Patent Number: 
Section: description

1. Field of Invention The invention relates to the design of plasma based fusion energy devices, specifically to the incorporation of apparatus for providing ionized fuel inside such devices and for improving the power balance of such devices. 2. Prior Art The Need for Fusion Fueled Power Plants The energy needs of the world are growing exponentially. Energy consumption is projected to double by the year 2050 and to meet these growing needs a thousand new coal-burning power plants are planned and/or under construction. These power plants will cost approximately 4 trillion dollars to build. Even worse than this expense, burning coal increases air pollution and carbon emissions. These side effects cause global warming and degrade the health of people around the world. Nuclear power plants offer an attractive alternative to coal powered power plants. Nuclear fission reactors operate like a slow atomic (“A”) bomb, giving off energy from splitting heavy plutonium or uranium atoms into smaller atoms. France generates most of its electricity from fission reactors and has achieved a good safety record. Reactors in some other countries have not had such good safety records. Three-mile Island, Chernobyl, and Fukushima are examples of reactors which have accidentally melted down and devastated the local environment. These disastrous meltdowns have created widespread mistrust of fission reactors as a practical alternative to coal burning plants. Nuclear fusion reactors do not melt down and do not pollute. They are designed to operate like a slow and safe hydrogen (“H”) bomb, fusing light isotopes of hydrogen, helium, and/or boron. Fusion devices are classified by the methods used to confine and heat a plasma of fuel ions mixed with electrons. Since the early 1950's, much research has been directed toward developing different fusion concepts. At this time the concept known as “tokamak” has become the favorite of the international fusion community. ITER, the latest multinational tokamak experiment, is currently under construction in the south of France. ITER will cost tens of billions of dollars to build and operate. Unfortunately, the first power plant based on ITER will not be ready until the mid-2040's at best. And worse, the complicated design of ITER makes it doubtful that it will ever be used for commercial power generation. At a recent international fusion conference, senior D.C. Energy Adviser Robert Hirsch criticized ITER, “First, we have to recognize that practical fusion power must measure up to or be superior to the competition in the electric power industry. Second, it is virtually certain that tokamak fusion as represented by ITER will not be practical.” ITER and other tokamak designs have serious disadvantages when compared to Inertial Electrostatic Confinement (IEC) fusion. The tokamak has a toroidal shape, leading to magneto-hydrodynamic (MHD) instabilities. Instabilities cause excessive plasma losses through the outside edge of the torus. In ongoing attempts to patch the loss points, the design of the tokamak has evolved to incorporate an expensive, super-conducting magnet design. In contrast, IEC devices confine the plasma into a quasi-spherical shape, which is MHD stable. Stability allows IEC devices to have a simpler design than ITER. By overcoming ITER's drawbacks, as pointed out by Hirsch (above), these simpler IEC designs will be more acceptable to the power industry. One example of an IEC design intended for power production was disclosed in a 2004 U.S. Pat. No. 8,059,779 to Greatbatch. The Greatbatch patent claims, “An electrostatic fusion device, comprising: a vacuum chamber; a potential well disposed in said vacuum chamber; a partial vacuum environment in said vacuum chamber containing fusion reaction ions; . . . .” (Here ends the quotation from Greatbatch.) Unfortunately, Greatbatch's patent lacks any description of how the “fusion reaction ions” came to be inside the potential well in the first place. Getting the ions into the potential well is a big problem not dealt with in the Greatbatch patent. Without an adequate fuel supply the proposed 2004-Greatbatch device cannot produce useful energy. The Polywell Reactor Concept The most promising example of an IEC fusion device was disclosed in pending U.S. Pat. 2010/0284501A1 by Rogers, entirely incorporated herein by reference. The 2010-Rogers application teaches an improvement on the well-known Polywell IEC reactor design. Polywell was originally patented by Robert Bussard in 1989 U.S. Pat. No. 4,826,646. Polywell has been the subject of extensive research by Energy Matter Conversion Corporation (EMC2) of Santa Fe, N. Mex. Bussard served as the CEO of this Company until his death in 2007. The Company's research was continuously funded by the U.S. Navy from 1991 to 2014. Shortly before his death, Bussard wrote a final report documenting his concerns about the unsolved problems with Polywell. Bussard's final report, “Polywell Results and Final Conclusions,” is hereinafter referred to as 2007-Bussard. The following excerpts from 2007-Bussard retain the same paragraph numbering as in the original report: 4. “Large scale vacuum pumping is required to avoid high-voltage arcing. But such vigorous pumping produces a core fuel density so low that it cannot produce significant fusion rates inside the machine . . . . Thus, some means must be found to ensure large electron density within the machine.” 5. “This requires that the ionization (of neutral gas) density within the machine must be very large relative to that outside; and this can be attained only by neutral gas injection directly into the machine, followed by subsequent very rapid ionization of this gas, before it can escape into the exterior region. In small machines this is difficult . . . .” 6. “Thus, in small systems there is a big incentive to attempt to fuel the machine with ions injected from ion guns . . . [but] they can not be fully magnetically shielded . . . . In this situation, it appears that the only way to test these principles in small machines is to try to use capacitor discharge drives . . . .” 11. “Thus, full-scale machines and their development will cost in the range of ca $180-200 million, depending on the fuel combination selected . . . . USNavy costs expended to date [i.e. 2007] in this program have been approximately $18 million over about 10 years . . . .” Only one public announcement has come from EMC2 since Bussard's death in 2007. In 2014, a research paper entitled “High Energy Electron Confinement in a Magnetic Cusp Configuration” was published by EMC2. First author of the paper was Dr. Jaeyoung Park, CEO of the Company. This paper, hereinafter called 2014-Park, reports experiments confirming the existence of the “wiffle-ball effect.” Coined by Bussard in 1991, “wiffle-ball effect” is a term used to describe the diamagnetic closing of electron-loss channels at high plasma density. The existence of the wiffle-ball in Polywell is essential if the Polywell design is to be used for practical power production. Wiffle-ball was predicted theoretically by Bussard in 1991 but had not been seen experimentally until the work reported in 2014-Park. The 2014-Park paper is timely and important for validating the Polywell concept. The machine design disclosed by this patent application goes far beyond the work reported in 2014-Park. The main flaw of the Park paper is that their experimental device operated in pulsed mode and without proper cooling. In pulsed mode, fusion energy output lasts only for a tiny fraction of a second. Net-power reactors must operate for months and years, not milliseconds. In addition, the power to heat the plasma came from external plasma guns. By nature, these guns are hopelessly inefficient for net energy production. To operate in a net-power mode, plasma-heating power must come from a high-voltage electron injector, not from a plasma injector. No high-voltage power supply was used in the work reported in 2014-Park. Without efficient plasma heating there is no hope that a Polywell device will ever produce more power than it consumes just to stay hot. Small-scale Polywell devices always consume more power than they produce. On the other hand, building a large-scale (i.e. break-even) device would cost hundreds of millions of dollars. To attract private investors it is now necessary to build and test structurally-correct, small-scale machines. Then keeping to a proven design, larger and larger scale-models can be built. At each stage of development the performance of the scale-model reactor can be compared with computer simulations. Once tested, the simulations can then be used to predict the performance of the next larger scale-model. In this way, designing the expensive net-power machines can be approached gradually and with confidence. Polywell, when properly fueled, can reach break-even and still avoid the complexity of tokamaks. Problems with Polywell—FIGS. 1A, 1B Pulsed operation, as described in 2007-Bussard and 2014-Park, is inadequate for demonstrating the Polywell principle. When the machine is operated pulsed, power is produced for only a tiny fraction of a second at a time. A viable power-reactor must demonstrate long-term, steady-state operation to earn the confidence of the power