Abstract:
In accordance with an embodiment of the invention, there is provided a device for generating electrical energy using a thermal cycle of a working gas. The device comprises at least one piston movably mounted in a container to form a working chamber between the at least one piston and the container, the working chamber containing the working gas performing the thermal cycle. An electrical circuit is mounted stationary relative to the container, the electrical circuit being electromagnetically coupled to provide a motive force to the at least one piston. An electronic power converter is electrically connected to the electrical circuit and to an electrical bus, and an electrical storage device is electrically connected to the electrical bus. The at least one piston is movably mounted such that its motion electromagnetically induces current in the electrical circuit. An electronic controller is electronically connected to the electronic power converter to control motion of the at least one piston to perform, in the thermal cycle, at least one of: (i) expanding the working gas beyond the volume at which compression of the working gas is begun within the thermal cycle or (ii) exhausting the working gas to a remaining volume less than the smallest volume of compressed gas within the thermal cycle. The electronic controller further controls flow of electrical energy to and from the electrical bus to effect a net positive average power transfer from the working gas to the electrical bus over the course of the thermal cycle.

Description:
RELATED APPLICATIONS 
       [0001]    This application is a divisional of Ser. No. 13/009,252 filed Jan. 19, 2011 which claims the benefit of U.S. Provisional Application No. 61/311,479, filed on Mar. 8, 2010, Attorney Docket No. 3129.1001-001, and claims the benefit of U.S. Provisional Application No. 61/296,140, filed on Jan. 19, 2010, Attorney Docket No. 3129.1001-000. The entire teachings of the above applications are incorporated herein by reference. 
     
    
     BACKGROUND OF THE INVENTION 
       [0002]    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. 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. 
         [0003]    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. 
         [0004]    By contrast with such conventional heat engines that use mechanical means for cyclic energy storage, U.S. Pat. No. 7,690,199 B2 of Wood, entitled “System and Method for Electrically-Coupled Thermal Cycle,” the disclosure of which is incorporated herein by reference in its entirety, describes an electrically-coupled thermal cycle. 
         [0005]    There is an ongoing need to produce fuel efficient engines, vehicles and thermal cycles. 
       SUMMARY OF THE INVENTION 
       [0006]    In accordance with an embodiment of the invention, there is provided a device for generating electrical energy using a thermal cycle of a working gas. The device comprises at least one piston movably mounted in a container to form a working chamber between the at least one piston and the container, the working chamber containing the working gas performing the thermal cycle. An electrical circuit is mounted stationary relative to the container, the electrical circuit being electromagnetically coupled to provide a motive force to the at least one piston. An electronic power converter is electrically connected to the electrical circuit and to an electrical bus, and an electrical storage device is electrically connected to the electrical bus. The at least one piston is movably mounted such that its motion electromagnetically induces current in the electrical circuit. An electronic controller is electronically connected to the electronic power converter to control motion of the at least one piston to perform, in the thermal cycle, at least one of: (i) expanding the working gas beyond the volume at which compression of the working gas is begun within the thermal cycle or (ii) exhausting the working gas to a remaining volume less than the smallest volume of compressed gas within the thermal cycle. The electronic controller is further electronically connected to the electrical bus to control both (i) flow of electrical energy produced by the current induced in the electrical circuit to the electrical bus, and (ii) flow of electrical energy from the electrical bus to the electrical circuit to electromagnetically provide the motive force to the at least one piston, and to effect a net positive average power transfer from the working gas to the electrical bus over the course of the thermal cycle. 
         [0007]    In further, related embodiments, the device may comprise a combustion device to combust the working gas in the thermal cycle. The device may comprise at least one orifice to effect intake and exhaustion of the working gas from the container, the thermal cycle comprising combustion of the working gas; or the device may comprise at least one orifice to effect intake and exhaustion of the working gas from the container without combustion of the working gas in the thermal cycle. The working gas may be air. An exterior surface of the container may be configured to conduct heat energy to the working gas. The at least one piston may comprise two pistons sharing a common working chamber. The two pistons may be in axial opposition to each other. The electronic controller may be configured to control motion of the pistons in the container to perform, in the thermal cycle, expansion of the working gas during motion of the pistons away from each other, and at least one of: (i) exhaustion of the working gas during motion of both pistons in the same direction relative to the container or (ii) exhaustion of the working gas while one piston is held at or near a fixed position relative to the container. The electronic controller may comprise a binary counter with a state corresponding to each stroke of the thermal cycle, the strokes of the thermal cycle comprising induction, compression, expansion, and exhaustion. 
         [0008]    In further, related embodiments, the electronic controller may be configured to control the at least one piston to perform a thermal cycle comprising strokes of induction, compression, expansion and exhaustion, and a duration of any one of the thermal cycle strokes of induction, compression, expansion, and exhaustion may differ from the duration of any of the other said strokes. A distance traversed by the at least one piston relative to the container in any one of the strokes of induction, compression, expansion, and exhaustion may differ from a distance traversed by the at least one piston relative to the container during any of the other strokes. The electronic controller may be configured to control the at least one piston to perform more than one thermal cycle, and a duration of any one complete thermal cycle may differ from a duration of any other complete thermal cycle, of the more than one thermal cycle. The working chamber may comprise a single orifice for the intake and exhaustion of working gas. The single orifice may intake from, and exhaust to, ambient air. The thermal cycle may comprise combustion of the working gas, or may be without combustion of the working gas. 
         [0009]    In other, related embodiments, the at least one piston may be entirely contained within the container. A mechanical support rigidly attached to the container may intrude into the at least one piston. The support may comprise a heat pipe for the transport of heat out of the container. The working chamber may comprise an orifice device for the intake or exhaustion of the working gas, said orifice device comprising an orifice device container, an orifice device piston and an orifice device electrical circuit, said orifice device electrical circuit being electromagnetically coupled to provide a motive force to the orifice device piston, and said orifice device piston being magnetically held in either of two positions within the orifice device container in the absence of electric current in the orifice device electrical circuit. The container and the at least one piston may each comprise a permanent magnet, the permanent magnet of the container and the permanent magnet of the at least one piston being mounted to be mutually repulsive. The container and the at least one piston may be mounted such that the weight of the at least one piston opposes a motion of expansion during the thermal cycle. The at least one piston may comprise an orifice for the intake or exhaustion of the working gas into or out of the working chamber. The container may comprise at least one orifice for the intake or exhaustion of the working gas into or out of the working chamber, said at least one orifice being shielded from the working chamber by the at least one piston for a portion of the thermal cycle. The container may comprise at least one magnetically-permeable spiral element electromagnetically coupled to the electrical circuit. 
         [0010]    In further, related embodiments, an expansion ratio of the working gas may be related to a compression ratio of the working gas only by a temperature rise ratio and an adiabatic constant, the temperature rise ratio being an inherent chemical property of the working gas and being equal to the highest absolute temperature achieved by the working gas in the thermal cycle divided by the absolute temperature of the working gas at the end of the compression stroke of the thermal cycle. The relation of the expansion ratio to the compression ratio may be given by: 
         [0000]    
       
      
       E/K=τ 
       1/γ 
      
     
         [0011]    where E is the expansion ratio, K is the compression ratio, γ is the adiabatic constant and τ is the temperature rise ratio. A ratio of exhaust gas absolute temperature of the working gas to inlet gas absolute temperature of the working gas may depend only on a temperature rise ratio and on a value of an adiabatic constant, the temperature rise ratio being an inherent chemical property of the working gas and being equal to the highest absolute temperature achieved by the working gas in the thermal cycle divided by the absolute temperature of the working gas at the end of the compression stroke of the thermal cycle. The ratio of exhaust gas absolute temperature to inlet gas absolute temperature may be given by: 
         [0000]        T   E   /T   I =τ 1/γ 
 
         [0012]    where T E  is the exhaust gas absolute temperature, T 1  is the inlet gas absolute temperature, γ is the adiabatic constant and τ is the temperature rise ratio. Efficiency of the device may be a function only of a temperature rise ratio, a value of an adiabatic constant and a compression ratio of the working gas, the temperature rise ratio being an inherent chemical property of the working gas and being equal to the highest absolute temperature achieved by the working gas in the thermal cycle divided by the absolute temperature of the working gas at the end of the compression stroke of the thermal cycle. Efficiency of the device may be given by the relation: 
         [0000]      η=1−[γ(τ (1/γ) −1)/( K   (γ-1) (τ−1)]
 
