referring to fig1 this embodiment of a thermoacoustically driven thermoacoustic refrigerator consists of two stack and heat exchanger assemblies contained in an acoustic resonator , that is effectively one half wavelength long , and contains pressurized inert gas . fig1 depicts a functional experimental apparatus . the resonator and pressure vessel 1 consists of a driver cylindrical tube 2 , having a diameter smaller than the driver stack tube 75 , and terminated by a driver large spherical volume 3 ; as well as refrigerator cylindrical tube 77 , having a diameter smaller than refrigerator stack tube 76 , and terminated by refrigerator large spherical volume 4 . the standing wave generated inside the resonator vessel is effectively one half of one wavelength , with the pan ( pressure antinode ) located at position 5 and the two van &# 39 ; s ( velocity antinode &# 39 ; s ) located at positions 6 and 7 . there are two stack and heat exchanger assemblies ; the thermoacoustic driver assembly 8 , and the thermoacoustic refrigerator assembly 9 , which are discussed in more detail below . the reasons for the diameter changes in the driver cylindrical tube portion 2 of the vessel are summarized as follows : the diameter of the driver stack tube 75 is reduced by the driver tube reducer 10 typically by a factor of 1 . 5 to 2 . this diameter change achieves two benefits compared to a constant diameter tube . first , the length of the resonator is reduced , for a given operating frequency , making the device more compact . second , the acoustic power dissipated at the internal walls of the tube is greatly reduced . the dissipation is reduced partially because the length is reduced . more detail is given in hofler u . s . pat . no . &# 39 ; 201 . the refrigerator tube reducer 11 coupled to the refrigerator stack assembly 76 serves the same function also . the shape of reducers 10 and 11 should have a gradual and smooth diameter change so as to avoid flow separation caused by relatively high acoustic velocities . typically , the diameter changes discussed in the previous paragraph are adjusted so as to minimize acoustic dissipation in the resonator and maximize the overall efficiency of the engine . a third possible benefit is that the diameters can be adjusted so as to minimize engine vibration and noise . the diameter ratio of tube 2 to tube 75 can be made significantly different than the tube 77 to tube 76 diameter ratio . resonator dissipation may be increased slightly , adversely impacting engine efficiency . but the net oscillatory gas momentum in tube 2 or tube 77 is very diameter dependent . if the diameter of tube 2 is made smaller , the gas momentum is reduced and the gas momentum can be made equal in magnitude , and opposite in direction , to that of tube 77 . by this means the gas momentum of the entire engine can be made to cancel , thereby reducing engine vibration and audible noise . the tube reducer at location 5 serves a different function . the object is to scale the overall power capacity of each of the two stack assemblies via their diameter . the independence of relative power capacity thus achieved is useful for purposes of efficiency optimization and / or improving the ease of engine start - up or limiting the hot temperature . since the diameter changes rather abruptly at a point where the acoustic velocity is very low and largely resistive in phase ( i . e . the acoustic velocity here is transferring acoustic power and is not involved in the reactive oscillatory energy ) the reactive acoustic velocity elsewhere in the resonator is not affected by this diameter change . this means that the relative acoustic velocity or pressure in the two stack assemblies is dependent primarily on the distance from the pan and nothing else . thus the power capacity of each stack assembly will scale with diameter . conversely , if the diameter change were to be made a location where the acoustic velocity is predominantly reactive , such as between the two stacks in fig . a from patent &# 39 ; 441 , then there would be a large change in acoustic velocity that would negate the desired power capacity change . finally , flow separation is unlikely at location 5 because of the low acoustic velocity . the tapered tube reducers 29 and 30 make the transitions to the spherical volumes 3 and 4 . since the acoustic velocity is very high at these transitions , flow separation and associated acoustic dissipation is likely . tapered reducers 29 and 30 are sometimes called &# 34 ; diffusers &# 34 ; and their function is to slow down the acoustic velocity at the junction to the spherical volumes and reduce the severity of the flow separation and amount of acoustic dissipation . to discuss the stack and heat exchanger assemblies of fig1 we now refer to the enlarged view of the central portion of this engine shown in fig2 . the driver and refrigerator assemblies 8 and 9 are comprised of driver thermoacoustic stack 12 and refrigerator thermoacoustic stack 13 and two heat exchangers for each stack , one adjacent to each end of the stack . the driver thermoacoustic stack 12 consists of many wire mesh disks stacked up to make a porous cylindrical plug . the wire is typically stainless steel . the point contacts between wires of two adjacent mesh disks greatly reduces the conductive heat flow down the temperature gradient in the stack . this is the same arrangement as in a typical stirling engine regenerator , except that the spacing between wires in a disk is about a factor of 10 larger than for a regenerator , so that the thermodynamic processes in the stack are thermoacoustic and not isothermal , as in a stirling cycle . the stack could also be fabricated from a spiral roll of stainless steel foil with gaps between