ELECTRODYNAMIC INERTIAL FUSION GENERATORS AND FISSION SATELLITES

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1 Invited paper presented at the Thorium nergy Alliance 4th Annual Future o nergy Conerence, Loyola University, Water Tower Campus, Chicago, Illinois, USA, May 31 June 1st LCTRODYNAMIC INRTIAL FUSION GNRATORS AND FISSION SATLLITS Magdi Ragheb and Monish Singh Department o Nuclear, Plasma and Radiological ngineering University o Illinois at Urbana-Champaign, 216 Talbot Laboratory, 104 South Wright Street, Urbana, Illinois 61801, USA. mragheb@illinois.edu msingh22@illinois.edu ABSTRACT The use o Diode and Wile Ball (WB) cusped magnetic ield conigurations is discussed in the context o their use as compact drivers in lectrostatic and lectrodynamic Inertial Coninement (IC) Fusion, or a Fusion-Fission Hybrid using a thorium molten salt breeder. The use o a usion ission thorium hybrid in association with these conigurations considering the catalyzed DD and the DT usion reactions and a molten salt using Th 232 as a U 233 breeder is analyzed. nergy and material balances in the coupled system as well as neutronic and photonic computations are conducted. They shows that the energy multiplication in the coupled system approaches ininity as the conversion ratio o the ission satellites approaches unity. Such a coniguration would allow enough energy breakeven or a sustainable long term energy system with a practically unlimited uel supply base. Deuterium can be extracted rom water in the world oceans, and thorium is our times more abundant than uranium in the arth s crust. The approach would provide the possibility or the eventual introduction o aneutronic usion cycles such as the pb 11 cycle or energy production as well as or space propulsion. Such an alternative sustainable paradigm would provide the possibility o an optimized usion-ission thorium hybrid or long term uel availability with the added advantages o higher temperatures thermal eiciency or process heat production or a uture hydrogen economy, prolieration resistance and minimized waste disposal characteristics. INTRODUCTION Cusped magnetic ield conigurations have been considered in usion research in several contexts since they oer a situation where the conined plasma is stable against perturbations. A linear cusped coniguration was earlier proposed by Ragheb et al. in 1985 or the magnetic protection o the irst wall o a DHe 3 low-tritium inventory usion inertial coninement reactor using heavy ions as drivers [1, 2]. It protected the wall rom the impingement o the charged particles and diverted them to collectors or direct energy conversion into electricity at a high conversion eiciency. The cusped coniguration was modiied, upon review, into an

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3 electrodynamic usion in a concept called the Polywell concept. The idea is to trap high densities o energetic electrons within a quasi-spherical magnetic ield into which a current o high energy electrons is injected. The electrons orm a deep negative potential well, without the need or mechanical grids. A small deviation rom charge neutrality o 10-6 o ions versus electrons is required to make the potential well as deep as the electron drive energy [4]. The ions to be used are then dropped at the edge o the created well. They all into the center with an 1/r 2 distribution o increasing density acquiring enough kinetic energy to make usion reactions possible as they collide at the core region. Whenever scattering occurs, the ions recirculate back up the well and then all in again when they reach the edge. ventually, similar to the electrons, the ions gyro motion in the increasing edge magnetic ield o the system. The critical consideration is the power balance between the usion power generation and the electron drive power loss. This depends on the ability o the magnetic ield to keep the ions trapped in the quasi-sphere electron-driven electrostatic potential well. The usion generation process and the electron trapping and losses are decoupled and can be optimized separately. Table 1: Catalyzed DD and DT Fusion Reaction nergetics. Reaction Total nergy rom usion, Charged Particle nergy (MeV) Neutron nergy (MeV) Fraction o energy to neutrons, n Number o Neutrons (MeV) (%) DT reaction D + 1T 2He (3.52) + 0n (14.06) Catalyzed DD reaction * (a) D + 1D 1T (1.01) + 1H (3.03) (b) /2 1D + 1D 2He (0.82) + 0n (2.45) /2 (c) 1D + 1T 2He (3.52) + 0n (14.06) (d) 1D + 2He 2He (3.67) + 1H (14.67) D 2He + 1H + 0n * DD reactions (a) and (b) are assumed to have a branching ration o ½ and proceed at an equal rate: R R1 = R DD 2 = 2 DT and DHe 3 reactions (c) and (d) proceed at the same rate as the two DD reactions. As initially suggested in 1987, coil conductors with zero cross sectional radius were placed exactly at the vertex edges with sharp corners where the coils came together. This leads to a unny cusp where an odd point/radial line appear sat such corners with a zero magnetic ield at a zero radius. SYMBIOTIC COUPLING OF FUSION BRDRS AND FISSION SATLLITS, NRGY AND MATRIAL BALANCS

