Abstract:
A cellular electron cooled storage ring system and method for achieving particle-fusion based energy, including a vacuum chamber to allow electron beam and ion beam merging and separation, cathodes to generate the electron beams, collectors to collect the electron beams, and magnetic field generation devices to guide the electrons and ions on their desired trajectories as well as contain neutralizing particles. By overlapping the electron and ion beams, thermal energy is transferred from the ion beams to the electron beams, which allows the invention to overcome particle losses due to resonances, scattering and heating of the ion beams. Advantageously, ions are accelerated to an energy that is near optimum for fusion reactions to occur, and uses electron energies that maintain this advantageous situation. Advantageously, the recirculation of ions that do not fuse or scatter at too large of an angle is allowed, giving such ions additional chances to participate in a desired fusion reaction. Advantageously, the invention allows for a continual addition of new ions to be added to the circulating ions already in the system. This combination of advantages results in a significant improvement in the predicted output power to input power ratio over previous particle fusion technologies. The invention will also enable improved yields of fast neutrons for materials testing.

Description:
REFERENCES CITED 
     Referenced by 
     U.S. Patent Documents 
       [0000]    
       
         U.S. Pat. No. 5,854,531 December 1998 Young, et al. 
         U.S. Pat. No. 5,152,955 October 1992 Russell 
         U.S. Pat. No. 5,138,271 August 1992 Ikegami 
         U.S. Pat. No. 5,001,438 March 1991 Miyata, et al. 
         U.S. Pat. No. 4,867,939 Sep. 19, 1989 Deutch 
       
     
       Other Documents 
       [0000]    
       
         G. I. Budker, The 1966 Proc. Int. Symp. Electron and Positron Storage Rings, Saclay. Atomnaya Energiya vol. 22 p. 346, 1967. 
         L. Spitzer, “Physics of Fully Ionized Gases”, (New York: Interscience, 1956) pp. 80-81. 
         G. I. Budker, et al., Particle Accelerators, Vol. 7, 197-211 (1976). 
         M. Bell, et al., Physics Letters, Vol. 87B, No. 3, (1979). 
         T. Ellison, et al., IEEE Trans. Nuc. Sci., Vol. NS-30, No. 4, 2636-2638, (1983). 
         D. J. Larson, et al., “Operation of a prototype intermediate-energy electron cooler”, NIM, A311, 30-33 (1992). 
         F. Krienen, “Electron Cooling”, Chapter 2 in “Handbook of Accelerator Physics and Engineering”, Eds. Wu Chao and Tigner, ISBN 9810235005, World Scientific, Singapore (1999, reprinted 2002). 
       
     
       FIELD OF THE INVENTION 
       [0013]    The present invention relates to a device intended to induce particle beam collisions for the purpose of creating fusion energy and fast neutrons, more particularly, to a method and system that achieves extremely high density, low energy ion beams by overlapping the beams with a properly formed electron beam, and furthermore, guides and focuses the ion beams into collision with each other within a very small collision area. Each of the colliding beams is contained in its own storage ring, with electron cooling sections on opposing sides of the ring. Each storage ring also has one or more sections that overlap a section from an adjacent storage ring, and it is in these overlapping sections that the beams are brought into collision and fusion energy and fast neutrons are released. 
       BACKGROUND OF THE INVENTION 
       [0014]    It has been known for decades that the power generated by the stars, including our own sun, comes from a chain of nuclear reactions that fuse hydrogen into heavier elements. One reaction in particular which has been of great interest is 
         [0000]        D+T −&gt;He 4   +n+ 17.6 MeV.  (1)
 
         [0015]    The reaction of Eq. (1) has a very high probability of occurrence, with a cross section reaching about 5 barns at a center of mass energy of about 100 keV. The output energy of the reaction of Eq. (1) is about ten million times the output energy of typical chemical reactions. The fuel sources for the reaction of Eq. (1) are isotopes of hydrogen. One of the isotopes, deuterium (D), is readily available in enormous quantities in sea water, and the other, tritium (T), can be generated by placing Lithium blankets around a fusion device. The neutron (n) generated in Eq. (1) can react with the Lithium (Li) through the reaction 
         [0000]        n +Li 6 −&gt;T+He 4 +4.8 MeV.  (2)
 
