FIG. 8  illustrates a portion of the cooler of  FIG. 1  illustrating a network of inertances and flow resistances between the pulse tube and the reservoir. 
         FIG. 9  is a chart illustrating cooler efficiency (y-axis) as a function of reservoir volume (x-axis). 
         FIG. 10  illustrates one embodiment of a pulse tube cooler with a variable phase control device configured to vary the flow resistance and/or inertance of the phase control device during the thermodynamic cycle of the cooler. 
         FIG. 11  illustrates one embodiment of a variable inertance device. 
         FIG. 12  illustrates another embodiment of a variable inertance device. 
         FIG. 13  illustrates one embodiment of a variable inertance gap device. 
         FIG. 14A  illustrates one embodiment of a variable flow resistant device in a low resistance configuration. 
         FIG. 14B  shows the device of  FIG. 14A  in a higher flow resistance configuration. 
         FIG. 15  is a chart showing a plot of orifice diameter versus compressor stroke position that was used in a model of the cooler of  FIG. 10 . 
         FIG. 16  is a chart illustrating the results of the model of the cooler of  FIG. 10 . 
         FIG. 17  illustrates one embodiment of a multistage pulse tube cooler with two stages. 
         FIG. 18  illustrates one embodiment of a multistage pulse tube cooler having control valves positioned between the respective pulse tubes and the reservoirs. 
         FIG. 19  illustrates one embodiment of a multistage pulse tube cooler having a control valve positioned between the pulse tubes of the stages. 
         FIG. 20  is a chart showing results of a computer model of the multistage pulse tube coolers of  FIGS. 17, 18 and 19 . 
     
    
    