4 Figure 2. nergy and material lows in the symbiotic coupling o usion breeder drivers and ission satellites. The purpose o a symbiotic system is to provide issile uel bred in the usion reactors or satellite ission burners o the uel. Material and energy lows balances are necessary to optimize the coupling and identiy the best conigurations. The driven system shown in Fig. 2 is considered. Let be the usion energy output per unit usion reaction. One DT reaction releases a neutron having an energy o MeV and the catalyzed DD reaction releases a neutron having an average energy o 8.26 MeV. From Table 1: MeV ( DT ) = 17.57[ ], usion MeV ( DD) = 21.62[ ]. usion PLASMA POWR AMPLIFICATION FACTOR An important design parameter or a magnetic usion reactor is its plasma power ampliication actor Q p, deined as the ratio o the thermonuclear power produced to the power input to generate and heat the plasma to thermonuclear usion temperatures: Q p

5 Q p = P thermonuclear usion energy generated in the plasma P = = energy required to heat the plasma (1) input h In a closed system, such as a toroidal Tokamak or Stellarator device, large values o are possible. Once the energy in the ions released rom the usion reactions in the plasma exceeds the radiation and other losses, plasma ignition should occur. The use o neutral ion beams injection or microwave radiorequency heating can thus be stopped, and the plasma burn becomes sel-sustained, as long as the usion uel continues being supplied, and the plasma remains conined. In an open system such as a mirror or a cusped coniguration usion reactor, because o the inevitable end losses, it is unlikely that ignition can be achieved. Such devices would have to be used as a driven power ampliier. With a low value o Q p, energy would have to be supplied continuously and the usion reaction would ampliy the energy input to the plasma by the actor Q p. In a single-cell plasma, Q p may not exceed about 1.2. The magnetic usion approach attempts at developing devices with a high value o Q p. Compact devices have low values o Q p o about The enhancement o Q p involves the reduction o end losses in open systems, particularly o high energy ions and electrons. FUSION NRGY BALANC I h is the energy input or heating the plasma, then = Q (2) p h Q p where Q p is the plasma power ampliication actor. The h variable is also related to the recycle energy or particle injection and heating energy, by rec = η, h I rec or, using q. (1), rec = (3) Q η p I where η I is the beam injection and plasma heating eiciency. The term h reappears with as output energy rom the plasma and is considered to be directed to the thermal conversion cycle.

6 energy, The usion energy,, appears as both charged particles energy, cp and neutron n. I n is the raction o usion energy carried away by the neutrons, then = (4) n n and As shown in Table 1, = (1 ) (5) cp n n( DT ) = 0.80, ( DD) = n In the usion blanket, the neutron energy n gets multiplied through the breeding and usion processes by the total Blanket nergy and Multiplication Factor, BMRF. The blanket energy output is obtained using q. 3 as b = BMRF. = BMRF.. n n (6) where: BMRF MeV Th( n, ) ission = BMR + source neutron energy (MeV) (7) and BMR = Blanket nergy Multiplication Ratio neutron and gamma ray energy deposited in the blanket (MeV) = source neutron energy (MeV) (8) Table 2: Comparison o the nergy Deposition Rates and Blanket Multiplication Ratios in a molten salt thorium blanket or dierent neutron sources [5]. Neutron Source Neutron Heating Rate (W per n/s) Gamma Ray Heating Rate (W per n/s) Total Heating Rate (W per n/s) Th(n, ) reactions (n/s) BMR BMRF Total nergy Deposition (MeV/source neutron) (Na-Th-F-Be) Molten Salt 2.45 MeV