         [0013]    where η is efficiency, γ is the adiabatic constant, τ is the temperature rise ratio and K is the compression ratio of the working gas. 
         [0014]    In further, related embodiments, the device may be capable of operating on a variety of different fuels. The device may be capable of operating on a fuel from the group consisting of: methanol, ethanol, propanol, benzene, octane, hydrogen and ammonia. The device may be capable of operating on a fuel that does not include carbon, such as hydrogen or ammonia. The electrical storage device may comprise at least one of a capacitor and a battery. The container may comprise a cylinder. The electronic controller may be electronically connected to the electronic power converter to control motion of the at least one piston to perform, in the thermal cycle, both: (i) expanding the working gas beyond the volume at which compression of the working gas is begun within the thermal cycle and (ii) exhausting the working gas to a remaining volume less than the smallest volume of compressed gas within the thermal cycle. The electronic controller may be configured to control the at least one piston to perform more than one thermal cycle, wherein an energy output of any one complete thermal cycle differs from an energy output of any other complete thermal cycle, of the more than one thermal cycle. The electronic controller may be electronically connected to the electronic power converter to control motion of the at least one piston to perform, in the thermal cycle: an induction stroke wherein working gas flows into the container during a motion of the at least one piston, an adiabatic compression stroke wherein the volume of the working gas is reduced during a motion of the at least one piston, a heating period wherein the temperature of the working gas rises, an adiabatic expansion stroke wherein the volume of the working gas is increased during a motion of the at least one piston beyond the volume at which compression of the working gas is begun within the thermal cycle, and an exhaustion stroke wherein the volume of the working gas is expelled from the container during a motion of the at least one piston to a remaining volume less than the smallest volume of compressed gas within the thermal cycle. 
         [0015]    In further related embodiments, the electronic controller may be electronically connected to the electronic power converter to control motion of the at least one piston to perform, in the thermal cycle, at least one of: (i) expanding the working gas to atmospheric pressure or (ii) exhausting the working gas to a remaining volume that is less than the smallest volume of compressed gas within the thermal cycle and that is as small as practicable. The electronic controller may be electronically connected to the electronic power converter to control motion of the at least one piston to perform, in the thermal cycle, both: (i) expanding the working gas to atmospheric pressure and (ii) exhausting the working gas to a remaining volume that is less than the smallest volume of compressed gas within the thermal cycle and that is as small as practicable. 
         [0016]    In another embodiment according to the invention, there is provided a device for pumping heat using electrical energy, the pumping of heat comprising performing a thermal cycle of a working gas. The device comprises at least one piston movably mounted in a container to form a working chamber between the at least one piston and the container, the working chamber containing the working gas performing the thermal cycle. An electrical circuit is mounted stationary relative to the container, the electrical circuit being electromagnetically coupled to provide a motive force to the at least one piston. An electronic power converter is electrically connected to the electrical circuit and to an electrical bus; and an electrical storage device is electrically connected to the electrical bus. The at least one piston is movably mounted such that its motion electromagnetically induces current in the electrical circuit. An electronic controller is electronically connected to the electronic power converter to control motion of the at least one piston to perform, in the thermal cycle, at least one of: (i) compressing the working gas over a volume greater than the volume through which the working gas is expanded within the thermal cycle or (ii) exhausting the working gas to a remaining volume less than the smallest volume of compressed gas within the thermal cycle. The electronic controller is further electronically connected to the electrical bus to control both (i) flow of electrical energy produced by the current induced in the electrical circuit to the electrical bus, and (ii) flow of electrical energy from the electrical bus to the electrical circuit to electromagnetically provide the motive force to the at least one piston, and to effect a net positive average power transfer from the electrical bus to the working gas over the course of the thermal cycle. 
         [0017]    In further, related embodiments, the device may comprise at least one orifice to effect intake and exhaustion of the working gas from the container. The working gas may be air. An exterior surface of the container may be configured to conduct heat energy from the working gas. The at least one piston may comprise two pistons sharing a common working chamber. The two pistons may be in axial opposition to each other. The electronic controller may be configured to control motion of the pistons in the container to perform, in the thermal cycle, compression of the working gas during motion of the pistons toward each other, and at least one of: (i) induction of the working gas during motion of both pistons in the same direction relative to the container or (ii) induction of the working gas while one piston is held at or near a fixed position relative to the container. The electronic controller may comprise a binary counter with a state corresponding to each stroke of the thermal cycle, the strokes of the thermal cycle comprising induction, compression, expansion, and exhaustion. 
         [0018]    In further, related embodiments, the electronic controller may be configured to control the at least one piston to perform a thermal cycle comprising strokes of induction, compression, expansion and exhaustion, and a duration of any one of the thermal cycle strokes of induction, compression, expansion, and exhaustion may differ from the duration of any of the other said strokes. A distance traversed by the at least one piston relative to the container in any one of the strokes of induction, compression, expansion, and exhaustion may differ from a distance traversed by the at least one piston relative to the container during any of the other strokes. The electronic controller may be configured to control the at least one piston to perform more than one thermal cycle, and a duration of any one complete thermal cycle may differ from a duration of any other complete thermal cycle, of the more than one thermal cycle. The working chamber may comprise a single orifice for the intake and exhaustion of working gas. The single orifice may intake from, and exhaust to, ambient air. The at least one piston may be entirely contained within the container. A mechanical support rigidly attached to the container may intrude into the at least one piston. The support may comprise a heat pipe for the transport of heat into or out of the container. 
         [0019]    In further, related embodiments, the working chamber may comprise an orifice device for the intake or exhaustion of the working gas, said orifice device comprising an orifice device container, an orifice device piston and an orifice device electrical circuit, said orifice device electrical circuit being electromagnetically coupled to provide a motive force to the orifice device piston, and said orifice device piston being magnetically held in either of two positions within the orifice device container in the absence of electric current in the orifice device electrical circuit. The container and the at least one piston may each comprise a permanent magnet, the permanent magnet of the container and the permanent magnet of the at least one piston being mounted to be mutually repulsive. The container and the at least one piston may be mounted such that the weight of the at least one piston assists a motion of compression during the thermal cycle. The at least one piston may comprise at least one orifice for the intake or exhaustion of the working gas into or out of the working chamber. The at least one orifice may be shielded from the working chamber by the at least one piston for a portion of the thermal cycle. The container may comprise at least one magnetically-permeable spiral element electromagnetically coupled to the electrical circuit. The electrical storage device may comprise at least one of a capacitor and a battery. The container may comprise a cylinder. 
         [0020]    In further, related embodiments, the electronic controller may be electronically connected to the electronic power converter to control motion of the at least one piston to perform, in the thermal cycle, both: (i) compressing the working gas over a volume greater than the volume through which the working gas is expanded within the thermal cycle and (ii) exhausting the working gas to a remaining volume less than the smallest volume of compressed gas within the thermal cycle. The electronic controller may be configured to control the at least one piston to perform more than one thermal cycle, and a heat output of any one complete thermal cycle may differ from a heat output of any other complete thermal cycle, of the more than one thermal cycle. The electronic controller may be electronically connected to the electronic power converter to control motion of the at least one piston to perform, in the thermal cycle: an induction stroke wherein working gas flows into the container during a motion of the at least one piston, an adiabatic compression stroke wherein the volume of the working gas is reduced during a motion of the at least one piston over a volume greater than the volume through which the working gas is expanded within the thermal cycle, a cooling period wherein heat flows from the working gas out of the container, an adiabatic expansion stroke wherein the volume of the working gas is increased during a motion of the at least one piston, and an exhaustion stroke wherein the volume of the working gas is reduced to a remaining volume less than the smallest volume of compressed gas within the thermal cycle during a motion of the at least one piston. The electronic controller may be electronically connected to the electronic power converter to control motion of the at least one piston to perform, in the thermal cycle, at least one of, or both of, (i) compressing the working gas over a volume greater than the volume through which the working gas is expanded within the thermal cycle and/or (ii) exhausting the working gas to a remaining volume that is less than the smallest volume of compressed gas within the thermal cycle and that is as small as practicable. 
         [0021]    In another 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 at least one piston in a container, containing the working gas performing the thermal cycle, to electromagnetically induce current in an electrical circuit mounted stationary relative to the container, the electrical circuit being electrically connected to an electronic power converter. Electrical energy, produced by the current induced in the electrical circuit, is transferred to an electrical bus electrically connected to the electronic power converter and electrically connected to an electrical storage device. Electrical energy from the electrical bus is transferred to the electrical circuit to electromagnetically provide a motive force to the at least one piston. The transferring the electrical energy to the electrical bus and the transferring the electrical energy from the electrical bus effect a net positive average power transfer from the working gas to the electrical bus over the course of the thermal cycle. The motion of the at least one piston is used to perform, in the thermal cycle, at least one of: (i) expanding the working gas beyond the volume at which compression of the working gas is begun within the thermal cycle or (ii) exhausting the working gas to a remaining volume less than the smallest volume of compressed gas within the thermal cycle. 
         [0022]    In further, related embodiments, the method may comprise combusting the working gas in the thermal cycle. The method may further comprise intaking and exhausting the working gas to and from the container, and combusting the working gas in the thermal cycle; or may comprise intaking and exhausting the working gas to and from the container, without combusting the working gas in the thermal cycle. The working gas may be air. The method may further comprise conducting heat energy to the working gas through an exterior surface of the container. The method may comprise using two pistons sharing a common working chamber to perform the thermal cycle. The method may comprise using two pistons in axial opposition to each other to perform the thermal cycle. The method may comprise performing, in the thermal cycle, expansion of the working gas during motion of the pistons away from each other, and at least one of: (i) exhaustion of the working gas during motion of both pistons in the same direction relative to the container or (ii) exhaustion of the working gas while one piston is held at or near a fixed position relative to the container. The method may further comprise controlling the thermal cycle with a binary counter with a state corresponding to each stroke of the thermal cycle, the strokes of the thermal cycle comprising induction, compression, expansion, and exhaustion. 
         [0023]    In further, related embodiments, the thermal cycle may comprise strokes of induction, compression, expansion and exhaustion, and a duration of any one of the thermal cycle strokes of induction, compression, expansion, and exhaustion may differ from the duration of any of the other said strokes. A distance traversed by the at least one piston relative to the container in any one of the strokes of induction, compression, expansion, and exhaustion may differ from a distance traversed by the at least one piston relative to the container during any of the other strokes. The method may comprise performing more than one thermal cycle, and a duration of any one complete thermal cycle may differ from a duration of any other complete thermal cycle, of the more than one thermal cycle. The method may comprise intaking and exhausting the working gas through a single orifice in the working chamber. The method may comprise intaking from, and exhausting to, ambient air through the single orifice. The method may comprise combusting the working gas in the thermal cycle, or may be without combustion of the working gas. 
         [0024]    In further, related embodiments, the at least one piston may be entirely contained within the container. The method may comprise supporting the at least one piston using a mechanical support rigidly attached to the container that intrudes into the at least one piston. The support may comprise a heat pipe for the transport of heat out of the container. The method may comprise intaking the working gas to, or exhausting the working gas from, the working chamber using an orifice device, said orifice device comprising an orifice device container, an orifice device piston and an orifice device electrical circuit, said orifice device electrical circuit providing a motive force to the orifice device piston, and said orifice device piston being magnetically held in either of two positions within the orifice device container in the absence of electric current in the orifice device electrical circuit. The method may comprise mounting a permanent magnet on the container and mounting a permanent magnet on the at least one piston, the permanent magnet of the container and the permanent magnet of the at least one piston being mounted to be mutually repulsive. The method may comprise using the weight of the at least one piston to oppose a motion of expansion during the thermal cycle. The method may comprise intaking or exhausting the working gas into or out of the working chamber through an orifice in the at least one piston. The method may comprise intaking or exhausting the working gas into or out of the working chamber through at least one orifice, said at least one orifice being shielded from the working chamber by the at least one piston for a portion of the thermal cycle. The method may comprise electromagnetically coupling at least one magnetically-permeable spiral element of the container to the electrical circuit. 
         [0025]    In further, related embodiments, an expansion ratio of the working gas may be related to a compression ratio of the working gas only by a temperature rise ratio and an adiabatic constant, the temperature rise ratio being an inherent chemical property of the working gas and being equal to the highest absolute temperature achieved by the working gas in the thermal cycle divided by the absolute temperature of the working gas at the end of the compression stroke of the thermal cycle. The relation of the expansion ratio to the compression ratio may be given by: 
         [0000]    
       
      
       E/K=τ 
       1/γ 
      
     
         [0026]    where E is the expansion ratio, K is the compression ratio, γ is the adiabatic constant and τ is the temperature rise ratio. A ratio of exhaust gas absolute temperature of the working gas to inlet gas absolute temperature of the working gas may depend only on a temperature rise ratio and on a value of an adiabatic constant, the temperature rise ratio being an inherent chemical property of the working gas and being equal to the highest absolute temperature achieved by the working gas in the thermal cycle divided by the absolute temperature of the working gas at the end of the compression stroke of the thermal cycle. The ratio of exhaust gas absolute temperature to inlet gas absolute temperature may be given by: 
         [0000]        T   E   /T   I =τ 1/γ 
 
         [0027]    where T E  is the exhaust gas absolute temperature, T 1  is the inlet gas absolute temperature, γ is the adiabatic constant and τ is the temperature rise ratio. Efficiency of a device performing the method may be a function only of a temperature rise ratio, a value of an adiabatic constant and a compression ratio of the working gas, the temperature rise ratio being an inherent chemical property of the working gas and being equal to the highest absolute temperature achieved by the working gas in the thermal cycle divided by the absolute temperature of the working gas at the end of the compression stroke of the thermal cycle. Efficiency of a device performing the method may be given by the relation: 
         [0000]      η=1−[γ(τ (1/γ) −1)/( K   (γ-1) (τ−1)]
 