companies. FIG. 1A shows a drawing of a magnet module (200) from the prior art. This drawing is copied from FIG. 3c of 2010-Rogers. The module shown was designed for steady-state, not pulsed, operation. According to the design, six or more similar modules are mounted on the faces of a polyhedron. Inside the polyhedron a plasma of electrons and ions is confined and heated. An ion gun (460) injects ions along the axis of one of six coil magnets (410). Finding a suitable place to position the ion gun was the main problem with this design. The central axis of the magnet must be kept open to allow high-energy electrons to circulate in and out of the core. The problem was that there was no workable position for the ion gun, i.e. where it avoids being hit by electrons. Electrons are born in an electron source (414). From the source, the electrons accelerate along the coil axis, i.e. in an upward direction in the Figure. Trapped electrons form a potential well inside the polyhedron. The potential well accelerates and traps ions born in the ion gun. The potential well has a roughly circular shape, like a volcano. Newborn ions are emitted from the source positioned at a point high on the rim of the well. The ions then fall down the inner wall of the potential well. Ions stream continuously into the core, each ion accelerated to fusion energy. Once in the core, each ion bounces many times back and forth across the well. After many passes through the center of the reactor, each ion either fuses or up-scatters out of the well. Whether lost to fusion or up-scattering, lost ions must be continuously replaced from the ion source to maintain the plasma density and temperature at constant values. Input power to the reactor is provided by a high-voltage power supply, not shown in this Figure. The power enters the magnet on wires inside insulated legs (404). The power supply biases the magnets on all (six or more) modules to a high-voltage, typically in the range 10-500 kilovolts. The positive voltage on the magnets attracts the negatively charged electrons. Electrons accelerate from the ground-potential source (414) to the center of the coil. Momentum carries the electrons through the magnet and on into the core of the reactor. The electron energy is transferred to ions through the action of the potential well. The well has the feature that the magnitude of the ion's energy is approximately equal to the magnitude of the incoming electron's energy. The voltage of the power supply is selected to give the ions the optimum energy for fusing. Different fuel choices require different voltages. FIG. 1B shows a graph of the fusion cross-section for four useful fuel choices. The curve labeled “DT” (102) shows the cross-section for fusing ions of deuterium (D) with ions of tritium (T). This reaction has the highest cross-section among all the possible light element combinations. This is the fuel choice of the ITER project. The “DD” curve (104) shows the cross-section for fusing deuterium ions with deuterium ions. The “DD” fuel choice has a lower cross-section than “DT.” Because of the lower cross-section, a D+D fueled power-reactor will be bigger in size than a D+T reactor producing the same power level. However, size is not the only selling point of a reactor design. Drawbacks with tritium fuel are that tritium is radioactive and expensive. These drawbacks are not shared with deuterium. Deuterium is stable and plentiful compared to tritium. D+D fuel is called an “advanced fuel” in the prior art. A major advantage of the subject invention over ITER is that, in some embodiments, the new design burns D+D fuel in a break-even reactor with a reactor size projected to be smaller than ITER. Avoiding the troublesome tritium as fuel is a great step forward from the prior art. Returning attention to FIG. 1A, in the prior art the ion gun (460) is not shielded by the magnetic field. The ion gun attracts electrons and thus bleeds them from the confined plasma. To maintain the density and temperature of the plasma, lost electrons must be replaced by fresh electrons that draw energy from the high-voltage power supply. The input power required to replace the lost electrons reduces the power balance of the model reactor. Greater-than-unity power balance is needed for net-power operation. Power balance can always be increased by making the reactor larger. But then the resulting break-even Polywell reactor size would be even larger than ITER. Until solved by this invention, prior-art fueling solutions lead to unacceptably large reactor sizes. Other features of the prior art, as indicated by FIG. 1A (205), (400), (405), (409), and (418), may prove useful in building and testing model reactors according to the invention. These features would function as described in 2010-Rogers, as incorporated herein. It might be tempting to modify the 2010-Rogers design by moving the ion gun OUTWARD from where it is shown in FIG. 1A. If the ion gun were located behind the magnet, it would be better shielded by the magnetic field. The ions might then be shot inward along an axis of the cylindrical coil. To accomplish this, the velocity of the ions coming out of the ion gun would need to just match the height of the flank of the potential well at the position where they enter the core. The height of the flank of the potential dictates a magic velocity at which the ions can enter the well and be trapped. However, if the velocity is even a tiny amount higher than this magic velocity, the ions will fly across the well and escape the opposite side. The need for precise adjustment of the ion velocity results in an impractically small operating range for the reactor. The idea of moving the ion guns outside the magnets will not work due to this drawback. The following “thought experiment” is proposed to illustrate the drawback: Suppose we wish to fill an extinct volcano with soccer balls. The volcano is like the potential well in an IEC reactor. The soccer balls are like fuel ions. The force of gravity is like the electrostatic force acting on the ions. We imagine the inside of the volcano as a perfectly smooth, frictionless bowl. The insides of the bowl rise to a circular rim all around. Outside the rim the flanks of the volcano fall away to level ground on all sides. The potential well is invisible in the IEC reactor; thus, we imagine the volcano to be invisible. Suppose it is shrouded in mist so that we cannot see it. We stand on level ground and kick the first ball toward the volcano. The ball rolls into the mist and then comes rolling back. Gradually, we kick the soccer ball harder and harder. Finally, we kick it hard enough that it rolls all the way up to the rim and falls into the volcano. But suppose we kicked it a little too hard. It rolls across the bowl, up the far wall, over the rim, and is lost. We adjust the strength of our kicks until some of the balls don't come back and don't exit the far side of the volcano. But even so, we still lose a lot of soccer balls. Minor variations in the strength of our kicks and in the height of the rim always cause most of the balls to be lost over the rim. Our efforts to trap all the soccer balls in the volcano are unsuccessful. And so is the problem of fueling Polywell with ion guns also intractable. In addition to the problems described above, ion guns have another serious problem. They consume a lot of power to produce only a tiny amount of ion current. The typical ion gun, such as the commercial one shown in 2010-Rogers (FIG. 4G), produces a maximum current of around 0.1 microamperes of ions. The ion current needed to stabilize the plasma in small-scale Polywell is in the milliampere range. It would take thousands of ion guns operating in parallel to produce even 1 milliampere of ions. Needless to say, operating thousands of ion guns is not practical for a myriad of reasons. The following conclusions summarize why existing ion sources are NOT suitable for fueling a Polywell type IEC reactor: (1) The reactor can only operate in millisecond-pulse mode. If the pulse lasts longer than a millisecond, the high-voltage arcs and fries the magnets. (2) Commercial ion sources are too big and too weak to be used inside the bore of the electromagnet. They cannot be shielded and they produce too little current. (3) Injecting ions from external ion guns is impractical because the ions cannot efficiently cross the flanks of the potential well. From the above analysis we see an apparatus for fueling an IEC reactor is needed. Without it fusion power cannot become a practical reality. The present patent application teaches how to build and use such an apparatus.  