     DESCRIPTION 
       FIG. 1  illustrates one embodiment of a pulse tube cooler  100 . The cooler  100  comprises various components in fluid communication with one another and filled with a working fluid (e.g., helium gas). For example, the cooler  100  may comprise a compressor  102  for providing pressure/volume (PV) work. The compressor  102  may be of any suitable compressor type and, in various embodiments, may be a linear compressor or rotary compressor. In various embodiments, the compressor  102  may comprise a piston  118  and a cylinder  120 . In addition, the cooler  100  may comprise a regenerator  104 , a pulse tube  106  and a reservoir  108 . A first heat exchanger  110  may be positioned between the compressor  102  and the regenerator  104 . A cold end heat exchanger  112  may be positioned at a cold end  99  of the pulse tube  106  near the regenerator  104 . A hot end heat exchanger  114  is positioned at a hot end  98  of the pulse tube  106  near the reservoir  108 . The reservoir  108  and the pulse tube  106  may be connected by a phase control device  116  that may comprise one or more sub-devices having an inertance and/or a resistance to the flow of working fluid, as described below. The phase control device  116  may be embodied as one or more separate components, as a portion of the pulse tube  106 , as a portion of the reservoir  108 , or as any combination thereof. 
     The compressor  102 , may drive the thermodynamic cycle of the cooler  100  at various frequencies. For example, in various embodiments, one thermodynamic cycle of the cooler  100  may correspond to one complete cycle of the piston  102  or other mechanism of the compressor  102 . According to the thermodynamic cycle of the cooler  100 , the compressor  102  may provide work W o  to compress a portion of the working fluid, adding heat Q o  and causing the temperature T o  of the working fluid to rise at heat exchanger  110 . As the compressor  102  further compresses the working fluid, warm working fluid is passed through the regenerator  104  where part of the heat of compression Q o  is removed and stored. Working fluid already present in the pulse tube  106  may be at a relatively lower pressure than that entering the pulse tube via  106  via the regenerator  104 . Accordingly, the working fluid entering the pulse tube  106  via the regenerator  104  may expand in the pulse tube  106 , causing cooling Q c  at the exchanger  112  at a temperature T c . Excess pressure in the pulse tube  106  from the expansion may be relieved across the phase control device  116  into the reservoir. As the cycle continues, the compressor  102  begins to draw the working fluid from the cold end  99  of the pulse tube  106  back through the regenerator  104 , where the stored heat is reintroduced. Resulting low pressure in the pulse tube  106  also causes working fluid from the reservoir  108  to be drawn across the phase control device  116  into the pulse tube  106 . This working fluid from the reservoir  108  is at a higher pressure than that already in the pulse tube  106  and, therefore, enters with heat energy Q h  and at a temperature T h  that is relatively warmer than that of the other working fluid in the pulse tube  106 . A new cycle may begin as the compressor  102  again reverses and begins to compress the working fluid. Examples of the operation of pulse tube coolers are provided in commonly assigned U.S. Patent Application Publication Nos. 2009/0084114, 2009/0084115 and 2009/0084116, which are incorporated herein by reference in their entirety. 
     The performance of the pulse tube cooler  100  depends on the generated phase shift between the pressure waves and mass flow waves generated by the compressor  102  in the working fluid. This phase shift is a function of the volume of the reservoir  108  and the inertance and/or flow resistance of the phase control device  116 . To achieve optimal performance, the phase shift may be approximately 0°, or slightly negative, such that the mass wave and pressure wave roughly coincide at the coldest portion of the pulse tube  106  (e.g., the cold end  99 ). According to various embodiments, the mechanical/fluid flow properties causing the phase shift may behave in a fashion analogous to the properties of an inductor-resistor-capacitor (LRC) electronic circuit that cause phase shifts between voltage and current. In the context of the pulse tube cooler  100 , resistance is analogous to the flow resistance impedance caused by the phase control device  116 . Inductance is analogous to the inertance introduced by the phase control device  116 . Capacitance is analogous to the heat capacity of the system and is a function of the geometry of the reservoir  108  and the heat capacity of the working fluid. 
     According to various embodiments, the phase control device  116  may comprise various components that introduce resistance and or inertance into the system. For example,  FIG. 2  illustrates one embodiment of the cooler  100  where the phase control device  116  consists of a flow resistive orifice  202 . The orifice  202  resists the flow of working fluid from the pulse tube  106  to the reservoir  108 , thus contributing to the phase shift between the pressure wave and mass wave. The flow resistance provided by the orifice  202  may be a function of the size and shape of the orifice. For example, for a circular orifice  202 , the resistance may depend on the orifice diameter. The orifice  202  may be embodied as a part of the pulse tube  106 , a part of the reservoir  106 , a separate component, or any combination thereof. It will be appreciated that a resistive orifice  202  may be associated with an irreversible energy loss that can serve as a drag on efficiency. 
       FIG. 3  illustrates one embodiment of the cooler  100  where the phase control device  116  comprises an inertance tube  204 . The inertance tube  204  may be several meters in length, which may be coiled, as shown in  FIG. 3 , or straight. By increasing the distance that the working fluid must traverse between the pulse tube  106  and the reservoir  108 , the inertance tube  204  may increase the time that the working fluid takes to reach the reservoir  108 , while only minimally affecting the timing of the pressure wave. In this way, the inertance tube  204  may introduce a phase shift between the pressure wave and the mass wave. For the inertance tube geometry shown in  FIG. 3 , the inertance (L) and flow resistance (R) of the tube  204  may be given by Equations 1 and 2 below where l t , d and v, respectively, are the length, diameter and internal volume of the inertance tube  204 . 
                   L   =       4   ⁢           ⁢     l   t         π   ×     d   2                 (   1   )               R   =       128   ⁢           ⁢     l   t     ⁢   η       (     π   ×   ρ   ×     d   4       )               (   2   )               
The inertance tube  204  may be embodied as a portion of the pulse tube  106 , a portion of the reservoir  108 , a separate component, or any combination thereof.
 
