Abstract:
In one embodiment according to the invention, there is provided a method for generating electrical energy using a thermal cycle of a working gas. The method comprises using the motion of a piston in a cylinder, containing the working gas performing the thermal cycle, to electromagnetically induce current in an electrical circuit coupled to the cylinder; using the electrical circuit to store the electrical energy, produced by the current induced in the electrical circuit, in an electrical storage device; and using the electrical energy stored in the electrical storage device to electromagnetically provide a motive force to the piston. Cyclically using the electrical circuit to store the electrical energy and using the stored energy to provide a motive force to the piston effect a net positive average power transfer into the electrical storage device over the course of the thermal cycle.

Description:
RELATED APPLICATION 
     This application is a divisional of U.S. application Ser. No. 11/338,421, filed Jan. 24, 2006, now U.S. Pat. No. 7,690,199, the entire teachings of which application are incorporated herein by reference. 
    
    
     BACKGROUND OF THE INVENTION 
     A thermal cycle of a heat engine that employs a quantity of gas as an operating medium can be described by reference to a pressure-volume (P-V) diagram.  FIGS. 1 and 2  show P-V diagrams for two well-known thermal cycles, the Carnot cycle ( FIG. 1 ), and the ideal Sterling cycle ( FIG. 2 ). 
     The net energy delivered from one thermal cycle is the area of the loop swept out by the operating path in the P-V plane. In the course of each cycle, energy is delivered by the engine for part of the cycle, and is absorbed by the engine for the remainder of the cycle. For some parts of some cycles, energy is neither stored nor delivered. For instance, in the ideal Sterling cycle, mechanical energy is neither absorbed nor delivered during those parts of the cycle where the trajectory is parallel to the P-axis. 
     By necessity, part of the system used for extracting a net positive average power output must include a device for storing and returning energy out of and into the heat engine, on a cyclic basis. In conventional heat engines, this cyclic energy storage is accomplished by mechanical means, for example via the rotational inertia of a crankshaft with flywheel attached. 
     SUMMARY OF THE INVENTION 
     It is desirable to be able to convert heat into electricity by means of a method in which the equipment is reliable, efficient, quiet, free of vibration, and capable of operating from a variety of fuels. 
     It is also desirable to be able to use electricity to effect heat transfer by means of equipment with such attributes. 
     To achieve these and other objectives, an embodiment of the invention provides a method for generating electrical energy using a thermal cycle of a working gas. The method comprises using the motion of a piston in a cylinder, containing the working gas performing the thermal cycle, to electromagnetically induce current in an electrical circuit coupled to the cylinder. The electrical circuit is used to store the electrical energy, produced by the current induced in the electrical circuit, in an electrical storage device; and the electrical energy stored in the electrical storage device is used to electromagnetically provide a motive force to the piston. Cyclically using the electrical circuit to store the electrical energy and using the stored energy to provide a motive force to the piston effect a net positive average power transfer into the electrical storage device over the course of the thermal cycle. 
     The electrical circuit may comprise an electronic power converter, and the method may further comprise using the electronic power converter to perform closed-loop electronic control of the motion of the piston. The electronic power converter may perform the closed-loop control based on electrical signals related to the state of the working gas. At least one of a temperature sensor, a pressure sensor, and a position sensor may be used to deliver the electrical signals related to the state of the working gas to the electronic power converter. 
     The thermal cycle may approximate a Sterling cycle, a Carnot cycle, an Otto cycle, or another thermal cycle. The thermal cycle may receive heat from external combustion, or the working gas may be cycled through an internal combustion cycle. 
     Compression and expansion of the working gas between a first piston and a second piston may be used to perform the thermal cycle. The electrical circuit may comprise a set of windings coupled to the cylinder, and the method may comprise using the motions of a first permanent magnet attached to the first piston and a second permanent magnet attached to the second piston to electromagnetically induce current in the set of windings. Further, the motions of the first piston and the second piston may be used to move the working gas along the cylinder to effect successive heat transfer with a heating zone and a cooling zone of the cylinder. 
     At least part of the shaft of the first piston may move concentrically within a shaft of the second piston. The electronic power converter may be used to control timing of the thermal cycle by controlling the motions of the first piston and the second piston; including by controlling the motions of the first piston and the second piston such that the working gas moves between a heating zone, a cooling zone, and a neutral zone of the cylinder. A thermal shade may be attached to the first piston or the second piston to insulate non-working gas within the cylinder; and a paddle may be attached to the first piston or the second piston to create turbulence in the working gas. An external flow return may be used to flow non-working gas between a first end zone and a second end zone of the cylinder. The first piston and the second piston may be mounted around a common centering shaft. 