A steady-state fusion energy device solving the above described fueling problems consists of a vacuum tank, coil electromagnets arranged on the faces of a polyhedron, electron-emitters mounted on the inner surfaces of the vacuum tank, a high-voltage power supply to bias the magnets, and most importantly, gas-cells mounted inside the bores of the magnets. The magnetic fields combine with the bias on the magnets to compress the electrons into narrow beams flowing in and out through the magnets. Locating the gas-cells at the points where the electron beams are narrowest allows the gas to be largely confined by pairs of metal plates with small holes to let the beams pass in and out of the cells. The holes' small diameters limit the flow of neutral gas out of the cells. Leaking gas must be pumped away by vacuum pumps to maintain a low pressure outside the gas-cells. The lower the leakage rate, the less expensive are the vacuum pumps. Vacuum pumps already represent a major portion of the capital cost of IEC reactors. The technique of maintaining a pressure differential across “choking” apertures is called differential pumping. The design and usage of differentially pumped gas-cells in nuclear physics experiments is familiar from the scientific literature. This invention is believed to be the first application of differential pumping to fuel fusion reactors. The immediate use of the embodiments disclosed will be in building and testing small-scale model-reactors. Small-scale reactors consume more power than they produce, but they must be built and tested first before committing billions of dollars to develop net-power reactors. The size of the scale-models will be increased step-by-step. With each size increase, the models will approach closer and closer to break-even. Constructing larger and larger scale models is a development path similar to the path that tokamak development has taken over the past 50 years. Fortunately, with the advantage of MHD stability, these embodiments have a much better chance of success than tokamaks ever did. The differentially pumped ion source, a central element of the embodiments, will be crucial both in building scale-models and in building net-power reactors. Larger model reactors require larger amounts of ions. Larger and larger amounts of ions can be produced economically by simply turning up a regulator-knob to control the pressure of the gas in the gas-cells. Electrons circulate in and out through the bores of the magnets. When an electron approaches one of the tank walls, it is slowed by a retarding electric field. Electrons stop just short of hitting the tank walls, reverse their trajectories, and fall back into the core under the influence of the electric field. Electrons circulate in and out of the reactor core many times until they up-scatter, hit the tank wall, and are lost. The continual loss of electrons forms a steady power drain from the steady-state reactor. Power drain is the main limiting factor to getting net-power from small-scale reactors. Large-sized reactors produce more fusion power than the electrons' power drain. The break-even reactor size is the size that produces the same amount of fusion power as the input power required to maintain the plasma. A predictable break-even size characterizes each reactor design. The smaller the size of the break-even reactor, the more economical the design is to build and operate. This invention leads to smaller break-even reactors. Continuous electron injection maintains a potential well that traps ions. In the embodiments of the invention disclosed, the same electrons also create fuel ions inside the reactor. The physics of ionization of gas by fast electrons is well understood. Monte Carlo modeling was used to simulate the production of ions, including effects of electron-velocity, electron-density, gas-pressure and gas-temperature. The computer algorithm that does the modeling was developed at Berkeley with hundreds of man-years of labor invested over several decades. The algorithm is described in Birdsall's 1991 publication, “Particle-in-Cell Charged-Particle Simulations Plus MonteCarlo Collisions with Neutral Atoms, PIC-MSS”, hereinafter called 1991-Birdsall. Gas is fed through a narrow-gauge tube into the gas-cells at a rate fast enough to just balance ions consumed by fusion plus ions lost to hitting internal structures. In order to avoid wasting drive power, it is important that the power lost to ions hitting internal structures be made smaller than the electron power loss described above. A certain minimum rate of loss to up-scattered electrons is unavoidable. However, the power lost to escaping ions can be, and has been, greatly reduced by the design features of these embodiments. By reducing the power lost to ions to be less than to electrons, the power balance of the model reactors was vastly improved over 2014-Park. Multiple gas-cells can be used by placing similar cells in more than just one magnet. An advantage of using multiple cells is that two different ion fuel species can be supplied by different gas-cells. This allows the fuel gas mixture to be adjusted in real-time while the reactor is running. The density of the gases in the gas-cells can be optimized by varying the mixture for maximum power output. For example, using the the p+B11 fusion reaction, one gas-cell could produce hydrogen ions (p) and another gas-cell could produce boron-11 ions. Once created by gas ionization, most ions accelerate from their birthplace into the core through the inner aperture of the gas-cell. The energy gained by each ion in this initial acceleration depends only on the distance from its birthplace to the center of the potential well. By minimizing the spacing between the apertures, the initial ion velocity varies only over a narrow range of velocities. This allows the ion energy to be precisely adjusted to the exact ion energy that maximizes fuel reactivity. This optimum energy can be determined for each fuel choice by analyzing the cross-section data shown in FIG. 1B. Some ions are also produced outside the gas-cells due to the necessary leakage of some gas out of the gas-cells through the apertures. These ions do not fall down the potential well at the place required for them to reach fusion energy. Because of the steep fall-off of the reactivity with energy, many ions born outside the gas-cells will never fuse. These ions are wasted. They needlessly consume drive power. The complete operation of a model reactor has been simulated by particle-in-cell techniques combined with Monte Carlo techniques. Different fuel mixtures will result in different sizes for the break-even reactor. A cube-shaped reactor fueled by D+D has been modeled in detail and found to predict a break-even reactor size of 18-25 meters. Fueling with D+T would give a much smaller reactor, but the D+T fuel choice may be unattractive because tritium (T) fuel is not only expensive but also radioactive. D+D is often called an “advanced” fuel because it avoids the problems inherent with tritium. An important feature of the embodiments is that the predicted IEC reactor size is smaller than ITER, even though the IEC reactor burns advanced fuels. Thus, the break-even IEC reactor is expected to be simpler and smaller, and therefore less expensive than any break-even tokamak, including ITER. Correcting the Over-Optimistic Size Prediction of the Prior Art In the present patent application, computer simulation was used to predict the sizes of break-even reactors constructed according to the embodiments. The reason for relying on simulation was that building full-scale reactors is too expensive to be undertaken without reliable theoretical guidance. Instead, trial and error experiments have traditionally been done with computer models to save the expense of constructing unproven designs that do not work. The most relevant computer simulation prior to 2010-Rogers is found in the patent application of Bussard, as reported in US20080187086A1, hereinafter called 2008-Bussard. The main difference between 2008-Bussard and this application is the predicted size of the break-even reactor. Both applications rely on computer simulations. Both analyze a theoretical model comprised of six electromagnets arranged on a cubic polyhedron. But 2008-Bussard predicts the break-even D+D reactor would be 1.5 to 2.5 meters diameter, while this Specification says a similar design would need to be 25 meters diameter to reach break-even. Careful analysis of 2008-Bussard was made in an effort to uncover the source of his vastly different predictions for the size of the break-even reactor. The difference discovered was that 2008-Bussard's computer simulation failed to properly account for the transverse momentum imparted to ions reflected from the edge of the “quasi-spherical” potential well. Bussard's simulation assumed that the well was perfectly spherical, not quasi-spherical. A perfectly spherical well would indeed result in convergence of in-falling ion positions to form a dense core at the center of the cube. Such convergence was not seen in the more realistic simulation disclosed in this Specification. To understand where 2008-Bussard went wrong, selected passages of the publication will be briefly analyzed here. The bracketed [numbers] below were copied from Bussard's USPTO publication. These numbers can serve as reference points to the USPTO's text to further validate the analysis. Quoting from 2008-Bussard: “[0060] According embodiments of the invention, particle injection (ion or electron) may be along the magnetic cusp field axes, . . . . Of course, in any realistic source of electrons (and of ions) there will always be a transverse component of energy, transverse to the radial motion due to the well gradient, that will prevent some of the particles from reaching the exact center of the potential well. Thus there will always exist a central ‘core’ whose size (rc) will depend on the ratio of transverse