adjacent layers . the gaps would be oriented parallel to the acoustic flow . the steel foil would have a substantially large amount of thermal conduction heat flow reducing the driver &# 39 ; s efficiency . the refrigerator thermoacoustic stack 13 is fabricated from a spiral roll of plastic film with gaps between adjacent layers , as in patent &# 39 ; 201 . the plastic film has low thermal conductivity compared to stainless steel . this stack could also be fabricated in the same manner as the driver stack 12 . at each end of both stacks are heat exchangers . a fine scale metal finned structure is located immediately adjacent to each stack end . the fins are made by pairing a copper or nickel ribbon with an aluminum ribbon and winding the pair in a spiral with adhesive , thereby forming a pancake disk . the disk is mounted and a heavy layer of copper or nickel is electroplated on one face of the disk . the plated layer is milled exposing the ribbon except for radial ribs bonded to the ribbon edges . the aluminum ribbon is dissolved with acid which opens the gaps between the layers of ribbon which is held in place by the radial ribs . in fig2 the fine finned components are items 14 , 15 , 16 , and 17 . the radial ribs holding the fins in alignment are items 18 , 19 , 20 , and 21 . a plan view of one heat exchanger is shown in fig3 with 32 radial ribs 18 . the fine scale fins are not shown in fig3 but would cover the top of ribs 18 . the spacing between adjacent heat exchanger fins is typically 1 / 2 to 3 / 4 the size of the gaps or pores in stacks 12 and 13 . the smaller spacing allows the height of the fins ( i . e . width of ribbon ) to be very short , while maintaining good thermal contact with the gas . reducing the finned surface area improves engine efficiency . given the high heat power density of the engine and the small volume of fin material , it is very easy to thermally overload the heat conductance of the fins . for this reason , materials that are more exotic than copper may be desirable . ribbon made of highly - oriented - pyrolytic - graphite can have a thermal conductivity 2 or 3 times that of copper . for applications requiring very small engines , deposition of synthetic diamond or sapphire on a metal ribbon substrate would produce enhanced thermal conductance . in fig3 the group of 32 radial ribs 18 are soldered or brazed onto the group of 7 tubes 22 that are the heat source or sink to regions external to the resonator vessel . these tubes can carry pumped water or anti - freeze , or they can be part of a heat pipe or thermal siphon ( a gravity assisted heat pipe ). they can also have electrical heater cartridges inserted into them as a heat source , or they could carry air / fuel combustion gases as a heat source . in fig2 the fluid carrying tubes are groups 22 , 23 , and 24 ; and the tubes 25 have heater cartridges inserted into them . tube group 22 is also shown in fig3 . the tubes in each fluid carrying group are oriented parallel to one another and are coupled to external inlet and outlet manifolds ( not shown ). typically , the flow resistances of the tubes are plumbed in parallel by the manifolds . the heater cartridge tubes in group 25 are oriented radially , and are co - aligned with the plated radial ribs . these four heat exchanger units are organized thermally as follows : note that the term heat sink or source is in reference to the internal heat loading of the stack , not the external loading . items 14 , 18 , and 22 are the driver &# 39 ; s ambient temperature heat sink . items 15 , 19 , and 25 are the driver &# 39 ; s hot ( typically 400 ° c .) heat source . items 16 , 20 , and 23 are the refrigerator &# 39 ; s ambient temperature ( typically 35 ° c .) heat sink . and items 17 , 21 , and 24 are the refrigerator &# 39 ; s cold ( typically - 5 ° c .) heat source . heat can be carried convectively from the hot exchanger components 15 , 19 , and 25 to the refrigerator &# 39 ; s ambient exchanger components 16 , 20 , and 23 . thin porous disks 26 and 27 help prevent this convective heat transport without dissipating any significant amount of acoustic energy . the disks also help reduce radiative heat transfer from the hot exchanger components . the location of the two disks is very near , and on either side of , the pan . since disks 26 and 27 will be moderately hot , they are typically comprised of one or a few sheets of stainless steel wire mesh . the wire size and spacing is roughly half that of the material used in either of the stacks 12 or 13 . since the driving impedance for the convective steady flow is very low , and the driving impedance for the acoustic flow is very high at this location , the flow impedance of the disks should be moderately high . the position of the pan 5 , relative to the two stacks is very critical for achieving the desired thermoacoustic performance from the engine . if the pan is too close to the driver stack , the engine will not oscillate . if the pan is too far from the driver stack , the efficiency will be poor . for this reason , it is desirable to dynamically adjust the position of the pan while the engine is operating , by some means . however , another even more important reason exists for dynamically adjusting the pan position . getting the engine started is usually difficult . prior to start - up , the cooler stack has no temperature gradient and is at ambient temperature . in this state , the potential acoustic load represented by the cooler stack is much larger than when it is cold . (&# 34 ; potential &# 34 ; refers to acoustic behavior prior to the existence of the wave .) if the cooler &# 39 ; s potential acoustic power load is larger than the potential power output of the driver , the engine will not start . once