7 DT Catalyzed DD (Li-Th-F-Be) Molten Salt 2.45 MeV DT Catalyzed DD The ollowing values rom the calculation results in Table 2 are adopted: BMRF( DT ) = 1.29 BMRF( DD) = 1.38 Considering the charged particles produced in the usion process, a actor γ is deined as the raction o the charged particle energy that olws to the direct energy converter and that is not converted into radiation or conveyed to the thermal conversion cycle. In the DT system, γ(dt) = 0.0, since direct converters are not normally used. However, or a DD system, γ ranges rom a low value o 0.42 or a low-β system to 0.54 or a high-β system. In the calculations that ollow, a value o γ(dd) = 0.42 is adopted. By using q. 4, the charged particle energy reaching the direct energy converter is cpdc = γ cp = γ (1 ) n (9) And or the energy reaching the thermal conversion cycle, cph = (1 γ ) cp = (1 γ )(1 ) n (10) I η dc is the charged particle conversion eiciency, then the electrical energy output rom the direct energy converter is given by = η dc dc cpdc = η γ(1 ) dc n (11) I δ is the raction o energy rejected by the direct energy converter that is recoverable through the thermal cycle, the energy available to the thermal conversion cycle rom the direct energy converter is = (1 η ) δ dch dc cpdc = (1 η ) δγ (1 ) dc n (12) The energy input to the thermal conversion cycle could be converted into electrical energy through an overall thermal cycle eiciency η th as

8 or, using the equations above, = η ( ), tc th dch cph b h 1 tc = ηth (1 ηdc) δγ (1 n) + (1 γ )(1 n) + BMRF. n + Qp (13) The combined electrical output rom the thermal cycle and the direct energy converter will be p = tc + dc (14) rom which an amount rec, given by q. 2, is recycled or particle injection and plasma heating, so that the electrical output capacity or the usion plant can be written as = = + out p rec tc dc rec ( usion) 1 1 = η th (1 ηdc) δγ (1 n) + (1 γ )(1 n) + BMRF. n + + ηdcγ (1 n) Qp Qpη I (15) and the net output is =. CF (16) ' out out usion ( usion) ( usion) where CF usion is the usion plant capacity actor. FISSIL NRGY AND MATRIAL BALANCS To determine the electrical energy production rom the ission reactors satellites, a material low balance is perormed. The rate o issile material production in the usion reactor blanket is where dm M kg = US. n. C1 ( ) (17) dt N year 0

9 U = issile nuclei yield per source neutron S n M N 0 = neutron source strength = atomic weight o the bred issile nuclide = Avogadro's number = kg. s g. yr 4 C1 conversion actor = ( ) The neutron source strength, S n can be written as where P = usion power 1 S = P.. C. CF (18) n 2 usion = energy release per usion event = W. MeV MW. J 18 C2 conversion actor = ( ) Combining qs. 14 and 15 yields where dm P M = U... C3. CFusion (19) dt N C3 = C1 C2. 0 The rate o issile material consumption, given by m c, in the ission satellites converter reactors is where P C tc ission dmc P M tc = (1 C)(1 + α).. C3. CFission (20) dt N ission = thermal power o the ission converter satellites = energy release per ission event number o issile nuclei produced = conversion ratio = number o issile nuclei consumed 0 α σ = capture to ission ratio= c σ For steady state operation, the rate o issile material production should equal the rate o consumption:

10 dm dt dm dt c =, or P tc ission P (1 C)(1 + α). CFission = U.. CFusion. NRGY AMPLIFICATION FACTOR AND SUPPORT RATIOS by The energy ampliication actor or ission to usion energy multiplication, is then given P tc ission U CFusion = =.. (21) P (1 C)(1 + α) CF ission Then, P = P and = (22) tc tc where tc is the energy production over a time interval τ in the usion and ission reactors. The electrical output rom the ission reactors is given by = η... CF (23) ' out th, s ission ( ission) where η th, s is the thermal cycle eiciency I the ission reactors, NRGY AND LCTRICAL SUPPORT RATIOS Three igures o merit can be suggested or the assessment o the symbiotic usion and ission combination. 1. The ission to usion energy ampliication actor deined by q. 18. It measures the multiplication o the energy external to the usion generators in the ission reactors satellites when the bred issile uel releases its energy content. ission U CFusion =.. (21) (1 C)(1 + α) CF ission The energy ampliication is increased at a irst level by the actor

