Patent Publication Number: US-10758888-B1

Title: Simultaneous generation of electricity and chemicals using a renewable primary energy source

Description:
CROSS REFERENCE TO RELATED PATENT APPLICATIONS 
     The present application is a continuation-in-part application of U.S. patent application Ser. No. 14/537,792, entitled “Simultaneous Generation of Electricity and Chemicals using a Renewable Primary Energy Source” by Ronny Bar-Gadda, filed on Nov. 10, 2014, which claims the benefit of U.S. Provisional Patent Application No. 62/061,578, titled “The Simultaneous Generation of Electricity and Chemicals using a Renewable Primary Energy Source,” filed Oct. 8, 2014, which applications are hereby incorporated herein by reference in their entirety. 
    
    
     BACKGROUND 
     A. Technical Field 
     The present invention relates to the generation and storing of electricity and chemical products and, more particularly, to systems, devices, and methods of concurrently generating power and electromagnetic radiation using renewable sources while producing chemical reactants. 
     B. Background of the Invention 
     Existing methods of generating electrical power through combustion of conventional fossil fuel energy sources are typically based on the utilization of a working fluid such as a gas or boiler-generated stream in a thermodynamic cycle in order to generate a motive force for rotating the shaft of a turbine, thereby, transforming chemical energy into an electromotive force that generates electrical energy. These methods are inherently limited by the maximum achievable Carnot cycle efficiency. In addition, the change of phase of material, such as the transformation of the water to steam requires large quantities of energy, most of which is lost in the form of heat due to condensation after exiting the turbine. 
     Alternative technologies that generate electrical power in the form of current and voltage from non-carbon-based sources suffer similarly from respective theoretical maximum efficiencies, for example, 59.3% for wind technology. 
     In contrast, solar cell technology using the photovoltaic effect undergoes an isothermal process that is not subject to power cycle analysis and the limitations of the Carnot cycle efficiency. Energy from the sun in the form of photons carrying energy or electromagnetic radiation can be harnessed directly to induce an electromotive force on free electrons to generate electrical power. Unfortunately, solar cells have inherent losses, such as FR losses, and the energy produced in the cell still needs to be stored before it can be transported and used. Until now, this made solar energy unattractive for applications such as the industrial-scale production of chemicals in capital-intensive facilities. What is needed are environmentally friendly systems and processes that efficiently produce chemicals while overcoming the above-described limitations. 
     SUMMARY OF THE INVENTION 
     In embodiments, a power generating apparatus includes: an emitter to convert a first current that has been derived from a solar cell into a coherent electron beam, the emitter having a first single potential; a collector having a second potential to accelerate electrons in the coherent electron beam, the collector provides a second current that is capable of driving a load, the collector comprises a surface that has a material with favorable secondary electron emission characteristics to generate secondary electron emission; and an electromagnetic radiation device to generate electromagnetic radiation at a frequency substantially equal to an absorption frequency of a predetermined chemical reactant to generate hydrogen from water vapor. 
     In embodiments, a power generating apparatus includes a power generation system to generate energy from a renewable energy source. The power generation system includes: an apparatus that generates a first current from a solar cell; an emitter to convert the first current into a coherent electron beam, the emitter having a first single potential; a collector having a second potential to accelerate electrons in the coherent electron beam, the collector providing a second current, the collector comprises a surface that has a material with favorable secondary electron emission characteristics to generate secondary electron emission; a converter that converts the second current to a power source capable of driving a load; and an electromagnetic radiation device that generates electromagnetic radiation at a frequency substantially equal to an absorption frequency of a predetermined chemical reactant to generate hydrogen from water vapor. 
    
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
       Reference will be made to embodiments of the invention, examples of which may be illustrated in the accompanying figures. These figures are intended to be illustrative, not limiting. Although the invention is generally described in the context of these embodiments, it should be understood that this is not intended to limit the scope of the invention to these particular embodiments. 
       FIGURE (“FIG.”)  1  is a general illustration of a system to generate energy from a renewable energy source according to various embodiments of the invention. 
         FIG. 2  is an exemplary schematic of a power generator to generate energy from a renewable energy source according to various embodiments of the invention. 
         FIG. 3  is an exemplary a power generator capable of generating phased electrical power according to various embodiments of the invention. 
         FIG. 4  illustrates a power generator capable of producing electromagnetic radiation at a specific microwave frequency according to various embodiments of the invention. 
         FIG. 5  illustrates a power generator capable of producing high frequency electromagnetic radiation via transverse motion of an electron beam, according to various embodiments of the invention. 
         FIG. 6  illustrates a power generator that uses a selection of a narrow range of electron velocities in an electron beam to reduce the number of collector electrodes and accompanying power supply. 
         FIG. 7  illustrates a power generator in which the electron beam is a plasma electron beam, according to various embodiments of the invention. 
         FIG. 8  is a flowchart of an illustrative process for power generation from a renewable energy source in accordance with various embodiments of the invention. 
         FIG. 9  is an exemplary schematic of a system to generate energy from a renewable energy source according to various embodiments of the invention. 
         FIG. 10  is an exemplary schematic of a system to generate energy from a renewable energy source according to various embodiments of the invention. 
         FIG. 11  is an exemplary schematic of a system to generate energy from a renewable energy source according to various embodiments of the invention. 
         FIG. 12  shows an exemplary arrangement of electron collectors according to various embodiments of the invention. 
         FIG. 13  is an exemplary schematic of a power generator having a communication device according to various embodiments of the invention. 
         FIG. 14  is an exemplary schematic of a chemical reacting system according to various embodiments of the invention. 
         FIG. 15  is an exemplary schematic of a chemical reacting system according to various embodiments of the invention. 
         FIGS. 16A and 16B  show exemplary arrangements of minors according to various embodiments of the invention. 
         FIG. 17  is an exemplary schematic of a chemical reacting system according to various embodiments of the invention. 
         FIG. 18  illustrates an exemplary energy band structure of an emitter according to various embodiments of the invention. 
     
    
    
     DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     In the following description, for the purpose of explanation, specific details are set forth in order to provide an understanding of the invention. It will be apparent, however, to one skilled in the art that the invention can be practiced without these details. One skilled in the art will recognize that embodiments of the present invention, described below, may be performed in a variety of ways and using a variety of means. Those skilled in the art will also recognize that additional modifications, applications, and embodiments are within the scope thereof, as are additional fields in which the invention may provide utility. Accordingly, the embodiments described below are illustrative of specific embodiments of the invention and are meant to avoid obscuring the invention. 
     Reference in the specification to “one embodiment” or “an embodiment” means that a particular feature, structure, characteristic, or function described in connection with the embodiment is included in at least one embodiment of the invention. The appearance of the phrase “in one embodiment,” “in an embodiment,” or the like in various places in the specification are not necessarily referring to the same embodiment. 
     Furthermore, connections between components or between method steps in the figures are not restricted to connections that are affected directly. Instead, connections illustrated in the figures between components or method steps may be modified or otherwise changed through the addition thereto of intermediary components or method steps, without departing from the teachings of the present invention. 
       FIG. 1  is a general illustration of a system to generate energy from a renewable energy source according to various embodiments of the invention. System  100  comprises solar cell  1 , voltage regulator  2 , battery  3 , power supply  4 , power generator  5 , inverter  6 , load  7 , fuel cell  8 , hydrogen storage  9 , oxygen storage  10 , metal halide compressor  11 , condenser  13 , separation unit  15 , nitrogen compressor  17 , and ammonia converter  18 . Solar cell  1  typically comprises a plurality of a solar panels that convert photons from sunlight into voltage. In one embodiment, solar cell  1  is implemented as a high voltage solar panel that outputs a sufficiently high voltage to replace power supply  4 . 
     Solar cell  1  is coupled to voltage regulator  2  that in operation regulates the output voltage of solar cell  1  to smooth out voltage variations due to varying insolation caused by natural variations in the sun&#39;s position relative to solar cell  1  and meteorological conditions, such as clouds causing a reduction in the intensity of sunlight incident on the surface of solar cell  1 . Battery  3  provides energy, especially, it instances where the sun&#39;s insolation is reduced to a level that causes the power output of power generator  5  to fall below a minimum value. Battery  3  may advantageously be operated at nighttime to enable continuous power delivery by system  100  to load  7 , which is an electric motor or any other electric device. Likewise, metal hydride compressor  11  may be used in conjunction with fuel cell  8  to generate electricity during hours when the solar insolation falls below a critical level of performance in which the solar panel delivers power at a rate that cannot meet demand. Power supply  4  may provide direct or alternating current to power generator  5 . In one embodiment, power generator  5  is designed to generate high frequency electromagnetic radiation that may be used, for example, to generate hydrogen from water vapor. 
     The electromagnetic radiation is generated by resonant or non-resonant structures designed to interact with an electron beam to generate one or more high frequencies. Ideally, the frequencies fall in a range of absorption frequencies useful for creating desired chemical compounds. The operation of sections of system  100  under vacuum conditions allows for the generation of the water vapor taking advantage of the depressed boiling point at sub-atmospheric pressures. In one embodiment, hydrogen is generated from water vapor using electromagnetic radiation by generating frequencies equal to the optimum frequency for absorption of energy in water molecules. 
     Water vapor may be produced by any method known in the art, including evaporation by solar heating or electrical heating, e.g., using electrical energy provided by solar cell  1 . Water from any source, including waste water and salt water, may be dissociated into its elements, hydrogen and oxygen, and burned to form purified water. The resulting combustion heat may be used to produce electricity via conventional turbine technology. The so generated energy can then power, for example, water pumps that distribute the generated water. 
     In example in  FIG. 1 , oxygen generated in power generator  5  is delivered to oxygen storage unit  10 , while generated hydrogen is delivered to storage unit  9 . Fuel cell  8  generates electricity for night time operation of system  100 . Fuel cell  8  derives its hydrogen fuel from hydrogen storage unit  9  and air or oxygen from oxygen storage  10 . A compressor (not shown) may be advantageous placed between hydrogen storage unit  9  and fuel cell  8  to increase the pressure of the hydrogen entering fuel cell  8 . Since solar power is direct current in nature, inverter  6  may be used to generate an alternating current depending on the requirements of power generator  5 , whose components and function are described further below with respect to  FIG. 2 , but may not be necessary in DC applications of power generator  5  and in single or three-phase power generation application, as described further below. 
     In one embodiment, system  100  in  FIG. 1  is designed to produce ammonia in addition to producing hydrogen and oxygen. If carbon dioxide is used as a reactant instead of nitrogen, other chemicals such as methane or methanol may be produced. Since ammonia is thermodynamically favored at high pressure and low temperatures, as can be derived from its stoichiometry, a compressor, e.g., metal hydride compressor  11 , can be used to increase the pressure to meet desired reaction conditions. Similarly, nitrogen compressor  17  is utilized in order to raise the nitrogen pressure. In one embodiment, hydrogen from metal hydride compressor  11  and nitrogen from 17 are combined in ammonia converter  18  in order to produce ammonia products  19 . Unlike existing methods that generate pure nitrogen from the air using conventional separation methods such as cryogenic or membrane separation, the concomitant production of noble gases and pure water along with nitrogen using system  100  optimizes the economics and efficiency of the overall production of ammonia. 
     Condenser  13  located at the exit of fuel cell  8  recovers the water generated as pure condensed water  14  byproduct of the electricity generation process. Condensed water  14  may be gathered and sold or serve other process functions, such as cooling. The remaining residual gases flow to separation unit  15  where noble gases are removed, shown as exit stream  16  in  FIG. 1 . Their constituents can be removed separately through many different methods. For example, separation unit  15  may be an adsorption column, whereby separation of the various gaseous components are eluded according to their adsorption coefficient on the surface of the material used for the separation. These materials are commonly found in adsorption columns in gas chromatographic processes. The remaining constituent, nitrogen, enters nitrogen compressor  17  for use in the ammonia synthesis process. 
     Since air contains both nitrogen and noble gases (e.g., helium, argon, xenon, krypton) as well as oxygen, these materials as well as the product of the fuel cell process, i.e., water, can be recovered as byproducts. In one embodiment, the oxidizer for fuel cell  8  may operate with air  12  instead of pure oxygen from oxygen storage  10 , and noble gases are recovered. Nitrogen may also be recovered from exit stream  16  since its separation properties are sufficiently distinctive from that of oxygen. The two key products; namely, hydrogen and nitrogen, may be combined in the correct ratio to produce ammonia. Other commercial chemicals such as methanol, ethanol, hydrocarbons, ethers, longer chain alcohols, aldehydes, ketones, phenols, heterocyclic compounds, etc. may be produced from CO 2 , which may be obtained from a variety of sources. 
       FIG. 2  is an exemplary schematic of a power generator to generate energy from a renewable energy source according to various embodiments of the invention. Power generator  200  comprises solar cell  20  comprising p-n junction  21 , transformer  34 , heater  43 , emitter  35 , grid  37 , collector  42 , and power conditioner  39 . In operation, solar cell  20  receives electromagnetic radiation in the form of sun light  22  that is captured, temporarily stored in p-n junction  21 , and output to both transformer  34  and heater  43 . Heater  43  performs thermionic generation of electrons from emitter  35 , while transformer  34  raises the voltage on emitter  35  to higher levels. Electrons emitted from emitter  35  form a coherent train of electrons or an electron beam that is directed through grid  37 . 