       FIG. 4  illustrates one embodiment of the cooler  100  where the phase control device  116  comprises an inertance gap device  206 . The inertance gap device  206  may be a portion of the pulse tube  106 , a portion of the reservoir  108 , a separate component, or any combination thereof. The inertance gap device  206  may behave similarly to the inertance tube  204 , but may have smaller physical dimensions. For example, while the intertance tube  204  may be several meters long, the inertance gap device  206  may have a length on the order of several inches.  FIG. 5  illustrates one example configuration of an inertance gap device  500  comprising parallel plates  502 ,  504 . The working fluid of the cooler  100  may pass between the parallel plates  502  as it travels between the pulse tube  106  and the reservoir  108 . The path of the working fluid through the inertance gap device  500  is indicated by arrows  506 . The inertance and flow resistance of the inertance gap geometry shown in  FIG. 5  are given by Equations 3 and 4 below, where l g , w and s are the length, width, and thickness of the gap. 
     
       
         
           
             
               
                 
                   L 
                   = 
                   
                     
                       l 
                       g 
                     
                     
                       w 
                       × 
                       s 
                     
                   
                 
               
               
                 
                   ( 
                   3 
                   ) 
                 
               
             
             
               
                 
                   R 
                   = 
                   
                     
                       12 
                       ⁢ 
                       
                           
                       
                       ⁢ 
                       
                         l 
                         g 
                       
                       ⁢ 
                       η 
                     
                     
                       ρ 
                       × 
                       w 
                       × 
                       
                         s 
                         3 
                       
                     
                   
                 
               
               
                 
                   ( 
                   4 
                   ) 
                 
               
             
           
         
       
     