11 ission ission 190 = = 10.8,or DT usion = = 8.8,or Catalyzed DD usion The energy multiplication is decreased by the actor containing the capture to ission ratio α given in Table 3 or various nuclides. A choice o the smallest value would avor the energy ampliication actor. In this case, the choice o U 233 in the thorium cycle with a α value o is avored to the choice o U 235 with a value o or Pu 239 with a value o , in the uranium-plutonium uel cycle. Table 3: Nuclear cross section or some issile and issionable nuclides at the thermal energy o ev. Nuclide Absorption cross section [barn] σ a Fission cross section [barn] σ Radiative capture cross section [barn] σ c Capture to ission ratio α Th Th Th Pa <0.1 U U U U U U Np <1 Pu Pu Pu Pu <0.2 1 barn=10-24 cm 2. A much more notable contribution can be noticed by the actor: conversion actor C is deined as 1 1 C, where the average number o issile nuclides produced C = average number o issile nuclides consumed As the value o the conversion actor C approaches unity, an ininite energy multiplication actor ensues:

12 ission U CF usion lim = lim.. = C 1 C 1 (1 C)(1 + α) CFission In more detail, when N nuclei o issile uel are consumed, NC nuclei o ertile uel are converted into issile nuclei. I the process is repeated, the consumption o N uel nuclei results in the conversion o a total number o issile nuclei as: N N NC NC NC NC total = (1...) = N + C+ C + C + C +... (24) 1 = N, 0 < C < 1. 1 C When C = 1, an ininite amount o issile uel can be converted rom a starting amount o ertile uel. When C > 1 the sequence diverges since more than a issile nucleus is created rom a ertile nucleus and cannot be summed mathematically. In this case C is designated as B, the breeding ratio. I only n recycles are involved, due to the accumulation o undesirable isotopes that could aect the recycling process, q. 24 reduces to: 2 3 n Ntotal = N + NC + NC + NC NC = N + C+ C + C + + C 2 3 n (1... ) n+ 1 1 C = N, 0 < C < 1. 1 C (25) 2. The thermal energy support ratio, R tc = cp + b + n, (26) 3. The electrical energy support ratio, S e =, (27) ' out ( ission) ' out ( usion) From the derived equations or the energy and material balances, a system analysis can be attempted. The results rom a detailed neutronics calculation o a molten salt blanket shown in Table 4 are adopted [5]. Table 4: Fissile and usile breeding or sodium and lithium salts in DT and DD symbiotic usionission uel actories. Blanket thickness = 42 cm, relector thickness = 40 cm; no structure in the salt region.

13 Source Li-Be-Th-F Salt Na-Be-Th-F Salt Li 6 (n,α)t Li 7 (n,n α)t Be 9 (n,t) F(n,T) Total T Th(n,γ) Be 9 (n,t) F(n,T) Total T Th(n,γ) (Nuclei / usion source neutron) DD x x x x x % 2.45 MeV DT x x x x x % MeV Catalyzed DD 50% 2.45 MeV 50% MeV x x x x x A point calculation can be glanced by using the calculated and representative data values listed in Table 5. Table 5: Parameter values or the symbiotic usion and ission coupling. Parameter Symbol Catalyzed DD DT Beam injection and plasma heating eiciency η I Fraction o usion energy carried by neutrons n Fusion energy output per usion reaction (MeV/usion) Total blanket energy multiplication BMRF Fraction o usion charged particles energy lowing to direct γ converter Direct conversion eiciency Fraction o energy rejected by the direct converter recoverable through thermal conversion Fusion thermal conversion cycle eiciency Fission thermal conversion cycle eiciency Fusion plant capacity actor Fission plant capacity actor nergy release per ission event (MeV/ission) η dc δ η th η th, s CF usion CF ision ission Capture to ission ratio α Conversion ratio o converter reactors C Fissile nuclei yield per source neutron U Plasma power ampliication actor Q p TH DIOD LCTROSTATIC INRTIAL CONFINMNT, IC ALTRNATIV