     In one embodiment, the electron beam is employed to generate pulsed or alternating current. The electrons are subsequently deposited on one or more collector electrodes  42  in order to capture the energy in the electron beam. In one embodiment, multiple collector electrodes  42  within varying bias voltages may be positioned in such a manner as to capture electrons having different levels of the kinetic energy. The collected electrons generate a current that can be filtered and otherwise processed to drive various types of loads (not shown). 
     The method of accelerating electrons in example in  FIG. 2  may be used to generate coherent electromagnetic radiation  70  using various structures, such as resonating cavities, magnets or coils, dielectric liners, etc. In embodiments, coherent electromagnetic radiation  70  is tuned to a specific frequency or band of frequencies that is used to perform specific tasks, as will be discussed with respect to  FIG. 4  through  FIG. 7  below. 
       FIG. 3  is an exemplary a power generator capable of generating phased electrical power according to various embodiments of the invention. Power generator  300  comprises power supply  34 , emitter  35 , grid power supply  36 , grid  37 , collector power supply  38 , collector electrodes  42 , heater power supply  43 , inverter  39 , transformer  40 , and load  41 . Although power generator  300  may produce electromagnetic radiation, it is not optimized to produce a coherent electron beam at a specific or band of frequencies. Grid  37  is a fine mesh to allow the electron beam to pass through or be stopped according to the desired outcome. The mesh is used to allow electrical continuity and a path for the applied charge. 
     In operation, cathode power supply  34  provides power for emitter  35 . Grid power supply  36  controls the space charge in drift tube  49  by superimposing a forcing function, e.g., a pulsed or sinusoidal waveform, on the electron beam in order to simulate an alternating current. Using three grids  37  permits three-phase electrical power generation in that each grid has a sinusoidal forcing function that is 120 degrees out of phase with the other two sinusoids. The net result of this operation is a three-phase alternating beam current. The advantage of this embodiment is that inverter  39  is not needed, such that (e.g., after a filtering step) the current can go directly to transformer  40  and to load  41 . 
     In one mode of operation, the electron beam is pulsed. This may easily be accomplished by turning on and off the current and voltage applied to grid  37  by grid power supply  36  in order for the electron beam to mimic the properties of grid  37 . Optional heater power supply  43  is coupled to emitter  35  (e.g., field emission emitter) to support the creation of thermionic electrons. As shown in example in  FIG. 3 , collector power supply  38  is referenced to cathode power supply  34 . The potential of collector electrodes  42  are matched to the potential of the electrons in the electron beam in order to recover the energy of the beam. 
     In instances where grid  37  is not used as a means to convert a direct current electron beam into alternating current, inverter  39  may be used to provide that functionality. In addition, inverter  39  may comprise power conditioning circuitry to process the power output from collector electrodes  42 . For example, inverter  39  may be designed to eliminate noise and spurious signals, such as unwanted spikes. Transformer  40  typically converts a low current at a high voltage present at the output of inverter  39  into a relatively lower voltage but higher current, prior to delivering power to load  41 . 
     While  FIG. 3  depicts an embodiment comprising three grids  37  designed to generate three-phase power, it is understood that other phases, e.g., single-phase power may equally be generated by power generator  300  by utilizing a single grid  37 . One of ordinary skill in the art will appreciate that also different waveforms may be generated using various methods known in the art, including amplitude modulation, pulsed code modulation, pulsed duration modulation, pulsed position modulation, pulsed amplitude modulation, and frequency modulation. 
       FIG. 4  illustrates a power generator capable of producing electromagnetic radiation at a specific microwave frequency, according to various embodiments of the invention. Power generator  400  comprises emitter power supply  34 , emitter or cathode  35 , collector power supply  38 , inverter  39 , transformer  40 , and load  41 , collector electrodes  42 , heater power supply  43 , magnetron injection gun  44 , magnets  45 , anode  46 , magnetic assembly  47 , port  48 ,  51 , drift tube  49 , window  50 , inner tube  52 , outer tube  53 , and exit ports  54  and  55 , respectively. For clarity, components similar to those shown in  FIG. 3  are labeled in the same manner. 
     As shown in  FIG. 4 , electromagnetic reactor section of power generator  400  consists of two coaxial concentric tubes, inner tube  52  and outer tube  53 . Inner tube  52  typically comprises a porous wall or membrane that allows for selective diffusion of products generated in inner tube  52  to exit from outer tube  53 . Outer tube  53  forms a non-porous walls of the reactor. In one embodiment, a difference in pressure between inner tube  52  and outer tube  53  causes selective diffusion of one component so that outer tube  53  is enriched in one component over another component. Conversely, reactants may enter outer tube  53  and exit after passing through the membrane of inner tube  52 . 
     In order to maintain high voltage on emitter  35 , power supply  34  may be employed. Power supply  34  derives its power from a renewable energy resource, such as the solar panel assembly mentioned previously. In one embodiment, a to-be-amplified signal from an electromagnetic source (e.g., IMPATT diode, RF, Microwave, sunlight, etc.) is provided through port  48 . It is noted that port  48  may be used to extract energy as well as add energy to an existing electron beam. 
     In one embodiment, magnetron injection gun  44  is energized by supply  43  to generate a “hollow” electron beam via emitter  35 . Anode  46  is positioned in a manner such as to cause the electron beam to initiate a rotational motion, while magnets  45  are strategically placed to aid in compressing the beam and directing it into drift tube  49 . As the beam enters the drift tube  49 , magnet  47  promotes the cyclonic and rotational movement of electrons in the beam and cause the electron beam to generate radiation at high frequency. The energy of the electron beam is captured by collector electrodes  42 , which are powered by supply  38  and referenced to cathode power supply  34 . The current then flows through power conditioner and inverter  39 . As with embodiments related to  FIG. 3 , the beam may be modulated such as to establish an alternating current, thus, eliminating the need for inversion. The power conditioner may also filter out extraneous noise and signals in order to ensure a clean power signal entering transformer  40  and/or load  41 . 
     It is known that some reactant molecules, such as water, have pronounced absorption frequencies that lie in the infrared, visible, and ultraviolet regions of the electromagnetic spectrum. Therefore, in one embodiment, power generator  400  is designed to generate specific frequencies, allow the electromagnetic portion of the beam to travel through window  50 , and facilitate energy coupling to chemicals in the reactor section of power generator  400  in order to perform desired chemical reactions. In one embodiment, the frequencies generated in drift tube  49  correspond to absorption frequencies of reactant molecules entering reactor  53  through port  51 . 
     Once the electromagnetic radiation imposed on the molecules is sufficiently strong to break the valence bonds between atoms, the reactant molecules dissociate into chemical products. For example, if the generated frequencies correspond to frequencies of maximum absorption for water vapor in a region of interest, then dissociation takes place once sufficient vibrational energy is generated to break the hydroxyl bonds to create hydrogen and oxygen. Gaseous products are separated through the membrane of inner tube  52 , which may be designed to be selective to only one of the gases. The separated gases leave the reactor through exit ports  54  and  55 , respectively. 