       FIG. 6  illustrates another example configuration of an inertance gap device  600  comprising concentric tubes  602 ,  604 . The working fluid passes between the tubes on its way from the pulse tube  106  to the reservoir  108  and back. The direction of the working fluid is indicated by arrows  606 . The inertance and resistance of the gap geometry shown in  FIG. 6  may be a function of the distance between the two concentric tubes  602 ,  604  and the length of the device  600 . 
     According to various embodiments, the LRC circuit analogy introduced above may be exploited in the design of the phase control device  116  in order to fine tune the performance of the pulse tube cooler  100 . For example, instead of comprising just one orifice or just one inertance tube or gap, the phase control device  116  may be constructed from a network of various inertance and flow resistant devices. LRC circuit principles may be used to design networks of inertance and flow resistant devices in order to provide a desired phase shift. Also, because the phase shift of the cooler  100  depends both on the phase control device  116  and the volume of the reservoir  108 , modifying the inertance and flow resistance properties of the phase control device  116  may allow the cooler  100  to be constructed with a reservoir  108  having a smaller volume. This may beneficially reduce the total size and weight of the cooler  100 . 
       FIG. 7  illustrates one embodiment of the cooler  100  where the phase control device  116  comprises a network  208  comprising an orifice  212  and an inertance device  210  arranged in parallel. In other words, both the inertance device  210  and the orifice  212  have one end in fluid communication with the hot end of the pulse tube  106  and an opposite end in fluid communication with the reservoir  108 . The inertance device  210  may be any kind of inertance device including, for example, an inertance tube and/or an inertance gap. The overall flow resistance and inertance of the network  208  may be found according to LRC circuit principles based on the flow resistance of the orifice  212  and the inertance and flow resistance of the inertance device  210 . The dimensions and/or other properties of the orifice  212  and the inertance device  210  may be selected to fine tune the phase difference between pressure waves and mass flow waves in the cooler  100 . In various embodiments, the network  208  may be designed to provide a desired phase difference (and hence desired cooler performance) with a reservoir volume  108  that is relatively smaller than that which is practically possible with a single element phase control device  116 . 
       FIG. 8  illustrates a portion  800  of the cooler  100  illustrating a network  214  of inertances and flow resistances between the pulse tube  106  and the reservoir  108 . The network  214  comprises three flow resistive orifices  216 ,  218 ,  220  and two inertance devices  222 ,  224 . The inertance devices  222 ,  224  may be inertance tubes, parallel plate inertance gaps, concentric circle inertance gaps, or any combination thereof. Resistive orifice  216  may have a first end  802  in fluid communication with the cold end  99  of the pulse tube  106  and a second end  804 . The resistive orifice  218  may have a first end  806  in fluid communication with the reservoir  108  and a second end  808  in fluid communication with the second end  804  of the orifice  216 . The inertance device  222  may have a first end  808  in fluid communication with the cold end  99  of the pulse tube  106  and a second end  810 . The inertance device  224  may have a first end  812  in fluid communication with the reservoir  108  and a second end  814  in fluid communication with the second end  810  of the inertance device  222 . A resistive orifice  220  may have a first end  816  in fluid communication with the second end  810  of the inertance device  222  and the second end  814  of the inertance device  224 . The orifice  220  may also have a second end  818  in fluid communication with the second end  804  of the orifice  216  and the second end  808  of the orifice  218 . 
     It will be appreciated that the sizes and values of the inertance devices  222 ,  224  and the flow resistive orifices  216 ,  218 ,  220  may be optimized based on the size of various other components (e.g., the regenerator  104 , pulse tube  106  and reservoir  108 ) and on the operating conditions. In one embodiment, the regenerator  104  may be 20.8 centimeters (cm) long with a diameter of 3.95 cm. The pulse tube  106  may be 20.13 cm long with a diameter of 2.54 cm. The inertance device  222  may be a concentric gap with a diameter of 1.297 cm, a length of 6.3 cm and a gap width of 23.59 microns. The inertance device  224  may also be a concentric gap with a diameter of 2.54 cm, a length of 7 cm and a gap width of 100 microns. The orifice  216  may have a diameter of 7.103×10 −4  meters. The orifice  218  may have a diameter of 12.12×10 −4  meters. Also, the orifice  220  may have a diameter of 1.869×10 −4  meters. 