         [0028]    where η is efficiency, γ is the adiabatic constant, τ is the temperature rise ratio and K is the compression ratio of the working gas. 
         [0029]    In further, related embodiments, the working gas may comprise a fuel from the group consisting of: methanol, ethanol, propanol, benzene, octane, hydrogen and ammonia. The working gas may comprise a fuel that does not include carbon. For example, the fuel may comprise hydrogen or ammonia. The electrical storage device may comprise at least one of a capacitor and a battery. The container may comprise a cylinder. The method may comprise performing, in the thermal cycle, both: (i) expanding the working gas beyond the volume at which compression of the working gas is begun within the thermal cycle and (ii) exhausting the working gas to a remaining volume less than the smallest volume of compressed gas within the thermal cycle. The method may comprise performing more than one thermal cycle, wherein an energy output of any one complete thermal cycle differs from an energy output of any other complete thermal cycle, of the more than one thermal cycle. The method may comprise performing, in the thermal cycle: an induction stroke wherein working gas flows into the container during a motion of the at least one piston, an adiabatic compression stroke wherein the volume of the working gas is reduced during a motion of the at least one piston, a heating period wherein the temperature of the working gas rises, an adiabatic expansion stroke wherein the volume of the working gas is increased during a motion of the at least one piston beyond the volume at which compression of the working gas is begun within the thermal cycle, and an exhaustion stroke wherein the volume of the working gas is expelled from the container during a motion of the at least one piston to a remaining volume less than the smallest volume of compressed gas within the thermal cycle. The method may comprise performing, in the thermal cycle, at least one of, or both of, (i) expanding the working gas to atmospheric pressure and/or (ii) exhausting the working gas to a remaining volume that is less than the smallest volume of compressed gas within the thermal cycle and that is as small as practicable. 
         [0030]    In another embodiment according to the invention, there is provided a method for pumping heat using electrical energy, the pumping of heat comprising performing a thermal cycle of a working gas. The method comprises using the motion of at least one piston in a container, containing the working gas performing the thermal cycle, to electromagnetically induce current in an electrical circuit mounted stationary relative to the container, the electrical circuit being electrically connected to an electronic power converter. Electrical energy, produced by the current induced in the electrical circuit, is transferred to an electrical bus electrically connected to the electronic power converter and electrically connected to an electrical storage device. Electrical energy is transferred from the electrical bus to the electrical circuit to electromagnetically provide a motive force to the at least one piston. The transferring the electrical energy to the electrical bus and the transferring the electrical energy from the electrical bus effects a net positive average power transfer from the electrical bus to the working gas over the course of the thermal cycle. The motion of the at least one piston is used to perform, in the thermal cycle, at least one of: (i) compressing the working gas over a volume greater than the volume through which the working gas is expanded within the thermal cycle or (ii) exhausting the working gas to a remaining volume less than the smallest volume of compressed gas within the thermal cycle. 
         [0031]    In further, related embodiments, the method may comprise intaking and exhausting the working gas from the container through at least one orifice. The working gas may be air. The method may comprise conducting heat energy from the working gas through an exterior surface of the container. The method may comprise using two pistons sharing a common working chamber to perform the thermal cycle. The two pistons may be used in axial opposition to each other to perform the thermal cycle. The method may comprise performing, in the thermal cycle, compression of the working gas during motion of the pistons toward each other, and at least one of: (i) induction of the working gas during motion of both pistons in the same direction relative to the container or (ii) induction of the working gas while one piston is held at or near a fixed position relative to the container. The method may comprise controlling the thermal cycle with a binary counter with a state corresponding to each stroke of the thermal cycle, the strokes of the thermal cycle comprising induction, compression, expansion, and exhaustion. 
         [0032]    In further, related embodiments, the method may comprise performing a thermal cycle comprising strokes of induction, compression, expansion and exhaustion, wherein a duration of any one of the thermal cycle strokes of induction, compression, expansion, and exhaustion differs from the duration of any of the other said strokes. A distance traversed by the at least one piston relative to the container in any one of the strokes of induction, compression, expansion, and exhaustion may differ from a distance traversed by the at least one piston relative to the container during any of the other strokes. The method may comprise performing more than one thermal cycle, wherein a duration of any one complete thermal cycle differs from a duration of any other complete thermal cycle, of the more than one thermal cycle. The method may comprise intaking the working gas to, and exhausting the working gas from, the working chamber through a single orifice. The method may comprise intaking from, and exhausting to, ambient air through the single orifice. 
         [0033]    In further, related embodiments, the at least one piston may be entirely contained within the container. The method may comprise supporting the at least one piston with a mechanical support rigidly attached to the container that intrudes into the at least one piston. The support may comprise a heat pipe for the transport of heat into or out of the container. The method may comprise intaking the working gas to, or exhausting the working gas from, the working chamber using an orifice device, said orifice device comprising an orifice device container, an orifice device piston and an orifice device electrical circuit, said orifice device electrical circuit being electromagnetically coupled to provide a motive force to the orifice device piston, and said orifice device piston being magnetically held in either of two positions within the orifice device container in the absence of electric current in the orifice device electrical circuit. The method may comprise mounting a permanent magnet on the container and mounting a permanent magnet on the at least one piston, the permanent magnet of the container and the permanent magnet of the at least one piston being mounted to be mutually repulsive. The method may comprise using the weight of the at least one piston to assist a motion of compression during the thermal cycle. The method may comprise intaking or exhausting the working gas into or out of the working chamber through an orifice in the at least one piston. The method may comprise intaking or exhausting the working gas into or out of the working chamber through at least one orifice, said at least one orifice being shielded from the working chamber by the at least one piston for a portion of the thermal cycle. 
         [0034]    In further, related embodiments, the method may comprise electromagnetically coupling at least one magnetically-permeable spiral element of the container to the electrical circuit. The electrical storage device may comprise at least one of a capacitor and a battery. The container may comprise a cylinder. The method may comprise performing, in the thermal cycle, both: (i) compressing the working gas over a volume greater than the volume through which the working gas is expanded within the thermal cycle and (ii) exhausting the working gas to a remaining volume less than the smallest volume of compressed gas within the thermal cycle. The method may comprise performing more than one thermal cycle, wherein a heat output of any one complete thermal cycle differs from a heat output of any other complete thermal cycle, of the more than one thermal cycle. 
         [0035]    In further, related embodiments, the method may comprise performing, in the thermal cycle: an induction stroke wherein working gas flows into the container during a motion of the at least one piston, an adiabatic compression stroke wherein the volume of the working gas is reduced during a motion of the at least one piston over a volume greater than the volume through which the working gas is expanded within the thermal cycle, a cooling period wherein heat flows from the working gas out of the container, an adiabatic expansion stroke wherein the volume of the working gas is increased during a motion of the at least one piston, and an exhaustion stroke wherein the volume of the working gas is reduced to a remaining volume less than the smallest volume of compressed gas within the thermal cycle during a motion of the at least one piston. The method may comprise performing, in the thermal cycle, at least one of, or both of, (i) compressing the working gas over a volume greater than the volume through which the working gas is expanded within the thermal cycle and/or (ii) exhausting the working gas to a remaining volume that is less than the smallest volume of compressed gas within the thermal cycle and that is as small as practicable. 
         [0036]    In another embodiment according to the invention, there is provided a device for generating electrical energy using a plurality of thermal cycles of a plurality of working gases. The device comprises a plurality of containers, a plurality of pistons and a plurality of electrical circuits. At least one of said pistons is movably mounted in each of said containers to form a working chamber between the at least one piston and the said container, the working chamber containing the working gas performing a thermal cycle. One of said electrical circuits is mounted stationary relative to each of said containers, the electrical circuits being electromagnetically coupled to provide motive forces to the at least one pistons. An electronic power converter is electrically connected to the electrical circuits and to an electrical bus. An electrical storage device is electrically connected to the electrical bus. Each of the at least one pistons is movably mounted such that its motion electromagnetically induces current in its associated electrical circuit. An electronic controller is electronically connected to the electronic power converter to control motion of the plurality of pistons to perform, in the thermal cycles, at least one of: (i) expanding each of the working gases beyond the volume at which compression of the working gas is begun within the associated thermal cycle or (ii) exhausting the working gas to a remaining volume less than the smallest volume of compressed gas within the associated thermal cycle. The electronic controller is further electronically connected to the electrical bus to control both (i) flow of electrical energy produced by the currents induced in the electrical circuits to the electrical bus, and (ii) flow of electrical energy from the electrical bus to the electrical circuits to electromagnetically provide the motive forces to the plurality of pistons, and to effect a net positive average power transfer from each of the working gases to the electrical bus over the course of each of the thermal cycles. 
         [0037]    In another embodiment according to the invention, there is provided a device for pumping heat using electrical energy, the pumping of heat comprising performing a plurality of thermal cycles of a plurality of working gases. The device comprises a plurality of containers, a plurality of pistons and a plurality of electrical circuits. At least one of said pistons is movably mounted in each of said containers to form a working chamber between the at least one piston and the said container, the working chamber containing the working gas performing a thermal cycle. One of said electrical circuits is mounted stationary relative to each of said containers, the electrical circuits being electromagnetically coupled to provide motive forces to the at least one pistons. An electronic power converter is electrically connected to the electrical circuits and to an electrical bus. An electrical storage device is electrically connected to the electrical bus. Each of the at least one pistons is movably mounted such that its motion electromagnetically induces current in its associated electrical circuit. An electronic controller is electronically connected to the electronic power converter to control motion of the plurality of pistons to perform, in the thermal cycles, at least one of: (i) compressing each of the working gases over a volume greater than the volume through which the working gas is expanded within the associated thermal cycle or (ii) exhausting the working gas to a remaining volume less than the smallest volume of compressed gas within the associated thermal cycle. The electronic controller is further electronically connected to the electrical bus to control both (i) flow of electrical energy produced by the currents induced in the electrical circuits to the electrical bus, and (ii) flow of electrical energy from the electrical bus to the electrical circuits to electromagnetically provide the motive forces to the plurality of pistons, and to effect a net positive average power transfer from the electrical bus to each of the working gases over the course of each of the thermal cycles. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0038]    The foregoing will be apparent from the following more particular description of example 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 embodiments of the present invention. 
           [0039]      FIG. 1  is a cross-section of a machine to generate electricity from a combustible mixture of gases, in accordance with an embodiment of the invention. 
           [0040]      FIG. 2  shows an electrical arrangement for an electrically-coupled heat engine, in accordance with an embodiment of the invention. 
           [0041]      FIG. 3  shows a pressure-volume diagram for advantageous operation of the machine of the embodiments of  FIGS. 1 and 2 , in accordance with an embodiment of the invention. 
           [0042]      FIG. 4  is a graph of volume versus time in operation of the machine of the embodiments of  FIGS. 1 and 2 , in accordance with an embodiment of the invention. 
           [0043]      FIG. 5  is a graph of pressure versus time in operation of the machine of the embodiments of  FIGS. 1 and 2 , in accordance with an embodiment of the invention. 
           [0044]      FIG. 6  shows the idealized Otto Cycle for a conventional internal combustion engine. 
           [0045]      FIG. 7  is a pressure-volume diagram illustrating differences between a complete internal combustion electricity generator cycle in accordance with an embodiment of the invention and the cycle of a conventional internal combustion engine. 
           [0046]      FIG. 8  is a comparative plot of the efficiencies for a complete internal combustion electricity generator cycle in accordance with an embodiment of the invention and for the conventional ideal Otto cycle. 
           [0047]      FIG. 9  is a pressure-volume diagram for a cycle using a partially truncated expansion stroke, in accordance with an embodiment of the invention. 
           [0048]      FIG. 10  is a pressure-volume diagram for a cycle using a fully truncated expansion stroke, in accordance with an embodiment of the invention. 
           [0049]      FIG. 11  is a pressure-volume diagram for a family of four internal combusion electricity generator cycles of varying energy content, in accordance with an embodiment of the invention. 
           [0050]      FIG. 12  is a schematic diagram of an electronic controller, in accordance with an embodiment of the invention. 
           [0051]      FIG. 13  is a schematic diagram of a simplified electronic controller, in accordance with an embodiment of the invention. 
           [0052]      FIG. 14  is a diagram of a machine in which two assemblies of the embodiment of  FIG. 1  are integrated to share a common combustion chamber, in accordance with an embodiment of the invention. 
           [0053]      FIG. 15  is a diagram of a machine using a shaft support, in accordance with an embodiment of the invention. 
           [0054]      FIG. 16  is a diagram of a machine in which a heat pipe is used to remove heat from a central shaft, in accordance with an embodiment of the invention. 
           [0055]      FIG. 17  is a diagram of a machine in which the inlet valve and exhaust valve are located away from the center line of the assembly, asymmetrically disposed, in accordance with an embodiment of the invention. 
           [0056]      FIG. 18  is a graph of displacement versus time for two pistons performing a complete internal combustion electricity generator cycle in accordance with an embodiment of the invention. 
           [0057]      FIG. 19  is a diagram of a machine in which an inlet valve and exhaust valve are integral to a lower piston head, in accordance with an embodiment of the invention. 
           [0058]      FIG. 20  is a diagram of a magnetically bistable valve, in accordance with an embodiment of the invention. 
           [0059]      FIG. 21  is a diagram of windings for use in an internal combustion electricity generator, in accordance with an embodiment of the invention. 
           [0060]      FIG. 22  is a diagram of coils connected electrically in series, in accordance with an embodiment of the invention. 
           [0061]      FIG. 23  is a set of graphs of coil currents, plotted in amplitude versus shuttle distance, in accordance with an embodiment of the invention. 
           [0062]      FIG. 24  is a diagram of a winding arrangement in which a magnetically-permeable cylinder has teeth surrounding the winding coils, in accordance with an embodiment of the invention. 
           [0063]      FIG. 25  is a perspective view of toothed laminations, in accordance with an embodiment of the invention. 
           [0064]      FIG. 26  is a diagram of an arrangement of magnets for use in the magnetic shuttle of an internal combustion electricity generator, in accordance with an embodiment of the invention. 
           [0065]      FIG. 27  is a diagram of a further arrangement of magnets for use in the magnetic shuttle of an internal combustion electricity generator, in accordance with an embodiment of the invention. 
           [0066]      FIG. 28  is a cross-section of a machine to generate electricity from a source of heat, in accordance with an embodiment of the invention. 
           [0067]      FIG. 29  is a graph of pressure versus time in operation of the machine of the embodiments of  FIGS. 1 and 2 , in accordance with an embodiment of the invention. 
           [0068]      FIG. 30  is a graph of volume versus time in operation of the machine of the embodiments of  FIGS. 1 and 2 , in accordance with an embodiment of the invention. 
           [0069]      FIG. 31  is a diagram illustrating a method of using a single valve for the intake and exhaustion of air into and out of the working cylinder in an internal combustion electric generator (ICEG), in accordance with an embodiment of the invention. 
           [0070]      FIG. 32  shows a pressure-volume diagram for advantageous operation of the machine of the embodiments of  FIGS. 28 ,  31  and  2  when operated as a heat pump, in accordance with an embodiment of the invention. 
           [0071]      FIG. 33  is a graph of pressure versus time in operation of the machine of the embodiment of  FIG. 31 , in accordance with an embodiment of the invention. 
           [0072]      FIG. 34  is a graph of volume versus time in operation of the machine of the embodiment of  FIG. 31 , in accordance with an embodiment of the invention. 
       
    
    