energy at the edge of the well (dEtrans) to the well depth (Ewell), such that the fractional core size will be approximately <rc>=(rc/R)=(dEtrans/Ewell)1/2.” “[0064] . . . the convergence of the quasi-spherical geometry of the polyhedral configurations of interest increases the local dynamic pressure by the square of the inverse ratio of radii from the outer (electron injection) radius to the inner (ion dynamic pressure confinement) radius, rc . . . .” “[0071] . . . In-falling ions will converge as the inverse square of the radius, thus the reaction rate will tend to vary as the inverse fourth power of the radius. This very rapid dependence ensures that nearly all of the fusion energy generated in such a device will be generated in and around the center of the (structurally-empty) cavity . . . .” “[0072] Numerical calculations show that the ion current densities required for total fusion power output at ‘useful’ levels for certain applications is much larger than those required for power balance makeup against electron losses. To achieve this state requires a current multiplication or ‘gain’ (Gj) achieved by the recirculation of ion (and electron) currents across the machine volume many times, until a sufficient ion density is achieved . . . it is clear that there must exist a size sufficiently large that the ‘gain’ may be unity (Gj=1), and that no current multiplication is required for operation of the machine at a breakeven power balance. Numerical calculations show that this size is approximately R≅10-20 m, . . . .” “[0208] . . . collective phenomena beyond start-up (from low- to high beta) . . . have been readily modelled successfully by a major plasma phenomenological code (the EIXL code) developed by EMC2 since 1990. This is a 1.5-dimensional Vlasov-Maxwell code, . . . which includes such phenomena as central core inertial-collisional compression effects which can apply to core ion compression in Polywell devices.” Here ends the quotation from 2008-Bussard. The following numbered paragraphs analyze the errors of the preceding “quoted” paragraphs, keyed to the same paragraph [numbers] used by the USPTO. The term “radial motion due to the well gradient” in that paragraph is misleading. The motion, due to the well gradient, is by no means “radial.” The well has a scalloped edge due to the bumpy nature of the confining magnets' field. The formula for “rc” at the end of the paragraph is incorrect because the in-falling ions travel on curved paths, not the radial paths assumed. The formula describes straight-line paths which do not exist. The phrase “the convergence of the quasi-spherical geometry” is self-contradicting. The “quasi-spherical geometry” produces divergence, not “convergence.” The simulation in 2008-Bussard describes an idealized spherical geometry, not the realistic “quasi-spherical geometry” of the actual device. The first statement, “In-falling ions will converge” is probably correct, at least for the first pass of newborn ions. The second statement, “thus the reaction rate will tend to vary as the inverse fourth power of the radius,” does not follow logically from the first statement. It is certainly not correct. The in-falling ions may indeed converge, but only on their first pass. The convergence is lost on subsequent bounces. The ions bounce many times back and forth before they fuse. Their directions gradually change, in random directions, from their original direction. After many bounces the accumulation of small turns has wiped out any convergence the ions might have had on their first pass through center. The paragraph says “output at ‘useful’ levels . . . is much larger than those required for power balance makeup against electron losses.” This statement is unrealistically optimistic. In this paragraph Bussard seems to be saying that lesser power levels, which he admits could be improved by simply going to larger reactors, would be useless; that is, the opposite of “useful.” In the present patent application the applicant discloses a useful design in which the break-even output power is definitely greater than the electron losses. The design results in a larger reactor than Bussard predicted. “Larger” break-even size is definitely not “useless” break-even size. “Useless” is a subjective term that loses its impact once it is realized that convergence does not exist. In this paragraph the simulation code used by Bussard is called “a 1.5-dimensional Vlasov-Maxwell code.” The jargon “1.5-dimensional” is the well-known name for a code one-dimensional (1D) in spatial variation and 2D in velocity. The meaning of this jargon would be obvious to anyone skilled in the art of plasma simulation. The simulated in-falling ions were confined by the simplicity of the code to travel along purely radial orbits. By assuming spherical symmetry, convergence was artificially imposed on the simulation results. In contrast, the present invention is supported by a 2.5-dimensional PIC code, which is inherently 2D in the spatial variable (x and y) and, by the way, 3D in velocity. As will become obvious in the description of the embodiments to follow, 2D spatial simulation is sufficient to show the greater complexity of the ion's trajectories. The trajectories certainly do not converge as claimed by Bussard. The existence of a convergence radius “rc” was postulated by Bussard in his paragraph [00060], quoted above. The existence of such a convergence radius was not confirmed by any measurement or realistic simulation in 2008-Bussard. The only simulation documented in 2008-Bussard is the “1.5-dimensional Vlasov-Maxwell code,” just discussed. No further details of the code are disclosed in the 2008-Bussard publication beyond those shown in the paragraph [0208] quoted above. It seems likely that the “core ion compression” feature claimed for the code was added into the basic physics by assuming a value of a hypothetical transverse energy for the ions at birth. The value selected for the transverse energy then would become an ad hoc parameter that could be chosen to produce any desired value for “rc,” the core radius. The value <rc> equal to 0.1 was chosen “as an example” in 2008-Bussard. This assumed value of “rc” resulted in a small break-even reactor-size prediction, but its assumption seems to be unsupported either by experiment or adequate theory. The PIC simulation presented in this Specification is 2.5-dimensional, in other words 2-dimensional in space and 3-dimensional in velocity. The extra spatial dimension led to predicting increased transverse momentum as a natural result of the ions' multiple reflections on the quasi-spherical potential well. A flat density profile resulted, reaching from cube center all the way out to the magnets. In the terminology of 2008-Bussard, such a flat density profile would be described by Gj=1. According to paragraph [0072] above, Gj=1 would produce a break-even radius of 10-20 m. Bussard called this radius “practically infeasible” in the same paragraph. However, once Bussard's quest for central convergence is abandoned, his break-even prediction comes into agreement with these PIC results. Obviously, a 10-20 meter break-even radius is not perfect, but it is feasible. Fortunately, there is another, better way to obtain a small break-even reactor size. This better way is disclosed as the second embodiment of this invention.  200 prior art magnet module. 205 module vacuum flange. 400 spacer flange. 404 hollow leg. 405 insulating section. 409 chamfered edge. 410 magnet box. 414 electron gun. 418 gas nozzle. 460 internal ion source. 102 graph of DT cross-section. 104 graph of DD cross-section. 110 highest sampled ion energy. 111 2nd-highest ion energy. 112 3rd-highest ion energy. 113 4th-highest ion energy. 120 energy axis. 121 cross-section axis. 220 vacuum tank. 225 gas-cell. 230 electron emitter. 282 copper magnet coils. 222 cell aperture plates. 224 left-hand gas-cell. 225 right-hand gas-cell. 226 top-magnet coil. 227 right-hand magnet coil. 228 bottom-magnet coil. 229 left-hand magnet coil. 230 electron emitter. 232 simulated electron positions. 234 gap between adjacent magnets. 236 horizontal (x) position scale. 238 vertical (y) position scale. 250 origin of Time axis. 252 particle counts axis. 254 graph of electrons' counts. 256 graph of ions' counts. 258 end of Time axis. 270 center-point of potential. 272 equipotential contour. 310 face cusp-line. 320 corner cusp-line. 340 narrowest part of cusp. 350 reduced-size apertures. 428 fast ion near center. 430 ion born in tank corner. 432 ion born near magnet. 434 ion born near center. 440 gas concentrated in gas-cells. 460 ions' left-hand bounce point. 462 ions' right-hand bounce point. 470 diagnostics, 10% background gas. 472 diagnostics, 1% background gas. 474 diagnostics, 0.1% background gas. 475 energy scale in electron-volts 476 graph of average electron energy. 477 ion energy with 10% background. 478 ion energy with 1% background. 749 ion energy with 0.1% background. 480 Time axis, background test. 481 Time of density declining. 482 Time of density leveling. 486 3-pairs of apertures on left. 487 3-pairs of apertures on right. 488 gas-cell with mulltistage pumping. 489 path of electrons recirculating. 490 vacuum pump pumping tank. 492 pump pumping inner volume. 493 pipe to inner volume. 