       FIG. 9  is a chart  900  illustrating cooler efficiency (y-axis) as a function of reservoir volume (x-axis). The chart  900  was generated by modeling various embodiments of the cooler  100  using the SAGE software package available from Gedeon Associates of Athens, Ohio. On the y-axis, cooler efficiency is represented as an input power necessary to bring about 20 Watts of cooling. Reservoir volume is represented on the x-axis in cubic meters. All of the plots  902 ,  904 ,  906 ,  908  shown in  FIG. 9  were modeled as including (i) a regenerator with a diameter of 3.95 centimeters (cm) and a length of 20.8 cm, and (ii) a pulse tube with a diameter of 2.54 cm and a length of 20.13 cm. Each of the plots  902 ,  904 ,  906 ,  908  corresponds to a different configuration of the phase control device  116 . Plot  908  shows results of the embodiment of the cooler  100  shown in  FIG. 2  where the phase control device  116  comprises a single flow resistive orifice  202 . The diameter of the single flow resistive orifice  202  was optimized for the component dimensions above by the SAGE software package. Plot  906  shows results of the embodiment of the cooler  100  shown in  FIGS. 3 and 4  where the phase control device  116  comprises a single inertance device, which may be an inertance tube or any kind of inertance gap. The dimensions of the inertance gap were optimized for the component dimensions above by the SAGE software package. Plot  904  shows results of the embodiment of the cooler  100  shown in  FIG. 7  having an inertance device (e.g., a tube or gap) and a resistive orifice in parallel. The dimensions of the inertance and resistance devices were optimized for the component dimensions above by the SAGE software package. Plot  902  shows results of the embodiment of the cooler  100  shown in  FIG. 8  having the network  214  of inertances and resistances as shown with the dimensions set forth above with respect to  FIG. 8 . It can be seen that plot  904  corresponding to the embodiment shown in  FIG. 7  and plot  902  corresponding to the embodiment shown in  FIG. 8  provide superior efficiency, with the plot  902  demonstrating superior efficiency over the range of reservoir volumes modeled, especially at smaller reservoir volumes. 
     During the thermodynamic cycle of a pulse tube cooler, such as the cooler  100  described above, the properties of the various components including, for example, the temperature of the working fluid, may change. This may, in turn, cause changes to the performance of the cooler including, for example, changes to the inertance and flow resistance of various components of the phase control device. Increased performance of the cooler, therefore, may be obtained by varying the inertance and/or flow resistance of the phase control device during the thermodynamic cycle of the cooler. 
       FIG. 10  illustrates one embodiment of a pulse tube cooler  1000  configured to vary the flow resistance and/or inertance of the phase control device  1010  during the thermodynamic cycle of the cooler  1000 . The cooler  1000  may comprise a compressor  1002 , a regenerator  1004 , a pulse tube  1006  and a reservoir  1008 . These components may operate, for example, as described above. For example, the pulse tube  1006  may have a cold end  1099  and a hot end  1098 . The variable phase control device  1010  may be any device having a variable inertance or flow resistance. The inertance and/or flow resistance of the device  1010  may be controllable. Examples of such devices are described below with reference to  FIGS. 11-13, 14A and 14B . A control circuit  1014  may control the inertance and/or flow resistance of the device  1010 . 
     The control circuit  1014  may be in communication with one or more sensors  1012  that may capture data indicative of the position of the cooler  1000  in its thermodynamic cycle. For example, the position of the compressor  1002  may track the position of the cooler  1000  in its thermodynamic cycle. Accordingly, the sensor  1012  may be positioned to sense the position of the compressor  1002 . For example, when the compressor  1002  is a piston-driven compressor, the sensor  1012  may track the position of the piston and/or a motor driving the piston. Also, for example, the sensor  1012  may sense the pressure at different positions of the compressor  1002  and, thereby, indirectly track the position of the compressor  1002 . According to various embodiments, the sensor  1012  may track the position of the cooler  1000  in its thermodynamic cycle in other ways. For example, the sensor  1012  may monitor the temperature, pressure and/or mass flow at different portions of the regenerator  1004 , pulse tube  1006  and/or reservoir  1008 . In operation, the control circuit  1014  may vary the resistance and/or inertance of the phase control device  1010  based on the position of the cooler  1000  in its thermodynamic cycle. For example, the control circuit  1014  may vary the resistance and/or inertance of the phase control device  1010  periodically based on a period of the thermodynamic cycle of the cooler  1000 . For example, the period of the phase control device  1010  may be equal to the period of the thermodynamic cycle of the cooler  1000 . Also, for example, in some embodiments, the period of the phase control device  1010  may be a multiple of the period of the thermodynamic cycle of the cooler  1000 . The multiple may be greater than or less than one. In various embodiments, the sensor  1012  may be omitted. The period of the thermodynamic cycle of the cooler  1000  may be known and the control circuit  1014  may drive the phase control device  1010  at a period equal to the known thermodynamic cycle of the cooler  1000 . The cooler  1000  may be calibrated so that any phase differences between the period of the phase control device  1010  and the cooler  100  may be reduced or eliminated. 