         [0016]    The reaction of Eq. (2) allows even more energy to be generated from the fusion reaction as well as generating more fuel for the reaction of Eq. (1). The end products of the reactions (1) and (2) are two Helium nuclei (He). Thus the fusion reactions result in reaction products that are not themselves radioactive, leading to the expectation that fusion energy generation will be clean—there will be no radioactive waste, no biological waste, and no green house gas waste directly produced from the reactions in Eqs. (1) and (2). (Of course, considerable activation of surrounding materials can occur for those neutrons that do not interact via Eq. (2).) 
         [0017]    Leading existing schemes for attempting to induce useful levels of fusion energy involve tokamaks and inertial confinement devices. Tokamaks work by heating a plasma of ions and electrons to a level where some of the ions will undergo fusion, while inertial confinement devices impinge beams of either particles or photons (light) upon a small target of fusable materials. In both of these conventional techniques, the ions have random velocity directions and magnitudes and only a small fraction of the ion pairs have the optimum conditions for a fusion event to occur. 
         [0018]    In addition to tokamaks and inertial confinement devices, numerous other approaches to fusion have been attempted as well. Muon induced fusion involves the use of muons to form atomic states of deuterium bound to tritium wherein the bound molecule is so tightly bound that fusion occurs. Cold fusion experiments were done with electrolysis of deuterated water, with some evidence of fusion occurring within the cells. Sonic wave induction of imploding bubbles in deuterated water is also being investigated. 
         [0019]    But despite all of the many and diverse efforts to date, no fusion energy production system has come close to the goal of serving as a useful source for electric energy. Accordingly, there is a need for an improved method and system for generating fusion energy. 
         [0020]    Use of colliding beam systems to produce fusion reactions have been described, but such conventional systems cannot produce useful electric energy because various scattering processes lead to particle beam loss that in turn leads to power losses far in excess of the fusion energy produced. Accordingly, there is a need for an improved method and system that is capable of reducing the power losses associated with colliding beam systems in order to explore the use of such systems for generating fusion energy. 
         [0021]    Electron cooling is a technique that has been described wherein an electron beam is overlapped with an ion beam in order to reduce velocity spreads in the ion beam. Electron cooling is conventionally used to increase the density of ion beams so that experiments will produce a higher number of reactions. Electron cooling is also conventionally used to increase the lifetime of stored ion beams. To date, electron cooling has not been applied to reduce scattering losses in colliding beam fusion devices. Accordingly, there is a need for an improved method and system that is capable of using electron cooling to reduce the power losses associated with colliding beam systems in order to explore the use of such systems for generating fusion energy. 
         [0022]    There is also a need for fast neutrons for materials testing in both the fission and fusion research communities. 
       SUMMARY OF THE INVENTION 
       [0023]    The present invention, which addresses the above desires and provides various advantages, resides in a method and system for generating large levels of output fusion energy. The system includes particle supplies for generating beams of projectile particles, overlapping storage rings for containing and recycling the projectile particles, electron cooling systems for stabilizing and restoring energy to the projectile particles, and interaction regions where the storage rings overlap for initiating nuclear fusion reactions with the projectile particles to generate the desired energy source. The system also includes a plurality of dipoles, quadrupoles, torroids and solenoids selectively situated around the rings to “bend” the direction of travel of the projectile particles within the system as well as to focus the beams down to a small size when they come into collision. 
         [0024]    By providing closed storage rings, the particle beams are contained within the system to repeatedly recirculate inside the storage rings. Particles that do not undergo fusion or are scattered at too large of an angle are given another chance to fuse every time they circulate within the system. And, as the particle supplies continuously inject low currents of additional particles into the storage rings which merge with previously injected particles circulating in the rings, relatively high intensity beams develop and are effectively stored in the system, even though the input currents used to populate the system remains relatively low throughout the operation of the system. While a small fraction of particles is lost to fusion reactions, scattering, recombination and charge exchange, the particle beams eventually increase in intensity as they circulate the ring, until equilibrium is reached between the additional currents injected into the system and the currents lost to fusion reactions, scattering, recombination and charge exchange. 
         [0025]    Distinctly, the present invention effectively retains and conserves the energy introduced into the system by recycling and reusing the projectile particles. In particular, the bulk of the energy expended in the initial provision of the particle beams is not dissipated as excess heat, but retained in the particle beams as the projectile particles are enabled for repeated encounters with each other with each revolution. 
         [0026]    Because the projectile particles are permitted to circulate in the system, instabilities could build up in the particle beams due to particle-particle interactions or particle-electromagnetic-field interactions. Advantageously, the system maintains the particle beams within optimal reaction parameters by providing the electron cooling systems to stabilize or “cool” the particle beams. Without the electron cooling systems, the particle beams would develop internal trajectories that would cause such a significant loss of beam particles that the device would not produce useful energy. 
         [0027]    The electron cooling systems include electron injectors which inject electron beams into the storage rings, into the path of the particle beams, and electron capture devices which capture the electron beams. The electrons are injected with a predetermined amount of energy to cause the projectile particles to move at an ideal velocity. By traveling and interacting with the particle beams, the electron beams maintain the particle beams within parameters that optimize fusion energy production. Any heating, scattering and deceleration that would otherwise adversely affect the particles stored in the system are effectively compensated for by the electron beams. Accordingly, scattering and energy loss in the beams is substantially continuously compensated for before significant instabilities have an opportunity to develop. In this manner, events that would typically cause significant instabilities in the particle beams are minimized if not eliminated. 
         [0028]    In order for the invention to produce large levels of fusion reactions it is important that the colliding particle beams be focused onto a small spot. Advantageously, the invention uses magnetic solenoids and quadrupoles that are arranged to have fields which, in concert with the magnetic dipoles and drift lengths, focus the particle beams into a very small size at the point they are passing by each other. By arranging for the high intensity and very small size at the collision region, large levels of fusion output reactions are generated. As a byproduct, large levels of fast neutrons are also generated. 
         [0029]    As a result of the small spot size “beam halo” is formed in the particle beams. Beam halo is a significant but minority portion of the beam that has different characteristics than does the majority portion of the beam. Due to its different characteristics, particles contained within the beam halo would be lost from the system if no means is supplied to prevent that from happening. Advantageously, the invention employs magnetic devices placed where the majority beam is smallest in order to separately affect the beam halo trajectories. Magnetic focusing devices more strongly affect particles farther from the beam axis than they do particles close to the beam axis. By placing such focusing devices at places where the majority beam is much smaller than the beam halo, the invention advantageously is able to significantly reduce particle losses due to beam halo formation. 
         [0030]    High intensity particle beams generate significant levels of electromagnetic fields due to the particle&#39;s electric charge and motion. Background particles formed from the ionization of the residual gas in the system will neutralize most of the electric fields present in the system. (The electric fields that remain will be found near the outer portion of the beams; it is these fields along with some strong scattering events that cause the beam halo to form.) In the region where the particle beams overlap the magnetic fields of the two beams cancel. (This is true both for the region where the ion beams overlap and for the region where the electron and ion beams overlap.) However, in the transport regions where there is no beam overlap, significant magnetic fields due to the particle beam&#39;s electric charge and motion will remain. 
         [0000]    Advantageously, the invention places magnetic focusing devices at the correct placement and with the correct field strength so as to recirculate the beam particles in the presence of the self field forces. The invention also uses tunable magnetic focusing devices so that changes in operational characteristics (during device turn on, for instance) can be handled by the beam optics of the device. 
         [0031]    Other features and advantages of the present invention will become apparent from the following detailed description of the preferred embodiments, taken in conjunction with the accompanying drawings, which illustrate by way of example the principles of the invention. 
     
    
     
       BRIEF DESCRIPTION OF THE DRAWINGS 
         [0032]    The invention is explained in more detail below with reference to the accompanying drawings in which: 
           [0033]      FIG. 1  is a schematic view of a system employing two electron-cooled intersecting storage rings for use in the invention and depicts particle beam positions within the invention; 
           [0034]      FIG. 2  is a schematic view of a system employing three electron-cooled intersecting storage rings for use in the invention and depicts particle beam positions within the invention; 
           [0035]      FIG. 3  is a schematic view of a system employing two electron-cooled intersecting storage rings for use in the invention to depict the placement of the subcomponents; 
           [0036]      FIG. 4  is a schematic view of a system employing three electron-cooled intersecting storage rings for use in the invention to depict the placement of the subcomponents; 
           [0037]      FIG. 5  is a schematic view of the ion injection and electron cooling system employed as part of the intersecting storage rings shown in  FIG. 1 ,  FIG. 2 ,  FIG. 3  and  FIG. 4 ; 
           [0038]      FIG. 6  is a schematic view of the electron cooling system that has no ion source which is employed as part of the intersecting storage rings shown in  FIG. 1 ,  FIG. 2 ,  FIG. 3  and  FIG. 4 ; 
           [0039]      FIG. 7  is a schematic view of the left end transport system of the intersecting storage rings shown in  FIG. 1 ,  FIG. 2 ,  FIG. 3  and  FIG. 4 ; 
           [0040]      FIG. 8  is a schematic view of the right end transport system of the intersecting storage rings shown in  FIG. 1 ,  FIG. 2 ,  FIG. 3  and  FIG. 4 ; 
           [0041]      FIG. 9  is a schematic view of the interaction transport system of the intersecting storage rings shown in  FIG. 1 ,  FIG. 2 ,  FIG. 3  and  FIG. 4 . 
       
    
    