     Two cylinders operating according to the invention may be operated in axial opposition to each other. Similarly, four cylinders may be operated in a bundle with parallel axes of the cylinders, two of the cylinders being operated antiparallel to the other two cylinders of the bundle. 
     In another embodiment according to the invention, there is provided a method for powering a heat pump using electrical energy, the heat pump performing a thermal cycle. The method comprises using electrical energy stored in an electrical storage device to electromagnetically provide a motive force to a piston in a cylinder containing the working gas performing the thermal cycle. The motion of the piston is used to electromagnetically induce current in an electrical circuit coupled to the cylinder; and the electrical circuit is used to store the electrical energy, produced by the current induced in the electrical circuit, in the electrical storage device. Cyclically using the stored energy to provide the motive force to the piston and using the electrical circuit to store the electrical energy effect a net positive average power transfer out of the electrical storage device over the course of the thermal cycle. Similar methods as those used with the method for generating electrical energy, above, may be used with the method for powering a heat pump. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       The foregoing and other objects, features and advantages of the invention will be apparent from the following more particular description of preferred embodiments of the invention, as illustrated in the accompanying drawings in which like reference characters refer to the same parts throughout the different views. The drawings are not necessarily to scale, emphasis instead being placed upon illustrating the principles of the invention. 
         FIG. 1  shows a pressure-volume diagram for a Carnot cycle, known in the art; 
         FIG. 2  shows a pressure-volume diagram for an ideal Sterling cycle, known in the art; 
         FIG. 3A  shows an arrangement of coils, magnets, and pistons for an external combustion cylinder according to an embodiment of the invention; 
         FIG. 3B  shows a separate view of a piston for the embodiment of  FIG. 3A ; 
         FIG. 4  is a schematic diagram of electrical components that are coupled to the external combustion cylinder arrangement of  FIGS. 3A-3B ; 
         FIG. 5A  illustrates an alternative embodiment that may be used in place of the mechanical arrangement of  FIG. 3A , in accordance with an embodiment of the invention; 
         FIGS. 5B and 5C  show separate views of pistons for the embodiment of  FIG. 5A ; 
         FIG. 6  is a timing diagram for the heat engines of  FIGS. 3A and 5A  when operated as electricity generators per the Sterling cycle depicted in  FIG. 2 , in accordance with an embodiment of the invention; 
         FIG. 7  is a P-V diagram for a Sterling cycle heat pump operated in accordance with an embodiment of the invention; 
         FIG. 8  is a timing diagram for the Sterling cycle heat pump of  FIG. 7 ; 
         FIG. 9  illustrates an alternative embodiment that may be used in place of the mechanical arrangements of  FIGS. 3A-3B  and  5 A- 5 C, in accordance with an embodiment of the invention; 
         FIG. 10  shows an axially opposed heat engine according to an embodiment of the invention; 
         FIGS. 11A and 11B  illustrate an arrangement of four of the cylinder assemblies of the type shown in  FIG. 5A  placed side-by-side with parallel central axes, according to an embodiment of the invention; 
         FIG. 12  is a timing diagram for the heat engines of  FIGS. 3A and 5A  when operated as electricity generators per the Carnot cycle depicted in  FIG. 1 , in accordance with an embodiment of the invention; 
         FIG. 13  is a cross-sectional view of a piston arrangement for an internal combustion generator, in accordance with an embodiment of the invention; 
         FIG. 14  is a timing diagram for an internal combustion generator, in accordance with an embodiment of the invention; and 
         FIG. 15  is a P-V diagram of an Otto cycle by which an internal combustion generator may be operated, in accordance with an embodiment of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
     Rotational inertia has been the method of choice for cyclic energy storage in heat engines since their development in the eighteenth century. Thus, the devices used for cyclically storing and returning energy out of and into the heat engine are typically mechanical. For example, an engine may use the rotational inertia of a crankshaft with flywheel attached for cyclical energy storage. In this way, conventional heat engines can be said to use mechanically-coupled thermal cycles. 