     In the region where water vapor dissociation is optimum (e.g. ultraviolet, microwave, and infrared regions of the electromagnetic spectrum), the combination of inner and outer tubes  52 ,  53  may be considered a coaxial waveguide for electromagnetic waves generated in drift tube  49 . The waveguide structure enables efficient decomposition of water vapor by dissociating water molecules entering outer tube  53 . Since hydrogen possesses a higher molecular velocity than oxygen, it diffuses through the membrane of inner tube  52  to accumulate at high concentration in inner tube  52  from which it flows to exit port  55 . The membrane may have a non-permeable coating (e.g., palladium, copper-palladium, silver-palladium, etc.) and be porous or selective to hydrogen so that relatively little or no oxygen molecules tend to diffuse from outer tube  53  to exit port  55 . Conversely, water molecules may enter through port  51  and exit through port  55  instead of port  54  via an opening in the membrane of inner tube  52 . One skilled in the art will appreciate that other classes of zeolites and activated carbons may be used. 
       FIG. 5  illustrates a power generator capable of producing high frequency electromagnetic radiation via transverse motion of an electron beam, according to various embodiments of the invention. Power generator  500  comprises emitter power supply  34 , emitter or cathode  35 , collector power supply  38 , inverter  39 , transformer  40 , and load  41 , collector electrodes  42 , heater power supply  43 , magnet  47 , port  48 ,  51 , drift tube  49 , window  50 , inner tube  52 , outer tube  53 , exit port  54 - 55 , mirror  56 , alternating magnetic assembly  57 , and dielectric liner  58 . 
     In example in  FIG. 5 , alternating magnetic assembly  57  is disposed between drift tube  49  and magnet  47 . In operation, alternating magnetic assembly  57  maximizes a transvers motion of electrons in the electron beam. Mirror  56  aids in the generation of a coherent electromagnetic radiation that is used to produce a resonance effect within drift tube  49 . Optional grid  37  may be used to operate power generator  500  in a way produce alternating current mentioned previously. 
     In one embodiment, alternating magnetic assembly  57  is replaced with a traveling wave guide structure in which a traveling wave is generated along a coil (not shown). The traveling wave enters drift tube  49  through port  48  and carries a high frequency wave. Under proper conditions, energy is exchanged between the electron beam and the traveling wave in order to amplify the wave or increase the energy of the electron beam. Magnetic assembly  47  may create a longitudinal magnetic field that compresses the electron. Magnetic assembly  47  may also create a cyclonic motion within the electron beam. The rotational component of the electrons generates a radiation field that interacts with the traveling wave of the coil. 
     In one embodiment, alternating magnetic assembly  57  and magnet  47  are replaced with a resonator structure to generate high frequency waves along which power can be extracted from an electron beam comprising bunched or bunching electrons. This embodiment may be used to amplify the resonant frequency in drift tube  49  to generate frequencies that otherwise are difficult to generate. For example, port  48  may receive electromagnetic waves having at certain frequencies. As the wave enters drift tube  49 , under proper conditions, amplification of the electromagnetic waves occurs when energy is extracted from the electron beam. Part or all of the remaining energy of the electron beam is captured through collector electrodes  42  and processed as described elsewhere with respect to other embodiments. Port  48  may also be used to generate alternating current by injecting a wave having a frequency of, for example, multiples of 60 Hz. Power generator  500  may be designed to generate frequencies in any of the sub-millimeter, millimeter, infrared, visible, and ultraviolet regions of the electromagnetic spectrum to facilitate absorption by reactant molecules with corresponding absorption frequencies. 
     For example, at 22.235 GHz, a water molecule will absorb energy at the 5 −1 -6 −5  transition. In addition, water absorbs greater amounts of energy in the sub millimeter region. Absorption peaks at 183.31 GHz (k=1.635 mm), 321.225 GHz (k=0.933 mm), 325.152 GHz (k=0.922 mm), 380.197 GHz (λ=0.7885 mm) are just a few of the absorption frequencies for water vapor. There are numerous such frequencies in the sub-millimeter and far infrared region, including 448.001 GHz (λ=0.6696 mm), 556.936 GHz (λ=0.5386 mm), 620.700 GHz (λ=0.4833 mm), 752.033 (λ=0.3989 mm), 916.171 GHz (λ=0.3274 mm), 970.315 GHz (λ=0.3091 mm), 987.926 GHz (λ=0.3036 mm), 1.0973 THz (λ=0.2733 mm), 1.11342 THz (λ=0.2694 mm), 1.16291 THz (λ=0.2579 mm), 1.20763 THz (λ=0.2484 mm), 1.22878 THz (λ=0.2441 mm), 1.41061 THz (λ=0.2126 mm), 1.60221 THz (λ=0.1872 mm), 1.66100 THz (λ=0.1806 mm), 1.66990 THz (λ=0.1796 mm), 1.71676 THz (λ=0.1747 mm), 1.79478 THz (λ=0.1671 mm), 1.79715 THz (λ=0.1669 mm), 1.86774 THz (λ=0.1606 mm), and 1.91935 THz (λ=0.1563 mm). 
     In the infrared range of 4 to 13 microns, there are a number of absorption frequencies in which the absorption coefficient is high enough so that the electromagnetic radiation couples well to the water vapor molecule. In this range, they are: 44.9 THz (λ=6.68 μm), 45.2 THz (λ=6.64 μm), 48.0 THz (λ=6.26 μm), 53.2 THz (λ=5.64 μm), 53.8 THz (λ=5.58 μm), 55.3 THz (λ=5.52 μm). 
     Throughout the spectrum there are special frequencies where the water vapor molecule favors maximum energy absorption. For example, 94.5 THz (λ=3.17 μm), 110 THz (λ=2.73 μm), 113 THz (λ=2.66 μm), 160 THz (λ=1.88 μm), 206 THz (λ=1.45 μm), 218 THz (λ=1.38 μm), 264 THz (λ=1.13 μm), 318 THz (λ=0.94 μm), 331 THz (λ=0.906 μm), 365 THz (λ=0.822 μm), 377 THz (λ=0.796 μm), 415 THz (λ=0.723 μm), 430 THz (λ=0.698 μm), 460 THz (λ=0.652 μm), 475 THz (λ=0.632 μm), 505 THz (λ=0.594 μm), 507 THz (λ=0.592 μm), 525 THz (λ=0.572 μm), 1.82 PHz (λ=0.1650 μm), and 2.42 PHz (λ=0.1240 μm). 
       FIG. 6  illustrates a power generator that uses a selection of a narrow range of electron velocities in an electron beam to reduce the number of collector electrodes and accompanying power supply. Components similar to those shown in  FIG. 5  are labeled in the same manner. Power generator  600  comprises parallel electrostatic deflection plates  60  and magnets  47  arranged in a perpendicular fashion within drift tube  49 , as depicted in  FIG. 6 . The electrostatic field residing on electrostatic deflection plates  60  may be provided by cathode power supply  34 . Deflection plates  60  generate an electrostatic field that is mutually perpendicular to the magnetic field generated by magnets  47 . Both fields are positioned orthogonal manner to the path of the electron beam, resulting in a certain number of electrons having a specific velocity and trajectory to travel directly to collector electrode  42  in a straight line undeflected from their original path. Applying a perpendicular magnetic field relative to the velocity of the electron beam without electrostatic deflection plates parallel to the electron beam, allows for targeted separation electrons of different velocities, and hence different potentials. This, in effect, allows for selective filtering of beam electrons having a specific velocity. 
     In one embodiment, additional collector electrodes having varying potential are placed on either side of a main collector electrode  42  for the purpose of accepting a matching electron potential at each respective collecting electrode. As a result, the number of electrons captured by the multiple collector electrodes is increased with the electron distribution being centered about the main collector electrode  42 . Additionally, it is possible to generate a pseudo-sinusoidal electron beam in order to stimulate an alternating current. 
     In one embodiment, an electron entering the magnetic field experiences a downward force due to the combination of the forward component of their velocity and the transverse magnetic field. This force is directed downward if the initial electron velocity is greater than that at which the electric and magnetic forces balance. The result of the downward component of velocity and the transverse magnetic field produces a backward component of force that may be sufficient to cause the electron to turn a loop. If the initial velocity is less than that for which the electric and magnetic forces are in balance, the electron will experience an upward force, which, in turn, gives a forward acceleration. The result is an undulating forward progression. This undulating forward progression resembles a sinusoid and can be used to convert the beam to an alternating current having a period that is a function of the magnetic field strength. Thus, an electron beam can directly generate an alternating current. 
       FIG. 7  illustrates a power generator in which the electron beam is a plasma electron beam, according to various embodiments of the invention. Components similar to those shown in  FIG. 6  are labeled in the same manner. For purposes of brevity, a description or their function is not repeated here. The plasma electron beam consists of neutral as well as charged species (i.e., ions and electrons). If the plasma electron beam travels at a velocity,  , and a magnetic field is established perpendicular to the beam, with a magnetic field strength, B app , the interaction between the two fields induces an electric field, E ind , that is at right angles to both   and B app  and given by the equation
 