     DESCRIPTION OF THE PREFERRED EMBODIMENTS 
     Summary Description of Preferred Embodiment Operation 
       [0042]    An electron-cooled intersecting storage ring system  10 A employing two intersecting storage rings for achieving large amounts of fusion reactions is shown in  FIG. 1 . An electron-cooled intersecting storage ring system  10 B employing three intersecting storage rings for achieving large amounts of fusion reactions is shown in  FIG. 2 . Preferred embodiments can contain four, five, or more intersecting storage rings. This description of the preferred embodiments will use deuterium and tritium as the example ions, but, as mentioned in the claims, other ions could be used in the invention as well. 
         [0043]    The electron-cooled intersecting storage ring system  10  utilizes a combination of elements, including an ion source  20  for supplying ions  22 , an electron source  24  for supplying electrons  26 , a vacuum chamber  28  for containing particles within a region of low pressure, solenoidal wire windings  30  and torroidal wire windings  32  to provide guiding and containing magnetic fields for electron  26  beam transport, an electron collector  34  to collect the electrons  26  after they have performed their function, solenoid magnets  36  and quadrupole magnets  38  to focus the ions  22  and dipole magnets  40  to bend the ions  22 . The ion source  20 , electron source  24 , vacuum chamber  28 , solenoidal wire windings  30 , torroidal wire windings  32 , electron collector  34 , solenoid magnets  36 , quadrupole magnets  38  and dipole magnets  40  can be made of off the shelf standard contemporary materials. 
         [0044]    The direction of particle motion for an embodiment of the invention using two storage rings is shown in  FIG. 1 . In the storage ring on the left (denoted as storage ring A) electrons  26  in one electron cooling system  14 A leave the electron source  24  near position A 10 , are guided by fields produced in solenoidal wire windings  30 , and further are guided and bent by fields produced in the torroidal wire windings  32  so that they pass near position A 12 . The electrons  26  are guided then by fields produced in solenoidal wire windings  30  in the long straight section, eventually passing first near position A 14  and then near position A 16 . After Passing near position A 16  the electrons  26  enter the downstream torroidal region where they are guided and bent by fields produced in the torroidal wire windings  32 , passing near position A 18 , and then are guided by fields produced in solenoidal wire windings  30 , with the electrons  26  collected near position A 20 . The electrons  26  in the system  14 B ( 14 B is depicted below the system  14 A) follow similar trajectories to the electrons  26  in the system  14 A. Deuterium ions  22 A are produced in an ion source  20  near position A 22  and enter the long straight section of the system  14 A at a small angle, where they then merge with the electron  26  beam near position A 24 . Small angle Coulomb scattering collisions bend the deuterium ions  22 A until they are moving substantially in the same direction as the electrons  26  when the deuterium ions  22 A pass near position A 16 . Due to their large mass, the deuterium ions  22 A travel nearly straight through the solenoidal wire windings  30  and torroidal wire windings  32 , and are then focused by solenoid  36  and quadrupole  38  magnets, and arrive at a dipole  40 A. The deuterium ion  22 A trajectories are bent in the dipole  40 A field, passing near position A 26 , and are then focused by solenoid  36  and quadrupole  38  magnets until they arrive at a second dipole  40 A. The deuterium ion  22 A trajectories are bent in the dipole  40 A field, passing near position A 28  and then exit the dipole  40 A and are focused in solenoid  36  and quadrupole  38  magnets, and then pass through solenoidal wire windings  30  and torroidal wire windings  32  of the electron cooling system  14 B, are then focused by solenoid  36  and quadrupole  38  magnets, and eventually enter a merging and separating dipole  40 B near position A 30 . The deuterium ion  22 A trajectories are bent in the dipole  40 B field, and are merged to fully overlap the on-coming tritium ion  22 B trajectories near position A 32 . The deuterium ion  22 A trajectories then travel through the interaction region where they are focused tightly into two small regions by solenoids  36 . A first overlap section exists between the merging and separating dipole containing positions A 30  and A 32  and the merging and separating dipole containing positions A 34  and A 36 . It is in the small regions within the first overlap section that the fusion interactions predominantly occur, since the oncoming tritium ions  22 B are also focused tightly into these regions and the relative velocities between the deuterium ions  22 A and tritium ions  22 B are appropriate for fusion to occur. The deuterium ion  22 A trajectories then enter a second merging and separating dipole  40 B passing near position A 34  and are bent and separated from the oncoming tritium ions  22 B, with the deuterium ions  22 B next passing near position A 36 . After leaving the merging and separating dipole  40 B, the deuterium ions  22 A pass through solenoid  36  and quadrupole magnets  38  which focus the beam and then the deuterium ions  22 A re-enter the electron cooling system  14 A, passing near position A 14  and then near position A 16 . The deuterium ions  22 A then continue to cycle around the system from a position near A 16  to a position near A 26  to a position near A 28  to a position near A 30  to a position near A 32  to a position near A 34  to a position near A 36  to a position near A 14  and back to near the position A 16  again. 
         [0045]    The tritium ions  22 B in  FIG. 1  follow trajectories similar to what was just described for the deuterium ions  22 A, except that the positions are labeled as B in the figure and the order of traversal of the subcomponents is different. (In A, the deuterium ions  22 A traverse an electron cooling system  14 A, an end region  16 A, an electron cooling system  14 B, and an interaction transport system  18 . In B, the tritium ions  22 B traverse an electron cooling system  14 A, an interaction transport system  18 , an electron cooling system  14 B, and an end region  16 B.) The tritium ions  22 B in the storage ring B start in the ion source  20  near position B 22  and then travel to a position near B 24  to near B 16  to near B 26  to near B 28  to near B 30  to near B 32  to near B 34  to near B 36  to near B 16  again. The tritium ions  22 B then continue to cycle around the system from near B 16  to near B 26  to near B 28  to near B 30  to near B 32  to near B 34  to near B 36  to near B 14  and back to near B 16  again. The electrons  26  in the electron cooling system  14 A that overlap the tritium ions  22 B leave the electron source  24  near position B 10 , are guided by fields produced in solenoidal wire windings  30 , and further are guided and bent by fields produced in the torroidal wire windings  32  so that they pass first near position B 12 , then near position B 14 , then near position B 16 , then near position B 18 , until they are finally collected then near position B 20 . The electrons  26  in the system  14 B ( 14 B is depicted below the system  14 A) follow similar trajectories to the electrons  26  in the system  14 A. 
         [0046]      FIG. 2  shows positions of particle travel within a preferred embodiment of the invention making use of three intersecting storage rings. In this case, deuterium ions  22 A and their associated electrons  26  will follow trajectories A and B as described in the preceding paragraphs, while tritium ions  22 B and their associated electrons  26  will follow trajectories C. The storage ring C is slightly different than what has been described above in that it has two interaction transport systems  18 , one on each end, rather than one end transport system  16  and one interaction transport system  18  on its ends; a second overlap section exists between the merging and separating dipole that contains the positions C 26  and C 28  and the merging and separating dipole that contains the positions C 30  and C 32 ; a third overlap section exists between the merging and separating dipole that contains the positions C 34  and C 36  and the merging and separating dipole that contains the positions C 38  and C 40 . But despite this slight difference the transport through its individual components is similar to what has been described above. The tritium ions  22 B in the storage ring C start in the ion source  20  near position C 22  and then travel to a position near C 24  to near C 16  to near C 26  to near C 28  to near C 30  to near C 32  to near C 34  to near C 36  to near C 38  to near C 40  to near C 16  again. The tritium ions  22 B then continue to cycle around the system from near C 16  to near C 26  to near C 28  to near C 30  to near C 32  to near C 34  to near C 36  to near C 38  to near C 40  to near C 14  and back to near C 16  again. The electrons  26  in the electron cooling system  14 A that overlap the tritium ions  22 B leave the electron source  24  near position C 10 , are guided by fields produced in solenoidal wire windings  30 , and further are guided and bent by fields produced in the torroidal wire windings  32  so that they pass first near position C 12 , then near position C 14 , then near position C 16 , then near position C 18 , until they are finally collected then near position C 20 . The electrons  26  in the system  14 B ( 14 B is depicted below the system  14 A) follow similar trajectories to the system in  14 A. 
         [0047]    Any number of storage rings (D, E, F, etc.) could be added, and the relevant point is that every other storage ring should contain deuterium ions  22 A, with the remainder containing tritium ions  22 B. (Storage ring A will always contain deuterium ions  22 A. Storage ring B will contain tritium ions  22 B if there are an even number of intersecting storage rings, and it will contain deuterium ions  22 A if there are an odd number of intersecting storage rings.) The added storage rings (D, E, F, etc.) would have a configuration identical to storage ring C. 
         [0048]    As seen in  FIG. 1  and  FIG. 2  the direction of ion  22  motion is counter clockwise within each storage ring. Significantly, where any two storage rings overlap the ion beams  22  are moving in opposing directions. Hence the ions  22  are brought into collision in the overlapping region. 
         [0049]    By arranging for the appropriate ion  22  energies the reaction probability will be near optimal, with all collisions occurring at an energy that is close to the optimum energy for fusion reactions to occur. The ion  22  energies are initially established by the voltages present in the ion source  20 , and are later affected by the electron cooling and space charge forces within the system  10 . The center of momentum will be arranged to be close to the maximum of the fusion reaction cross section. However, due to electron scattering off of residual ions, it is advisable for the deuterium-tritium case that the energy be somewhat higher than the energy at the peak of the cross section. For the preferred embodiment described herein, the deuterium  22 A beam will have an energy of about 240 keV in the interaction transport system  18  while the tritium  22 B beam will have an energy of about 160 keV. This choice of energies results in a center of mass energy of about 400 keV, which is above the peak of the fusion energy cross section, but where the fusion interaction cross section is still high. (The peak of the cross section is about 5 barn and occurs at a center of mass energy of about 100 keV. At 400 keV the cross section is about 0.85 barn. A better device operation would likely be obtained by lowering the beam energies somewhat below 400 keV, but above the 100 keV where the electron scattering is a problem.) A significant advance of this invention is that it arranges almost all colliding particles  22  to have an energy close to what is desired for fusion reactions to occur, since conventional approaches such as tokamaks, inertial confinement, and sonic implosion involve fusable particles that have a thermal distribution wherein only a relatively small percentage of the particles have the appropriate energy for fusion to occur. 
         [0050]    Not only does the invention arrange for the ions  22  to have the optimum energy for fusion reactions to occur, but the invention also arranges for the ions  22  to be focused to a very small area at interaction regions within the overlap portion of the interaction transport system  18 . The invention achieves this condition through the use of dipole magnets  40 , quadrupole magnets  38 , and solenoidal magnets  36  each with an advantageous magnetic field configuration, and with each situated at advantageous positions. By focusing the ions  22  into a very small area, the number of collisions will be maximized, resulting in the maximum fusion output power. 
       Component Specifications for a Preferred Embodiment 
       [0051]    Component specifications for a preferred embodiment will now be presented. It should be understood that what follows is one concrete example of a preferred embodiment using specific values but that the specific values listed below are meant only as approximate values.  FIG. 1  and  FIG. 2  likewise represent two specific arrangements of the invention. Obviously, the invention could be embodied in a wide variety of shapes and sizes. 
         [0052]      FIG. 3  depicts the same electron-cooled intersecting storage ring system  10 A employing two intersecting storage rings as shown in  FIG. 1 , except that  FIG. 3  identifies sub-systems of the system. It is seen that each storage ring consists of: 1) an electron cooling system  14 A capable of cooling ions  22  and allowing ion  22  beam injection; 2) an end transport system  16  capable of transporting the ions  22  between two electron cooling systems  14 ; 3) an electron cooling system  14 B capable of cooling ions  22 ; and 4) an interaction transport system  18  that allows overlapping transport of the ions  22  of two adjacent storage rings and providing focusing to enhance fusion reactions. 
         [0053]      FIG. 4  depicts the same electron-cooled intersecting storage ring system  10 B employing three intersecting storage rings as shown in  FIG. 2 , except that  FIG. 4  identifies sub-systems of the system. In  FIG. 4  it is seen that the interior storage ring consists of 1) an electron cooling system  14 A capable of cooling ions  22  and allowing ion  22  beam injection; 2) an electron cooling system  14 B capable of cooling ions  22 ; and 3) two interaction transport systems  18  that allow overlapping transport of the ions  22  of two adjacent storage rings and providing focusing to enhance fusion reactions. 
         [0054]    The sub-systems are depicted in  FIG. 5 ,  FIG. 6 ,  FIG. 7 ,  FIG. 8  and  FIG. 9 .  FIG. 5  depicts the electron cooling system  14 A,  FIG. 6  depicts the electron cooling system  14 B,  FIG. 7  depicts the end transport system  16 A,  FIG. 8  depicts the end transport system  16 B and  FIG. 9  depicts the interaction transport system  18 . Individual components are indicated on each of the sub-system depictions, and the component specifications for the preferred embodiment will now be described. 
         [0055]    Table 1 presents a listing of the magnetic configurations used in the interaction transport system  18  of the preferred embodiment, while Listing 1 gives the nominal and approximate lengths of the components used in the interaction transport system  18 . 
         [0056]    Table 2 presents a listing of the magnetic configurations used in the end transport system  16  of the preferred embodiment, while Listing 2 gives the nominal lengths of the components used in the end transport system  16 . 
         [0057]    The electron cooling system  14  of the preferred embodiment includes a solenoid winding  30 A surrounding the electron source  24 , torroidal wire windings  32 A and solenoidal wire windings  30 B to merge the electron  26  beam with the ion  22  beam, a long solenoid winding  30 C in the electron cooling region, torroidal wire windings  32 B and solenoidal wire windings  30 D to separate the electron  26  and ion  22  beams, and a solenoid winding  30 E surrounding the electron collector  34 . The central magnetic field within all of the solenoidal wire windings  30  and torroidal wire windings  32  of the electron cooling system  14  will be 100 Gauss in the preferred embodiment. The length in the beam direction of the long solenoid wire windings  30 C will be about 14 meters to perform the cooling function and can be longer to arrange for proper joining of the subsystems. The radius of curvature in the electron  26  beam center within the torroidal wire windings  32  is one meter and the angular deflection of the electron  26  beam center within the torroidal wire windings  32  is 45 degrees in the preferred embodiment. 
         [0058]      FIG. 5  shows an ion  22  injection system that injects ions  22  at a large angle, and does so in order to clearly show the concept of the invention. In a preferred embodiment, the angle of ion  22  injection will be much smaller. A smaller injection angle can be obtained either by having the injection line be in the plane perpendicular to the plane of the drawing, or by including a small dipole magnet  40  at the end of the ion  22  injection line. 
       Listing 1. Elements Used in the Interaction Transport System  18 . 
       [0059]    Element 1—a 30 cm long magnetic solenoid,  36 A.
 