     However, in such a mechanically-coupled thermal cycle the motion of the pistons is constrained by the motion of the crankshaft. The pistons therefore cannot move in a manner that allows the state of the working gas to closely follow the desired P-V cycle. The relative amounts of time devoted to each segment of the cycle are fixed by the mechanical constraints on the motion of the flywheel. Moreover, mechanically-coupled heat engines are constrained in their reliability and efficiency, the amount of noise and vibration they generate, and their ability to operate from a variety of fuels. 
     In order to improve on these characteristics, an embodiment according to the invention uses an electricity storage device to accommodate the cyclic flow of energy from a thermal cycle. The thermal cycle can therefore be described as electrically-coupled. An embodiment uses direct electric drive of pistons by means of electromagnetic shear. 
     Electricity storage devices suitable for this application include, for example, capacitors, batteries, and (if available) superconducting coils. Direct electric drive using electromagnetic shear may be accomplished with the use of permanent magnets attached to each piston assembly, and with the use of controlled electric currents in coils or windings to provide force to, or electromagnetic induction from, the permanent magnets. 
     Embodiments of an electrically-coupled thermal cycle may be used for the generation of electricity from a thermal cycle, such as to charge a battery using the external or internal combustion of a gas; or for electrical powering of a thermal cycle, such as using a battery or other source of direct current to power a heat pump. 
     In accordance with the invention, power electronic circuits can be built which permit the motion of the pistons to be controlled so as to follow as closely as possible any desired path in the P-V plane. The necessary energy cycling required to extract average power from a heat engine can be effected via electrical energy storage. The use of electric coupling in this manner allows for variation of the amounts of time spent in each segment of a P-V cycle, thereby allowing for high thermal cycle efficiencies. 
     Therefore, by comparison with prior systems in which energy was cyclically stored mechanically, an embodiment according to the invention uses electrical storage of cyclical energy flow. In addition, use of electrical circuitry allows closed-loop electrical control of piston motion. 
     In the prior art, refrigeration devices are known that are driven by electronic linear drive motors, such as in U.S. Pat. No. 4,761,960 of Higham et al.; U.S. Pat. No. 4,697,113 of Young; and U.S. Pat. No. 5,040,372 of Higham. Further, such linear drive motors may be battery-powered, with the delivery of current from the battery being electrically controlled, as in U.S. Pat. No. 5,752,385 of Nelson and U.S. Pat. No. 4,434,617 of Walsh. Also, free-piston hydraulic engines are known, such as in U.S. Pat. No. 4,215,548 of Beremand. 
     However, an embodiment according to the present invention is fundamentally different from such previously known systems because it employs electrical storage of cyclical energy flows to and from the thermal cycle. Thus, within a thermal cycle, an embodiment according to the invention cycles energy into and out of an electrical storage device that is electrically coupled to a cylinder containing the piston. By contrast, such previously known systems did not use electrical storage of cyclical energy flow. Some such prior systems may instead use a form of mechanical resonance for cyclical energy flow. For example, in U.S. Pat. No. 4,434,617, a mechanical resonance is used between the mass of the piston and the compressed end-zone gas, which acts as a spring, for cyclical energy flow. Although a synchronized electrical drive is used to assist and maintain the mechanical resonance, the system does not use an electrical storage device to absorb the cyclical energy flow from the thermal cycle. Such systems therefore do not allow the potential improvements in thermal efficiency provided by using electrical storage of cyclical energy flows from a thermal cycle, and electronic control of the cyclical energy flows, according to an embodiment of the invention. 
     A description of preferred embodiments of the invention follows. 
       FIGS. 3A and 3B  show an arrangement of coils, magnets, and pistons for an external combustion generator according to an embodiment of the invention. In the cross-sectional view of  FIG. 3A , a closed gas containment cylinder  301  contains a body of gas, a portion of which becomes the working gas  302 . The working gas  302  is the subset of the total gas within the cylinder  301  that lies between two pistons  303  and  304 , which slide within the cylinder  301 . The pistons  303  and  304  maintain a tolerably good gas seal with the inner wall of the cylinder  301  without creating undue friction. Conventional piston rings, for example, may be employed for this purpose. The cylinder  301  will typically be of circular cross section, but may have other cross sectional shapes. The working gas  302  may be any gas suitable for the purpose, such as air, nitrogen, helium, or hydrogen. 