494 inner volume. 496 pump pumping outer volume. 497 pipe to outer volume. 498 outer volume. 510 brace opening Variables' block. 512 typical comment line. 513 blank comment line. 514 typical variable definition. 516 equals symbol for assignment. 518 typical assignment expression. 520 linear variable dependence. 521 quadratic variable dependence. 522 magnet current scaling. 524 magnet definition block. 525 assigning magnets' corner gap. 526 operational parameters block. 527 cells per size scaling factor. 528 assigning PIC cell-size. 529 cell count per tank diameter. 530 magnets' bias-voltage. 531 electrons' initial velocity. 532 time-step vs. Velocity. 533 electron emitter current. 534 extractor definition block. 536 assigning extractor size. 537 assigning extractor position. 540 gas-cell definition block. 550 gas-fill definition block. 552 assigning gas density. 553 background/cell density ratio. 554 assigning background density. 555 assigning electron ionization factor. 556 assigning diagnostic-time duration. 560 typical wire coordinate. 561 modulus operator usage. 563 example of assigned-variable usage. 564 brace ending Variables Block. 570 simulation control block. 571 assigning initial values. 572 automatic x-coordinate. 573 automatic y-coordinate. 574 assigning “Bx” magnetic field. 576 assigning “By” field. 580 defining electron properties. 582 Monte-Carlo Collisions block. 584 assigning neutral gas properties. 585 pre-loading PIC-cells with gas. 586 use of ionization scale factor. 588 brace ending MCC block. 590 extractor properties block. 592 charge-bleeding option. 598 end of extractor definition block. 610 y-axis ions per square-meter. 612 x-axis, 0 to 0.62 meters. 624 left-hand ion surface. 626 right-hand ion surface. 620 ions' central density level. 622 electrons' central density level. 630 electrons' trapped in cusps. 640 white box marking waist. 642 x-coordinate of waist. 644 y-coordinate of waist. 646 central x-coordinate. 647 x-axis spanning tank edge. 648 extended horizontal lead line. 650 equipotential at electrons' surface. 660 By scale calibrated in Tesla. 662 By as a function of x. 666 line marking By value. 670 line at x-center position. 671 one x-interval off center. 672 two x-intervals off center. 673 three x-intervals off center. 674 four x-intervals off center. 680 ion velocity at center. 681 velocity 1-off center. 682 velocity 2-off center. 683 velocity 3-off center. 684 velocity 4-off center. 686 ions' x-velocity axis. 687 ions' x-position axis. 690 boundary of interior electrons. 692 interior electron's trajectory. 694 exterior electron's trajectory. 696 limiting exterior B-field line. 697 2D plot of electron density. 698 central-cell setting scale. 699 typical electron trapping regions. 700 table for numerical integration. 702 index of table entries. 704 x-positions of integrand sampling. 706 ion velocities sampled. 708 ions' kinetic energy (doubled). 710 angle averaged cross-section. 712 integrand at sample points. 714 Simpson's rule weight factors. 716 integrand samples to be summed. 802 ions' tank loss current. 804 nine-microsecond time span. 806 average loss current extrapolated. 808 loss-axis calibrated in amperes. 812 bottom corner ion loss spectrum. 813 face-cusp ion loss spectrum. 814 top corner ion loss spectrum. 816 ions' energy origin. 817 ions' energy maximum. 818 ions' average energy. 819 ions' position axis. 832 electron's energy-spectrum. 834 electrons' lost-energy axis. 836 electrons' energy centroid. 910 electron-extractor electrode. 912 steady-state electron positions. 914 typical corner-cusp endpoint. 916 typical face-cusp endpoint. 918 tank wall clear of losses. 919 electrons in cusp at extractor. 920 ions' 2D positions, 2nd embodiment. 922 ions escaping in corner cusp. 924 ions escaping in face cusp. 1002 ions' x-velocities vs. x-positions, 2nd embodiment. 1020 electron loss current on tank. 1022 ion loss current on tank. 1024 latest time in start-up. 1026 average electron loss current. 1028 average ion loss current. 1030 position axis, 0 to 0.62 m. 1032 max potential measured in volts. 1040 electrons' spectrum on electrode. 1042 electrons' position axis. 1044 cell at midpoint of electrode. 1048 electrons' energy axis. 1050 1st embodiment loss vs. Time. 1052 current constant at 2.0 amperes. 1060 electrons' loss on extractor. 1062 ions' loss on extractor. 1064 electron current 1.3 amperes. 1065 ion current 0.008 amperes.  In the First Embodiment, the largest single source of power loss was from electrons hitting the tank walls. Electron power loss dominated over magnet and ion power losses in determining Pin. The electron power loss of the central slab was computed from the simulation diagnostics by a method similar to the one described in the previous section for the ions. FIG. 8C shows the energy/position spectra of electrons hitting the left-hand tank wall. Once again the energy spectra appeared divided into 3 peaks. The 3 peaks again were separated in distance along the left-hand tank wall, as indicated on the position axis (819). A smaller peak (832) occurred at center and two larger peaks occurred at the bottom and top ends of the wall. The lengths of the vertical lines inside the 3 peaks measured the number of electrons hitting the wall at each electron-energy and electron-position. In this Figure, the energy axis (834) spans a smaller range, zero to 1e4 electron-volts. Energy divisions are at 1 keV intervals along this axis (834). A value for the average electron energy was needed to compute the power loss. The mathematical centroid of the electrons' energy distributions is shown marked with a dashed line (836). The average energy of all the lost electrons was read as the intersection point of the dashed line with the energy axis (834). This method determined the average lost-electrons' energy to be 1.5 keV per electron. Also needed to compute the electrons' power-loss was the electrons' loss-current on the tank walls. This number could have been read from a diagnostic display similar to FIG. 8A for ions. More accurately, the electron current was calculated from the physics principles of particle- and charge-conservation. By the definition of steady-state, the total number of electrons in the plasma was constant in time. To maintain this condition, the net current of electrons into and out-of the tank must total zero. The flow of electrons into the tank was known to be the sum of current from the electron-emitter plus a current of electrons created by gas ionization. The emitter current had been optimized by trial and error to give the best model-reactor power-balance. This optimized value of current, 2.0 amperes, was assigned as the variable “eleclgnitionCurrent,” as shown in FIG. 5B (533). By charge and particle conservation, the lost-electron current from gas ionization must be equal to the lost-ion current. The lost-ion current was determined in the previous section to be 0.017 A. This is a very small current compared to the 2.0 amperes from the electron-emitter. Two significant digits were all that were needed to compute the electron power loss. The small additional current from gas ionization could be ignored compared to the 2.0 amperes from the electron-emitter. Returning to FIG. 8C, the 10 keV energy range spanned by the electrons' energy axis (834) was 5 times smaller than the ions' energy range in the previous Figure (816,817). The electrons' average-energy at the wall was much smaller than the ions' average-energy. In traveling from the core to the tank walls, electrons run uphill against the potential. By doing this, they convert most of their kinetic energy to potential energy before hitting the wall. This conversion of kinetic to potential energy occurs in vacuum and so is entirely lossless. This process enables an efficient resetting of up-scattered electrons' energies. In a net-power reactor, the energy lost by electrons at the tank wall will be converted to electricity and re-injected via the high-voltage power supply. Such recycling of lost energy is limited by the efficiency factor η, as discussed previously. Inefficient recycling applies only to a small fraction of injected energy, only the fraction remaining to an up-scattered electron after its uphill run to the tank. The efficient correction of up-scattering, using lossless conversion of kinetic to potential energy, is an important feature of Polywell confinement. When combined with the new ion source specified in this embodiment, it produces a superior fusion reactor design. The electron power loss was computed as the product of electron energy, expressed in volts, times electron current, expressed in amperes. The electron power loss was 1.5 kilovolts times 2.0 amperes which equals 3.0 kilowatts. This was the simulated power carried away by the electrons lost from the central slab of the cubic reactor. In computing the central-slab's power loss, this 3.0 kilowatts adds to the 680 watts lost by the ions, as computed in the previous section of this Specification. Evaluating the 3D Power Loss from the Simulated 2D Power Loss by Stacking Slabs Adding the electrons' 3.0 kilowatts to the ions' 680-watt power loss, the total particle power loss from the central slab was 3.7 kilowatts, again expressed to two significant digits. To extrapolate to the power loss of the