     DETAILED DESCRIPTION OF THE INVENTION 
       [0073]    A description of example embodiments of the invention follows. 
         [0074]    It is desirable to be able to convert fuel into electricity by means of a method in which the equipment is efficient, reliable, quiet and vibration free, and in which the equipment operates from a variety of fuels. 
         [0075]    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. 
         [0076]    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. 
         [0077]    In order to improve on these characteristics, the invention of U.S. Pat. No. 7,690,199 B2 of Wood, entitled “System and Method for Electrically-Coupled Thermal Cycle,” the disclosure of which is incorporated herein by reference in its entirety, 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. 
         [0078]    An embodiment according to the present invention likewise provides an electrically-coupled heat engine and thermal cycle. 
         [0079]    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. 
         [0080]    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 combustion of a gas. 
         [0081]    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. 
         [0082]    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 electronic circuitry allows closed-loop electrical control of piston motion. Open-loop control may also be used. 
         [0083]    An embodiment according to the present invention 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. Such a use of electrical storage of cyclical energy flow contrasts with the conventional use a form of mechanical resonance for cyclical energy flow, for example when a mechanical resonance is used between the mass of a piston and compressed end-zone gas, which acts as a spring, for cyclical energy flow. 
         [0084]    An embodiment according to the invention may use electrical storage of cyclical energy flows to and from the thermal cycle, without mechanical storage of such energy flows. An embodiment according to the invention may be without any attached crankshaft, attached flywheel, moving displacer or other mechanical means of cyclical energy storage attached to the cylinder. For a multiple cylinder machine in accordance with an embodiment of the invention, energy transfer is shared on a common electrical bus. 
       Implementation of an Internal Combustion Electricity Generator. 
     a) Mechanical Arrangement 
       [0085]      FIG. 1  is a cross-section of a machine to generate electricity from a combustible mixture of gases, such as a conventional air-fuel mixture, in accordance with an embodiment of the invention. A combustion cylinder  101  houses a piston assembly consisting of a piston head  102  attached to a central shaft  103 . Between the piston head and one end of the combustion cylinder  101  is a combustion chamber  104 . Piercing the combustion cylinder  101  are an inlet valve  105 , an exhaust valve  106 , and an optional spark plug  107 . Although valves are shown here and in other embodiments herein, the term “orifice” is used herein to indicate that other types of openings may be used. In the embodiment of  FIG. 1  (and other embodiments herein), a fuel injector could be used in place of the inlet valve. The surface  117  of the combustion cylinder  101  that opposes the piston head  102  is referred to as the cylinder head. These opposing surfaces need not be flat as shown in  FIG. 1 . Typically, but not necessarily, the inlet valve  105 , the exhaust valve  106 , and the optional spark plug  107  pierce the cylinder head  117 . 
         [0086]    Attached to the central shaft  103 , away from the piston head  102 , is a magnetic shuttle assembly in the form of a spool, consisting of two discs  109  and  110  surrounding the central shaft  103 . Between shuttle discs  109  and  110 , and surrounding central shaft  103 , is an array  112  of permanent magnets. Central shaft  103  is fabricated from a thermally-non-conductive material, whereas piston head  102  may be metallic, and may have a ceramic or other thermally-non-conductive surface coating. Shuttle discs  109  and  110  are made of magnetically-permeable material such as iron or magnet-grade steel. 
         [0087]    Surrounding shuttle discs  109  and  110  is a non-magnetic cylinder  115  which serves to support electric windings  113  which are wound on the outside of cylinder  115 . Surrounding electric windings  113  is a magnetically-permeable cylinder  114 , typically made of laminations of magnet-grade steel. Magnetically-permeable cylinder  114  may have slots to secure or encompass the windings  113 , as is the manner in electric machines. Arranged together, magnet array  112 , shuttle discs  109  and  110 , and laminations  114  form a magnetic circuit, whose flux intersects windings  113 . Accordingly, whenever piston head  102  moves axially within combustion cylinder  101 , a voltage is induced in windings  113  by the shuttle discs  109  and  110 . Conversely, whenever an electric current is passed through windings  113 , an axial force is exerted on the shuttle discs  109  and  110  by the windings  113 . This force is translated by the central shaft  103  to the piston head  102 . Position sensors (not shown in  FIG. 1 ) provide information to an electronic controller. 
         [0088]    Winding support cylinder  115  is attached to combustion cylinder  101  by a thermally-insulating disc  116 . Attached to the opposing end of winding support cylinder  115  is a shaft support disc  118 . Central shaft  103  passes through and is supported by a sleeve bearing  117  located at the inner diameter of shaft support disc  118 . Piston head  102  typically features piston rings (not shown in  FIG. 1 ) for mechanical contact with the inside wall of combustion cylinder  101 . To avoid mechanical wear, a small clearance is maintained between the inside wall of support cylinder  115  and shuttle discs  109  and  110 . Orifice  108  at the inner diameter of insulating disc  116  restricts airflow between the combustion cylinder  101  and the winding support cylinder  115 , while maintaining a small clearance between the central shaft  103  and the insulating disc  116 , to avoid mechanical wear. 
         [0089]    Shaft support disc  118  typically is perforated with a plurality of orifices (not shown in  FIG. 1 ) to allow for atmospheric air flow into and out of winding support cylinder  115 , thereby proving air cooling for the magnet array  112 . Lower shuttle disc  109  may similarly be perforated with a plurality of orifices (not shown in  FIG. 1 ) to allow for air cooling of the magnet array  112 . Air cooling of the magnets may be assisted by a cooling fan (not shown in  FIG. 1 ). Upper shuttle disc  110  may have thermal insulation (not shown in  FIG. 1 ) on its upper surface (facing insulating disc  116 ) to resist heat flow from the combustion cylinder  101  toward the magnet array  112 . 
         [0090]    In an alternative embodiment, shaft support disc  118  is omitted from the structure of  FIG. 1 , and sleeve bearing  117  is located at the center of insulating disc  116 , replacing orifice  108 . 
         [0091]    In  FIG. 1  winding support cylinder  115  is depicted as having a larger diameter than combustion cylinder  101 . In other embodiments, these two cylinders may have the same diameter, or the combustion cylinder  101  may have a larger diameter than the winding support cylinder  115 . An encompassing cylinder or jacket (not shown in  FIG. 1 ) may be located around the combustion cylinder  101  to restrict heat loss from the exterior surface of the combustion cylinder. Inlet valve  105  and exhaust valve  106  may be actuated by electric solenoid action, under control from an electronic controller.  111  depicts an inlet fuel passage, and  119  depicts an exhaust passage. 
       b) Electrical Arrangement 
       [0092]      FIG. 2  shows the general electrical arrangement of an electrically-coupled heat engine, in accordance with an embodiment of the invention. The windings  201  connect to an electronic power converter  202 .  FIG. 2  shows two isolated windings for illustrative convenience, but any number of separate windings may be employed, as necessary. Also connected to electronic power converter  202  are signals from an electronic controller  208 , which receives signals from position sensors  203 . Although two sensors are shown in  FIG. 2 , any number of position sensors may be employed. The position sensors  203  give the electronic controller  208  the information that it needs for it to know the exact location of the shuttle discs  109  and  110  at any instant in time. 
         [0093]    Electronic power converter  202  is also connected to a DC bus  207 , to which is also attached a capacitor (or supercapacitor)  204  and a battery  205  and an electric load  206 . The electric load may be disconnected from the bus when not required, while the electronic power converter  202  continues to charge the battery  205 . Electronic controller  208  also receives current and voltage signals from the DC bus  207 , as well as current and voltage signals from the windings  201 . 
         [0094]    During operation of the system, the electronic controller  208  controls the flow of electric current into and out of the windings in such a manner as to cause the motion of the shuttle to move up and down (i.e., axially) so as to effect energy transfer from an ignited fuel-air mixture in the combustion chamber through the windings, and through the electronic power converter  202  to the electric load  206 . The capacitor  204  and battery  205  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  202  stores little or no energy, and transfers power between the DC bus  207  and the windings  201  in a highly efficient manner. 
       c) Thermal Cycle 
       [0095]    The operation of a heat engine that employs a quantity of gas as an operating medium may be described by reference to a pressure-volume diagram, hereinafter referred to as a P-V diagram. 
         [0096]      FIG. 3  shows a pressure-volume diagram for advantageous operation of the machine of the embodiments of  FIGS. 1 and 2 , the Internal Combustion Electricity Generator, hereinafter referred to as the “ICEG,” in accordance with an embodiment of the invention. The pressure P represented in  FIG. 3  is the pressure within the combustion chamber  104  of  FIG. 1 , and the volume V represented in  FIG. 3  is the volume of gas within that combustion chamber. The cycle of operation depicted in  FIG. 3  will hereinafter be referred to as the Complete ICEG Cycle. (Truncated versions of the Cycle will be described below.) Motion in the time domain is depicted in  FIGS. 4 and 5 , which display volume V and pressure P versus time, in accordance with an embodiment of the invention. In addition to being defined by a P-V cycle, an ICEG Cycle in an embodiment according to the invention may be defined by a time domain sequence. 
         [0097]    Consider a single cycle of operation beginning at point  305  in  FIG. 3 . The volume of gas is zero, indicating that the piston shaft  103  has moved to its uppermost limit, leaving no space at all between piston head  102  and cylinder head  117 . (In this explanation it is assumed that the spark plug and valves take up no volume inside the combustion cylinder.) At point  305  in  FIG. 3  the pressure is 1 atmosphere, (following an exhaustion stroke at atmospheric pressure.) 
       Step i), Induction: 
       [0098]    Following closure of the exhaust valve  106  and opening of inlet valve  105 , a fuel-air mixture is drawn into the combustion chamber  104  at atmospheric pressure during t 0  to t 1 , until point  301  is reached as determined by the electronic controller  208 . Let the volume of the combustion chamber  104  at point  301  be K. 
         [0000]    Step ii), Compression: 
         [0099]    Following closure of the inlet valve  105  during t 1  to t 2 , and with the exhaust valve  106  remaining closed, the fuel-air mixture is now compressed adiabatically (i.e., with no thermal losses) during t 2  to t 3  in the combustion chamber  104  until point  302  is reached as determined by the electronic controller  208 . Let us arbitrarily define the volume of the combustion chamber  104  at point  302  to be 1 unit. 
         [0000]    Step iii), Ignition: 
         [0100]    At point  302  the compressed fuel-air mixture is now ignited via the spark plug  107 , or is self-detonated in the manner of a diesel engine. The electronic controller  208  initiates no further action until the pressure P has risen maximally to point  303 . As indicated in  FIGS. 4 and 5 , this pressure rise step takes finite time, from t 3  to t 4 . 
         [0000]    Step iv), Expansion: 
         [0101]    At point  303  the electronic controller  208  initiates an adiabatic expansion of the combusted gas in the combustion chamber  104 , until the pressure has fallen during t 4  to t 5  all the way back to unity (atmospheric pressure) at point  304 . Let the volume of the combustion chamber  104  at point  304  be E. 
       Step v), Exhaustion: 
       [0102]    At point  304 , exhaust valve  106  is opened during t 5  to t 6 , following which the electronic controller  208  causes upwards motion of the piston shaft  103  during t 6  to t 7  until all gas in the combustion chamber  104  is exhausted. Exhaust valve  106  is closed from t 7  to t 8 , thereby completing the ICEG cycle. Another cycle may or may not be initiated immediately, as determined by the electronic controller  208 . 
         [0103]    It should be noted that times taken for each of the major strokes (induction, compression, expansion, exhaustion) need not be the same, as is the case in a conventional internal combustion engine, and may be varied relative to each other by an electronic controller, in accordance with an embodiment of the invention. Note also that with expansion all the way to atmospheric pressure being possible in an embodiment according to the invention, the audible sound of exhaust may be lower than conventional internal combustion engines, and may allow the reduction in size of, or elimination of, the muffler. 
         [0000]    Comparison with a Conventional Internal Combustion Engine: 
         [0104]      FIG. 6  shows the idealized cycle for a conventional internal combustion engine, commonly known as the Otto Cycle. By comparison with the Complete ICEG Cycle of the embodiment of  FIG. 3 , two differences between the cycles are apparent. (The ignition stage in  FIG. 6  between points  602  and  603  corresponds to the ignition stage in  FIG. 3  between points  302  and  303 .) 
         [0105]    A first difference is that for the Otto Cycle, expansion is terminated at point  604  where the expanded volume equals the starting volume at point  601  prior to compression. This represents a loss of energy, some of which is manifest in the explosive exhaust sound in the absence of a muffler, and the rest of which is rejected as waste heat. 
         [0106]    A second difference is that for the Otto Cycle, exhaustion at point  605  is incomplete, with some of the exhaust gas mixture remaining in the combustion chamber. This represents a loss of efficiency. 
         [0107]    A third difference between the cycle for a real conventional internal combustion engine and the Complete ICEG Cycle is not apparent from the P-V diagrams of  FIGS. 3 and 6 , but is illustrated in the timing diagrams of  FIGS. 4 and 5 . This difference results from the dwell periods taken in the Complete ICEG Cycle to ensure that the state actually reaches into the corners of the desired P-V diagram. These dwell periods are t 1  to t 2 , t 3  to t 4 , t 5  to t 6 , and t 7  to t 8  in  FIGS. 4 and 5 . 
         [0108]    Taken together, these three differences between the Complete ICEG Cycle in accordance with an embodiment of the invention and the cycle of a conventional internal combustion engine represent efficiency advantages for the ICEG.  FIG. 7  is a pressure-volume diagram illustrating differences between a Complete ICEG cycle in accordance with an embodiment of the invention and the cycle of a conventional internal combustion engine. Interior to the conventional ideal Otto loop is an interior loop  701  showing that, in practice, the state of a conventional internal combustion engine does not reach into the corners, with resulting loss of efficiency. Also shown are the expansion tail  702  and the exhaustion tail  703  of an embodiment according to the invention, both missing from the conventional Otto cycle. 
         [0109]    It should be noted that a variety of fuel types can be used with an ICEG according to an embodiment of the invention. In particular, the fuel used in an ICEG may be a fuel that does not include carbon, for example hydrogen or ammonia. Other fuels may be used in an ICEG, for example the fuels discussed in the section that follows. 
       Thermodynamic Formulae 
       [0110]    Without wishing to be bound by theory, some theoretical considerations are set forth here, relating to embodiments described herein. Consider a mass m of ideal gas with specific heat at constant volume c v . Let the absolute temperature of the gas be T. If a quantity ΔQ of heat is added to that mass m of gas, the resulting temperature rise ΔT is given by: 
         [0000]      Δ Q=mc   v   ΔT   (Equation 1)
 
         [0111]    Suppose that the mass m of gas is constrained at constant volume, as is the case between  302  and  303  in  FIG. 3 . Then the temperature rise ΔT takes the gas from pressure P 1  and temperature T 1  to pressure P 2  and temperature T 2 , and 
         [0000]        T   2   =T   1   +ΔT   (Equation 2)
 
         [0000]        P   2   /P   1 =T 2 /T 1   (Equation 3)
 
         [0112]    Let q m  be the Specific Combustion Energy of a combustible mixture of gases, e.g., an air-fuel mixture. 
         [0000]        q   m   =ΔQ/m   (Equation 4)
 
         [0000]      Hence: 
         [0000]      Δ T=q   m   /c   v   (Equation 5)
 
         [0000]      Then: 
         [0000]        P   2   /P   1 =1 +q   m /( c   v   *T   1 )  (Equation 6)
 
         [0113]    We shall use the symbol τ to denote this ratio of pressures P 2 /P 1  or temperatures T 2 /T 1 , and we shall refer to τ as the Temperature Rise Ratio, which is inherent to the chemical properties of the combustible mixture. Thus: 
         [0000]      τ=1 +q   m /( c   v   *T   1 )  (Equation 7)
 
         [0114]    As an illustrative example for determination of the value of τ, consider a stoichiometric (chemically balanced) mixture of ethanol and air. The chemical equation of combustion is: 
         [0000]      C 2 H 5 OH+3O 2 +12.9N 2 =2CO 2 +3H 2 0+12.9N 2   (Equation 8)
 
         [0115]    In equation 8, the constitution of air is approximated as 21% oxygen and 79% nitrogen gas, by weight. From reference texts, the calorific value q f  for ethanol is in the vicinity of 28.4 kJ/gm. From equation 8, the ethanol percentage by weight of the stoichiometric mixture is 100×46/503=9.15%. Accordingly, letting α represent the fraction by weight of fuel in the mixture, the calorific value q m  for the ethanol/air mixture is given by Equation 9: 
         [0000]        q   m   =q   f *α  (Equation 9)
 
         [0000]    Thus q m  for the ethanol/air mixture is in the vicinity of 28.4×0.0915=2.60 kJ/gm. For air, c v =0.712 J/gm.K. Hence, for an assumed inlet gas temperature T 1  of 373 K (=100° C.), we have: 
         [0000]    
       
         
           
             
               
                 
                   τ 
                   = 
                     
                    
                   
                     1 
                     + 
                     
                       2 
                       , 
                       
                         600 
                         / 
                         
                           ( 
                           
                             0.712 
                             × 
                             373 
                           
                           ) 
                         
                       
                     
                   
                 
               
             
             
               
                 
                   = 
                     
                    
                   10.8 
                 
               
             
           
         
       
     
         [0116]    By way of comparison, Table 1 shows τ values for seven types of fuel. 
         [0000]                                                              TABLE 1                       Fuel   q f  (kJ/gm)   α   τ                                        Methanol   15.1   0.1228   8.0           Ethanol   28.4   0.0915   10.8           Propanol   42.0   0.0805   13.7           Benzene   67.9   0.0639   17.3           Octane   113.2   0.0565   25.1           Hydrogen   136.2   0.0256   14.1           Ammonia   18.6   0.1295   10.1                        
The τ values in Table 1 were determined on the same basis as used above for the case of ethanol, and on the following set of corresponding chemical equations:
 
         [0000]      CH 3 OH+1.5O 2 +6.45N 2 ═CO 2 +2H 2 0+6.45N 2   (Equation 10)
 
         [0000]      C 2 H 5 OH+3O 2 +12.9N 2 =2CO 2 +3H 2 0+12.9N 2   (Equation 8)
 
         [0000]      C 3 H 7 OH+4.5O 2 +19.35N 2 =2CO 2 +3H 2 0+19.35N 2   (Equation 11)
 
         [0000]      C 6 H 6 +7.5O 2 +33.25N 2 =6CO 2 +3H 2 0+33.25N 2   (Equation 12)
 
         [0000]      C 8 H 18 +12.5O 2 +53.75N 2 =8CO 2 +9H 2 0+53.75N 2   (Equation 13)
 