     As shown in  FIG. 3B , each of the two pistons  303  and  304  is in the form of a plate. Attached centrally and perpendicular to each plate  303  and  304  is a shaft  307  and  308  attached at its other end to a permanent magnet plate  305  and  306 . The permanent magnet plates  305  and  306  contain permanent magnets within them, suitably arranged, together with magnetic path material such as iron or a suitable grade of steel. The arrangement of the permanent magnets and magnetic path material is such as to produce magnetic flux emanating from the outer edges of the permanent magnet plates  305  and  306 , which cuts through the drive windings  309  and  310  surrounding the cylinder  301  ( FIG. 3A ). The cylinder  301  is made of nonmagnetic materials. A plurality of such materials may be employed to construct cylinder  301 . For example, a material such as aluminum may be used for regions such as  313  and  314 , where heat flow is required; and a material such as ceramic or fiberglass may be used for regions such as  317 , where heat flow is not required. Surrounding the drive windings  309  and  310  are magnetic field return paths  311  and  312  made of magnetic path material. 
     Also surrounding the cylinder  301  are two heat transfer zones  313  and  314  made of thermally conductive material such as copper or an aluminum alloy. A heating zone  313  accepts heat from an external heat source, for example a flame or solar collector, and transfers that heat into the working gas  302  at an appropriate time, as described below. Likewise, a cooling zone  314  extracts heat from the working gas  302  at an appropriate time, also described below. The heat transfer zones  313  and  314  are separated from each other by a thermally insulated neutral zone  317 . The three zones  313 ,  314 , and  317  are shown in the accompanying figures to be of comparable lengths, which is not necessarily required, but may be advantageous with regard to optimization of overall power output. 
       FIG. 4  is a schematic diagram of electrical components that are coupled to the external combustion cylinder arrangement of  FIGS. 3A-3B , in order to accommodate the cyclic flow of energy from the thermal cycle in accordance with an embodiment of the invention. Drive windings  409 ,  410 ,  443 , which are the drive windings depicted as  309 ,  310  of  FIG. 3A , connect to an electronic power converter  435 .  FIG. 4  shows three isolated windings  409 ,  410 ,  443  for illustrative convenience, but any number of separate windings may be employed, as necessary. Also connected to the electronic power converter  435  are signals from position sensors  436 , a temperature sensor  440 , and a pressure sensor  441 . It will be appreciated that any appropriate number of such position, temperature, and pressure sensors may be employed. The position sensors  436  give the electronic power converter  435  the information it needs to know the exact location of each piston at any instant in time. The temperature sensor  440  and pressure sensor  441  inform the electronic power converter  435  of the state of the working gas  302  at any instant. 
     Electronic power converter  435  is connected to a DC Bus  442 , to which is connected a capacitor  437  and/or a battery  438 , and an electric load  439 . The electric load  439  may be disconnected from the DC Bus  442  when not required, while the electronic power converter  435  continues to charge the battery  438 . Suitable batteries for battery  438  include lithium or other modern types of batteries configured for energy cycling applications, with better performance gained by lithium or other types of batteries capable of cycling energy at a rate of a few cycles per second or faster. 
     During operation of the system, the electronic power converter  435  of  FIG. 4  controls the flow of electric current into and out of the windings  309  and  310  of  FIG. 3A  such that pistons  303  and  304  move up and down within the cylinder  301  to cause the working gas  302  to follow a desired P-V cycle. The capacitor  437  and battery  438  act as the energy reservoir for the system, and absorb the cyclic energy variations which are integral to the cycles of heat engines. The electronic power converter  435  stores little or no energy, and transfers power between the DC Bus  442  and the windings  309  and  310  in a highly efficient manner. 
     In this way, the embodiment of  FIGS. 3A-4  provides an electrically-coupled external combustion generator. Energy released from external combustion is transferred into the cylinder  301  through heating zone  313 , a pressure-volume cycle is produced in working gas  302 , and cyclic energy storage is performed by the electrical circuitry of  FIG. 4 . In one application, for example, the external combustion of a gas may therefore be used to store electrical charge in battery  438  without using any moving parts other than the pistons  303  and  304 . 