cubic reactor required an estimate of how many slabs must be stacked up to make a cube of plasma. By symmetry, the stacked plasma cube must have the same height as the width of the square plasma cloud in the slab. The number of slabs required was computed as the width of the plasma square divided by the thickness of the slab, both width and thickness to be determined. The thickness of the simulated slab was computed as the ratio of the 2D electron-density divided by the 3D electron-density. The simulated central electron density was read from FIG. 6B as the position where the dashed line (622) intersected the vertical axis (610). This density reads as 4e14 electrons per square meter. The 3D density was previously computed as ne=5.6e16 electrons per cubic meter. Combining these factors, the slab thickness was found to be (4e14 m−2)/(5.6e16 m−3), which equals 0.0071 meters. This slab thickness was surprisingly found to be approximately equal to the PIC cell-size. To see this, PIC cell-size can be computed by hand from diagnostics. Cell-size is the ratio of tank diameter in meters divided by tank diameter in cells, 0.622 m/72=0.0086 m. PIC cell-size was originally specified to be just small enough to avoid artifacts in simulating the smallest in-plane plasma features. Fortuitously, the slab thickness (0.0071 m) turned out to be about the same size as the cell-size. The previously-selected cell-size (0.0086 m) was therefore already small enough to validate this method of determining slab thickness as 2D density divided by 3D density. Since the plasma cloud is cube-shaped, determining its width also determines its height. The width was determined from the marked position of the surface point (640) in FIG. 6C. The x-coordinate of this point, marked by the vertical line (642), was noted previously as x=0.19 m. By symmetry, the diameter of the square containing the central cloud of electrons is twice the distance of this edge-point from the cube's center-point. The x-coordinate of the cube's center-point is 0.311 m, as marked in FIG. 6C (646). The horizontal dimension of the plasma cube, by this measure, was computed to be 2(0.311 m−0.19 m), which equals 0.24 m. The number of slabs to make a cube was computed to be this diameter of the electron cloud divided by the slab thickness, 0.24 m/0.0071 m which equals 34 slabs. It would take 34 slabs stacked up to make a cube-shaped volume of electron plasma. The power lost by particles from the entire cubic reactor was computed as the product of the number of slabs (34) times the power lost from the simulated central slab (3.7 kilowatts). This product equals 126 kilowatts, the total power loss of the ions and electrons from the whole cubic reactor. Adding the power loss of the magnets (6.0 kilowatts) gave the total power loss of the whole reactor as 132 kilowatts. This is the value of Pin required to compute the power balance for a D+D fueled model reactor in the First Embodiment of the invention. Retrieving the value of Pout computed previously, the power balance follows immediately to be Qm=Pout/Pin=1.65e-5/132e3=1.22e-10. This power balance was used in the empirical scaling formula to compute the break-even reactor size as follows: Determining the Exponent “s” in the Power Balance Scaling Formula The whole point of carefully computing the power balance has been to use it to estimate the size of a break-even reactor to be constructed according to the First Embodiment. The numerator of Qm is known to scale as the 7th power of magnet size. The exponent governing the scaling of the denominator of Qm was determined as follows: FIG. 8C showed that the magnets' face cusps (832) leak electrons at a much lower rate that the corner cusps. The corner-cusp peaks, shown above and below the face-cusp peak (832), have many more electron counts, as shown by the lengths of the vertical bars forming the peaks. The dominance of the corner cusps over the face cusps continues to increase as the size of the magnets grows toward break-even. As an approximation, the electron leakage through the face cusps was ignored in deriving the scaling of Pin. This approximation gets better as the size of the simulated reactor was increased. Ignoring the face cusps, the electron leakage scales as the 2nd power of the reactor size. This scaling was derived by the following logical argument. Electron power loss has been shown to be proportional to the number of slabs and inversely proportional to the slab thickness. The number of slabs is proportional to the linear size of the reactor. The slab thickness, like the PIC cell-size, is inversely proportional to the size of the reactor. The product of these two factors increases as the 2nd power of size. This logic leads directly to a 2nd power scaling of electron power loss with magnet size. Ions' losses are also expected to scale approximately as the 2nd power of size. As seen in FIG. 8B, ions' losses are also dominated by corner-cusps' losses, though not as completely as electrons' losses. The approximate dominance of the corner cusps was enough to show the ions' losses scale approximately as the 2nd power. Ions contribute only a small fraction to the overall particle losses; therefore, approximate loss-scaling is good enough to enable a valid scaling of power-balance to break-even. The 2nd power scaling of particle losses with magnet size has also been confirmed by Bussard's experiments on actual Polywell reactors. Quoting from 2008-Bussard, “[0207] Tests made on a large variety of machines, over a wide range of drive and operating parameters have shown that the loss power scales as . . . the square of the system size (radius).” Pin is the sum of particles' power loss plus magnet resistive power loss. The magnet power loss also scales as the 2nd power of size. This is known theoretically from the properties of liquid cooled copper conductors. Resistive power loss is produced in proportion to the cross-sectional area of the magnet coils. This area increases as the 2nd power of the coil diameter. This theoretical scaling of magnet power loss was empirically verified by comparing the power requirements of all the standard magnets in the GMW Associates catalog. Drive-power requirements were seen to vary from magnet to magnet in proportion to coil-area. Pin is the sum of two contributions, both of which scale as the 2nd power of magnet size. It does not matter in what proportions the power loss is divided between particles' lost power and magnets' lost power. As long as both terms scale with the same exponent (=2), the sum still scales as the 2nd power of size. The combined effect of the numerator scaling as the 7th power of size and the denominator scaling as the 2nd power of size makes the quotient Pout/Pin scale as the 5th power of size. The logic of this section leads to the conclusion that the scaling exponent “s” equals 5. Applying the Power Balance Scaling Formula to Predict Break-Even Reactor Size The power balance scales with reactor size in a predictable fashion. As the size of the model reactor increases toward break-even size, the magnetic field strength will rise in proportion to the increase in magnets' size. The scaling relationship between magnet size and power balance results in the following expression for break-even magnet size as a function of model power balance: Db=Dm/(Qm)(1/s), where Db is the diameter of the break-even magnet, Dm is the diameter of the model magnet, Qm is the power balance of the model reactor, and “s” is a scaling exponent, now known to be s=5, as shown in the previous section. Substituting the values of Dm, Qm, and “s” from the previous analyses resulted in the following estimate of break-even magnet size for a D+D fueled reactor built according the First Embodiment of the invention: Db(DD)=(0.75*0.315 m)/(1.22e-10)(1/s)=0.26 m/0.0104=25 meters. This size estimate is coincidentally the same size as ITER. The embodiment has a decided advantage over ITER in that it burns “advanced” fuel instead of ITER's troublesome tritium. A still smaller break-even size was desirable. To compare directly with ITER, the fuel was changed from D+D to D+T, leaving the other reactor design parameters the same. At the crucial sample points shown in FIG. 1B (111, 112, and 113), the cross-section curve for DT (102) is approximately parallel to the curve for DD (104). The D+T fusion cross-section (102) is seen to be a factor 160 times larger than the D+D cross-section (104). The factor of 160 holds for all three sample points (111, 112, and 113). Applying this scaling factor to the integral in FIG. 7 (716) was the only adjustment needed to replace the D+D fuel by D+T fuel. Applying this factor resulted in a 160-fold increase in the model reactor's power balance. The power balance increased from the Qm(DD)=1.22e-10, shown above, to 160 times 1.22e-10, which made the new power balance Qm(DT)=2.0e-8. Using the same formula, Db=Dm/(Qm)(1/s), resulted in the break-even size estimate for a D+T reactor Db(DT)=Db(DD)/(160)(1/s)=25 m/2.8=9 meters. Burning D+T fuel instead of D+D fuel would reduce this embodiment's break-even reactor's magnet size from 25 meters to 9 meters diameter. Not only is the size of the break-even reactor of interest, the power output is too. Pout rises as the 7th power of size. The ratio of the break-even size to the model size, in the case of D+D fueled reactor, was 25 m/0.26 m=96. For a 96-fold increase in size, the fusion power output would rise by a factor of 967, which is 7.6e13. Multiplying this factor by the model Pout gave the projected power output of a break-even D+D reactor to be 1.65e-5 watts times 7.6e13 which equals 1.25 gigawatts (GW). If electrical power is produced from thermal power by the Rankine cycle, an efficiency factor of η=0.4 applies. The resulting net electrical power then projects to be 1.25 GW times 0.4 which equals 0.5 GW. This level of power output is well within the range of power output covered by the many conventional nuclear reactors operating in the U.S. Nuclear reactors in the U.S. range in power output from 0.5 to 4.0 GW. D+D fueled reactors built according to the First Embodiment may well replace all the nuclear reactors currently in the U.S.   