     The control circuit  1014  may comprise any suitable form of analog or digital control device or devices. According to various embodiments, the control circuit  1014  may comprise one or more digital processor with associated memory. The memory may comprise instructions that, when executed by the one or more digital processors, cause the control circuit  1014  to control the inertance and/or flow resistance of the phase control device  1010  as described herein. 
       FIG. 11  illustrates one embodiment of a variable inertance device  1100  that may be controlled by the control circuit  1014 . As illustrated, the device  1100  is positioned between and partially within the pulse tube  106  and the reservoir  108 . A spacer  1114  may be positioned between the reservoir  108  and the pulse tube  106 . A flange  1112  may be positioned at a transition between the pulse tube  106  and the spacer  1114 . A plunger  1102  may be positioned within the flange  1112 . The plunger  1102  and the flange  1112  may define a gap  1110  between them that may serve as an inertance gap. The size of the gap  1110  may change as the plunger  1102  moves in and out with respect to the flange  1112 . Accordingly, the inertance and flow resistance of the gap  1110  may vary depending on the position of the plunger  1102 . A linear motor  1108  may provide motive force to translate the plunger  1102  back and forth within the flange  1112  in the direction of arrow  1116  based on a control signal received from the control circuit  1014 .  FIG. 12  illustrates another embodiment of a variable inertance device  1200 . The device  1200  may operate in a manner similar to that of the device  1100  described above. Flange  1206  and plunger  1202  of the device  1200 , however, have shapes that narrow towards the pulse tube  106 , giving the device  1200  different flow resistance and inertance properties than the device  1100  for a given gap size. 
       FIG. 13  illustrates one embodiment of a variable inertance gap device  1300 . The device  1300  comprises a piston  1302  and a housing  1304  that collectively define an inertance gap  1306 . A motor  1308  (e.g., a linear motor) may drive the piston  1302  back and forth in the direction of the arrow  1310  based on a control signal received from the control circuit  1014 , thus alternately enlarging and contracting the inertance gap  1306 . The device  1300  is illustrated in cross section, such that working fluid would flow between the pulse tube  106  and the reservoir  108  through the gap  1306  in a direction into and out of the page. Accordingly, as the piston  1302  is moved to change the diameter of the gap  1306 , the inertance and resistance of the device  1300  may change. 
       FIG. 14A  illustrates one embodiment of a variable flow resistance device  1400  in a low resistance configuration. The device  1400  comprises a ring  1406  made up of shaped plates  1404  capable of sliding over one another and defining an orifice  1402 . The size of the orifice  1402  may define the flow resistance of the device, with larger orifice sizes corresponding to lower flow resistances.  FIG. 14B  shows the device  1400  in a higher flow resistance configuration. As illustrated, the plates  1404  have slid over one another causing the size of the orifice  1402  to be reduced. The device  1400  may be transitioned from the low flow resistance configuration shown in  FIG. 14A  to the high flow resistance configuration shown in  FIG. 14B  by any suitable mechanism based on a control signal received from the control circuit  1014 . For example, the device  1400  may operate in a manner similar to that of mechanical irises used in the optical arts. Motive force to change the diameter of the orifice  1402  may be provided by any suitable device including, for example, a stepper motor (not shown). 
     The pulse tube cooler  1000  was modeled using the SAGE software described above. Three configurations were modeled. In a first configuration, the phase control device  1010  was modeled as a fixed diameter (e.g., non-varying) orifice. The SAGE software package was utilized to optimize the fixed diameter based on the dimensions of the other components. In a second configuration, the phase control device  1010  was modeled as a fixed inertance tube. Again, the SAGE software package was utilized to optimize the fixed inertance based on the dimensions of the other components. In a third configuration, the phase control device  1010  was a variable diameter orifice device similar to the device  1400  shown in  FIG. 14 . The diameter of the orifice opening was varied with the stroke of the compressor.  FIG. 15  is a chart showing a plot  1500  of orifice diameter versus compressor stroke position that was used in the model. In all of the modeled configurations, the regenerator  1004  was 3.144 cm in length and 0.6185 cm in diameter. Also, in all of the modeled configurations, the pulse tube  1006  was 3.144 cm in length and 0.5396 cm in diameter. 