 E   ind   =     ×B   app .
 
     It is noted that a sufficiently strong magnetic field renders a conducting gas anisotropic and, thus, the conductivity becomes a tensor quantity rather than a scalar used here for purposes of simplification. Then, per Ohm&#39;s law, the density of the current induced in the conductive fluid (i.e., the plasma) becomes
 
 J   ind   =σE   ind .
 
     Simultaneously with the induced current ponder-motive force, F ind , is induced and given by the vector product
 
 F   ind   =J   ind   ×B   app .
 
     This force occurs because, as in an electric generator, the conducting fluid cuts the lines of the magnetic field. The equation above yields a vector perpendicular to both J ind  and B app . The induced force is parallel to   but opposite in direction. In  FIG. 7  an electric field, E app , is applied at right angles to both B app  and  , but opposite in direction to J ind . The current density due to this applied electric field is denoted by J cond  and called conduction current. The net current density, J, through the conducting fluid is then
 
 J =σ( E   app   +     ×B   app )=σ( E   app   +E   ind ).
 
     The ponder-motive or Lorentz force associated with the conduction current is then
 
 F=J×B   app =σ( E   app   +     ×B   app )× B   app  
 
     If E app &gt; ×B app , we obtain an accelerator that can enhance power production as well as electromagnetic wave generation. This approach is superior to conventional means of producing power in that the acceleration of the fluid occurs by electromagnetic fields rather than by using large quantities of thermal energy that limit the amount of power produced and, thus, efficiency and cause thermal deterioration of the turbine generator walls. Unlike conventional magneto-hydrodynamic (MHD) power generation, this embodiment avoids the high temperatures required to generate a gas that is sufficiently ionized to have the desired high conductivity for electromagnetic acceleration. 
     Additional advantages over MHD reactors include that no difficult to handle and toxic (e.g, mercury or liquid sodium) conducting liquids are used. The flow of liquid metals, such as molten sodium-potassium eutectic solutions, in MHD reactors necessitates unusual pumping, controlling, and measurement techniques. In addition, cooling of the walls of the reaction chamber requires not easily obtained high heat transfer rates. Furthermore, to sufficiently cool the reactor walls that are in constant contact with the hot conductive gas, oftentimes magnets designs are employed that are fairly difficult to implement and prone to causing flow instabilities. 
     Power generator  700  in  FIG. 7  comprises electrodes  61  and collector power supply  38  coupled to both electrodes  61  and collector electrodes  42 . Electrodes  61  are arranged as a series of parallel plate pairs that are symmetrically distributed at either side of the plasma electron beam along the top and bottom ends of drift tube  49 , i.e., parallel to the direction of motion for the plasma beam. However, this is not intended as a limitation, as electrodes  61  may have any shape and be positioned at other suitable locations within power generator  700 . Electrodes  61  may be arranged according to sequentially decreasing negative potential, for example, to allow for different ionized species formed in the electron beam having different velocities due to their different ionic weights to be captured at more than one potential. 
     In order to provide ions for the plasma beam, port  62  may be used to admit gases that can be ionized in the plasma beam. These include inert gases, hydrogen, and alkali metals. 
     In example in  FIG. 7 , electrodes  61  have a higher negative potential than cathode  35  in order to attract positive ions from the plasma beam. The high negative potential of electrodes  61  permits electrons to travel from cathode  35  to the relatively lower negative potential of collector electrodes  42  without being prematurely captured by electrodes  61 . Collector electrodes  42  are arranged as a series of multi-electrode collectors whose potential matches the beam potential and have a relatively higher potential than electron emitting cathode  35 . This facilitates capture of electrons by electrodes  42  and provides for the recovery of energy from the plasma beam. 
       FIG. 8  is a flowchart of an illustrative process for power generation from a renewable energy source in accordance with various embodiments of the invention. At step  802 , a current is generated from a p-n junction of a solar cell. 
     At step  804 , a part of the current is applied to an emitter that emits electrons. 
     At step  806 , a high potential is generated on the emitter, for example, by applying a part of the current to the emitter. 
     At step  808 , current is converted into an electron beam that is emitted from the emitter. 
     At step  810 , the emitted electrons are accelerated to a high kinetic energy level. 
     At step  812 , an alternating potential is applied between the emitter and a collector in order to generate an alternating current. 
     At step  814 , the electrons from the accelerated electron beam are collected, for example, to provide a second current at a potential that is lower than the emitter potential in order to drive a load. 
     Finally, at step  816 , chemical reactants are created, for example, by using high frequency radiation created by the electron beam. 
       FIG. 9  is an exemplary schematic of a system  900  to generate energy from a renewable energy source according to various embodiments of the invention. One or more solar panels  71  may be used depending on the amount of electrical power that needs to be amplified. Input of solar energy is converted to electrical charges in the form of the solar panel  71 . The output of a solar panel goes into a dc-dc voltage regulator  72  and charge controller that is necessary to smooth out any variations of the output of a solar panel. This is due to the varying insolation of the Sun resulting from the variations in the Sun&#39;s position and meteorological conditions. In embodiments, fluctuations of photon capture may be mitigated by using a dc-dc voltage regulator  72 . 
     A set of batteries (optional)  73  provide energy in these instances where the Sun&#39;s insolation is reduced to a level in which the stored hydrogen is utilized to generate electricity from a fuel cell to provide power. 
     A power supply  74  operates the solar amplifier. The input of the power supply may use either direct or alternating current. It is preferred that the power supply run on dc since the output of the regulator is dc. Since solar power is direct current in nature, an additional inverter is needed for the power supply if it is an alternating current power supply. The solar amplifier  75   a  takes the input from the power supply  74  in order to amplify the current generated in the amplifier. The collector  75   b , which is a component of the solar amplifier whose purpose is to collect the high energy electrons generated by the emitter (not shown) and let it be converted to a conductive current. The current output goes to a transformer to step down the voltage and filter out any noise that may have been generated, where the transformer and filter are collectively referred to as the power conditioning unit  76 . Power from the power conditioning unit  76  is split into two streams. One circuit goes to generate hydrogen in the electrolysis unit  77 . The produced hydrogen is sent to a storage unit  78 , which is used by the fuel cell  79  in order to provide electrical power to the power supply when the solar insolation is not sufficient enough to warrant the use of the solar panel. Inverter  80  is an optional component only if the solar amplifier is run in dc mode. The output of the power conditioning unit  76  then goes to an electrical load. 
       FIG. 10  is an exemplary schematic of a system  1000  to generate energy from a renewable energy source according to various embodiments of the invention. The system  1000  is similar to the system  900 , with a difference that the electromagnetic waves generated by the accelerating electrons in the solar amplifier ( 75   a  and  75   b ) produce coherent electromagnetic radiation that may dissociate water vapor under certain conditions. 
     One or more solar panels  71  may be used depending on the amount of electrical power that needs to be amplified. Input of solar energy is converted to electrical charges in the form of a solar panel  71 . The output of a solar panel goes into a dc-dc voltage regulator  72  and charge controller that is necessary to smooth out any variations of the output of a solar panel. This is due to the varying insolation of the Sun resulting from the variations in the Sun&#39;s position and meteorological conditions. 
     A set of batteries (optional)  73  provides in order to provide energy in these instances where the Sun&#39;s insolation is reduced to a level in which the stored energy from the battery or alternatively of stored hydrogen generated from the production of electromagnetic radiation tuned to various absorption frequencies of water vapor is utilized to generate electricity from a fuel cell to provide power. A power supply  74  operates the solar amplifier. The input of the power supply  74  may use either direct current from a fuel cell  79  or if enough hydrogen has been stored, the fuel cell may be used as a power source during night time hours. The advantage of using the power supply in conjunction with a fuel cell is that the consumption of hydrogen in the fuel cell is greatly reduced since the power supply is generating the high potential energy needed to increase power output. It is preferred that the power supply run on dc since the output of the regulator is dc. 
     The solar amplifier  75   a  takes the input from the power supply  74  in order to amplify the current generated in the amplifier. Both ac and dc current can be generated in the solar amplifier. The collector  75   b , which is a component of the solar amplifier whose purpose is to collect the high energy electrons generated by the emitter (not shown) and let it be converted to a conductive current. The current output goes to a transformer to step down the voltage and filter out any noise that may have been generated. The advantage of this configuration is that none of the electrical power of the beam is used to produce hydrogen such as shown in  FIG. 9 . 
     The electrons accelerating in the space between the emitter/cathode and the collector produce coherent electromagnetic waves that can be manipulated to selectively be absorbed in the water vapor molecule. If the energy density is high enough, then dissociation occurs and hydrogen and oxygen can be recovered separately via a membrane. The oxygen can be stored in a storage  81  or vented since the oxygen from the air could be used as an oxidizing source for the fuel cell. The reaction chamber  82  is designed in such a way as to fully utilize the energy in the electromagnetic wave by generating a geometry so as to create a resonating structure (see  FIGS. 16A, 16B, 17 ). The produced hydrogen is sent to a storage unit  78 , which is used by the fuel cell  79  in order to provide electrical power to the power supply when the solar insolation is not sufficient enough to warrant the use of the solar panel. Inverter  80  is an optional component only if the solar amplifier is run in dc mode. The output of the power conditioning unit  76  then goes to an electrical load. 
       FIG. 11  is an exemplary schematic of a system  1100  to generate energy from a renewable energy source according to various embodiments of the invention. The system  1100  is similar to the system  1000 , with a difference that a solar panel  71  possessing a higher potential energy output is used. By generating high potential energy, an important function of the power supply  74  may be eliminated. The use of the power supply at night is thereby optional as shown in  FIG. 11 . In embodiments, the high voltage panels  71  can be constructed using different paths. Since voltage is linearly additive, constructing a higher density of solar cells will increase the net output voltage. Another way is to use the anomalous photovoltaic effect. Some semiconductors in the form of a thin-layer exhibit a high voltage photovoltaic effect. Over distances of the dimensions of a standard solar panel (1 m 2 ), it is possible to generate very high voltages. One could also use the Dember effect to generate high voltages. 
     Thermionic emission is a process by which the emission of electrons may take place. If an electron, moving with a sufficiently high velocity, strikes a surface, the impact may cause other electrons to escape from the surface. These are called secondary electrons and the phenomenon just described is called secondary emission. The number of secondary electrons varies with the velocity of the impacting, or primary, electrons and with the chemical nature and the physical conditions of the surface on which they strike. 
     The secondary emission from any given surface increases with increasing velocity of the primary electrons passing through a maximum and then declining in number. The number of secondary electrons produced can vary with the material. There are several materials that have high emission of secondary electrons. The ratio or the number of secondary electrons 
     emitted per incident primary electron is called the secondary emission ratio 
               (     =       I   S       I   i         )     ,         
where, I s  is the electron current (number of secondary electrons) of secondary electrons generated, I i  is the primary electron current. In embodiments, one or more of MgO, ZnO, polycrystalline CVD diamond, AgMgO(Cs), CuBeO(Cs) and Al 2 O 3  are used as secondary electron emitters (more specifically, secondary emission coating) to increase the beam current in order to generate higher powers, as shown in  FIG. 12 .
 