       FIGS. 5A-5C  illustrate an alternative embodiment that may be used in place of the mechanical arrangement of  FIGS. 3A-3B , wherein the drive windings  509  and  510  are placed adjacent to each other and away from the heating zone  513 . By placing the permanent magnet plates  505  and  506  away from the heating zone  513 , this arrangement simplifies the design task of keeping the permanent magnets cool. Neodymium-iron permanent magnet material loses its magnetism when subjected to high temperatures, and is limited to working temperatures typically no higher than 150 to 200 C. As shown in  FIG. 5A , the shaft  507  of a longer piston assembly (shown separately in  FIG. 5B ) lies concentrically within the shaft  508  of a shorter piston assembly (shown separately in  FIG. 5C ). The mechanical fit between these two shafts  507  and  508  is such as to give a tolerably good gas seal between them without creating undue friction. The inner shaft  507 , which connects piston  503  to its permanent magnet plate  505 , is constructed to give minimal heat conduction from the hot upper end  503  to the permanent magnet plate  505  and to the shaft  508  surrounding it. This may be effected by using a thermally insulating material such as ceramic for shaft  507 , possibly with a metallic core for strength. The drive windings  509  for the longer piston assembly  503  are located further away from the cooling zone  514  than the drive windings  510  for the shorter piston assembly  504 . In  FIG. 5A  (unlike with plates  305  and  306  in  FIG. 3A ), permanent magnet plate  506  is located above permanent magnet plate  505 , because piston assembly  503  is longer than piston assembly  504 . The operation of the heat engine depicted in  FIG. 5A  is just as described above for the heat engine depicted in  FIG. 3A , with similar electrical coupling to circuitry such as that of  FIG. 4 . 
       FIG. 6  is a timing diagram for the heat engines of  FIGS. 3A and 5A  when operated as electricity generators per the Sterling cycle depicted in  FIG. 2 , in accordance with an embodiment of the invention. Curve  644  is the piston position profile for piston  303 ,  503 , and curve  645  is the piston position profile for piston  304 ,  504 , for a repeating cycle A-B-C-D-A. The piston positions are indicated by position levels  0  through  3  on the y-axis of  FIG. 6 , which correspond to cylinder positions indicated in  FIGS. 3A and 5A . The cooling zone  314 ,  514  extends from position level  0  to level  1  ; the neutral zone  317 ,  517  extends from position level  1  to level  2 ; and the heating zone  313 ,  513  extends from position level  2  to level  3 . Although  FIG. 6  shows the amount of time spent in each of the four segments of the thermal cycle as approximately equal, it is to be understood that the duration of each segment can be varied independently of the others, thereby allowing for power output variation and efficiency maximization. In varying the duration of the segments, there is an inherent conflict between the objectives of maximizing power output and maximizing efficiency; either objective can be satisfied, but not both simultaneously. 
     Between times A and B of  FIG. 6  the working gas  302 ,  502  is compressed at constant temperature T 1 . In the A-B path, piston  304 ,  504  is held at position Level  0  (shown on the y-axis of  FIG. 6 , and in  FIGS. 3A and 5A ) as shown by curve  645 , while piston  303 ,  503  is moved from position Level  2  to Level  1  as shown by curve  644 , thereby compressing the working gas  302 ,  502 . The motion  644  of piston  303 ,  503  for this segment is depicted as having a straight-line shape in  FIG. 6 , although in practice the motion will typically be nonlinear. 
     Between times B and C of  FIG. 6 , the working gas  302 ,  502  is held at constant volume and heated to temperature T 2 . In the B-C path, both pistons initially move quickly together such that piston  303 ,  503  is moved from position Level  1  to Level  3 , while piston  304 ,  504  is moved from position Level  0  to Level  2 , as indicated by curves  644  and  645 . For the duration of the B-C time segment, piston  304 ,  504  is held at position Level  2  (curve  645 ), and piston  303 ,  503  is held at position Level  3  (curve  644 ). 
     Between times C and D of  FIG. 6 , the working gas  302 ,  502  expands at constant temperature T 2 . In the C-D path, piston  303 ,  503  is held at position Level  3  (curve  644 ), while piston  304 ,  504  is moved from position Level  2  to Level  1  (curve  645 ). The motion of piston  304 ,  504  for this segment is depicted as having a straight-line shape in curve  645  of  FIG. 6 , although in practice the motion will typically be nonlinear. 
     Between times D and A of  FIG. 6 , the working gas  302 ,  502  is again held at constant volume and is cooled to temperature T 1 . In the D-A path, both pistons initially move quickly together such that piston  303 ,  503  is moved from position Level  3  to Level  2  (curve  644 ), while piston  304  is moved from position Level  1  to Level  0  (curve  645 ). For the duration of the D-A time segment, piston  304 ,  504  is held at position Level  0  (curve  645 ), and piston  303 ,  503  is held at position Level  2  (curve  644 ). 