       FIG. 16  is a chart  1600  illustrating the results of the model. The chart  1600  shows cold tip temperature at the cold end  1099  of the pulse tube  1006  on the x-axis and cooling capacity in Watts on the y-axis. Curves  1604  and  1606  show the results of the fixed orifice configuration and the fixed inertance configuration, respectively. Curve  1602  shows the results of the variable orifice configuration. It can be seen that across the full range of tested cold tip temperatures, the cooling capacity of the variable orifice configuration was greater than that of either of the fixed configurations. Although the described model tested only a variable flow resistance configuration, it is believed that similarly positive results would be obtained by utilizing a variable inertance device including, for example, those described above with respect to  FIGS. 11-13 . 
     According to various embodiments, a flow resistance device network, such as the networks  208 ,  214  shown in  FIGS. 7 and 8  may comprise one or more variable phase control devices. The variable phase control devices may have a variable inertance and/or a variable flow resistance. The flow resistance and or inertance of the variable phase control devices may be varied periodically within the thermodynamic cycle of the pulse tube cooler, for example, as described above with reference to  FIG. 10 . 
     To decrease cold end temperature, it may be desirable to combine multiple pulse tube coolers into a multistage cooler.  FIG. 17  illustrates one embodiment of a multistage pulse tube cooler with two stages,  1701 ,  1703 . A compressor  1702  may comprise a piston  1706  and a cylinder  1706 . The first stage  1701  comprises a first stage regenerator  1708 , a first stage reservoir  1730  and a first stage pulse tube  1718  having a cold end  1720  and a hot end  1722 . The compressor  1702  and the first stage regenerator may be in fluid communication with one another, for example, via a tube  1701 . The pulse tube  1718  and reservoir  1730  are connected via a first stage phase control device  1728 , which may be a flow resistive orifice and/or an inertance device (e.g., tube or gap). The second stage  1703  may comprise a second stage regenerator  1710 , a second stage reservoir  1726  and a second stage pulse tube  1712 , which may have a hot end  1716  and a cold end  1714 . The cold end  1714  of the second stage pulse tube  1712  may be in fluid communication with the second stage regenerator  1710 , for example, via tube  1715 . The second stage pulse tube  1712  and the second stage reservoir  1726  may also be connected via a phase control device  1724 . The phase control device  1724 , like the device  1728 , may be a flow resistive orifice and/or an inertance tube or gap. The cold end  1720  of the first stage pulse tube  1718  is in fluid communication with the second stage regenerator  1710 . For example, in the embodiment shown in  FIG. 17 , the cold end  1720  of the first stage pulse tube  1718  is connected to the second stage regenerator via tubes  1721  and  1723 . Although only two stages are shown, it will be appreciated that coolers may be constructed with an arbitrary number of stages. 
     In the multistage cooler  1700  shown in  FIG. 17 , the phase control devices  1728  and/or  1724  may be configured as described above. For example, one or both of the phase control devices  1728 ,  1724  may comprise a network of flow resistive orifices and/or inertance devices. Also, for example, one or both of the phase control devices  1728 ,  1724  may comprise at least one flow resistive orifice and/or inertance device having a resistance and/or inertance that varies with time, for example, based on the thermodynamic cycle of the cooler  1700  as described above. It will be appreciated that when coolers having more than two stages are used, the respective phase control devices of the different phases may also comprise a network of devices and/or a variable device, as described. 
       FIG. 18  illustrates one embodiment of a multistage pulse tube cooler  1800  having control valves  1802 ,  1804  positioned between the respective pulse tubes  1712 ,  1718  and the reservoirs  1726 ,  1730 . The control valves  1802 ,  1804  may be any suitable type of valve or variable diameter orifice. For example, in various embodiments, one or both of the valves  1802 ,  1804  may be needle-type valves. As shown, the control valves  1802 ,  1804  are separated from the respective reservoirs  1730 ,  1726  via the phase control devices  1728 ,  1724 . It will be appreciated, however, that the positions of the phase control devices  1728 ,  1724  and the control valves  1804 ,  1802  may be reversed. According to various embodiments, tuning the control valves  1802 ,  1804  may affect the relative cooling loads of the stages  1701 ,  1703 . 
     The control valves  1802 ,  1804  may act as flow resistive orifices and/or inertance gaps. Accordingly, changing the positions of the valves  1802 ,  1804  may change the resistance and/or inertance between the pulse tubes  1718 ,  1712  and their respective reservoirs  1730 ,  1726 . As the relative resistance and/or inertance values for each of the stages  1701 ,  1703  changes, the relative cooling load between the stages  1701 ,  1703  may also change. Accordingly, optimizing the positions of the valves  1802 ,  1804  may also have the effect of optimizing the cooling load between the stages  1701 ,  1703 . 