Element 2—a 30 cm long magnetic quadrupole,  38 A.
 
Element 3—a 60 cm long drift.
 
Element 4—a 20 cm long magnetic quadrupole,  38 B.
 
Element 5—a 20 cm long drift.
 
Element 6—a 10 cm long magnetic quadrupole,  38 C.
 
Element 7—a 10 cm long drift.
 
Element 8—a 62.832 cm central arc length dipole,  40 B, with bending radius of 40 cm, (90 degree bend, arc length=[π/2]r) full gap of 25.4 cm, an entrance angle on the pole piece of −30 degrees, and zero angle on the exit pole piece.
 
Element 9—a 12.8 kV deceleration due to self space charge fields.
 
Element 10—a 15 cm long solenoid,  36 B.
 
Element 11—an 11.21 cm long drift.
 
Element 12—a 20 cm long solenoid,  36 C.
 
Element 13—an 11.21 cm long drift.
 
Element 14—a 30 cm long solenoid,  36 D.
 
Element 15—an 11.21 cm long drift.
 
Element 16—a 20 cm long solenoid,  36 C.
 
Element 17—an 11.21 cm long drift.
 
Element 18—a 15 cm long solenoid,  36 B.
 
Element 19—a 12.8 kV acceleration due to self space charge fields.
 
Element 20—a 62.832 cm central arc length dipole,  40 B, with bending radius of 40 cm, (90 degree bend, arc length=[π/2]r) full gap of 25.4 cm, an entrance angle on the pole piece of 0 degrees, and a −30 degree angle on the exit pole piece.
 
Element 21—a 10 cm long drift.
 
Element 22—a 10 cm long magnetic quadrupole,  38 D.
 
Element 23—a 20 cm long drift.
 
Element 24—a 20 cm long magnetic quadrupole,  38 E.
 
Element 25—a 60 cm long drift.
 
Element 26—a 30 cm long magnetic quadrupole,  38 F.
 