14 arlier work by I. Langmuir and K. B. Blodgett [8] inspired conigurations that are electrostatic rather than electrodynamic in nature in the 1960s by Philo T. Farnsworth, the inventor o television and Frequency Modulated (FM) radio, and R. T. Hirsch [8, 9]. They used a diode coniguration in the orm o spherical screens grids biased to high negative potentials to energize ions and accelerate them to the center o the device, where usion ensues. This is not attainable with realistic inite size coil conductors. In its simplest two-grid coniguration, the usion ions such as deuterons are accelerated electrostatically through a nearly spherically symmetric ocal point. At the ocal point, the beams converge leading to the usion o the iond conined in the electrostatic potential well. This coniguration was extensively studied by George H. Miley at the University o Illinois. Ion collisions with the grids lead to unavoidable energy losses limiting the power gains to less than 0.1 percent. The University o Illinois Inertial lectrostatic Coninement (IC) device provides MeV DD neutrons / second when operated with a steady-state deuterium discharge at 70 kv. Being compact and lightweight, the IC potentially represents an attractive portable neutron source or activation analysis applications, oil well logging, airport luggage and port o entry ship containers inspection or explosive nitrogenous materials and even special issile materials. The plasma discharge in the IC is unique, using a spherical grid in a spherical vacuum vessel with the discharge ormed between the grid and the vessel wall, while the -70 kv grid (cathode) also serves to extract high-energy ions. A key eature o the IC discharge is the ormation o ion micro-channels that carry the main ion low through the grid openings [10]. IC is ideally suited or burning advanced neutronless uels such as D-He 3 and p-b 11 due to the beam-like energy and low electron temperature. nergetic usion products escape the well and can undergo direct conversion to electricity. The Star Mode Inertial IC is a simple and lightweight device. The charged particles beams are ocused through large openings to minimize the interception o grid wires and give a good ocus despite deviations rom the spheroid shapes. The preliminary design o a small 100-kWe p-b 11 space power unit was undertaken along with the possible extension to an ion thruster or space applications. Diiculties to be addressed include being able to scale up to higher powers needed or more ambitious uture space missions. The objective would be to use a usion powered IC or next generation power units in the 100- kwe range. The technology underlying the electrically-driven IC jet unit underpins the development o a next generation usion ion propulsion units or deep space spacecrat replacing chemical systems. A Modular approach takes advantage o inherently small size o the IC units. In a Magnetically Channeled Spherical Array (MCSA) the linked units have improved coninement and guide usion products out o the system. A null-ield region created within each pair o Helmholtz coils conine plasma which is conined by the peripheral magnetic ield and no grid structure. A cusp ield coniguration provides luid stability. The radial leakage is recirculated back into the coninement region and the axial leakage is retrapped in the neighboring cells.

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16 Figure 5. Inertial lectrostatic Coninement IC device operating in the jet mode. The Speciic Impulse I sp = 3,000 sec, Input power = Watt, Thrust T = 34 mn, Accelerating potential = 600 V, Jet power: P jet = 500 Watts, iciency: h t = percent [10]. Figure 6. Two-grid and Multigrid systems shown in their vacuum chambers [13]. Figure 7. Two grid system jet and star plasma modes [13].

17 Figure 8. Multigrid system star mode o operation [13]. A presumption is that the grid coniguration cannot generate net power because the conined ions collide with the grid too oten beore they get to the center where they would use. Magnetically shielding the grid may allow the ions to accelerate to the center with less grid collision rates. On the other hand, in the grid design, the ast ions also lose their energy and thermalize through multiple scattering collisions with the cold background medium. Other mechanisms would be ions sputtering rom the outer shell and accelerating back to the grid, and electron accelerating away rom the grid to the shell. A design actor to be considered is the need or cooling the central cathode to prevent it rom melting in a power production application. LCTRODYNAMIC INRTIAL CONFINMNT, IC Using a cusped coniguration, energetic electrons are trapped in a quasi-spherical polyhedral magnetic ield to create a spherical electric potential well in which ions can be dropped. I injected at its edge, they are accelerated to the center with an increase in density and kinetic energy and inducing usion. In this approach, the power loss problem is shited rom being an ion grid collision problem into electron transport losses across high magnetic ields to the conining magnets. The competing electron power loss and the usion energy gain are decoupled and can be optimized Cusp-axis ields o Gauss were generated and DD usion did occur. Deep electron created wells at 27 kv well depth, and were created with -30 kv electron drives [4]. CUSPD MAGNTIC FILD CONFIGURATIONS In most systems in which a plasma is conined by a magnetic ield that surrounds it smoothly without a discontinuity, there is a tendency toward the creation o instabilities. This is so because the magnetic lines o orce which are stretched around the plasma can shorten themselves by burrowing into the gas and thus orce it outward.