the engine has been running and the cooler stack is cold , its relative power load is much reduced . one solution is to greatly increase the driver &# 39 ; s hot heat exchanger temperature for start - up conditions . this is undesirable because of possible melt - down problems or the requirement for expensive ultra - high temperature materials . a better solution is to shift the position of the pan away from the driver stack . the downward shift of the pan in fig1 will make the driver stack generate more potential acoustic power and the cooler stack potentially dissipate less power and cause the acoustic oscillations to start . a very simple means of adjusting the position of the pan is an electrical heater tape 28 wound around a portion of the resonator vessel on the driver side , where the acoustic velocity is high . any controllable heat source could be used instead of an electrical heater . by increasing the temperature of the tube in this region , the location of the pan is shifted downward in fig1 . a small amount electricity or heat is wasted , but no moving parts are added . other acoustical geometries and packaging schemes can be used to make the cooling engine more efficient and / or more compact . fig4 is a schematic drawing of a heat driven cooling engine having two driver assemblies 31 and 32 and two refrigerator assemblies 33 and 34 in a toroidal resonator 35 that has an acoustic path length of exactly one acoustic wavelength . a driver / cooler pair of assemblies such as 31 and 33 is identical to the configuration shown in fig2 in both appearance and function . the standing wave is oriented in the resonator so that two pan &# 39 ; s exist at positions 36 and 37 , and two van &# 39 ; s exist at positions 38 and 39 . the advantage of this embodiment is that the engine is more compact because the bulky spherical volumes have been eliminated and because of the folded shape of the two u - tubes . also , the resonator dissipates less acoustic energy , improving the engine efficiency . residential air conditioning units having multi - ton cooling capacities can be built utilizing this embodiment , and result in a unit size that is almost as small as traditional vapor - compression machines . the disadvantage of this embodiment is that fabrication costs are increased because double the number of stack and heat exchanger components are required . yet another embodiment is shown in fig5 . this variation replaces the large spherical volumes 3 and 4 of fig1 with large elongated volumes 40 and 41 . the &# 34 ; folding &# 34 ; achieved by making the main resonator tube 46 reentrant with volumes 40 and 41 , in combination with their elongated shape , makes the engine considerably more compact . internal plate 42 and hemisphere 43 form a gas tight seal separating volumes 40 and 41 from volume 45 . while volumes 40 and 41 are acoustically active volumes , volume 45 is not . volume 45 contains a pressurized inert gas with good thermal insulating properties and is packed with fibrous insulating material . while the acoustically active resonator typically contains helium gas or helium mixtures having high thermal conductivity , the insulating gas in volume 45 is typically argon or krypton at approximately the same pressure as the helium . the presence of pressurized volume 45 provides continuity of the whole external pressure vessel 47 . while vessel 47 must be strong enough to contain the gas pressure , internal resonator tube 46 can be made with thin walls , even where the high temperatures exist . not only does the insulating gas of volume 45 provide direct insulating value , but the thin internal construction further reduces thermal conduction between the heat exchangers . also , the inert insulating gas in volume 45 helps prevent oxidation of hot internal heat exchanger components . finally , vessel 47 is near ambient temperature over its entirety , so its strength is not compromised by the hot heat exchanger temperature . internal plate 44 separates volume 45 into two portions . plate 44 prevents gross gas flow between the two portions while allowing a slight leakage between portions for pressure equalization . the function of plate 44 is to further improve the quality of thermal insulation around the cold portion of the refrigerator , especially with respect to the hot heat exchanger of the driver . the engine shown in fig5 can be folded yet again in the middle at the pan , where the acoustic velocity is small , as shown in fig6 . in addition to further improving the compactness of the engine , this modification exposes the hot face of the driver stack 83 to a focused solar radiation 80 heat source . the focused sunlight 80 passes through two transparent windows 81 into the pressurized acoustic space and impinges on the stack face 83 . note that no heat exchanger fins are required at face 83 . if the stack material is sufficiently optically opaque and absorptive , the light is directly converted to heat where the heat is required . transparent windows 81 can be made from a high temperature material such as fused quartz . the inner hot window has an equalized mean pressure on both sides to prevent creep flow of the window . the cooler outer window is insulated by the inner window and sustains the force of the internal mean pressure . connecting tube 82 couples the acoustic power generated by the driver to the refrigerator . the pan is located in tube 82 . the heat driven thermoacoustic motor of this invention can also be used for the purpose of generating electricity . a cross section of the first embodiment of the heat powered generator is shown in fig7 . the essence of this acoustic motor - generator is to couple the heat powered acoustic motor from the top half of fig1 to a linear