Element 27—a 40 cm long solenoid,  36 E.
 
Element 28—a 45 cm long drift.
 
Element 29—a 10 cm long magnetic quadrupole,  38 G.
 
Element 30—a 20 cm long drift.
 
Element 31—a 30 cm long magnetic quadrupole,  38 H.
 
Element 32—a 30 cm long solenoid,  36 F.
 
         [0000]    
       
         
               
             
               
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 1 
               
             
             
               
                   
               
               
                 Magnetic Excitations of Solenoids 36 and Quadrupoles 38 For  
               
               
                 Various Conditions Within the Interaction Transport System 18. 
               
             
          
           
               
                   
                 Deuterium, 
                 Deuterium, 
                 Deuterium, 
                 Tritium, 
                 Tritium 
               
               
                 Element 
                 full current 
                 half current 
                 no current 
                 full current 
                 no current 
               
               
                   
               
             
          
           
               
                 36A 
                 2.19  
                 kG 
                 2.60  
                 kG 
                 2.95  
                 kG 
                 2.18  
                 kG 
                 3.00  
                 kG 
               
               
                 38A 
                 −6.40  
                 G/cm 
                 −9.07  
                 G/cm 
                 −12.2  
                 G/cm 
                 −6.74  
                 G/cm 
                 −12.1  
                 G/cm 
               
               
                 38B 
                 27.7  
                 G/cm 
                 45.8  
                 G/cm 
                 82.5  
                 G/cm 
                 32.4  
                 G/cm 
                 81.6  
                 G/cm 
               
               
                 38C 
                 −251 
                 G/cm 
                 −205  
                 G/cm 
                 −322  
                 G/cm 
                 −278  
                 G/cm 
                 −324  
                 G/cm 
               
               
                 36B 
                 10  
                 kG 
                 10.5  
                 kG 
                 11  
                 kG 
                 10  
                 kG 
                 11  
                 kG 
               
               
                 36C 
                 6  
                 kG 
                 6  
                 kG 
                 6  
                 kG 
                 6  
                 kG 
                 6  
                 kG 
               
               
                 36D 
                 10  
                 kG 
                 10  
                 kG 
                 10  
                 kG 
                 10  
                 kG 
                 10  
                 kG 
               
               
                 36C 
                 6  
                 kG 
                 6  
                 kG 
                 6  
                 kG 
                 6  
                 kG 
                 6  
                 kG 
               
               
                 36B 
                 10  
                 kG 
                 10.5  
                 kG 
                 11 
                 kG 
                 10  
                 kG 
                 11  
                 kG 
               
               
                 38D 
                 −299  
                 G/cm 
                 −187  
                 G/cm 
                 −355  
                 G/cm 
                 −210  
                 G/cm 
                 −333  
                 G/cm 
               
               
                 38E 
                 29.3  
                 G/cm 
                 38.2  
                 G/cm 
                 82.9  
                 G/cm 
                 13.9  
                 G/cm 
                 80.2  
                 G/cm 
               
               
                 38F 
                 −6.35  
                 G/cm 
                 −9.07  
                 G/cm 
                 −12.2  
                 G/cm 
                 −6.74  
                 G/cm 
                 −12.1  
                 G/cm 
               
               
                 36E 
                 4.45  
                 kG 
                 4.67  
                 kG 
                 4.94  
                 kG 
                 4.30  
                 kG 
                 5.02  
                 kG 
               
               
                 38G 
                 2.06  
                 kG/cm 
                 2.06  
                 kG/cm 
                 2.06  
                 kG/cm 
                 1.56  
                 kG/cm 
                 1.56  
                 kG/cm 
               
               
                 38H 
                 −2.97 
                 G/cm 
                 −2.02  
                 G/cm 
                 −2.76  
                 G/cm 
                 0.1  
                 G/cm 
                 −2.02  
                 G/cm 
               
               
                 36F 
                 4.36  
                 kG 
                 4.50  
                 kG 
                 4.63  
                 kG 
                 4.37  
                 kG 
                 4.69  
                 kG 
               
               
                   
               
             
          
         
       
     
       Listing 2. Elements Used in the End Transport System  16 . 
       [0060]    Element 1—a 30 cm long magnetic solenoid,  36 G.
 
Element 2—a 30 cm long magnetic quadrupole,  38 I.
 
Element 3—a 120 cm long drift.
 
Element 4—a 62.832 cm central arc length dipole,  40 A, with bending radius of 40 cm, (90 degree bend, arc length=[π/2]r) full gap of 25.4 cm, an entrance angle on the pole piece of −30 degrees, and zero angle on the exit pole piece.
 
Element 5—a 15 cm long magnetic solenoid, 36H
 
Element 6—a 42.42 cm long drift.
 
Element 7—a 30 cm long magnetic quadrupole,  38 J.
 
Element 8—a 42.42 cm long drift.
 
Element 9—a 15 cm long magnetic solenoid,  36 I.
 
Element 10—a 62.832 cm central arc length dipole,  40 A, with bending radius of 40 cm, (90 degree bend, arc length=[π/2]r) full gap of 25.4 cm, an entrance angle on the pole piece of 0 degrees, and a −30 degree angle on the exit pole piece.
 
Element 11—a 120 cm long drift.
 
Element 12—a 30 cm long magnetic quadrupole,  38 K.
 
Element 13—a 30 cm long magnetic solenoid,  36 J.
 
         [0000]    
       
         
               
             
               
               
               
               
               
             
               
               
               
               
               
               
               
               
               
             
           
               
                 TABLE 2 
               
             
             
               
                   
               
               
                 Magnetic Excitations For Various Conditions  
               
               
                 in the End Transfer System 16. 
               
             
          
           
               
                   
                 Deuterium, 
                 Deuterium, 
                 Tritium, 
                 Tritium 
               
               
                 Element 
                 full current 
                 no current 
                 full current 
                 No current 
               
               
                   
               
             
          
           
               
                 36G 
                 2.15  
                 kG 
                 3.0  
                 kG 
                 2.2  
                 kG 
                 3.0  
                 kG 
               
               
                 38I  
                 2.57  
                 G/cm 
                 2.57  
                 G/cm 
                 2.60  
                 G/cm 
                 2.60  
                 G/cm 
               
               
                 36H 
                 9.79  
                 kG 
                 10.83  
                 kG 
                 9.93  
                 kG 
                 11.14  
                 kG 
               
               
                 38J  
                 130  
                 G/cm 
                 204  
                 G/cm 
                 134  
                 G/cm 
                 209  
                 G/cm 
               
               
                 36I  
                 9.79  
                 kG 
                 10.83  
                 kG 
                 9.93  
                 kG 
                 11.14  
                 kG 
               
               
                 38K 
                 1.69  
                 G/cm 
                 2.34  
                 G/cm 
                 1.78  
                 G/cm 
                 2.40  
                 G/cm 
               
               
                 36J  
                 2.11  
                 kG 
                 2.99  
                 kG 
                 2.16  
                 kG 
                 2.99  
                 kG 
               
               
                   
               
             
          
         
       
     
       Calculated Parameters of the Preferred Embodiment Assuming 10,000 Amperes of Stored Beam Currents 
       [0061]    The preferred embodiment may be operated over a wide range of stored beam currents, as the design is specified for operation between zero and 10,000 Amperes of stored electron, deuteron and triton currents. Design calculations will now be presented for the operation of the preferred embodiment assuming that the full design current of 10,000 Amperes can be achieved within the preferred embodiment. These calculations indicate that the preferred embodiment is of interest for advancing the science of fusion energy experimental devices. 
       10,000 Ampere Design Calculations: Power Output 
       [0062]    The power output from fusion reactions can be calculated from Eq. (3): 
         [0000]      Power Output=1.90×10 −27 (1 +v   D   /v   T )( LI   T   I   D   /ev   D   πr   2 ) m   2 MV.  (3)
 