FIG. 10B shows a wavy line (1022) graphing the ions' loss current on the tank, as a function of time. Except for the usual statistical variations, the current is seen to be constant in time, characteristic of steady-state. The line intersects the vertical axis at a point (1028) one small-division above zero. The vertical axis was calibrated in amperes. On this scale, one small-division equaled 0.008 amperes. The average lost ion current thus reads as 0.008 amperes. To compute the lost power loss in watts, the 0.008 amperes ion current was multiplied by the ion particles' average energy at the tank wall, expressed in electron-volts. Returning attention to FIG. 10C, up-scattered ions reach the tank by starting with near-zero kinetic energy at the peaks of the potential (460 or 462). From there they fall down the outer flanks of the potential, impacting one of the tank walls with the kinetic energy they gained in the fall. The tank walls were, by design, held at zero voltage. The left tank wall is shown as the left axis (1032) in the Figure. By the time they hit this wall, the ions have gained kinetic energy equal to the potential energy they had when they started from the potential peak (460). Reading the voltage where the dashed line intersects the vertical axis (1032) shows the ions started with approximately 40 kilovolts of potential. Multiplying this voltage times the ions' lost current gave the ions' power drain; 0.008 amperes times 40 kilovolts is 320 watts. This number is the ions' power drain in the simulated central slab. FIG. 8B showed that ion losses occurred mostly in the 4 corner cusps (812, 814). The dominance of the corner-cusp losses over face-cusp losses (813) will increase as the model reactor size grows toward break-even. Corner-cusp losses will be approximately the same in each of the slabs stacked up to make a cubic reactor. The number of slabs stacked to make a 3D reactor from a 2D simulation was the same here in the Second Embodiment as was found previously for the First Embodiment. Multiplying this number of slabs, 34, by the ion power loss to the central slab, 320 watts, yielded the estimate of 10.9 kilowatts for the ions' steady-state power-loss in the whole cube.        As disclosed so far, the Second Embodiment is characterized by an electron power-loss of 7.0 kilowatts and an ion power loss of 10.9 kilowatts. To these must be added the power lost to magnet heating. Magnet heating was the same as before, 6.0 kilowatts for the 6 magnets of the small-model cubic reactor. Adding the 3 contributions to Pin, the estimated power loss for a small-model D+D fueled reactor was 7.0+10.9+6.0=23.9 kilowatts. The power balance was computed as Qm=Pout/Pin=1.65e-5 watts divided by 23.9 kilowatts; Qm=6.9e-10. The estimated magnet size of the break-even reactor was computed by the same formula as before, substituting only the new value of Qm; Db=Dm/(Qm)(1/s)=0.26 m/(6.9e-10)0.2=0.26 m/0.0147=18 meters. This magnet size is significantly smaller than the 24-meter magnet diameter predicted for ITER. The main result of these disclosures is to specify a design that will produce a compact reactor to surpass the performance of other fusion reactor designs. In addition to its smaller size, the reactor designed according to the Second Embodiment can burn the advanced fuel, D+D, instead of ITER's troublesome tritium. The power output of the break-even reactor was estimated by multiplying Pout for the small-scale reactor by the 7th power of the ratio of magnet sizes between break-even and small-scale model. The size-ratio was 18 meters divided by 0.26 meters which equals 69. Raised to the 7th power, the power-ratio was 697 which equals 7.6e12. Multiplying Pout by this power-ratio and the Rankine-cycle efficiency (η=0.4) gave the break-even power output as 1.65e-5 watts times 7.6e12 times 0.4 which equals 50 megawatts electrical. This power output may be more useful than the 500-megawatts-electrical output predicted for the comparable reactor of the First Embodiment. For any reactor design, the break-even power output is the minimum useful output of a reactor of that design. Due to the 7th power scaling in these Embodiments, vast increases in power outputs can be obtained by increasing the size beyond break-even. For example, to double the power output would only require increasing the magnet size by a factor of 1.1 [=2(1/7)]. The 18 meter break-even size would need to only increase from 18 to 19.8 meters to double the power output. Reactors built according to the embodiments of the invention are envisioned to fill the needs of a wide range of applications from small-scale to large-scale power plants. Planes and rockets can use reactors only slightly larger than break-even (18 m), producing net power around 100 megawatts. Towns and cities will need larger reactors. The 7th power scaling of the power output with size allows the embodiments to serve a wide range of power needs from 100 megawatts upward to 100 gigawatts or more. Only the scale of the reactor need be increased to vastly increase its power output. Building a reactor twice the size increases the power 128-times (=27). Multiplying the break-even reactor's 50 megawatts by this factor yields 6.4 gigawatts as the electrical-power output of a reactor twice as large as the 18 m break-even one.      The reader accordingly will see that the fusion device of the inventive embodiments can be used to construct useful scale-model reactors. Building larger and larger scale-models will lead to development of economical net-power reactors. For the first time it is now possible to ionize and inject fuel ions into the core of an Inertial Electrostatic Confinement (IEC) reactor without consuming too much power in the process. Accurate and reliable computer simulations were disclosed to show that the size of a net-power, advanced-fuel reactor can be as small as 18 meters in diameter. The projected power output of an 18-meter reactor would be only 50 megawatts, making the design appropriate for a wide range of power-generating applications. These applications range from powering towns and cities to powering vehicles such as boats, planes, and spacecraft. Many fuel choices are available. Deuterium, tritium, helium, boron, etc. can be burned. Increasing the reactor size dramatically increases its power, up to hundreds of gigawatts. Mechanical and electrical construction is simple, providing for easy maintenance. Super-conducting magnets are optional, unlike ITER and tokamaks which require them. The basic design of the fusion device incorporates magnets mounted on all the faces of a predefined polyhedron. The magnets are all the same size and produce identical magnetic fields, all pointing inward toward the center of the polyhedron. This arrangement of magnetic fields creates a number of cusp-lines, one cusp-line down the bore of each magnet. Electrons circulate in and out of the reactor core along cusp-lines. Aligned with the central bores of some or all of the magnets are mounted gas-cells, electron-emitters, and optionally electron-extractors. These useful apparatuses, gas-cell, e-emitter, and e-extractor, may each be duplicated on any or all of the polyhedron-face cusp-lines. Two or 3 types may even be mounted on a single cusp-line. Only the extractor is necessarily opaque to electrons. Emitters of filament design are largely transparent to electrons and so may be mounted co-linearly on a cusp-line with a gas-cell and extractor. The number of each of the 3 types of apparatus may vary from application to application. The principles of the design of the embodiments admit to various number and placement of the 3 types of mounted apparatus. Many such variations may prove useful and all such variations are claimed in this patent application. A computer simulation was tailored to analyze a cubic reactor burning deuterium fuel. The cube is only one of the many polyhedra that could be chosen as the basic frame for mounting the magnets. Other polyhedra might be useful and might improve performance. For example, a reactor based on an icosahedron would have 20 magnets instead of six. The down-side of using more magnets is that extra input-power is required to power the magnets. Input-power is a factor in power balance. Increasing input-power would increase the size of the break-even reactor. Larger-sized reactors are more expensive to build and less efficient to operate. On