       FIG. 12  shows an exemplary arrangement of electron collectors according to various embodiments of the invention. In embodiments, a secondary emission coating may be disposed on the surface of one or more of the collectors. The momentum of the electrons coming from the electron beam causes the removal of more than one electron from the surface coating of the collector, thereby dislodging electrons on the surface of the collector. These materials have very low surface work functions, which is the energy needed to eject the electron from the material. Typical materials are made of compounds of silver-oxygen-cesium and antimony-cesium. As shown in the figure, there are a number of collector stages (or collector electrodes)  1202 , where electron multiplication takes place. The number of electrons increase as the number of stages increase until the last stage. If one electron can generate m secondary electrons at each collector stage, the current gain after N stages is,
 
 G=i   out   /i   in   =m   N  
 
     For example, if N=10 and m=5, then G=10 7  or a gain of 140 dB. A focusing electrode is used to direct the beam on the first stage collector. 
     Depending on the amount of power recovery, the collector may include one stage or multiple stages, i.e., the collector may include one or more collector electrodes  1202 . Each stage needs to have a potential that is near the potential of that part of the beam that matches it. As each part of the beam matches its potential with the collector potential, the sum total of those currents issuing from the multistage collector adds up to the total beam current. If the potential is in the thousands of volts, a step-down transformer may be applied to the multistage collector at various points on the high side of the transformer, in order to reduce voltages to a common useable voltage such as 110 or 120 volts. Each stage may have a coating of a high secondary emission material as described above or any from a class of compounds in which the secondary emission coefficient is &gt;1. The current is multiplied or amplified according to the process conditions of the device and the nature of the material and properties of the electron beam. In embodiments, the amount of current is related to the number of collector stages as: δ=(I s /I i ) n  where n is the number of stages of the collector. For example, a two-stage collector with a diamond coating could have an amplification of 6,400 times the original current. In addition, the same principle may be used to generate the primary electrons. For example, a thermionic emitter can be used to initiate an electron beam, the beam interacts with a number of stages in which it has a high secondary emissive material on its way to the collector, increasing the net beam current. As it travels through the drift tube which lies between the electron generator assembly and the collectors  100 , the beam encounters a multistage collector with additional stages to produce additional current if a secondary electron emissive surface is coated on each stage of the collector surface. Care needs to be taken to eliminate back recoil to the cathode in these instances. Also, in embodiments, in a manner similar to photomultiplier tubes, one may initiate the beam current by using the sunlight or a combination of photo-emissive and thermionic materials. 
     Focused electromagnetic radiation may be used to transmit and receive electromagnetic signals that may be used for a variety of communications as illustrated in  FIG. 13 .  FIG. 13  is an exemplary schematic of a power generator having a communication device  1300  according to various embodiments of the invention.  FIG. 13  illustrates one exemplary application of the power generators described in conjunction with  FIGS. 1-12 . 
     The acceleration of electrons can create coherent electromagnetic waves, with the judicious use of magnets and resonators as described earlier in the disclosure. As depicted in  FIG. 13 , in embodiments, the electromagnetic waves generated by the power generator system may be used to send information to and from the power generator system, using the communication device  1300 , such as antenna. In embodiments, since there is no limit on the frequency of transmission and reception, it is possible to have wide broadband communications with this embodiment of this invention. 
       FIG. 14  is an exemplary schematic of a chemical reacting system according to various embodiments of the invention. The reaction chamber is used to accept the coherent electromagnetic radiation. The coherent radiation is tuned to the absorption frequency of the reactant (in this case carbon dioxide). The reaction chamber may also contain a membrane for the separation of products. In this example, carbon dioxide is dissociated to carbon monoxide and oxygen. The carbon monoxide enters a second chamber with steam as a reactant to convert the steam into hydrogen. The oxygen reacts with the carbon monoxide molecule to form carbon dioxide as shown in the following formula,
 
CO+H 2 O=CO 2 +H 2  
 
       FIG. 15  is an exemplary schematic of a chemical reacting system  1500  according to various embodiments of the invention. This figure shows how a chemical reaction can be achieved. The output of these reaction, for example, CO 2 =CO+½O 2  and/or H 2 O=H 2 +½O 2  is electromagnetic radiation at specific frequencies that correspond to maximizing the absorption of electromagnetic radiation. As stated earlier in this disclosure, the various absorption frequencies for water vapor have been stated. In the case of another molecule, namely carbon dioxide, certain frequencies maximize absorption of radiation. Some of them are listed below: 
     667.3 cm −1 , 1285.5 cm −1 , 1388.3 cm −1 , 2349.3 cm −1 , 3609 cm −1 , 3716 cm −1    
     In this configuration, there are two mirrors on either side of the reactor chamber  83  as well as the diverging section of the nozzle  84 . This is done to create a standing wave as found in a typical laser geometry in order to maximize the intensity of the incoming radiation. A membrane at the diffuser end  85  of the converging-divergent nozzle arrangement is used to bring up the pressure to more easily effect separation. Detailed description of the mirrors in the system  1500  is given below in conjunction with  FIGS. 16A and 16B . 
     In order to sustain the electromagnetic wave, it is important to maintain the integrity of the wave. This is accomplished by using a resonating cavity. A resonating cavity is simply an enclosure where the primary energy wave becomes a standing wave. Thus, a wave and its harmonics may fill the entire cavity.  FIGS. 10, 11, 14 and 15  show the reaction chamber  82 . In embodiments, a resonating cavity is used so that the maximum efficiency is attained. In terms of efficiency, we can also measure that by using a factor called Q, quality or simply the quality factor. It is a measure of the cavity to maintain and store energy versus losses of energy leaving the cavity or,
 