         [0063]    Parameters used in the preferred embodiment are a length of the region where the beams are small of L=1.2 mm, a deuterium  22 A beam current of I D =10,000 A, a tritium  22 B beam current of I T =10,000 A, and a radius of the beams where they are small within the interaction transport system  18  of r=90 μm. For these parameters the density of deuterons  22 A within the small interaction volume is n D =5.12×10 17  cm −3 , the density of tritons  22 B within the small interaction volume is n T =7.66×10 17  cm −3  and the power output from one small interaction volume is 29.2 kW. For the preferred embodiment, there are two small interaction volumes in each interaction transport system  18 , and hence the power output will be 58.4 kW per interaction transport system  18  of the preferred embodiment. 
         [0064]    (Note that in the above expression it is assumed that r will be constant, when in fact it will vary considerably over the interaction region. In actuality, the power output will be 2.24×10 −27 (1+v D /v T )(I T I D /ev D π)m 2 MV∫dx/[a(x)b(x)], where dx is the differential unit of measure in the beam direction, a(x) is the beam horizontal size and b(x) is the beam vertical size. The integral is to be evaluated throughout the region where the beams collide. For the preferred embodiment, the quantity ∫dx/[a(x)b(x)]=139,000 m −1 , while the approximation L/r 2 =148,000 m −1 . Hence, it is a good approximation to use L=1.2 mm and r=90 microns when evaluating the power output.) 
       10,000 Ampere Design Calculations: Beam Neutralization 
       [0065]    If there were no compensating factor, the electric self charge of 10,000 A tritium  22 B beam currents at an energy of 160 keV would be too large to sustain the beam. A formula to estimate the beam center to beam edge electric potential is V=30I/β, where I is in Amperes, β is the beam velocity divided by the speed of light, and V is in volts. For 160 keV tritium  22 B beams, β=0.0107, and with I=10,000 A this leaves a beam center to beam edge potential difference of 28 MegaVolts, about 175 times greater than the tritium  22 B beam energy itself. Clearly, such a condition cannot be established. Nonetheless, it is possible to arrange for 10,000 Ampere beams at 160 keV, due to the trapping of free electrons within the beam. Electrons will be formed from the ionization of background gasses and they will be trapped by any electrostatic potential that is greater than their own kinetic energy. Calculations have shown that an equilibrium situation is obtained when an electrostatic potential of 5625 Volts is established between the beam edge and the beam center in the interaction region. In the non-interaction regions, the equilibrium is established at about 228 V for the tritium  22 B case, and 390 V for the deuterium  22 A case. In the region where the electron  26  beam overlaps the ion  22  beam, the neutralization occurs due to similar currents of oppositely charged particles. In the regions where the electrons  26  flow without overlapping ion  22  beams, residual ions will neutralize the electron  26  beam. 
       10,000 Ampere Design Calculations: Halo Formation and Control 
       [0066]    As just described, background particles will lead to electric field neutralization that will greatly reduce the self space charge electric fields of the particle beams used in the invention. However, some electric field will remain, as it is this remnant electric field that serves to contain the neutralizing particles. This electric field will manifest itself toward the outer regions of the particle beams, since it is the nature of plasmas (or any conductor) that residual charge migrates toward the outside. The presence of this electric field will lead to the formation of a portion of the beam that has a different ion  22  optical profile than the main core beam. This new profile is called “beam halo” since it is a faint amount of the beam that exists outside of the main beam at focal points. Advantageously, the invention uses magnets to focus this beam halo where the main core beam is small. This technique allows for independent focusing of the beam halo from the core beam, and is used to retain the beam halo particles in the system. While the beam halo must be cooled to return it to the main beam, the energy expended in cooling the beam halo is far less than what would be expended if the beam halo were lost from the system entirely and had to be replaced by additional injected beam. 
       10,000 Ampere Design Calculations: Self Magnetic Field Limitation on Currents 
       [0067]    It can be seen from Eq. (3) that the output fusion power scales as the deuterium  22 A current multiplied by the tritium  22 B current, among other factors. Hence it is advisable to maximize the beam currents within the device. However, Table 1 and 2 show that the magnetic fields employed in the components are already significantly affected by the design currents of 10,000 A and therefore the design current is appropriate for the analysis of the preferred embodiment. The invention advantageously uses tunable magnetic components to operate over a range of beam current conditions, allowing the invention to operate from the low initial startup beam currents all the way up to the full design current. The tunable magnetic components make the preferred embodiment excellent as a research device for fusion energy generation, as operation can be studied over a wide range of operating characteristics. 
       10,000 Ampere Design Calculations: Beam Energy Losses 
       [0068]    As particle beams traverse matter they lose energy via the dE/dx process. The rate of energy loss is given by the following formula: 
         [0000]        dE/dx=[ω   p   2   z   2   e   2   /v   2 ] ln(Λ v/ω   p   b   min )  (4)
 
         [0069]    In Eq. (4) Λ is a factor of order unity (and therefore not important since it is within the logarithm), b min  is the larger of either ze 2 /γmv 2  or /γmv, and ω p   2 =4πne 2 /m=4πnc 2 r e . Here n is the number of electrons per unit volume, and r e  is the classical radius of the electron, r e =2.82×10 −13  cm, e is the charge on the electron, m is the mass of the electron, c is the speed of light, v is the velocity of the ions  22  with respect to the matter being traversed, and z is the charge of the nuclei of the matter being traversed. γ is a relativistic factor that can be set equal to one here. 
         [0070]    The particle beams  22  will lose energy via Eq. (4) to background gas particles in the vacuum chamber  28  as well as to electrons trapped by the Coulomb potential within the beams. The dE/dx mechanism will in turn heat the background gas particles and trapped electrons. A detailed analysis has been done to calculate the expected dE/dx energy loss for the 10,000 A design, with the results given in Table 3 below. 
         [0000]    
       
         
               
             
               
               
             
           
               
                 TABLE 3 
               
             
             
               
                   
               
               
                 dE/dx Power Losses. 
               
             
          
           
               
                 Parameter 
                 Value 
               
               
                   
               
               
                 dE/dx Power Loss in One Interaction Region 
                  750 W 
               
               
                 dE/dx Power Loss in Tritium Non-Interaction Region 
                   22 W 
               
               
                 dE/dx Power Loss in Deuterium Non-Interaction Region 
                   12 W 
               
               
                 Deuterium dE/dx Power Loss to Background Gas 
                 31.5 W 
               
               
                 Tritium dE/dx Power Loss to Background Gas 
                 17.5 W 
               
               
                 dE/dx Power Electron Cooling Beam Loses to 
                  193 W 
               
               
                 Background Gas, Deuterium Case 
                   
               
               
                 dE/dx Power Electron Cooling Beam Loses to 
                 87.4 W 
               
               
                 Background Gas, Tritium Case 
                   
               
               
                 Energy Supplied by Electrons to Overcome Ion 
                  0.094 eV 
               
               
                 dE/dx Losses, Tritium Case 
                   
               
               
                 Energy Supplied by Electrons to Overcome Ion 
                 0.0644 eV 
               
               
                 dE/dx Losses, Deuterium Case 
               
               
                   
               
             
          
         
       
     
       10,000 Ampere Design Calculations: Intrabeam Scattering, Single Scattering, Multiple Scattering, Recombination and Charge Exchange 
       [0071]    Many scattering processes will exist within the storage ring system. The particles can scatter off of an oncoming beam, off of residual gas particles in the vacuum chamber  28 , off of charged neutralizing particles trapped by the Coulomb forces within the beams, and off of other particles within the same beam. These effects have been calculated in detail for the 10,000 A design, with the important results summarized in Tables 4, 5, and 6. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
               
             
               
               
               
             
           
               
                 TABLE 4 
               
             
             
               
                   
               
               
                 Single Scattering Parameters. 
               