the other hand, the shape of the icosahedron is closer to the shape of a sphere than is the shape of the cube. A perfect sphere would have perfect convergence. It might turn out that the central-density convergence sought by Bussard will someday be be found in the icosahedron. If convergence were obtained, it would raise the power output by raising the central ion density. The net effect of convergence would be to raise the power balance and thereby shrink the size of the break-even reactor, which would be a positive result. A more detailed computer analysis could answer the question of whether higher-order polyhedra might be better than the cube. The possibility of smaller reactor size makes the use of higher-order polyhedra a useful addition to these embodiments. The advantages of the disclosed ion-source and electron-extractor apply equally well to designs with higher-order polyhedra. The operating point of the reactor was characterized by simulating fixed knob values in software. In an actual reactor the electron current, electron energy, gas pressure, and ion density can be simultaneously varied by a human operator turning knobs. The operator would naturally “tune” the knob values to increase the power-balance. This tuning might well be faster in hardware than in software. For the same reason, the graphic-equalizer on a stereo amplifier is better tuned using more than one knob at a time, so might the reactor be better tuned varying more than one knob at a time. It was not possible to explore every possible knob value in simulation. The computer took about 100 hours to try just one set of knob values. It is to be understood that tuning might improve power-balance over the performance presented in these disclosures. A complete range of possible knob values, as provided by all possible adjustments of the hardware components, are obvious variants of the specified embodiments and so are also claimed below. The geometry of the model-reactor was set by making certain other choices in assigning the simulation variables. For example, the spacing of the magnets one from the other, the so called “gap width”, was fixed by setting the variable “magCornerGap,” as seen in FIG. 5A (525). Changing the value of this setting produced wide-ranging effects. The smaller the value, the stronger was the magnetic field in the corners between the magnets. Stronger field reduced the rate of electron leakage through the corners to the tank. But smaller “gap width” also caused more electrons to be lost by hitting the magnets. The ideal value for “gap width” might best be found by trial and error in hardware rather than running the simulation over and over. Other important variables' settings controlled the shape of the magnet coils. The coils in the simulation were taken from catalog specifications, approximately square in coil cross-section and round in plan-view. Many shapes of magnets can be produced by standard manufacturing techniques. The coils are made by winding copper wire on a spool with an open central bore. The technique of winding can produce magnets with a variety of cross-sectional shapes and a variety of plan-view shapes with equal ease. For example, a square spool would produce magnets having square plan-view instead of the round plan-view as shown in FIG. 2. Square coils would produce an equally narrow gap along the sides of the square faces of a cubic reactor. A long thin gap would have reduced electron leakage to the tank but would also suffer more electrons' lost to hitting the magnets. Different choices of plan-view are exemplary of the flexibility of the design. Exercising this flexibility can improve the performance of the model-reactor. Improvement in performance from such changes in magnet-spacing and magnet-shape are anticipated as obvious extensions of these disclosures. In addition to the shape of the coil winding spool, the cross-sectional shape of the coil may also be changed from what was simulated. FIG. 1A (410) shows an alternative chamfered coil shape, having a trapezoidal cross-section. A chamfered shape would allow magnets of a chosen outside-diameter to be mounted closer together, on a smaller polyhedron, thus increasing the corner magnetic-field and reducing corner particle-losses. The standard technique of building up a coil by winding many turns of copper wire on a spool can easily produce other cross-sectional shapes, not only the chamfered one shown in FIG. 1A. Different coil cross-sectional shapes may be combined with different coil plan-views, as described in the previous paragraph. These various shapes produce variants of the basic principles of the disclosed embodiments, and so are claimed. In addition to magnets wound from copper wire, magnets may be wound from super-conducting wire or tape. Super-conducting magnet coils may have advantages over copper-wound coils. Super-conducting coils have much reduced electrical resistance and therefore reduced resistive heating compared to copper. In principle, this feature would allow the coils to be smaller and still produce the strong fields required for break-even. The principle of the embodiments described would be the same with super-conducting coils as with copper coils. Super-conducting coils must be maintained at cryogenic temperatures which would require additional thermal insulation to protect the coils from the heat radiating from the plasma. The extra engineering required to keep the magnets cold poses a potential draw-back to using super-conducting coils. Even so, the principles of the designs disclosed in these embodiments apply equally well with super-conducting coils. Whether they give a net advantage will depend on the cost and size of the additional hardware needed to keep the super-conducting magnets cold. As described in the Specification, the vacuum tank had dual functions. It kept out the air and also functioned as a grounded electrode to accelerate electrons from the emitter. In an actual reactor, the grounded-electrode function might be provided by a separate Faraday cage disposed inside the vacuum tank and surrounding the magnets. Faraday cages are well-known devices for providing electrical shielding. In an actual reactor, a Faraday cage might have the same shape as the vacuum tank, or a different shape such as sphere or non-cubic polyhedron. One advantage provided by a Faraday cage would be to leave room outside the cage and inside the tank for mounting a spherical, direct-conversion energy-device such as disclosed in 2011-Greatbatch. The use of Faraday cages of various shapes would be extensions of the embodiments described and obvious to one skilled in the art of electrode design. The terminology “vacuum tank” and “Faraday cage” should be considered interchangeable and identical terms for means providing the functions of the outer, grounded-electrode described in the Specification. The next logical step in the time following this disclosure is to build and test one or more small-scale model reactors according to the disclosed embodiments. The measured power balance of such model reactors may well exceed the power balance predicted by the simulation disclosed herein. Diamagnetism is an important physical phenomena not yet included in the simulation. The true magnetic field at the surface of the plasma will be the sum of a field from the coil magnets plus an opposing field from the diamagnetism of the plasma. Diamagnetism is a well-known physics term for magnetic fields generated by internal currents in materials. Due to diamagnetic effects, the size of the actual plasma cloud will turn out to be larger than the simulated size. Diamagnetic fields can be simulated, but such simulations were beyond the capability of the applicant's computer. Diamagnetic effects in a cubic reactor have been measured and reported recently in 2014-Park. Park's coils measured 14 cm outside-diameter compared to 26 cm outside-diameter for the small-scale coils of this Specification. Diamagnetic fields generally increase the size of the plasma cloud when adding to the applied magnetic field. This size increase is what Bussard called the “wiffle-ball effect.” With diamagnetic fields properly included, the simulated power output from the plasma would increase as the 3rd power of the size increase caused by diamagnetism. This would improve the predicted power balance and shrink the predicted break-even magnet size. The net effect of including diamagnetism in the model analysis would be to improve simulated performance of the subject embodiments. Omitting diamagnetism from the simulation, as disclosed herein, set a lower limit on the power balance of the small-scale model. The predicted performance of the embodiments is already an improvement over the prior art. Diamagnetism will make it more so. Although the description above contains many specificities, these should not be construed as limiting the scope of the embodiments but as merely providing illustrations of some of the presently preferred embodiments. For example, the knob values controlling the reactor may be varied by a human operator; also magnet spacings and magnet currents may be changed to improve power balance. Thus, the scope of the embodiments should be determined by the appended claims and their legal equivalents, rather than by the examples given.