       FIG. 19  illustrates one embodiment of a multistage pulse tube cooler  1900  having an inter-stage flow control device  1902  positioned between the pulse tubes  1708 ,  1710  of the stages  1701 ,  1703 . The flow control device  1902  may be any sort of valve, variable diameter orifice, inertance device, or combination there of. For example, the flow control device  1902  may be a needle valve. The flow control device  1902 , as shown, connects the cold end of the first stage pulse tube  1718  to the hot end of the second stage pulse tube  1712 . In this way, the flow control device  1902  may control and regulate fluid pressure exchange between the stages  1701 ,  1703 . In use, the flow control device  1902  may allow some of the pressure from the first stage  1701  to bleed into the second stage  1703 . In this way, modifying the properties of the flow control device  1902  may serve to shift the cooling load between the stages  1701 ,  1703 . The cooler  1900  is illustrated as including phase control devices  1802 ,  1803  between the respective pulse tubes  1718 ,  1712  and reservoirs  1730 ,  1726 . It will be appreciated, however, that some embodiments including the flow control device  1902  may omit one or both of the phase control devices  1802 ,  1804 . 
     The SAGE software package available from Gedeon Associates of Athens, Ohio was used to model the coolers  1700 ,  1800 ,  1900  shown in  FIGS. 17, 18 and 19 , respectively. According to the model, the first stage regenerator  1708  was 13.93 centimeters (cm) in length and 8.29 cm in diameter. The first stage pulse tube  1718  was 25.0 cm in length and 2.672 cm in diameter. The second stage regenerator  1710  was 3.224 cm in length and 4.0 cm in diameter. The second stage pulse tube was 10.0 cm in length and 1.609 cm in diameter. The positions of the various valves  1802 ,  1804 ,  1902  were optimized based on these dimensions by the SAGE software package. 
       FIG. 20  is a chart showing results of the SAGE software&#39;s model. Values on the x-axis represent the temperature at the cold end  1714  of the second stage pulse tube  1712 . Values on the y-axis represent the second stage cooling capacity. It can be seen that the cooler  1800  with the control valves  1802 ,  1804  (line  2004 ) exhibited greater cooling capacity than the multistage cooler  1700  (line  2002 ) across the full range of second stage temperatures. The cooler  1900  with the flow control device  1902  between the respective pulse tubes  1712 ,  1718  (line  2006 ) performed better still with a greater cooling capacity than either of the coolers  1700 ,  1800  over the whole modeled range of second stage temperatures. The advantage of the cooler  1900  was pronounced at lower second stage temperatures. 
     It is to be understood that the figures and descriptions of the present invention have been simplified to illustrate elements that are relevant for a clear understanding of the present invention, while eliminating other elements, for purposes of clarity. Those of ordinary skill in the art will recognize that these and other elements may be desirable. However, because such elements are well known in the art and because they do not facilitate a better understanding of the present invention, a discussion of such elements is not provided herein. 
     In general, it will be apparent to one of ordinary skill in the art that at least some of the embodiments described herein, such as those including the control circuit  1014 , may be implemented utilizing many different embodiments of software, firmware, and/or hardware. The software and firmware code may be executed by a computer or computing device comprising a processor (e.g., a DSP or any other similar processing circuit). The processor may be in communication with memory or another computer readable medium comprising the software code. The software code or specialized control hardware that may be used to implement embodiments is not limiting. For example, embodiments described herein may be implemented in computer software using any suitable computer software language type, using, for example, conventional or object-oriented techniques. Such software may be stored on any type of suitable computer-readable medium or media, such as, for example, a magnetic or optical storage medium. According to various embodiments, the software may be firmware stored at an EEPROM and/or other non-volatile memory associated with a DSP or other similar processing circuit. The operation and behavior of the embodiments may be described without specific reference to specific software code or specialized hardware components. The absence of such specific references is feasible, because it is clearly understood that artisans of ordinary skill would be able to design software and control hardware to implement the embodiments based on the present description with no more than reasonable effort and without undue experimentation. 
     In various embodiments disclosed herein, a single component may be replaced by multiple components and multiple components may be replaced by a single component to perform a given function or functions. Except where such substitution would not be operative, such substitution is within the intended scope of the embodiments. 
     While various embodiments have been described herein, it should be apparent that various modifications, alterations, and adaptations to those embodiments may occur to persons skilled in the art with attainment of at least some of the advantages. The disclosed embodiments are therefore intended to include all such modifications, alterations, and adaptations without departing from the scope of the embodiments as set forth herein.