 Q =energy stored in the resonator/energy lost from the resonator
 
     In order to efficiently use the energy to its maximum for any given reaction of a chemical mixture, it is important to attain very high values of Q for endothermic reactions and low values of Q for exothermic reactions. In order to dissociate water or carbon dioxide to given as an example, the following chemical reaction and energy necessary to produce hydrogen and oxygen molecules and carbon monoxide and oxygen molecules are given below:
 
CO 2 =CO+½O 2  Delta H=+2.9 eV/molecule
 
H 2 O=H 2 +½O 2  Delta H=+2.6 eV/molecule
 
     The above two reactions require additional energy to break their bonds and recombine to products. The cavity with a very high Q factor may store energy to be used for bond dissociation. In addition, the effective absorption path is increased with higher quality factors. 
     There are other cases where a chemical mixture causes an exothermic reaction and it is important to reach low Q levels in order to remove energy from the resonating cavity reactor so only the forward reaction path is maintained. An example of an exothermic chemical reaction that produces hydrogen, may be:
 
CO+H 2 O=CO 2 +H 2  Delta H=−0.4 eV/molecule
 
     The above quantities for the energy is called the enthalpy of dissociation, Delta H, and is an equilibrium thermodynamic quantity assuming an infinite reaction time. In order to speed up the reaction, we may put energy in order to reduce the reaction time. Quickly overcoming the activation energy is the way to accomplish that goal. Increasing the energy density leads to higher energy states of the molecules which lead to dissociation. The is why focusing the electromagnetic energy into a smaller region as shown in  FIG. 16B  leads to high energy densities. Multiphoton absorption of the energy into the reactant molecule leads to higher energy states. In order to achieve that goal for any particular frequency focusing the energy into a smaller volume results in an improvement in the probability that the photon may be absorbed by the reactant molecule. As an example, here is a calculation determining the probability a photon will be absorbed by a water molecule. 
     The definition of irradiance is given below:
 
 I =Irradiance=energy/area*time
 
 I =(# photons)*(photon energy)/(volume*time/length)
 
 I =(# photons)*(photon energy)/(volume/speed of light)
 
Or,
 
 I=Nh   /( V/c )
 
Or,
 
 N =( I/ch   ) V  
 
     Where, N is the number of photons,   is the frequency of the radiation of absorption, c is the speed of light=3E08 meters per second, h is the Planck&#39;s constant=6.626E-34 Joule-seconds, NA is the Avogadro&#39;s number=6.02e23 molecules per mole, V is the volume of interest for the interaction of the photon with the molecule. The volume of a water molecule is 
     
       
         
           
             
               
                 
                   
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     The number of photons in this volume at a wavelength where water vapor absorbs electromagnetic radiation may be chosen from the absorption spectrum of water vapor. We also see from the above equation where the number of photons for absorption can increase if the irradiance level is high and also a frequency as low as possible for high absorption is also chosen. We may choose the sub-millimeter range in the water absorption spectrum at a frequency of 556.936 GHz (0.5386 mm) to show as an example because of its very high absorption characteristics. Therefore, 
     
       
         
           
             
               
                 
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     It is apparent from the above quantity of photons that the irradiance needs to be high in order to improve the probability of interaction of the photon with the water molecule. An irradiance of I=3.702×10 15  J secs −1  m 2  is necessary to have a probability of one photon interacting with one water molecule. It should be pointed out that the size of a photon in this case is huge since the wavelength of the photon wave is 0.536 mm or 538.6 microns in length compared to an average length of a water molecule to be around 3.1×10 −10  m or 3.1×10 −4  microns, or six orders of magnitude smaller. This high irradiance can be accomplished in different ways as taught in this disclosure. In order to obtain high irradiance several factors must be considered. First the Q of the resonating cavity must be at its highest. The energy may be further concentrated as shown in  FIGS. 16A and 17 . Lastly, pulsing the energy by Q switching and mode-locking is necessary to obtain high irradiances. In order to raise the value of Q we have to observe its relationship to the frequency,
 
 Q=     /Δ       
 
     where,   is frequency and Δ  is linewidth of the output of the electromagnetic radiation produced in the solar amplifier of this disclosure. 
     The narrower the bandwidth the greater the value of Q. The value for Q for two mirrors of different reflectivities, R 1  and R 2  with a separation between the mirrors of a length, d, we have,
 
 Q= 2π d   ( R   1   R   2 ) 0.25   /c [1−( R   1   R   2 ) 0.50 ]
 
     Or, for two mirrors with equal reflectivity, R 1 =R 2 , then,
 
 Q= 2π d   ( R   1 ) 0.50   //c [1− R   1 ]
 
     Using the above value for the frequency,  , R 1 =R 2 =0.99 and d=1 meter for the length of the cavity, we get Q=1.16638×10 8 , a very high value. In order to fulfill the other requirement to produce enough photons to sustain a high efficient absorption of electromagnetic waves into the water molecule, the irradiance needs to be above a certain critical value. 
     Another method for maximizing energy density in order to generate a chemical reaction is pulsing the coherent electron beam. This will generate huge power gradients in the resonating cavity, especially the configuration where there is a focus of the two mirrors (see FIGS.  16   b  and  17 ). The reactant molecules can be excited first by an electrical discharge, followed by a pulse of the electron beam, thereby generating focused electromagnetic radiation in the form of a pulse that travels through the excited reactant molecules, resulting in a chemical reaction. This is further enhanced by use of the geometric arrangement as illustrated in  FIGS. 16 b    and  17 . For example, if the electron beam is pulsed at 1 microsecond intervals (1 μsec=1×10 −6  secs) and the energy generated during the pulse is 1,000 Joules, the power produced during the pulse,
 