             
          
           
               
                 Parameter 
                   
                 Value 
               
               
                   
               
             
          
           
               
                 Single Scattering Angle Presumed Lost 
                   
                 0.2 
                 rad 
               
               
                 Cross Section for Single Scattering Loss 
                   
                 10.11 
                 barn 
               
             
          
           
               
                 Single Scattering off of Residual Gas 
                   
                 Negligible 
               
               
                 Single Scattering Effective Beam Emittance 
                 ε scat   
                 8.68 × 10 −8 π 
               
               
                 Single Scattering Beam Size in Cooler (Deuterium) 
                   
                 38.8 cm 
               
               
                 Single Scattering Beam Size in Cooler (Tritium) 
                   
                 39.5 cm 
               
               
                 Electrons that Scatter off Residual Ions at &gt;0.1 
                   
                  4.7% per meter 
               
               
                 radians, Tritium Cooling Case 
                   
                   
               
               
                 Electrons that Scatter off Residual Ions at &gt;0.1 
                   
                 0.66% per meter 
               
               
                 radians, Deuterium Cooling Case 
                   
                   
               
               
                 Single Scattering of Electron Beams off 
                   
                 Negligible 
               
               
                 Background Gas 
                   
                   
               
               
                 Heating of Electron Beam due to Ion Single 
                   
                 Negligible 
               
               
                 Scattering 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 5 
               
             
             
               
                   
               
               
                 Multiple Scattering Parameters. 
               
             
          
           
               
                 Parameter 
                   
                 Value 
               
               
                   
               
               
                 Multiple Beam-Beam Scattering Emittance Growth 
                 Δε nT   
                 6.65 × 10 −9 π m-r 
               
               
                 of the Tritium Beam (One Interaction Waist) 
                   
                   
               
               
                 Multiple Beam-Beam Scattering Emittance Growth 
                 Δε nD   
                 9.95 × 10 −9 π m-r 
               
               
                 of the Deuterium Beam (One Interaction Waist) 
                   
                   
               
               
                 Ion Multiple Scattering off of Residual Gas 
                   
                 Negligible 
               
               
                 Multiple Scattering of Electron Beams off 
                   
                 Negligible 
               
               
                 Background Gas 
                   
                   
               
               
                 Heating of Electron Beam due to Ion Multiple 
                   
                 Negligible 
               
               
                 Scattering 
                   
                   
               
               
                 Electron Multiple Scattering Emittance Growth 
                   
                  20% 
               
               
                 due to Residual Ions in 10 cm, tritium case 
                   
                   
               
               
                 Electron Multiple Scattering Emittance Growth 
                   
                 7.3% 
               
               
                 due to Residual Ions in 10 cm, deuterium case 
               
               
                   
               
             
          
         
       
     
         [0000]    
       
         
               
             
               
               
               
             
           
               
                 TABLE 6 
               
             
             
               
                   
               
               
                 Intrabeam Scattering Parameters. 
               
             
          
           
               
                 Parameter 
                   
                 Value 
               
               
                   
               
               
                 Deuterium Longitudinal Intrabeam Scattering 
                 Δdp/p 
                 4.2 × 10 −4   
               
               
                 Growth (per turn, two interaction Waists) 
                   
                   
               
               
                 Tritium Longitudinal Intrabeam Scattering Growth 
                 Δdp/p 
                 9.8 × 10 −4   
               
               
                 (per turn, two interaction Waists) 
                   
                   
               
               
                 Electron Heating Due to Intrabeam Scattering of 
                 ΔE ion   
                 0.39 eV 
               
               
                 Tritium 
                   
                   
               
               
                 Electron Heating Due to Intrabeam Scattering of 
                 ΔE ion   
                 0.19 eV 
               
               
                 Deuterium 
                   
                   
               
               
                 Growth in Electron Cooling Beam Radius Due to 
                   
                 2.04 mm 
               
               
                 Transverse Self Scattering 
                   
                   
               
               
                 Growth in Electron Cooling Beam Momentum 
                   
                 Negligible 
               
               
                 Spread Due to Longitudinal Self Scattering 
               
               
                   
               
             
          
         
       
     
       10,000 Ampere Design Calculations: Recombination and Charge Exchange 
       [0072]    Recombination of the free hydrogen ions  22  with the free electrons present in the system will result in a neutral hydrogen atom. Since the newly formed atom is now in an uncharged state, it will no longer be bound by the magnetic confinement fields and can therefore be lost. Generally this effect is considered too small to be considered in electron cooling experiments, as the loss rate is usually on the order of tens of particles per second. For the invention discussed herein, with 10,000 A currents, the expected loss rate will be about 2.6×10 −12  A, which is negligibly small. 
         [0073]    As the ions  22  traverse through the neutral gas atoms in the vacuum chamber  28  an electron can be exchanged from the gas atom to the ion  22  in the beam. This potential loss mechanism has been estimated to have an upper bound of 10 kW for the invention. 
       10,000 Ampere Design Calculations: Plasma Instabilities 
       [0074]    Plasma instabilities are important considerations for most hot fusion devices. An important number in this regard is the number of plasma oscillations that will occur within the system per unit time, which is related to the plasma frequency, ω p   2 =4πne 2 /m, where n is the number of electrons per unit volume, e is the charge of the electron, and m is the mass of the electron. For the invention described herein, the number of plasma oscillations that occur in various regions are summarized in Table 7. As can be seen from the table, about 29,000 plasma oscillations will take place during the passage of a tritium ion  22 B through one half cell of the invention, and 18,200 plasma oscillations will take place during the passage of a deuterium ion  22 A through one half cell of the invention. 
         [0000]    
       
         
               
             
               
               
               
             
               
               
               
             
           
               
                 TABLE 7 
               
             
             
               
                   
               
               
                 Number of Plasma Oscillations Within the System. 
               
             
          
           
               
                   
                 Parameter 
                 Number 
               
               
                   
                   
               
             
          
           
               
                   
                 Number of Plasma Oscillations During Deuteron 
                 5080 
               
               
                   
                 Transit of the Interaction Region 
                   
               
               
                   
                 Number of Plasma Oscillations During Triton 
                 7600 
               
               
                   
                 Transit of the Interaction Region 
                   
               
               
                   
                 Number of Plasma Oscillations During Deuteron 
                 5500 
               
               
                   
                 Transit of the Cooling Region 
                   
               
               
                   
                 Number of Plasma Oscillations During Triton 
                 9970 
               
               
                   
                 Transit of the Cooling Region 
                   
               
               
                   
                 Number of Plasma Oscillations During Deuteron 
                 7620 
               
               
                   
                 Transit of the Remaining Regions 
                   
               
               
                   
                 Number of Plasma Oscillations During Triton 
                 11400 
               
               
                   
                 Transit of the Remaining Regions 
               
               
                   
                   
               
             
          
         
       