         [0000]      2H 2 +O 2 +4.3N 2 =2CO 2 +3H 2 0+4.3N 2   (Equation 14)
 
         [0000]      4NH 3 +3O 2 +12.9N 2 =6H 2 0+14.9N 2   (Equation 15)
 
         [0117]    For an ideal gas, an adiabatic (thermally lossless) compression or expansion from a point (P 1 , V 1 ) to another point (P 2 , V 2 ) in the P-V plane follows this relationship, γ being known as the adiabatic constant: 
         [0000]        P   1   V   1   γ   =P   2   V   2   γ   (Equation 16)
 
         [0118]    With these relationships in place, formulae for motion around the Complete ICEG Cycle of  FIG. 3  are given by Table 2. 
         [0000]    
       
         
               
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Point 
                 P 
                 V 
                 T 
               
               
                   
               
             
             
               
                 301 
                 1 
                 K 
                 T 1   
               
               
                 302 
                 K γ   
                 1 
                 T 1  K γ−1   
               
               
                 303 
                 τ K γ   
                 1 
                 τ T 1  K γ−1   
               
               
                 304 
                 1 
                 K τ 1/γ   
                 T 1  τ 1/γ   
               
               
                   
               
             
          
         
       
     
         [0119]    From Table 2 it follows that: 
         [0000]        E/K=τ   1/γ   (Equation 17)
 
         [0120]    Equation (17) shows that the expansion ratio E is related to the compression ratio K only by the temperature rise ratio τ, an inherent chemical property of the combustible mixture, and on the value of γ. By way of example for τ=10.8 (per the above for the case of ethanol), and γ=1.30 (assumed), E/K=6.24, which means that the length of the intake stroke of the Complete ICEG Cycle is 16% of the length of the expansion stroke. Similarly from Table 2 it follows that: 
         [0000]        T   304   /T   301 =τ 1/γ   (Equation 18)
 
         [0121]    Equation (18) shows that the ratio of exhaust gas temperature to inlet gas temperature depends only on the temperature rise ratio τ and on the value of γ. 
         [0122]    Using the results of Table 2, it can be shown that the efficiency of the Complete ICEG Cycle (i.e., net mechanical work produced divided by thermal energy input) is: 
         [0000]    
       
         
           
             
               
                 
                   
                     
                       
                         
                           η 
                           ICEG 
                         
                         = 
                           
                          
                         
                           1 
                           - 
                           
                             Heat 
                              
                             
                                 
                             
                              
                             
                               Loss 
                               / 
                               Heat 
                             
                              
                             
                                 
                             
                              
                             Input 
                           
                         
                       
                     
                   
                   
                     
                       
                         = 
                           
                          
                         
                           1 
                           - 
                           
                             
                               
                                 γ 
                                  
                                 
                                   ( 
                                   
                                     
                                       T 
                                       4 
                                     
                                     - 
                                     
                                       T 
                                       1 
                                     
                                   
                                   ) 
                                 
                               
                               / 
                               
                                 ( 
                                 
                                   
                                     T 
                                     3 
                                   
                                   - 
                                   
                                     T 
                                     2 
                                   
                                 
                                 ) 
                               
                             
                              
                             
                                 
                             
                              
                             
                               ( 
                               
                                 Equation 
                                  
                                 
                                     
                                 
                                  
                                 20 
                               
                               ) 
                             
                           
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     19 
                   
                   ) 
                 
               
             
             
               
                 
                   
                     η 
                     ICEG 
                   
                   = 
                   
                     1 
                     - 
                     
                       [ 
                       
                         
                           γ 
                            
                           
                             ( 
                             
                               
                                 τ 
                                 
                                   ( 
                                   
                                     1 
                                     / 
                                     γ 
                                   
                                   ) 
                                 
                               
                               - 
                               1 
                             
                             ) 
                           
                         
                         / 
                         
                           ( 
                           
                             
                               K 
                               
                                 ( 
                                 
                                   γ 
                                   - 
                                   1 
                                 
                                 ) 
                               
                             
                              
                             
                               ( 
                               
                                 τ 
                                 - 
                                 1 
                               
                               ) 
                             
                           
                           ] 
                         
                       
                     
                   
                 
               
               
                 
                   ( 
                   
                     Equation 
                      
                     
                         
                     
                      
                     21 
                   
                   ) 
                 
               
             
           
         
       
     
         [0123]    From equation (21) it can be seen that the efficiency is a function of γ, τ, and K only. 
         [0124]    A well-known result from thermodynamics gives the efficiency of the ideal Otto cycle thus: 
         [0000]      η OTTO =1−1 /K   (γ-1)   (Equation 22)
 
         [0125]    A comparative plot of the efficiencies for the Complete ICEG Cycle in accordance with an embodiment of the invention per the above theory and for the ideal Otto cycle is given in  FIG. 8 , from which it can be seen that the Complete ICEG Cycle (upper curve) has a higher efficiency than the ideal Otto cycle (lower curve), particularly at low values of compression ratio K. 
         [0126]    It should be noted that in accordance with the thermodynamic formulae presented herein, the power conversion efficiency of an ICEG may depend on the Temperature Rise Ratio for the particular fuel used, in accordance with an embodiment of the invention. In particular, the power conversion efficiency of an ICEG increases with increasing values of the Temperature Rise Ratio τ, in accordance with Equation 21. 
       Variable Energy Output Per Cycle 
       [0127]    The output energy per cycle for an ICEG can be varied by altering the length of the intake stroke ( 305 - 301  in  FIG. 3 ), in accordance with an embodiment of the invention. The length of the stroke may be varied in real time by an electronic controller as the engine operates. In any given physical embodiment of an ICEG machine, there will be a practical limit to the expansion distance. If the inlet stroke magnitude is increased beyond the limit imposed by that expansion distance and by equation 10, then it will be necessary to partially truncate the expansion stroke, as shown in  FIG. 9 , in accordance with an embodiment of the invention. In the limiting case of a fully truncated expansion stroke as shown in the embodiment of  FIG. 10 , the inlet stroke and expansion stroke are of equal length as in the Otto cycle, but with the notable difference that exhaustion is still complete for the ICEG machine. 
         [0128]      FIG. 11  displays a family of four ICEG cycles of varying energy content, in accordance with an embodiment of the invention. The energy content may be varied in real time by an electronic controller as the engine operates. The first two cycles, with pressure peaks at points A and B, are Complete ICEG Cycles. The cycle with pressure peak at point C is a Partially Truncated ICEG Cycle. The cycle with pressure peak at point D is a Fully Truncated ICEG Cycle. 
       Electronic Controller Implementation 
       [0129]    An electronic controller can be implemented for an ICEG to follow the cycle of  FIG. 3 , without the need for the use of a microprocessor, in accordance with an embodiment of the invention. The absence of a microprocessor in the controller offers the advantages of inherent reliability, fast dynamics, minimal development time, and minimal development cost. Of course, a microprocessor-based controller may supplement or replace the controller described here. 
         [0130]      FIG. 12  is a schematic diagram of an electronic controller, in accordance with an embodiment of the invention, and can be used as the basis for either an all-hardware controller implementation, or a microprocessor-based implementation. In  FIG. 12 , functionality is shown only for the four major motions in the ICEG cycle of  FIG. 3 , in order to facilitate illustration of the method. The minor motions (dwell periods) can be implemented by techniques discussed below. 
         [0131]    The central component of the method of  FIG. 12  is a two-bit counter C 1 , the output [A,B] of which represents each of the four major motion states, as shown in Table 3: 
         [0000]    
       
         
               
               
               
               
             
           
               
                   
                 TABLE 3 
               
               
                   
                   
               
               
                   
                 A 
                 B 
                 Motion 
               
               
                   
                   
               
             
             
               
                   
                 0 
                 0 
                 Exhaust 
               
               
                   
                 0 
                 1 
                 Intake 
               
               
                   
                 1 
                 0 
                 Compression 
               
               
                   
                 1 
                 1 
                 Expansion 
               
               
                   
                   
               
             
          
         
       
     
         [0132]    When counter C 1  is in state (0,0), the velocity of the shuttle of  FIG. 1  is controlled to be −1, i.e., motion in the negative (volume reduction) direction at a speed of 1 arbitrary speed units. This is the exhaust stroke,  304  to  305  in  FIG. 3  and t 6  to t 7  in  FIGS. 4 and 5 . 
         [0133]    When counter C 1  is in state (0,1), the velocity of the shuttle of  FIG. 1  is controlled to be +1, i.e., motion in the positive (volume increase) direction at a speed of 1 arbitrary speed units. This is the intake stroke,  305  to  301  in  FIG. 3  and t 0  to t 1  in  FIGS. 4 and 5 . 
         [0134]    When counter C 1  is in state (1,0), the velocity of the shuttle of  FIG. 1  is controlled to be −2, i.e., motion in the negative (volume reduction) direction at a speed of 2 arbitrary speed units. This is the compression stroke,  301  to  302  in  FIG. 3  and t 2  to t 3  in  FIGS. 4 and 5 . 
         [0135]    When counter C 1  is in state (1,1), the velocity of the shuttle of  FIG. 1  is controlled to be +2, i.e., motion in the positive (volume increase) direction at a speed of 2 arbitrary speed units. This is the expansion stroke,  303  to  304  in  FIG. 3  and t 4  to t 5  in  FIGS. 4 and 5 . 
         [0136]    As noted elsewhere in this description, the speed of the shuttle need not be held constant at any point of the entire ICEG cycle, nor does the average speed of any stroke need to be constrained in its relationship with any other stroke. In this illustration, the choice of relative speeds for the exhaust and intake strokes is arbitrarily taken as one half of the speeds for the compression and expansion strokes, in order to simplify the description and to illustrate the ability for this system to employ intake and exhaust speeds that are lower than the speeds of the compression and expansion strokes, thereby effecting a reduction in energy losses resulting from higher gas velocities. 
         [0137]    At the end of each of the four major strokes, one of the sensors S 1  through S 5  shown in  FIG. 12  changes state, thereby initiating a single pulse from a single pulse generator (or monostable multivibrator, sometimes known in the electronics industry as a “one-shot”.) A pulse from any of the one-shot single pulse generators causes the output of OR gate OR 1  momentarily to go high, thereby incrementing the count of the two-bit counter C 1 , and initiating a new major stroke. The minor motions (dwell periods) can be implemented by the use of time delays or sensors acting as inputs to AND gates that are coupled with the sensing elements S 1  through S 5  of  FIG. 12 . 
         [0138]      FIG. 13  is a schematic diagram of an electronic controller in accordance with an embodiment of the invention in which a functional simplification of the arrangement of  FIG. 12  has been made, obtained by noting that the A output of counter C 1  corresponds to the desired speed of the shuttle (1 or 2), while the B output of counter C 1  corresponds to the desired direction of the shuttle (+ or −). 
       Axial Opposition. 
       [0139]      FIG. 14  shows an enhancement of the arrangement of the single shuttle scheme of  FIG. 1 , in accordance with an embodiment of the invention. In this enhancement, two complete (typically but not necessarily identical) shuttle and magnetic assemblies oppose each other in an integrated assembly, each with its associated electrical windings. Items  1402   a ,  1403   a ,  1408   a ,  1409   a ,  1410   a ,  1412   a ,  1413   a ,  1414   a ,  1415   a ,  1416   a ,  1417   a , and  1418   a  in the lower assembly, and items  1402   b ,  1403   b ,  1408   b ,  1409   b ,  1410   b ,  1412   b ,  1413   b ,  1414   b ,  1415   b ,  1416   b ,  1417   b , and  1418   b  in the upper assembly correspond respectively to their counterpart items  102 ,  103 ,  108 ,  109 ,  110 ,  112 ,  113 ,  114 ,  115 ,  116 ,  117 , and  118  in  FIG. 1 , as described above. Thus integrated, the two assemblies share a common combustion chamber  1404 , which features side-entry inlet and exhaust valves  1405   b  and  1406   b . The inlet valve  1405   b  may be a fuel injector. An optional side-entry spark plug may also pierce the combustion chamber  1404 . Such a spark plug is not shown in  FIG. 14 , to illustrate the option of a self-detonating arrangement, as in a diesel engine. Shown below is an alternative placement of the inlet and exhaust valves, in which the two piston heads can approach each other closely, thereby facilitating high compression ratios. 
         [0140]    The advantages of an axially opposed arrangement as illustrated in  FIG. 14  include:
       i. Mechanical balancing of forces (thereby reducing vibration),   ii. Elimination of the cylinder head  117  of  FIG. 1  with attendant cost savings,   iii. Facilitation of the use of high compression ratios, since the combustion cylinder  1401  takes the form of a pure cylinder, for which it is easier to ensure adequate strength against high compression forces than is the case if a cylinder head is included.       
 