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19 everywhere convex on the side toward the plasma. To satisy this curvature requirement, the magnetic ield must possess cusps, which are points or lines, or both, through which the magnetic ield lines pass radially outward rom the center o the coninement region as shown in Figs. 9, 10. A laboratory geometry o this kind is called a picket ence, and consists o two layers o parallel wires carrying currents in alternating directions so that the magnetic ield has a series cusps. The magnetic ields are generated in the vicinity o the walls decreasing the power needed in maintaining them. This advantage is superseded by the more important advantage o stable coninement. Another type o cusped geometry is the biconal cusp produced by a pair o magnetic ield circular coils with the currents in them lowing in opposite directions. A succession o cusped conigurations can generate a toroidal cusped system. I there is a loss o plasma rom the central volume, the lines o orce would have to stretch to ill the volume previously occupied by the plasma. Since this requires extra energy expenditure, this type o instability would not probably occur. In the cusped coniguration, a singular condition exists at the center where the magnetic ield goes exactly to zero. A particle passing through this point will experience a large ield change occurring in a time interval less than the gyromagnetic period, particularly as this period is lengthened by the decrease in the magnetic ield strength. The magnetic moment becomes no longer an adiabatic invariant o the system. In the special case o a particle actually passing through the point where the magnetic ield is zero, the particle will momentarily travel in a straight line and its motion will bear no relationship to that beore its passage through this point. The magnetic energy o the particle can theoretically reach an ininite value along the zero magnetic ield line. I one considers a conined plasma rather than a particle, one must consider the problem o Magneto Hydro Dynamic (MHD) cumulation o energy near a zero ield line. Let us consider a perectly conducting and incompressible cylindrical plasma to be immersed in a quadrupolar steady external magnetic ield: B = B xy. (28) e 0 In the absence o currents and velocities the plasma is under an unstable equilibrium to a linear velocity perturbation: v v x y = Ux, = Uy. (29) The MHD equations o motion which do not depend on the z axis variable can be exactly solved with the velocity perturbation as an initial condition. The motion generates an axial current j z in the z direction. Due to the pinch eect or the Lorentz orce: F = j B, (30)

20 the circular section o the cylinder is deormed into ellipses o axes (0x, 0y). Ater a time comparable to the ratio o the initial cylinder ration to the Alvèn velocity: V A B 0 = 1 (31) 2 ( 4πρ) a cumulation process occurs and the elliptical cross section is stretched along the x axis or the y axis depending on the relative values o the initial perturbation velocities U and V. The important result is that the plasma lattens and expands radially perpendicular to the z axis while the plasma kinetic energy and the current density increase without limit. The MHD equations can also be solved i the plasma is considered to be a perect gas with a inite electrical conductivity. At the inite cumulation time, the plasma initially contained within a circular cross section plasma would be squeezed within an ellipse o zero volume. The density, velocity V y, current density j z, as well as the internal kinetic or magnetic energies, all become ininite inside the limiting segments. The cumulation process requires an energy source supplied by the energy stored in the magnetic ield. An interesting consequence o the cumulation process is that the electron velocity J/n tends to ininity which could explain the process o acceleration o particles to extremely high velocities as is observed in cosmic ray particles. This suggests their origin as magnetic ield conigurations occurring in Gamma Ray Bursts (GRBs). The hot plasma in the magnetic ield would generate high energy radiation in the orm o synchrotron radiation. PLASMA STABILITY AND TH BTA FACTOR The pressure in a plasma o density as a unction o its temperature T in Kelvins and the Boltzmann constant k is pplasma = nkt (32) The pressure exercised on the plasma by the containing magnetic ield B is p magnetic 2 B = (33) 2µ The beta value is deined as the ratio o the plasma pressure to magnetic pressure β p nkt plasma = = (34) 2 pmagnetic ( B /2 µ ) The beta parameter is a measure o the kinetic to electromagnetic energy content o a plasma. There is a limit on the value o beta beore instabilities that would lead to the destruction o the plasma would occur.