     Examination of the timing diagram of  FIG. 6  shows that there are portions of the cycle wherein the pistons are stationary. These regions may afford an opportunity for efficiency improvement, whereby a mechanical means is used to hold each piston in its appointed place during a stationary portion of the cycle rather than relying on the flow of electric current in the drive windings, with its attendant ohmic losses. For instance, during the compression region A-B in  FIG. 6 , piston  304 ,  504  could be prevented from moving even lower than position Level  0  by a mechanical impediment. The state of pressure in the end zones  315 / 515 ,  316 / 516  will be a factor in the implementation of this technique, and the design of the end zones may need to be modified accordingly. 
     Such mechanical hard stops could, in principle, take the form of a mechanical barrier, or they may be effected by means of permanent magnets (and/or magnetic poles) attached rigidly either to the cylinder  301 ,  501  and/or to the piston assemblies. If a mechanical barrier is used, the power electronics can control the motion of the piston as it approaches the barrier so as to effect a “soft landing”. A soft, springy material attached to the barrier or to the piston may assist with ensuring a soft landing. Permanent magnets would have the advantage of maintaining a physical impediment to further motion, without the practical concerns of physical contact associated with mechanical barriers. The permanent magnets can be used either in the attraction mode or in the repulsion mode. If they are used in the attraction mode, the control electronics will need to provide an excess impulse of current in order to break the piston free from its magnetic confinement at the end of the stationary period. 
     Although a Sterling cycle has been described above, the general arrangement illustrated by  FIGS. 3A-5C  can be used for other types of thermal cycle, including one which approximates the Carnot cycle of  FIG. 1 . Such a Carnot Engine may operate, for example, via the timing diagram of  FIG. 12 , which applies to a physical arrangement in which the length of the neutral zone  317 ,  517  is three times that of the heating  313 ,  513  and cooling  314 ,  514  zones. In  FIG. 12 , curve  1244  is the piston position profile for piston  303 ,  503 , and curve  1245  is the piston position profile for piston  304 ,  504 , for a repeating cycle A-B-C-D-A. Because of the extended length of the neutral zone  317 ,  517 , the position levels are shown ranging from level  0  to level  5 , with the cooling zone  314 ,  514  extending from level  0  to level  1  , the neutral zone  317 ,  517  extending from level  1  to level  4 , and the heating zone  313 ,  513  extending from level  4  to level  5 . Time interval A-B corresponds to isothermal compression, interval B-C corresponds adiabatic compression, interval C-D corresponds to isothermal expansion, and interval D-A corresponds to adiabatic expansion. 
     While the embodiments of  FIGS. 3A-5C  have been described as generators, by which heat is converted to electricity, it is also possible to use an electrically-coupled thermal cycle in accordance with an embodiment of the invention to create an electrically-powered heat pump. In this case, the embodiments of  FIGS. 3A-5C  are essentially operated in reverse: energy stored in electrical circuitry such as that of  FIG. 4  is cycled in and out of a cylinder  301 ,  501  via windings  309 ,  509  and  310 ,  510 , so that the pistons  303 - 304  and  503 - 504  perform a heat pump cycle. Such a heat pump may be used to generate heat or to receive heat, which can be transferred to or from an external object through heating and cooling zones  313 - 314  and  513 - 514 . 
       FIG. 7  shows a P-V diagram for such a Sterling cycle heat pump (i.e., a refrigerator) operated in accordance with an embodiment of the invention. It can be seen that the path followed is that of  FIG. 2 , taken in reverse.  FIG. 8  gives the corresponding timing diagram, which can be understood by reference to the similar preceding explanation for  FIG. 6 . Curve  844  is the piston position profile for piston  303 ,  503 , and curve  845  is the piston position profile for piston  304 ,  504 , for a repeating cycle A-B-C-D-A. The piston positions are indicated by position levels  0  through  3  on the y-axis of  FIG. 8 , which correspond to cylinder positions indicated in  FIGS. 3A and 5A . The cooling zone  314 ,  514  extends from position level  0  to level  1  ; the neutral zone  317 ,  517  extends from position level  1  to level  2 ; and the heating zone  313 ,  513  extends from position level  2  to level  3 . 