Pulse power=pulse energy/pulse duration
 
     Or, 1000 joules/1×10 −6  secs=1,000 MW or 1′ GW 
     Q-switching and mode-locking are two methods by which short intense pulses of high energy can be generated. The standard method is to block one of the mirrors when the medium is active. By unblocking the mirror, a build-up of inverted molecules releases their photons to generate very high powers. Mode-locking allows the shortest pulses to be produced in a resonating cavity. The many longitudinal modes in the cavity are made to oscillate in phase. By inserting a special optical element in the cavity makes all the modes oscillate together. Q-switching is similar in nature in that a method or optical element is placed in the path of the light between the mirrors in order to generate high quantities of excited species. In this invention, high energy pulsed coherent electromagnetic radiation is generated by pulsing the electron beam in the solar amplifier ( 75   a ,  75   b ). A grid which lies between the cathode and collector is pulsed so that bundles of electrons in phase with each other are emitted. Due to the acceleration of these bunches of electrons, coherent radiation is emitted where it enters the reaction chamber  82 . If the reaction chamber  82  has excited species generated by a discharge, the pulse of electromagnetic radiation may increase the number of excited species and hence, the number of inverted molecules and amplify their presence. In embodiments, the entering focused electromagnetic radiation may enter the reaction chamber  82  through a window or lens if the energy density needs to increase further. 
       FIGS. 16A and 16B  show exemplary arrangements of minors according to various embodiments of the invention.  FIG. 17  is an exemplary schematic of a chemical reacting system  1700  according to various embodiments of the invention. In embodiments, as depicted in  FIG. 16A , a pair of flat minors may be used to form a resonating cavity. In alternative embodiments, as depicted in  FIG. 16B , a pair of confocal minors may be used to form a resonating cavity and also focus the electromagnetic radiation.  FIGS. 16A and 16B  illustrate two methods to achieve maximum utilization of the electromagnetic wave. Parallel plates or confocal minors are used to direct the radiation in order to setup a standing wave.  FIG. 16B  illustrates a standing wave with a focus midway between the two mirrors.  FIG. 17  illustrates this point with a membrane at the center of the focus. Reactant material may flow within the membrane (perpendicular to the page). The density of the radiation (where most of the reaction occurs) may be highest at the focal point. Products leave the membrane perpendicular to the flow as well as parallel in the direction of the flow within the membrane. 
     As a variant of this method, a second reactor as shown in  FIG. 14 , uses another reactant (in this illustration, steam) in order to use one of the products of the reaction chamber, carbon monoxide (CO), to produce hydrogen and carbon dioxide. The carbon dioxide is recycled to produce more CO. Other processes involving CO+H2 may be achieved by this method. In some cases, a catalyst may be needed to speed up the reaction. A catalyst may be used in either chamber in order to generate a myriad of chemicals. For example, reduction of metal ores to metals using carbon monoxide and/or hydrogen is an example. Another variation is illustrated in  FIG. 15 . In this approach, a first reaction chamber dissociates the reactant material as disclosed above. The products of that reaction then travel through a converging-diverging nozzle  84  in order to “freeze” the products. A second set of mirrors are used to generate standing waves for further reaction until separation of the products occur in the diffuser section  85  of the reaction zone. In  FIG. 17 , the membrane  86  separates the products. Both electromagnetic radiation and the generation of free electrons can be used to initiate and promote the dissociation of the reactant(s) to products. Supersonic speeds result in the diffuser section  85 . Carbon dioxide may be dissociated using He, N 2  and/or H 2 O as energy catalysts. 
     As shown in  FIG. 17 , the chemical reacting system  1700  may include a pair of confocal mirrors that form a resonance cavity and a membrane disposed inside the resonance cavity. The arrangement of  FIG. 17  leads to a further increase in the energy density, compare to the arrangements in  FIGS. 16A and 16B . 
       FIG. 18  illustrates an exemplary energy band structure of an emitter according to various embodiments of the invention. More efficient emitters can be used as shown in this figure. Improvement of emission can be attained through a deliberate modification of the energy band structure. In embodiments, the approach has been to reduce the electron affinity, Ea. Thus, permitting the escape of electrons which have been excited into the conduction band at greater depths within the material. If the electron affinity is made less than zero (the vacuum level is lower than the bottom of the conduction band, a condition described as “negative electron affinity” and illustrated in this figure. 
     Improvement of emission may be attained through a deliberate modification of the energy band structure. In embodiments, the approach has been to reduce the electron affinity, Ea, thus permitting the escape of electrons which have been excited into the conduction band at greater depths within the material. If the electron affinity is made less than zero (the vacuum level is lower than the bottom of the conduction band, a condition described as “negative electron affinity” and illustrated in  FIG. 18 . The escape depth may be as much as 100 times greater than for the normal material. For example, the escape depth of a photoelectron is limited by the energy loss suffered in phonon scattering. Within a certain period in time, typically on the order of 10 −12  seconds, the electron energy drops from a level above the vacuum level to the bottom of the conduction band from which it is not able to escape into the vacuum. On the other hand, the electron can stay in the conduction band in the order of 10 −10  seconds without further loss of energy, i.e. without dropping the valence band. If the vacuum level is below the bottom of the conduction band, the electron may be in an energy state from which it can escape into the vacuum for a period of time that is approximately 100 times longer than if an energy level above the bottom of the conduction band is required for escape. 
     In embodiments, several approaches to reduce the electron affinity may be applied. As an example, the semiconductor emitter is made strongly p-type by the addition of the proper “doping” agent. If gallium arsenide is the host material, zinc may be incorporated into the crystal lattice to a concentration of perhaps 1,000 parts per million. The zinc produces isolated energy states within the forbidden gap, near the top of the valence band, which are normally empty but which will accept electrons under the proper circumstances. The p-doped material has its Fermi level just above the top of the valence band. Next is to apply to a semiconductor a surface film of an electropositive material such as cesium. Each cesium atom becomes ionized through loss of an electron to a p-type energy level near the surface of the semiconductor and is held to the surface by electrostatic attraction. The changes which result in the energy band structure is two-fold in extent. First, the acceptance of electrons by the p-type impurity levels is accompanied by a downward bending of the energy bands. This bending could be understood by observing that a filled state must be, in general, below the Fermi level; the whole structure near the surface is bent downward to accomplish this result. Secondly, the potential difference between the charged electropositive layer (cesium) and the body charge (filled zinc levels) results in a further depression of the vacuum level as a result of a dipole moment right at the surface. The reduction of electron affinity can also be described if one were to consider the surface of the emitter as a capacitor. The charge on one side of the capacitor is represented by the surface layer of cesium ions; the other charge is represented by the region of filled acceptor levels. The reduction in the electron affinity is exactly equal to the potential difference developed across the capacitor. 
     Semiconductors with negative electron affinity provide an alternative way to achieve low work function materials because the Fermi level could be increased in the band gap by process and doping techniques, while the surface termination may maintain the vacuum level below the conduction band minimum. In a semiconductor, the electron affinity is the difference between the vacuum energy level and the conduction band minimum. The term negative electron affinity (NEA) refers to the condition where the vacuum level lies below the conduction band minimum. An electron with an energy greater than or equal to the conduction band minimum can escape into vacuum without an energy barrier at the surface of the semiconductor. Thus, an NEA surface may be expected to enhance cathode emission.  FIG. 18  shows the band diagram of an n-type semiconductor with a negative electron affinity. The work function of the material is very sensitive to the materials surface conditions, such as absorbed or evaporated layers, surface reconstruction, surface charging, oxide layer imperfections, surface and bulk contamination, etc. 
     The wide band gap semiconductors of diamond and AlxGa1-xN alloys have been shown to exhibit a small or negative electron affinity. This means that electrons excited into the conduction band may be emitted into a vacuum with little or no barrier. Thus n-type doping of the materials may provide electrons in the conduction band for efficient thermionic emission. The approach for preparing an n-type diamond can be accomplished employing nitrogen doping. Nitrogen is known to be a relatively deep donor with a level at 1.7 eV below the conduction band minimum. However, simple calculations indicate that at temperatures of 500-600 C, the Fermi energy would reside about 1.5 eV below the conduction band minimum resulting in an effective work function of 1.5 eV. Band bending effects would increase this value. 
     It will be appreciated by those skilled in the art that fewer or additional steps may be incorporated with the steps illustrated herein without departing from the scope of the invention. No particular order is implied by the arrangement of blocks within the flowchart or the description herein. 
     It will be further appreciated that the preceding examples and embodiments are exemplary and are for the purposes of clarity and understanding and not limiting to the scope of the present invention. It is intended that all permutations, enhancements, equivalents, combinations, and improvements thereto that are apparent to those skilled in the art, upon a reading of the specification and a study of the drawings, are included within the scope of the present invention. It is therefore intended that the claims include all such modifications, permutations, and equivalents as fall within the true spirit and scope of the present invention.