         [0144]    An electronic controller for the arrangement of  FIG. 14  could be a modification of the controller of  FIG. 13 , wherein a single two-bit counter C 1  controls both shuttles, and wherein sensors are located in each assembly, with sensing signals being combined in a logical OR manner, or in a logical AND manner, as appropriate. 
         [0145]    The terminology “horizontally opposed” may be used in place of the term “axially opposed.” 
       Compact Shaft Support. 
       [0146]      FIG. 15  shows an enhancement of the arrangement of the shuttle support scheme of  FIG. 1 , in accordance with an embodiment of the invention. In this enhancement, a shaft support  1520  fits inside a hollow central shaft  1503  to provide the lateral support that the sleeve bearing  117  provides in the arrangement of  FIG. 1 . Items  1501 ,  1502 ,  1503 ,  1504 ,  1505 ,  1506 ,  1507 ,  1508 ,  1509 ,  1510 ,  1511 ,  1512 ,  1513 ,  1514 ,  1515 ,  1516 ,  1517 ,  1518 , and  1519  correspond respectively to their counterpart items  101 ,  102 ,  103 ,  104 ,  105 ,  106 ,  107 ,  108 ,  109 ,  110 ,  111 ,  112 ,  113 ,  114 ,  115 ,  116 ,  117 ,  118 , and  119  in  FIG. 1 , as described above. 
         [0147]    The advantages of the arrangement of  FIG. 15  include the fact that the overall length required to accommodate the assembly is reduced. Shaft support disc  1518  typically is perforated with a plurality of orifices (not shown in  FIG. 15 ) to allow for atmospheric air flow into and out of winding support cylinder  1515 , thereby providing air cooling for the magnet array  1512 . 
       Central Shaft Cooling Method. 
       [0148]      FIG. 16  shows a method for removing heat from the central shaft of the arrangement of  FIG. 15 , in order to help reduce magnet temperatures, in accordance with an embodiment of the invention. Inside the compact shaft support  1620  is a heat pipe  1621  which rapidly removes heat from the shaft support  1620 , thereby drawing heat away from the central shaft  1603 , and from the magnet array  1612 . A set of cooling fins  1622  is shown as a means for dissipating the heat thus drawn, but other dissipating means can be employed, such as a fluid cooling circuit, or thermal conduction to other portions of the installation. Items  1601 ,  1602 ,  1603 ,  1604 ,  1605 ,  1606 ,  1607 ,  1608 ,  1609 ,  1610 ,  1611 ,  1612 ,  1613 ,  1614 ,  1615 ,  1616 ,  1617 ,  1618 , and  1619  correspond respectively to their counterpart items  1501 ,  1502 ,  1503 ,  1504 ,  1505 ,  1506 ,  1507 ,  1508 ,  1509 ,  1510 ,  1511 ,  1512 ,  1513 ,  1514 ,  1515 ,  1516 ,  1517 ,  1518 , and  1519  in  FIG. 15 , and to their corresponding counterpart items in  FIG. 1 , as described above. 
         [0149]    A heat pipe arrangement similar to the one shown in  FIG. 16  can also be employed with the arrangement of  FIG. 1 , whereby a heat pipe with terminating fins would fit inside the central shaft  103 . 
       First Alternative Location of Valves. 
       [0150]      FIG. 17  shows an alternative arrangement to that of  FIG. 14 , in which the inlet valve  1705  and exhaust valve  1706  are located away from the center line of the assembly, asymmetrically disposed, in accordance with an embodiment of the invention. The motivation for the arrangement of  FIG. 17  is to provide for an exceedingly small volume of the combustion chamber at the time of maximum compression, i.e., at point  302  of the ICEG cycle of  FIG. 3 . The arrangement of  FIG. 17  takes advantage of the fact that the inlet and exhaust valves are only open (in the ICEG cycle) when the pressure in the combustion chamber is atmospheric. Furthermore, when the point of maximum compression has been reached, the inlet and outlet valves have been bypassed by the piston. 
         [0151]      FIG. 18  is a graph of displacement of two piston heads  1702  and  1703  relative to the center line, versus time, so as to accomplish a complete ICEG cycle for the arrangement of  FIG. 17 , in accordance with an embodiment of the invention. Times t 0  through t 8  in  FIG. 18  correspond with times t 0  through t 8  in  FIGS. 4 and 5 . Trajectory  1801  shows the displacement of piston head  1703 , and trajectory  1802  shows the displacement of piston head  1702 . At the beginning of the ICEG cycle (point  305  in  FIG. 3 ), both piston heads are situated at a low extremity, near the lower level of the inlet and exhaust valves  1705  and  1706 . During the interval t 0  through t 1  with the inlet valve  1705  open, the lower piston head  1702  remains stationary while the upper piston head  1703  moves upward. When an adequate intake volume has been reached at point t 1 , inlet valve  1702  closes, until t 2 . Between t 2  and t 3 , upper piston head  1703  continues to move upward, while lower piston head  1702  moves upward in such a manner that when upper piston head  1703  arrives at half the desired compression distance above the center line, lower piston head  1702  arrives at half the desired compression distance below the center line. Between t 3  and t 4  ignition takes place. Between t 4  and t 5  expansion occurs, with the two piston heads moving apart at equal speed. Between t 5  and t 6  the exhaust valve opens. Then, between t 6  and t 7  exhaustion is accomplished by the downward motion of the upper piston head  1703  while the lower piston head  1702  remains stationary. Between t 7  and t 8  the exhaust valve closes and the inlet valve opens. Another cycle may or may not be initiated immediately, as determined by the electronic controller  208 . 
       Second Alternative Location of Valves. 
       [0152]    In the arrangement of  FIG. 17 , the sealing rings of the piston heads  1702  and  1703  are required to pass by the inlet and exhaust valves  1705  and  1706 . This may result in undesirable wear of the sealing rings as they pass over discontinuities in the cylinder wall.  FIG. 19  shows another arrangement, in accordance with an embodiment of the invention, wherein the piston heads do not pass over discontinuities in the cylinder wall. 
         [0153]    In the embodiment of  FIG. 19 , inlet valve  1905  and exhaust valve  1906  are integral to the lower piston head  1902 , and ride with it. Upper piston head  1903  does not carry valves. The shafts of inlet valve  1905  and exhaust valve  1906  pass through the lower piston head  1902 . Springs  1907  and  1911  hold the inlet and exhaust valves closed, except when these springs are compressed by the action of electromagnets  1909  and  1913  acting on permanent magnets  1908  and  1912 . Inlet manifold  1910  serves as a duct for incoming air or an air/fuel mixture, while exhaust manifold  1914  serves as a duct for the exhaust gases. An optional fuel injector may pierce the wall of the combustion chamber  1901  at or near the center line of the combustion chamber, 
       Gravity Assisted Energy Capture. 
       [0154]    During the expansion stroke ( 303  to  304  in  FIG. 3 , and t 4  to t 5  in  FIGS. 4 and 5 ), the windings  113  have the task of arresting the motion of the shuttle in finite distance. To assist this action, it may be effective in accordance with an embodiment of the invention to mount the complete engine as depicted in  FIGS. 1 ,  15 ,  16 ,  28  and  31  in an inverted position, so that during the expansion stroke ( 303  to  304  in  FIG. 3 ) the kinetic energy of the shuttle is converted in part to potential (gravitational) energy. This potential energy will then be recaptured during the exhaustion stroke ( 304  to  305  in  FIG. 3 .) 
       Magnetically Assisted Energy Capture. 
       [0155]    The task of assisting the windings  113  to arrest the motion of the shuttle in finite distance might also be achieved in accordance with an embodiment of the invention by the inclusion of repulsive permanent magnets between the shuttle lower disc  109  and the shaft support disc  118 . Kinetic energy retained by the shuttle at the end of the expansion stroke ( 303  to  304  in  FIG. 3 ) can be captured by the windings during the exhaustion stroke ( 304  to  305  in  FIG. 3 ) after the shuttle has bounced off the repulsive magnets that are attached to the shaft support disc  118 . 
       Magnetic Bumpers for Lossless Resting. 
       [0156]    In the gravity assisted energy capture arrangement described above, it may be advantageous to include repulsive permanent magnets between the shuttle upper disc  110  (which will actually occupy the physically lower position in the inverted arrangement) and the insulating disc  116 , in accordance with an embodiment of the invention. This will permit the indefinite resting of the shuttle between energy-conversion cycles (i.e., after the exhaustion stroke  304  to  305  and before the induction stroke  305  to  301 ) without the consumption of energy, and without mechanical contact. 
       Magnetically Bistable Valves. 
       [0157]      FIG. 20  is a diagram of an arrangement for the operation of a valve (inlet or exhaust) with minimal energy consumption, in accordance with an embodiment of the invention. Valve  2001  pierces a cylinder head  2002  (alternatively, a cylinder wall.) Attached to and surrounding the shaft of valve  2001  is a cylindrical magnet array  2003 . Surrounding magnet array  2003  is a winding (or windings)  2005  housed within a magnetically-permeable casement  2004 , through which the valve  2001  can slide freely. Casement  2004  is rigidly anchored to the cylinder head  2002  by an attachment  2006 . 
         [0158]    Cylindrical magnet array  2003  is shorter in length than casement  2004 , and by magnetic attraction will attach itself to either end of casement  2004 . A pulse of current of appropriate amplitude, polarity, and duration will dislodge cylindrical magnet array  2003  from whichever end of casement  2004  to which it is attached, and will cause cylindrical magnet array  2003  to move to and remain at the opposite end of casement  2004 . Immediately following cessation of the dislodging pulse of current, and while the cylindrical magnet array  2003  is still in motion, an applied driving voltage of opposite polarity to the dislodging voltage is applied to the winding  2005 . This reverse-polarity connection, with suitable drive electronics, will result in a return to the electrical supply of most the energy used in dislodgement of the cylindrical magnet array  2003 . 
       Periodic and Aperiodic Cycles. 
       [0159]    With reference to  FIGS. 3 and 11 , a new cycle may or may not be initiated immediately following the completion of any one cycle, in accordance with an embodiment of the invention. If a new cycle is initiated without delay, and if all cycles are identical, then fixed-frequency operation of an engine will result. Similarly, if a fixed time delay is inserted between each cycle and if all cycles are identical then fixed-frequency operation of an engine will again result. Average power output can be varied either by altering the time delay between cycles, or by varying the energy output per cycle as explained above or by a combination of both methods, in accordance with an embodiment of the invention. 
         [0160]    In cases where fixed-frequency operation results in a noisome droning or resonance, the ICEG can be operated in a non-periodic manner, wherein successful cycles are of differing energy content, or of differing duration, or of differing time separation, in accordance with an embodiment of the invention. This variation would be effected by the electronic controller, which may employ a pseudo-random sequence generator, or the action of a chaotically-behaved circuit, or a noise generator, in order to generate a sequence of cycles that is aperiodic, while maintaining a desired average power output. 
       Winding Arrangement. 
       [0161]      FIG. 21  shows a simplified arrangement of windings for use in an ICEG, in accordance with an embodiment of the invention. Such an arrangement may be referred to as a tubular synchronous motor, in accordance with an embodiment of the invention. Shuttle bobbin  2101  is made from permanent magnets and magnetically-permeable material, typically as described above in connection with  FIG. 1 . Between bobbin  2101  and magnetically-permeable cylinder  2102  are coils of wire  2103  through  2109 , wound on a non-magnetic non-conducting thin cylinder  2110 . In  FIG. 21 , the arrows marked on bobbin  2101  indicate the direction of the magnetic flux within the bobbin, and the arrows marked on cylinder  2102  indicate the direction of the magnetic flux within the cylinder. It is understood that shuttle bobbin  2101  in  FIG. 21  performs the function of the shuttle bobbins shown in FIGS.  1 , 14 ,  15 ,  16 , and  17 . 
         [0162]    As drawn in  FIG. 21 , each coil has four turns of wire, but any number of turns can be employed for each coil, in any number of layers of wire. Gaps shown between the coils are shown in  FIG. 21  for clarity, but are not necessary, and would typically be omitted in practice. At the instant depicted, current flows in all coils except  2106 . The standard convention is followed here for indicating current direction, namely, that a dot within a circle indicates a single wire with current flowing toward the viewer, and that a cross within a circle indicates a single wire with current flowing away from the viewer. As a combined result of the flux cutting through coils  2104  and  2108  and the simultaneous flow of current within those coils, a force (leftwards) will be exerted on the bobbin. Likewise, if the bobbin has velocity in either direction at the instant shown, a voltage will be induced in windings  2104  and  2108 . 
         [0163]    In order to arrange that coils  2104  and  2108  have the same magnitude of current flowing in them at any instant of time and in the correct directions, coils  2104  and  2108  are connected electrically in series as illustrated in the manner of the embodiment of  FIG. 22 , wherein only two turns per coil are shown for ease of interpretation. From  FIG. 22  it can be seen that the turns of coils  2104  and  2108  are wrapped around cylinder  2110  in opposing directions. Other coils (further along in the axial direction) can be placed in series with the coils depicted in  FIG. 22 , with alternating winding directions. Semiconductor switches can be used to steer current flow through only those coils that are active, i.e., that are cutting flux from the flanges of the shuttle bobbin. The switches can control individual coils, or pairs of coils, or groups of coils. 
         [0164]    For the instant depicted in  FIG. 21 , it can be seen that current flow in coil  2106  is not required in order to produce an axial force on bobbin  2101 . It can also be seen that if bobbin  2101  is allowed to move leftwards by four coil pitches such that its right-hand flange is aligned with coil  2104 , then the current direction in coil  2104  will need to be reversed from that shown, in order to produce a continuation of force in the leftwards direction.  FIG. 23  shows a sequence of the four sets of coil currents (plotted in amplitude versus axial shuttle distance s) such that axial motion of the bobbin will continue smoothly and without interruption, in accordance with an embodiment of the invention. Not shown in  FIGS. 21 and 22  are position-sensing devices to provide synchronizing information to the drive electronics that feeds the four sets (or “phases”) of coils. The motor depicted in  FIG. 21  acts as a four-phase linear motor. Other numbers of phases are possible, such as three, five, six, etc. Although the profiling of current pulses depicted in  FIG. 23  is square, the edges of the pulses may be rounded or tapered, even until the pulses become sinusoidal in shape. 
         [0165]      FIG. 24  shows a variation of the arrangement of  FIG. 21  in which the magnetically-permeable cylinder  2402  has teeth surrounding the winding coils, thereby providing for higher magnetic field strengths with resultant higher power output for a given size of windings and for a given quantity of permanent magnet material, in accordance with an embodiment of the invention. The toothed laminations run axially, and generally take the form shown in the perspective view given in the embodiment of  FIG. 25 , it being understood that the cross-sectional proportions of the laminations can be varied to suit any particular design. 
       Laminations. 
       [0166]    With a rectangular (straight-sided) cross-section as shown in the embodiment of  FIG. 25 , there will be tangential gaps between the laminations when they are juxtaposed around the perimeter of the non-magnetic non-conducting thin cylinder  2110 . These gaps act as electrical insulation between the laminations, thereby helping to reduce eddy-current losses within the laminations. It is also possible to locate the supporting thin cylinder ( 2110 ) on the outside of the laminations rather than on the inside, thereby permitting a smaller magnetic gap between the bobbin flanges and the lamination teeth. 
         [0167]    In accordance with an embodiment of the invention, the method for constructing laminations of the tubular synchronous motor of an ACEG machine may be as described above. For both the ICEG and ACEG machines, as well as for the external-combustion machines described in U.S. Pat. No. 7,690,199 B2 of Wood, it may be advantageous to construct the laminations in a somewhat spiral manner, rather than in an axially-straight manner. The result of such a spiral disposition will be to induce a gradual rotation of the shuttle as successive axial strokes are executed. Such rotation will result from the fact that the axial forces going and coming are not symmetrical. The benefit of such rotation will be smooth and even mechanical wear of the bearing surfaces over time, particularly of the piston rings. This will provide for the maintenance of higher efficiency operation as the machine wears with usage and age. 
       Axially-Magnetized Arrangement. 
       [0168]      FIG. 26  shows an alternative arrangement of magnets for use in the magnetic shuttle of an ICEG, in accordance with an embodiment of the invention. It is understood that the magnetic shuttle depicted in  FIG. 26  performs the function of the shuttle bobbins shown in  FIGS. 1 ,  14 ,  15 ,  16 ,  17 ,  28  and  31 . 
         [0169]    Shaft  2601  is made from non-magnetic material. Surrounding shaft  2601  are ring-shaped axially-magnetized permanent magnets  2602 ,  2603 ,  2604 , and  2605 . Interleaved between these magnets are rings of magnetically-permeable material,  2606 ,  2607 ,  2608 ,  2609 , and  2610 . 
         [0170]    In  FIG. 26 , the arrows marked on the permanent magnets and on the magnetically-permeable rings indicate the direction of the magnetic flux within the bobbin. Permanent magnets  2602 ,  2603 ,  2604 , and  2605  are placed with alternating axial directions, so that the outside faces of the magnetically-permeable rings have alternating magnetic polarity, (i.e., north-south-north-south, etc.). 
       Radially-Magnetized Arrangement. 
       [0171]      FIG. 27  shows another alternative arrangement of magnets for use in the magnetic shuttle of an ICEG, in accordance with an embodiment of the invention. Again, it is understood that the magnetic shuttle depicted in  FIG. 27  performs the function of the shuttle bobbins shown in  FIGS. 1 ,  14 ,  15 ,  16 ,  17 ,  28  and  31 . 
         [0172]    Shaft  2701  is made from magnetically-permeable material, and may have a hollow core. Surrounding shaft  2701  are ring-shaped radially-magnetized permanent magnets  2702 ,  2703 ,  2704 , and  2705 . Interleaved between these magnets are regions of non-magnetic material, which may be air, or may be solid material. Permanent magnets  2702 ,  2703 ,  2704 , and  2705  may have their volume enhanced by magnetically-permeable rings (not shown in  FIG. 27 ) located either on their outer faces, or on their inner diameters. 
         [0173]    In  FIG. 27 , the arrows marked on the permanent magnets and on the magnetically-permeable shaft  2701  indicate the direction of the magnetic flux within the bobbin. Permanent magnets  2702 ,  2703 ,  2704 , and  2705  are placed with alternating radial magnetic directions, so that their outside faces have alternating magnetic polarity, (i.e., north-south-north-south, etc.). 
         [0174]    It should be noted that in addition to being used with engines described herein, winding and magnet arrangements described herein in connection with  FIGS. 21 through 27  may also be used in electric motors generally. Further, such winding and magnet arrangements may also be used with internal and external combustion engines, including those described in connection with  FIGS. 3A ,  5 A and  13  and elsewhere in U.S. Pat. No. 7,690,199 B2 of Wood, entitled “System and Method for Electrically-Coupled Thermal Cycle,” the disclosure of which is incorporated herein by reference in its entirety. 
       Use in Vehicles 
       [0175]    Heat engine and thermal cycles described herein in accordance with embodiments of the invention may be useful in all manner of applications, including both stationary and mobile applications. In on embodiment according to the invention, electrically-coupled heat engines and thermal cycles described herein may be used for vehicle engines, with the electricity that is produced by the engine being used to drive electric motors, which may be located at or near some or all of the wheels of the vehicle. The foregoing is desirable to be performed with minimal storage of electricity, in order to minimize the weight of batteries used in the vehicle. Such minimal storage of electricity may be achieved by the use of multiple cylinders, each cylinder functioning as an electrically-coupled heat engine according to an embodiment of the invention. By using such multiple cylinders, the instantaneous power collection from the collection of cylinders may be configured to have a minimal ripple of power output, and therefore require less storage of electricity and therefore less weight of batteries. 
       Waste Heat Capture 
       [0176]    In accordance with an embodiment of the invention, waste heat given off by a heat engine in accordance with embodiments described herein, may be captured and used by an external combustion engine. For example, heat may be captured by a machine that receives its heat from an external heat source, such as the machine described in connection with  FIG. 3A  of, and elsewhere in, U.S. Pat. No. 7,690,199 B2 of Wood, entitled “System and Method for Electrically-Coupled Thermal Cycle,” the disclosure of which is incorporated herein by reference in its entirety; and also such as the air cycle machine described below (the “ACEG”). 
       Implementation of an External Combustion Electricity Generator. 
     a) Mechanical Arrangement 
       [0177]      FIG. 28  is a cross-section of a machine to generate electricity from a source of heat, in accordance with an embodiment of the invention. A working cylinder  2801  houses a piston assembly consisting of a piston head  2802  attached to a central shaft  2803 . Between the piston head and one end of the working cylinder  2801  is a working chamber  2804 . The end  2817  of the working cylinder  2801  that opposes the piston head  2802  is referred to as the cylinder head. An external source of heat is applied to cylinder head  2817 , it being understood that this source of heat is at a temperature higher than the air which is ambient to the cylinder head  2817 . 