     
         [0075]    Direct excitation of the resonant electron oscillations at a will not appear as there will be no electron cyclotron resonant power source in the invention. 
         [0076]    The Buneman instability (two stream instability) and various classes of the beam-plasma instabilities should not exist in the invention. The Buneman instability manifests itself in situations where the drift velocity is greater than the electron thermal velocity, and that condition is not present in the invention, since the dE/dx mechanism will quickly heat the plasma electrons to velocities in excess of the ion  22  beam drift velocities. The beam-plasma instability also relies on an interaction between plasma oscillations in the beam and the plasma. In the case of the invention, the temperature of the electron plasma is so high that the thermal motion of the electrons will cause such incoherence in the electron plasma that these instabilities can not grow. 
         [0077]    The resonant condition for ion motion occurs at the frequency ω i =(m/M i ) 1/2 ω p . For tritons  22 B, the square root of the mass ratio is (m/M T ) 1/2 =1/74, and therefore the number of natural ion  22 B oscillations that will take place during the triton&#39;s  22 B passage through an invention cell is about 390. For deuterons  22 A, the square root of the mass ratio is (m/M D ) 1/2 =1/61, and therefore the number of natural ion  22 A oscillations that will take place during the deuteron&#39;s  22 A passage through an invention cell is about 300. These times are too short for most plasma oscillations to present a problem for the invention considered herein. This is because the beam ions  22  are continuously passing through electrons and the oncoming ion  22  beams at different physical locations during even this short time. Hence, it should not be possible for oscillations to set up a positive feedback to beam density disturbances, and this is the root cause of plasma instabilities. With the root cause of plasma instabilities not present within the extremely short time scale of the interaction, no destructive plasma instabilities should occur. 
         [0078]    Any small beam density disturbance that does get started in a single pass through the invention cell will be eliminated during the passage through the electron cooling system  14 . The electrons  26  within the electron cooling system  14  are born anew (at the cathode of the electron source  24 ) continuously, and have no history of interaction with the ion  22  beams between subsequent passes. Hence, when the ions  22  come to equilibrium with the electrons  26  in the electron cooling system  14 , they do so with electrons  26  that have no correlation with electrons  26  on previous or subsequent turns. 
         [0079]    Note that the invention cell is considerably different from a tokamak in its approach to fusion energy generation. In a tokamak, the ion-electron plasma must exist for time scales on the order of a second (or, eventually, much longer), various beams are used for heating, and there is a magnetic confining field. For the invention discussed herein, the ions  22  only exist in the individual interaction plasmas for less than a nanosecond, there are no external energy sources beyond the beam  22  self motion, and there is no containing solenoidal field for the ions  22 . Therefore, many of the conditions required for plasma instabilities simply do not exist in the invention. 
         [0080]    Importantly, the preferred embodiment is designed to be able to operate over a wide range of beam currents, from 0 to 10,000 A. As such, the preferred embodiment is an excellent research device that can be used to investigate stable beam operation for colliding beam fusion devices over a wide parameter range. 
       10,000 Ampere Design Calculations: Beam Instabilities and Resonances 
       [0081]    In traditional storage rings instabilities arise because the large numbers of particles stored have a significant collective self space charge field. If a disturbance forms in the particle distribution, the field from the disturbance can affect the environment surrounding the beam, setting up oscillating electromagnetic fields. If those fields then act back on the space charge disturbance such that the disturbance grows, an instability exists which can destroy the beam. 
         [0082]    Resonant phenomena are also usually important to evaluate. Resonances occur when some of the particles circulate the device in such a way as to be at the same transverse position at every (or every other) turn around the device. Those particles which exhibit this behavior will see the same magnet imperfections on every (or every other) pass, and will be quickly lost from the device. 
         [0083]    In the invention described herein the problem of instability and resonant loss should not exist. The presence of strong electron cooling forces means that any small offset in particle momentum will be corrected on each pass. Cooling in a single turn means that the invention here is, from an accelerator physics standpoint, a single pass device, in which instabilities are known to be far less troublesome and in which resonances do not exist. 
       10,000 Ampere Design Calculations: Expected Power Input; Expected Q. 
       [0084]    The scientific Q is defined as the output power divided by the power input supplied to the various beams used in the invention. It is calculated above that the power output of a single interaction region is 29.2 kW, and herein it assumed that there are two interaction regions per interaction transport system  18 , which results in: 
         [0000]      Predicted Output Power=58.4 kW per interaction transport system 18.  (5)
 
         [0085]    The power input of the supplied tritium  22 B and deuterium  22 A beams is equal to the total energy supplied to these beams multiplied by the feed current required to keep the nominal beam currents at 10,000 A. The feed current must be equal to the ions  22  that are lost to fusion plus those that are lost to scattering. The fusion cross section is about 0.85 barn, while Table 4 specifies that the cross section for single scattering of the beams is about 10 barn. The remainder of Table 4 shows that other scattering processes have a negligible contribution to the particle loss rate. Also, the 0.85 barn fusion cross section is almost certainly contained within the 10 barn scattering cross section (as the 10 barn results from the nearest collisions, which are also those most likely to result in fusion). Hence, the feed current required is 10/0.85 times that which would result in the output power of 58.4 kW, or, (10×58.4 kW)/(0.85×22.4 MV)=30.7 mA. The required power input of the tritium  22 B beam is thus 30.7 mA×167 kV=5.1 kW, and the required power input of the deuterium  22 A beam is 30.7 mA×247 kV=7.6 kW, leaving: 
         [0000]      Required Ion 22 Beam Drive Power=12.7 kW.  (6)
 
         [0086]    For a single electron  26  beam to provide the tritium  22 B beam cooling, the beam energy that must be supplied is the sum of the energy lost, which is the 0.094 eV shown in Table 3 as the energy needed to overcome the dE/dx of the tritons  22 B being cooled, plus 0.01 eV which is the energy needed to overcome the dE/dx loss of the electrons  26  to the residual gas, plus the energy spread induced by the need to cool the intrabeam scattering, shown in Table 6 as 0.39 eV, all multiplied by 10,000 A: 
         [0000]      Tritium 22B cooling electron 26 beam drive power: 4.94 kW  (7)
 
         [0087]    For a single electron  26  beam to provide the deuterium  22 A beam cooling, the beam energy that must be supplied is the sum of the energy lost, which is the 0.0644 eV shown in Table 3 as the energy needed to overcome the dE/dx of the deuterons  22 A being cooled, plus 0.02 eV which is the energy needed to overcome the dE/dx loss of the electrons  26  to the residual gas, plus the energy spread induced by the need to cool the intrabeam scattering, shown in Table 6 as 0.19 eV, all multiplied by 10,000 A: 
         [0000]      Deuterium 22A cooling electron 26 beam drive power: 2.744 kW  (8)
 
         [0000]    Eqs. (5) through (8) leave the predicted scientific Q value for 10,000 A currents as: 
         [0000]        Q  scientific=58.4/(12.7+4.94+2.744)+1=2.86+1=3.86.  (9)
 
         [0088]    In Eq. (9) the addition of 1 to the ratio comes from the realization that the lost ion  22  and electron  26  power will also generate heat and contribute to the overall output power. Obtaining a Q value this high will enable the invention to be a major step forward in fusion power devices. 
       Other Preferred Embodiments 
       [0089]    The above preferred embodiment concerns use of the invention to achieve colliding beam fusion of deuterium  22 A and tritium  22 B with a center of mass energy of about 400 keV. The analysis indicates that gains can be made by lowering the center of mass energy. Also, the invention can be used with other ion combinations, including deuterium colliding with Helium-3, deuterium-deuterium, proton-Lithium-6 and proton-Boron-11 among others. The peak of the cross section occurs within operating ranges for these reactions of: 50 keV to 500 keV for deuterium-tritium; 200 keV to one MeV for deuterium-helium-3; and one MeV to four MeV for deuterium-deuterium. For the lower energies in this range, a simple ion source can be used for particle beam generation while for the higher energies an ion source and an injector accelerator could be used. Scattering losses, beam energy losses, and beam sourcing powers must be considered in detail before choosing an optimum operating point, but it is expected that the invention would optimally operate somewhere in these ranges for those species.