       FIG. 9  shows an alternative embodiment that may be used in place of the mechanical arrangements of  FIGS. 3A-3B  and  5 A- 5 C. A centering shaft  921  is located centrally and within the shaft  907  of piston assembly  903 , which in turn is located within the shaft  908  of piston assembly  904 . Again, the mechanical fit between the shafts  921 ,  907 , and  908  is such as to give a tolerably good gas seal between them without creating undue friction. Centering shaft  921  holds both piston assemblies  903 ,  904  centered within the cylinder  901 , so that they do not cling to one side of the cylinder via magnetic attraction, thereby causing excess friction and compromised gas sealing. The centering shaft  921  therefore assists to improve system efficiency. 
     In an alternative embodiment according to the invention, portions of centering shaft  921  may be made of magnetic path material encircled by field coils, to create an electromagnet, thereby providing a means for the elimination of permanent magnets in the plates  305  and  306  of  FIG. 3A . For example, using field coils wound around each end of such a magnetic centering shaft  921 , two electromagnets may be created, to replace the functional role of permanent magnets in plates  305  and  306 . Plates  305  and  306  are then made of magnetic path material. 
     Returning to the embodiment of  FIG. 9 , thermal shades  922  can be fitted to, or made part of the pistons  903  and  904 . The function of these thermal shades  922  is to impede the flow of heat through the heating  913  and cooling  914  zones during appropriate portions of the heat cycle. The thermal shades  922  are made of thermally insulating material, and are located close to, but not in contact with, the inside walls of the cylinder  901 . The thermal shades  922  extend around the entire inner perimeter of the inside walls of the cylinder  901 . They impede the flow of heat via radiation, conduction, and convection into and out of the non-working gas within the cylinder  901 , thereby improving system efficiency. 
     An external flow return  923  is a tube allowing non-working gas to flow from the upper end zone  915  to the lower end zone  916  to permit pressure equalization, which may be necessary to improve system efficiency. An alternative means for achieving this pressure equalizing gas flow, not shown in  FIG. 9 , is to provide an internal flow return in the form of a passageway inside the centering shaft  921 , which then takes the form of a hollow tube. The volume of the upper end zone  915  and lower end zone  916  relative to the size of the working region (that is, the region between piston position levels  0  and  3 ) may need to be adequately large in order to maintain system efficiency, by eliminating the requirement for excessive forces to compress the gas in the end zones  915  and  916 . To this end, the external flow return  923  may include one or more expansion chambers (not shown in  FIG. 9 ) along its length. 
     In order to improve the rate of heat transfer through the walls of the heating zone  913  into the working gas  902 , paddles  924  may be attached to the pistons  903  and  904 . These paddles  924  stir the working gas  902  as the pistons  903  and  904  move relative to each other, thereby causing turbulence and motion of the working gas  902 , and helping improve system efficiency. The paddles  924  also improve the rate of heat transfer from the working gas  902  through the walls of the cooling zone  914 . The paddles  924  may have a variety of shapes, consistent with not making contact with each other or with the other piston. 
       FIGS. 10-11B  illustrate methods for reducing vibrations in a power conversion system according to an embodiment of the invention. In  FIG. 10 , two of the cylinder assemblies of the type shown in  FIG. 5A  (or any other cylinder assemblies according to the invention) are arranged so that their central axes are coincident and opposing. The motion of the pistons for the system of  FIG. 10  is controlled by their power conversion electronics such that the corresponding pistons move in synchronism in exactly equal and opposite movements. Thus, the two piston assemblies  1003 / 1005  move toward or away from each other at exactly the same speed, and likewise the two piston assemblies  1004  move toward (or away from) each other in synchronism. The upper end zone  1015  is common to both sides of the engine, while there is a separate lower end zone  1016  at each end. Such an arrangement may be referred as an engine with “horizontally opposed” cylinders; or more generally, “axially opposed” cylinders, since the common axis need not necessarily be horizontal. A horizontal placement may have advantages for arrangement of the flow of combustion gases past the heating zones. 
     In  FIGS. 11A and 11B , four of the cylinder assemblies of the type shown in  FIG. 5A  (or any other cylinder assemblies according to the invention) are placed side-by-side so that their central axes are parallel and arranged in a diamond pattern as viewed end-on (shown in  FIG. 11B ). The controlling power electronics ensures that the pistons in cylinders A and C move together in the same direction and in exact synchronism. The pistons in cylinders B and D also move together in the same direction and in exact synchronism, but in exactly the opposite direction to those in A and C, as indicated by the cross and dot vector notation of  FIG. 11B . In order to keep the heating zones in all four cylinders close together, the two pairs of cylinders may need to be displaced axially relative to each other rather than having their ends coplanar. 