         [0178]    The opposing surfaces of cylinder head  2817  and piston head  2802  need not be flat as shown in  FIG. 28 . Non-flat shapes for these surfaces will allow for increased surface area for the conduction of heat from the heat source into the working cylinder  2801 . By arranging for the two surfaces to have complementary shapes so as to nestle close to each other, minimal volume of the working chamber  2804  is achieved at the time when the piston head approaches the cylinder head. To this end, these two opposing surfaces may be conical or hemispherical in shape. They may also have rings or fins that nestle together with minimal interstitial volume and without mechanical contact. 
         [0179]    Separating cylinder head  2817  and working cylinder  2801  is a thermally-insulating ring  2820 . At the end of working cylinder  2801  that is away from the cylinder head  2817  is a thermally-insulating disc  2816 , through which passes central shaft  2803 . Central shaft  2803  is typically made of thermally-insulating material, whereas piston head  2802  may be metallic, and may have a ceramic or other thermally-non-conductive surface coating. 
         [0180]    Heat sources for use with an embodiment of the invention include, but are not limited to, firewood and other forms of biomass, fossil fuels, geothermal energy, solar energy, nuclear energy, waste heat from industrial processes, waste heat from gas turbines, waste heat from heat engines including combustion engines, and waste heat from fuel cell system systems. Heat generated from any of these sources is delivered to cylinder head  2817  by standard heat-transfer techniques. 
         [0181]    Connecting the working chamber  2804  to the ambient air is a valve  2805 . Valve  2805  serves to allow both the inlet and exhaustion of ambient air to and from the working chamber  2804 . Typically, but not necessarily, valve  2805  pierces the cylinder head  2817 . Alternatively, valve  2805  may also pierce thermally-insulating ring  2820  or it may pierce working cylinder  2801 . There may also be a multiplicity of valves  2805  acting in a substantially, but not exactly, synchronous manner. Valve  2805  may be actuated by electric solenoid action, under control from an electronic controller. 
         [0182]    Attached to the central shaft  2803 , away from the piston head  2802 , is a magnetic shuttle assembly in the form of a spool, consisting of two discs  2809  and  2810  surrounding the central shaft  2803 . Between shuttle discs  2809  and  2810 , and surrounding central shaft  2803 , is an array  2812  of permanent magnets. Shuttle discs  2809  and  2810  are made of magnetically-permeable material such as iron or magnet-grade steel or ferrite. 
         [0183]    Surrounding shuttle discs  2809  and  2810  are electric windings  2813  embedded in or otherwise attached to magnetically-permeable cylinder  2814 , typically made of laminations of magnet-grade steel or of ferrite. Magnetically-permeable cylinder  2814  typically has slots to secure or encompass the windings  2813 , as is the manner in electric machines. Arranged together, magnet array  2812 , shuttle discs  2809  and  2810 , and laminations  2814  form a magnetic circuit, whose flux intersects windings  2813 . Accordingly, whenever piston head  2802  moves axially within working cylinder  2801 , a voltage is induced in windings  2813  by the shuttle discs  2809  and  2810 . Conversely, whenever an electric current is passed through windings  2813 , an axial force is exerted on the shuttle discs  2809  and  2810  by the windings  2813 . This force is translated by the central shaft  2803  to the piston head  2802 . Position sensors (not shown in  FIG. 28 ) provide information to an electronic controller. It is understood that shuttle discs  2809  and  2810  do not contact either the electric windings  2813  or the laminations  2814  at any time during their travel. 
         [0184]    Surrounding laminations  2814  is a winding support cylinder  2815 , which is attached to working cylinder  2801  by thermally-insulating disc  2816 . Attached to the opposing end of winding support cylinder  2815  is a shaft support disc  2818 . Attached centrally to shaft support disc  2818  is a shaft support pin  2821  that fits inside central shaft  2803 . Shaft support pin  2821  provides lateral support to the shuttle assembly made up of piston head  2802 , shaft  2803 , magnet array  2812 , and shuttle discs  2809  and  2810 . 
         [0185]    Piston head  2802  typically features piston rings (not shown in  FIG. 28 ) for mechanical contact with the inside wall of working cylinder  2801 . Orifice  2808  at the inner diameter of insulating disc  2816  restricts airflow between the working cylinder  2801  and the magnet array  2812 , while maintaining a small clearance between the central shaft  2803  and the insulating disc  2816 , to avoid mechanical wear. 
         [0186]    Shaft support disc  2818  typically is perforated with a plurality of orifices (not shown in  FIG. 28 ) to allow for atmospheric air cooling of the magnet array  2812 . Lower shuttle disc  2809  may similarly be perforated with a plurality of orifices (not shown in  FIG. 28 ) to allow for air cooling of the magnet array  2812 . Air cooling of the magnets may be assisted by a cooling fan (not shown in  FIG. 28 ). Upper shuttle disc  2810  may have thermal insulation (not shown in  FIG. 28 ) on its upper surface (facing insulating disc  2816 ) to resist heat flow from the working cylinder  2801  toward the magnet array  2812 . 
         [0187]    In  FIG. 28  winding support cylinder  2815  is depicted as having a larger diameter than working cylinder  2801 . In other embodiments, these two cylinders may have the same diameter, or the working cylinder  2801  may have a larger diameter than the winding support cylinder  2815 . An encompassing cylinder or jacket (not shown in  FIG. 28 ) may be located around the working cylinder  2801  to restrict heat loss from the exterior surface of the working cylinder. Valve  2805  may be actuated by electric solenoid action, under control from an electronic controller. 
       b) Electrical Arrangement 
       [0188]    The embodiment of  FIG. 28  may be operated with the general electrical arrangement shown in  FIG. 2 , in accordance with an embodiment of the invention. The windings  201  connect to an electronic power converter  202 .  FIG. 2  shows two isolated windings for illustrative convenience, but any number of separate windings may be employed, as necessary. Also connected to electronic power converter  202  are signals from an electronic controller  208 , which receives signals from position sensors  203 . Although two sensors are shown in  FIG. 2 , any number of position sensors may be employed. The position sensors  203  give the electronic controller  208  the information that it needs for it to know the exact location of the shuttle discs  2809  and  2810  at any instant in time. 
         [0189]    Electronic power converter  202  is also connected to a DC bus  207 , to which is also attached a capacitor (or supercapacitor)  204  and a battery  205  and an electric load  206 . The electric load may be disconnected from the bus when not required, while the electronic power converter  202  continues to charge the battery  205 . Electronic controller  208  also receives current and voltage signals from the DC bus  207 , as well as current and voltage signals from the windings  201 . 
         [0190]    During operation of the system, the electronic controller  208  controls the flow of electric current into and out of the windings in such a manner as to cause the motion of the shuttle to move up and down (i.e., axially) so as to effect energy transfer from compressed air in the working chamber through the windings, and through the electronic power converter  202  to the electric load  206 . The capacitor  204  and battery  205  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  202  stores little or no energy, and transfers power between the DC bus  207  and the windings  201  in a highly efficient manner. 
       c) Thermal Cycle 
       [0191]    The operation of a heat engine that employs a quantity of gas as an operating medium may be described by reference to a pressure-volume diagram, hereinafter referred to as a P-V diagram. 
         [0192]      FIG. 3  shows a pressure-volume diagram for advantageous operation of the machine of the embodiments of  FIGS. 28 and 2 , the Air Cycle Electricity Generator, hereinafter referred to as the “ACEG,” in accordance with an embodiment of the invention. The pressure P represented in  FIG. 3  is the pressure within the working chamber  2804  of  FIG. 28 , and the volume V represented in  FIG. 3  is the volume of gas within that working chamber. The cycle of operation depicted in  FIG. 3  will hereinafter be referred to as the Complete ACEG Cycle. (Truncated versions will be described below.) Motion in the time domain is depicted in  FIGS. 29 and 30 , which display pressure P and volume V versus time, in accordance with an embodiment of the invention. In addition to being defined by a P-V cycle, an ACEG Cycle in an embodiment according to the invention may be defined by a time domain sequence. 
         [0193]    Consider a single cycle of operation beginning at point  305  in  FIG. 3 . The volume of gas is zero, indicating that the piston shaft  2803  has moved to its uppermost limit, leaving minimal space between piston head  2802  and cylinder head  2817 . (In this explanation it is assumed that the valve  2805  takes up negligible volume inside the working chamber  2804 .) At point  305  in  FIG. 3  the pressure is 1 atmosphere, (following an exhaustion stroke at atmospheric pressure.) 
       Step i), Induction: 
       [0194]    With valve  2805  open, ambient air is drawn into the working chamber  2804  at atmospheric pressure during t 0  to t 1 , until point  301  is reached as determined by the electronic controller  208 . Let the volume of the working chamber  2804  at point  301  be K. 
         [0000]    Step ii), Compression: 
         [0195]    Following closure of the valve  2805  during t 1  to t 2 , the air in the working chamber  2804  is now compressed adiabatically (i.e., with no thermal losses) during t 2  to t 3  until point  302  is reached as determined by the electronic controller  208 . Let us arbitrarily define the volume of the working chamber  2804  at point  302  to be 1 unit. 
         [0000]    Step iii), Heating: 
         [0196]    Beginning at point  302 , the electronic controller  208  initiates no further motion, and holds the piston head  2802  stationary while heat flows into the working chamber  2804  through cylinder head  2817 . This heat flow continues until the pressure P has risen to point  303  as determined by the electronic controller  208 . As indicated in  FIGS. 29 and 30 , this pressure rise step takes finite time, from t 3  to t 4 . Note that for heat to flow in the required direction, the temperature of the external heat source must be higher than the temperature attained by the compressed air at point  302  of the cycle, i.e., at the end of the compression stroke. 
         [0000]    Step iv), Expansion: 
         [0197]    At point  303  the electronic controller  208  initiates an adiabatic expansion of the heated air in the working chamber  2804 , until the pressure has fallen during t 4  to t 5  all the way back to unity (atmospheric pressure) at point  304 . Let the volume of the working chamber  2804  at point  304  be E. 
       Step v), Exhaustion: 
       [0198]    At point  304 , valve  2805  is opened during t 5  to t 6 , following which the electronic controller  208  causes upwards motion of the piston shaft  2803  during t 6  to t 7  until almost all air in the working chamber  2804  is exhausted. Another cycle may or may not be initiated immediately, as determined by the electronic controller  208 . Valve  2805  remains open throughout the exhaustion and induction strokes. In order to minimize the intake of hot air that has just been exhausted, an external electronically-controlled flap or valve (not shown in  FIG. 28 ) may be employed to ensure that fresh cool air is drawn in through valve  2805  during the induction stroke. 
         [0199]    It should be noted that times taken for each of the major strokes (induction, compression, expansion, exhaustion) need not be the same, as is the case in a conventional internal combustion engine, and that these times may be varied relative to each other by an electronic controller, in accordance with an embodiment of the invention. Note also that with expansion all the way to atmospheric pressure being possible in an embodiment according to the invention, the audible sound of exhaust may be lower than conventional internal combustion engines, and may allow the reduction in size of, or elimination of, the muffler. 
       d) Variable Energy Output per Cycle 
       [0200]    The output energy per cycle for an ACEG can be varied by altering the length of the intake stroke ( 305 - 301  in  FIG. 3 ), in accordance with an embodiment of the invention. In any given physical embodiment of an ACEG machine, there will be a practical limit to the expansion distance. If the inlet stroke magnitude is increased beyond a certain limit imposed by that expansion distance in accordance with the laws of thermodynamics, then it will be necessary to partially truncate the expansion stroke, as shown in  FIG. 9 , which depicts a Partially Truncated ACEG Cycle. In the limiting case of a fully truncated expansion stroke as shown in  FIG. 10 , the inlet stroke and expansion stroke are of equal length, thereby yielding a Fully Truncated ACEG Cycle. 
         [0201]      FIG. 11  displays a family of four ACEG cycles of varying energy content, in accordance with an embodiment of the invention. The first two cycles, with pressure peaks at points A and B, are Complete ACEG Cycles. The cycle with pressure peak at point C is a Partially Truncated ACEG Cycle. The cycle with pressure peak at point D is a Fully Truncated ACEG Cycle. 
       e) Waste Heat Capture 
       [0202]    In accordance with an embodiment of the present invention, waste heat given off by another heat engine (such as an internal combustion engine) may be captured and used as the source of heat for an ACEG. For example, heat may be captured from an ICEG as described herein. Waste heat sources for use with the present invention include, but are not limited to, industrial processes, gas turbines, other heat engines including combustion engines, and fuel cell system systems such as those of the solid-oxide type. 
       f) Electronic Controller Implementation 
       [0203]    In accordance with an embodiment of the invention, an electronic controller can be implemented for an ACEG to follow the cycle of  FIG. 3  in a manner similar to that described above with reference to  FIGS. 12 and 13 . A difference between the ACEG controller in accordance with an embodiment of the invention and the ICEG controller is that, for the ACEG machine, at the end of the compression stroke (points  302 ,  2902 , and  3002  in  FIGS. 3 ,  29 , and  30 ) the controller must ensure that the shuttle is held stationary until the pressure reaches the requisite level (at point  2903  of  FIG. 29 ) before the shuttle is released for the expansion stroke. This high-pressure point will typically be detected by a pressure sensor, although a temperature sensor may also suffice. This decision point in the ACEG cycle replaces the corresponding decision point in the ICEG cycle at which ignition is detected. 
       g) Other Improvements 
       [0204]    Improvements described above can be applied to the ACEG machine, in accordance with an embodiment of the invention. These include employing axial opposition of cylinders, the use of heat pipes to assist the cooling of the permanent magnets, methods for constructing valves, methods for constructing the tubular synchronous motor, gravity-assisted energy capture, magnetically-assisted energy capture, magnetic bumpers for lossless resting, and cycles that are either periodic or aperiodic. 
         [0000]    h) Single valve ICEG 
         [0205]    In another embodiment according to the invention, the method of using a single valve for the intake and exhaustion of air into and out of the working cylinder as described above for an air-cycle electric generator (ACEG) may also be employed in an internal combustion electric generator (ICEG) of the general type as described above. The principle of such a scheme is illustrated in the ICEG of the embodiment of  FIG. 31 , the arrangement of which is similar to that of the ACEG of  FIG. 28  herein, with the difference that a fuel injector  3122  is included and the thermally-insulating ring  2820  is omitted. In addition, an air plenum  3123  surrounds air valve  3105 . 
         [0206]    Incoming air flows into one orifice of plenum  3123 , and exhaust air flows out of a second orifice of plenum  3123 . Inside plenum  3123  an electronically-controlled flap  3124  serves to divert the flow of air within the plenum. Motion of flap  3124  is synchronized with the thermal cycle in such a way that exhaust air flows out of working chamber  3104  through the exhaust duct, and inlet air flows through the inlet duct into the working chamber  3104  when required. 
         [0207]    Flap  3124  is shown in  FIG. 31  by way of illustrating the principle of operation of this embodiment of the invention. In practice, other methods of diverting air flow in the plenum may be employed, including the use of an electronically-controlled rotary valve in place of flap  3124 . By comparison with the requirements of valve  3105 , air-tightness is not required for the diverting means that performs the function of flap  3124 . Accordingly, advantages of an embodiment according to the present invention include reduced cost and improved reliability by comparison with an engine having two or more valves piercing the combustion chamber. 
       i) Heat Pump 
       [0208]    While the embodiments of  FIGS. 1 ,  2 ,  12 ,  13 ,  14 ,  15 ,  16 ,  17 ,  19 ,  28 , and  31  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 embodiments of the invention to create an electrically-powered heat pump. In this case, the embodiments of  FIGS. 1 ,  2 ,  12 ,  13 ,  14 ,  15 ,  16 ,  17 ,  19 ,  28 , and  31  are essentially operated in reverse: energy stored in electrical circuitry such as that of  FIG. 2  is cycled in and out of a working cylinder such as  2801  via windings  2813  so that piston head  2802  performs a heat pump cycle, and likewise for the other arrangements. Such a heat pump may be used to extract heat energy from ambient air, and to deliver that heat to an external heat sink by way of cylinder head  2817 . It may also be used to produce liquid and/or gaseous fuels from constituent elements, for instance to produce ammonia from a mixture of hydrogen and nitrogen. 
         [0209]      FIG. 32  shows a P-V diagram for such a heat pump (i.e., a refrigerator, or air conditioner) operated in accordance with an embodiment of the invention.  FIGS. 33 and 34  give the associated timing diagrams for pressure and volume versus time, in accordance with an embodiment of the invention. 
         [0210]    Consider a single cycle of operation beginning at point  3205  in  FIG. 32 . The volume of gas is zero, indicating that the piston shaft  2803  has moved to its uppermost limit, leaving minimal space between piston head  2802  and cylinder head  2817 . (In this explanation it is assumed that the valve  2805  takes up negligible volume inside the working chamber  2804 .) At point  3205  in  FIG. 32  the pressure is 1 atmosphere, (following an exhaustion stroke at atmospheric pressure.) 
       Step i), Induction: 
       [0211]    With valve  2805  open, ambient air is drawn into the working chamber  2804  at atmospheric pressure during t 0  to t 1 , until point  3201  is reached as determined by the electronic controller  208 . Let the volume of the working chamber  2804  at point  3201  be K. 
         [0000]    Step ii), Compression: 
         [0212]    Following closure of the valve  2805  during t 1  to t 2 , the air in the working chamber  2804  is now compressed adiabatically (i.e., with no thermal losses) during t 2  to t 3  until point  3202  is reached as determined by the electronic controller  208 . Let us arbitrarily define the volume of the working chamber  2804  at point  3202  to be 1 unit. 
         [0000]    Step iii), Cooling: 
         [0213]    Beginning at point  3202 , the electronic controller  208  initiates no further motion, and holds the piston head  2802  stationary while heat flows out of the working chamber  2804  through cylinder head  2817 . This heat flow continues until the pressure P has fallen to point  3203  as determined by the electronic controller  208 . As indicated in  FIGS. 33 and 34 , this fall in pressure takes finite time, from t 3  to t 4 . Note that for heat to flow in the required direction, the temperature of the external heat sink must be lower than the temperature attained by the compressed air at point  3202  of the cycle, i.e., at the end of the compression stroke. 
         [0000]    Step iv), Expansion: 
         [0214]    At point  3203  the electronic controller  208  initiates an adiabatic expansion of the air in the working chamber  2804 , until the pressure has fallen during t 4  to t 5  all the way back to unity (atmospheric pressure) at point  3204 . Let the volume of the working chamber  2804  at point  3204  be E. 
       Step v), Exhaustion: 
       [0215]    At point  3204 , valve  2805  is opened during t 5  to t 6 , following which the electronic controller  208  causes upwards motion of the piston shaft  2803  during t 6  to t 7  until almost all air in the working chamber  2804  is exhausted. Another cycle may or may not be initiated immediately, as determined by the electronic controller  208 . Valve  2805  remains open throughout the exhaustion and induction strokes. In order to minimize the intake of cool air that has just been exhausted, an external electronically-controlled flap or valve (not shown in  FIG. 28 ) may be employed to ensure that fresh air is drawn in through valve  2805  during the induction stroke. 
         [0216]    It should be noted that times taken for each of the major strokes (induction, compression, expansion, exhaustion) need not be the same, as is the case in a conventional mechanically-reciprocating machine, and that these times may be varied relative to each other by an electronic controller, in accordance with an embodiment of the invention. Note also that with expansion all the way to atmospheric pressure being possible in an embodiment according to the invention, the audible sound of exhaust may allow the reduction in size, or elimination of, a muffler. 
         [0217]    To illustrate the use of a heat pump of the type shown in  FIG. 28  for the production of a fuel, in accordance with an embodiment of the invention, we note that, with a suitable catalyst present, the application of heat and pressure to a mixture of hydrogen and nitrogen will yield ammonia in accordance with the following chemical equation: 
         [0000]      3H 2 +N 2 =2NH 3   (Equation 23)
 