oscillating variable reluctance generator . the thermoacoustic driver , consisting of stack and exchanger assembly 8 and resonator components , causes acoustic power to flow toward the pan at location 5 . the usual porous disks 26 and 27 are included to reduce the heat leak from the hot heat exchanger . below the pan is a linear oscillating piston assembly 49 consisting of two large diameter low - mass pistons 50 and 51 connected together by rod 52 which is also connected to cylindrical plug 53 . the material used for items 50 , 51 and 52 could be aluminum . cylindrical plug 53 is made of a high permeability magnetic material such as laminated iron sheets or ferrite ceramic . cylindrical plug 53 is part of a magnetic circuit formed by permanent magnet 55 and magnetic core 54 . the permanent magnet is a ceramic magnet or rare earth magnet , and the high permeability core is laminated iron . cooling water flowing in tube 58 is coupled thermally to thermally conductive porous disk 59 . disk 59 is a low heat power exchanger with low gas flow impedance . the object of disk 59 and cooling tube 58 is to prevent the generator piston assembly and magnetic components from becoming too hot . section b - b &# 39 ; of the fig7 is shown in fig8 and shows the magnetic circuit in more detail . cylindrical plug 53 moves into and out - of the plane of fig8 either interrupting the magnetic circuit of 54 and 55 , or completing the circuit in the middle position . if the plug completes the circuit , the field in core 54 is high , and if the circuit is interrupted , the field in core 54 is low . conducting coils 56 and 57 will generate a current in response to the varying magnetic flux in core 54 . while the direction of the flux in core 54 does not change , the flux magnitude does oscillate greatly . since the magnetic circuit is interrupted twice for each cycle of motion , the electrical frequency is twice the frequency of motion for plug 53 . the clearance between pistons 50 and 51 and their respective bores is sufficiently small such that the gas blow - by is negligible or modest at the acoustic frequencies . the clearance around pistons 50 and 51 is either maintained by the air - bearing effect of the gas blow - by , or by a flexible suspension not shown . the clearance between plug 53 and its bore need not block gas flow , but should be small enough to effectively complete the magnetic circuit . also , the cylinder 61 surrounding plug 53 should either be thin enough to not interrupt the magnetic circuit , or it should have enough magnetic permeability to not interrupt the circuit . below the bottom of the piston assembly in fig7 is a small volume 60 . volume 60 terminates and seals the pressurized vessel and together with piston 51 forms a gas compliance having a modest stiffness . the moving piston assembly has a mass and experiences a restoring force stiffness arising from several sources . the contributions to the restoring force stiffness are from : the gas stiffness of volume 60 acting on piston 51 , the magnetic force between 53 and 54 , the acoustic stiffness representing the reactive part of the standing wave acting on piston 50 , and any additional explicit spring or suspension ( not shown ) used to align the piston assembly . the mechanical reactance of all of these stiffness values should exactly cancel the reactance of the moving mass at the operating frequency . with the reactances being canceled , the resistive component of the standing wave acting on piston 50 then supplies the force required to power the magnetic forces in the generator . the object of pistons 50 and 51 having a large diameter and iron plug 53 having a small diameter , is to maintain a reasonably high operating frequency . the larger piston areas for 50 and 51 increase the effective acoustic stiffness on the assembly , and smaller sizes for plug 53 reduce mass . if the operating frequency is allowed to drop too low , then the length of the resonator vessel above stack and exchanger assembly 8 will become excessively large . fig9 shows another embodiment of the heat powered electricity generator . gas volumes 3 and 60 of fig7 have been eliminated and two stack and exchanger assemblies are combined with one variable reluctance generator . compactness and power density of the entire unit is improved as is efficiency , though construction costs are increased . the resonator vessel 70 of fig9 is similar to the toroidal vessel of fig4 . the standing wave is oriented in the resonator such that pan &# 39 ; s exist at locations 71 and 72 with a van located at 73 . thus the region of the vessel from 71 to 72 including 73 contains exactly one half of one wavelength . this means that region from 71 to 72 including the variable reluctance piston assembly appears to be effectively one half of one wavelength also . this is consistent with the piston assembly having a net mechanical reactance that is mass - like at the operating frequency , and represents an effective impedance change that is equivalent to 35 % to 40 % of a wavelength . finally , the electricity generator of fig7 and 9 need not be a variable reluctance generator . any electricity generating scheme incorporating a linear oscillating piston is possible . a good example is the moving magnet arrangement patented by sun power corp ., ( redlich , u . s . pat . no . &# 39 ; 174 ( above )). the moving magnet generator has better power density , but the magnetic core arrangement is more complicated and expensive . obviously many modifications and variations of the present invention are possible in light of the above teachings . it is , therefore , to be understood that the present invention may be practiced within the scope of the following claims other than as specifically described .