     The methods described above can be extended to the implementation of an internal combustion generator, in accordance with an embodiment of the invention. In a similar fashion to that described for  FIGS. 3A-4 , the electrical arrangement of  FIG. 4  may be used to perform cyclical energy storage for a mechanical piston arrangement of an internal combustion cycle.  FIG. 13  is a cross-sectional view of one possible such mechanical arrangement, which can be seen to incorporate features already explained with reference to  FIGS. 3A ,  5 A, and  9 . In  FIG. 13 , two concentric piston assemblies  1303  and  1304  surround a centering shaft  1321  in a cylinder  1301 , as in  FIG. 9 . An arrangement corresponding to  FIG. 3A  could also be implemented, wherein the piston assemblies are physically separate, with or without a centering shaft. In  FIG. 13 , a fuel/air mixture is fed into the working gas region  1302  via an inlet valve and port  1332 , and an outlet valve and port  1333  allows for exhaust gas to be ejected. A spark plug  1331  is located at the upper end of the working gas region  1302 . The walls of the working gas region  1302  are thermally insulated, and are made strong enough to withstand the forces associated with ignition of the fuel/air mixture. Other features may be similar to those described above, including concentric shafts  1307  and  1308 , permanent magnet plates  1305  and  1306 , drive windings  1309  and  1310 , magnetic field return paths  1311  and  1312 , and end zones  1315  and  1316 . Exhaust port  1334  provides a means of escape for gas in region  1316 , so that excessive compression forces are not required to compress the gas in region  1316 . 
       FIG. 14  shows a timing diagram that the internal combustion generator of  FIG. 13  may follow while performing an Otto cycle shown in the P-V diagram of  FIG. 15 , in accordance with an embodiment of the invention. Curve  1444  is the piston position profile for piston  1303 , and curve  1445  is the piston position profile for piston  1304 , for a repeating cycle A-B-C-D-A. The piston positions are indicated by position levels  0  and  1  on the y-axis of  FIG. 14 , which correspond to cylinder positions indicated in  FIG. 13 . 
     Between times A and B of  FIGS. 14 and 15 , the inlet valve  1332  of  FIG. 13  is open, allowing a fuel/air mixture to be drawn into the working gas region  1302  as piston  1303  is moved from position Level  0  to Level  1  (curve  1444 ). During this segment, piston  1304  is held at position Level  0  (curve  1445 ). The motion of piston  1303  for this segment is depicted as having a straight-line shape (curve  1444 ), although in practice the motion may be nonlinear. 
     Between points B and C of  FIGS. 14 and 15 , the working gas  1302  is compressed as piston  1304  is moved from position Level  0  to Level  1  (curve  1445 ), while piston  1303  remains at Level  1  (curve  1444 ). At point C, spark plug  1331  initiates combustion of the working gas  1302 , at which time the pressure of the working gas  1302  jumps immediately to the higher level shown at C′ in the P-V diagram of  FIG. 15 . 
     Between points C and D of  FIGS. 14 and 15 , the working gas  1302  expands, exerting mechanical force on the pistons, and forcing piston  1304  downward (curve  1445 ) while piston  1303  remains at position Level  1  (curve  1444 ). Again, the motion of piston  1304  for this segment is depicted as having a straight-line shape, although in practice the motion may be nonlinear. At point D, exhaust valve  1333  is opened, at which time the pressure of the working gas  1302  falls immediately to the lower level shown at D′ in the P-V diagram. 
     Between points D and A of  FIGS. 14 and 15 , the exhaust valve  1333  remains open, and the burnt working gas  1302  is ejected as piston  1303  is moved from position Level  1  to Level  0  (curve  1444 ), while piston  1304  remains at Level  0  (curve  1445 ). 
     It can therefore be seen that embodiments according to the invention provide a variety of different possible ways of using electrical storage of the cyclical energy required by a thermal cycle, including external and internal combustion generators, and electrically-driven heat pumps. 
     While this invention has been particularly shown and described with references to preferred embodiments thereof, it will be understood by those skilled in the art that various changes in form and details may be made therein without departing from the scope of the invention encompassed by the appended claims.