         [0218]    We refer again to  FIGS. 28 ,  32 ,  33 , and  34 . One cycle of ammonia production is completed as follows: 
       Step i), Induction: 
       [0219]    With valve  2805  open, a pre-heated mixture of hydrogen and nitrogen is drawn into the working chamber  2804  at a suitable pressure during t 0  to t 1 , until point  3201  is reached as determined by the electronic controller  208 . Let the volume of the working chamber  2804  at point  3201  be K. 
         [0000]    Step ii), Compression: 
         [0220]    Following closure of the valve  2805  during t 1  to t 2 , the pre-heated mixture of hydrogen and nitrogen in the working chamber  2804  is now compressed adiabatically (i.e., with no thermal losses) during t 2  to t 3  until point  3202  is reached as determined by the electronic controller  208 . Let us arbitrarily define the volume of the working chamber  2804  at point  3202  to be 1 unit. During this compression step of the cycle, and with a suitable catalyst present on the inside surfaces of the combustion chamber  2804 , ammonia is formed, in accordance with Equation 23. 
         [0000]    Step iii), Cooling: 
         [0221]    Beginning at point  3202 , the electronic controller  208  initiates no further motion, and holds the piston head  2802  stationary while heat flows out of the working chamber  2804  through cylinder head  2817 . This heat outflow may be used to pre-heat an incoming charge of hydrogen and nitrogen, thereby effecting an overall energy savings. Heat flow continues until the pressure P has fallen to point  3203  as determined by the electronic controller  208 . As indicated in  FIGS. 33 and 34 , this fall in pressure takes finite time, from t 3  to t 4 . Note that for heat to flow in the required direction, the temperature of the external heat sink must be lower than the temperature attained by the compressed mixture in the working chamber at point  3202  of the cycle, i.e., at the end of the compression stroke. 
         [0000]    Step iv), Expansion: 
         [0222]    At point  3203  the electronic controller  208  initiates an adiabatic expansion of the cooled ammonia in the working chamber  2804 , until the pressure has fallen during t 4  to t 5  all the way back to point  3204 . Let the volume of the working chamber  2804  at point  3204  be E. 
       Step v), Exhaustion: 
       [0223]    At point  3204 , valve  2805  is opened during t 5  to t 6 , following which the electronic controller  208  causes upwards motion of the piston shaft  2803  during t 6  to t 7  until almost all gas in the working chamber  2804  is exhausted. 
         [0224]    The teachings of all patents, published applications and references cited herein are incorporated by reference in their entirety. 
         [0225]    While this invention has been particularly shown and described with references to example 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.