21 WIFFL BALL CONFIGURATION Born in 1928, Robert W. Bussard was an American physicist working primarily in nuclear usion energy research. He received his Ph. D. rom Princeton University. He was as co-ounder and director o nergy/matter Conversion, MC2 Corporation. He held the post o Assistant Director to the USA Atomic nergy Commission and positions at Los Alamos National Laboratory (LANL), Oak Ridge National laboratory (ORNL), and the TRW Systems Company, a deense contractor. He acted as a designer o the Nerva motor, a governmentsponsored project to develop a nuclear powered rocket or heavy-lit applications in the late 1960's. Bussard is known or conceiving the Bussard ramjet, an interstellar spacecrat powered by hydrogen usion using hydrogen collected rom the interstellar gas medium utilizing a magnetic ield. He spent over 20 years developing a modiied Farnsworth-style Polywell compact usion device, successully generating over 100,000 times the output o Farnsworth's original experiments. In 2006, Bussard's Polywell design was awarded the Outstanding Technology o the Year Award by the International Academy o Sciences. The Bussard Ramjet is a modiied usion-drive starship proposed in the 1960's by Carl Sagan and urther popularized by authors such as Jerry Pournelle and Larry Niven. Bussard became disenchanted with the magnetic toroidal coninement Tokamak and Stellarator usion concepts. He returned to the roots o Farnsworth-style usion in the Polywell project that he initiated in He was unded or over 20 years by the Department o the Navy. Bussard's MC2 Corporation was tasked with solving 19 undamental challenges that stood in the way o designing commercially viable Farnsworth usors. Bussard's irst intended application was an 8-oot diameter naval reactor capable o generating 100 MWth o output power. Bussard's Polywell design is conceived or portability, making it perect or not only the Navy's intended use in powering ocean vessels and submarines, but also or providing high output thrust or proposed nuclear space-applications or high velocity trans-orbital spacecrat capable o reaching the moon in 8 hours. The 100 MWth nominal power is to insure getting above break-even conditions. It can be run at lower power. Thermal problems get worse with larger sizes. The usion reactor is a geometrical problem, more so than a ission reactor. Size does matter, and building a large unit insures that there is margin or error. The device uses a cusped usion coniguration. The earliest device was constructed in 1994 and named Wile Ball 2 or in short WB2. Another Polywell device designated as WB4 was constructed in These devices suered rom excessive electron losses. The WB6 device controlled the electron losses in Ater Bussard's death, the USA Navy went on to und the construction o a device designated as WB7. It was constructed, saw its irst plasma generation in January o 2008, and met expectations. The USA Navy was interested in the construction o a 100 MWth power reactor or naval propulsion applications.

22 Figure 11. Wile Ball toy. Figure 12. The Wileball cusped magnetic ields coniguration [14]. Figure 13. Cusped coniguration Wile Ball WB2, Source: MC2 Corporation [4].

23 Figure 14: Magnetic ields rom single and six current loops. Figure 15. Polywell usion Wile Ball WB4 device, Source: MC2 Corporation [4]. Figure 16. Wile Ball WB6 device achieved control o electron losses, Source: MC2 Corporation [4].

24 Figure 17. Wile Ball WB7 device using a He plasma. Source: MC2 Corporation [4]. WIFFLBALL XPRIMNTAL DVICS Bussard and his team at nergy/matter Conversion Corporation, over 20 years o research, explored the possibility o a neutronless pure usion process. The usion process avored by Bussard uses the pb 11 usion reaction producing a C 12 nucleus in its excited state. This excited C 12 nucleus decays to Be 8 and He 4. Be 8 within sec urther decays into two more He 4 nuclei. This is the only known nuclear-energy releasing process that releases usion energy and three helium atoms, but no initial neutrons. H + B C * C Be + He (3.76 MeV ) 12* Be He (2.46) MeV ) + He (2.46 MeV ) H + B 3 He MeV (35) This reaction appears to be radiation-ree, but even though it is 2-4 orders o magnitude less in terms o neutron production than the DT reaction, some side radiation producing reactions do occur, such as: H + B C + n 2.8 MeV H + B C + γ + 16 MeV D + B C + n MeV He + B N + n MeV He + B C + H He + B C + T

25 Some reactions will also occur with any B 11 impurity, and a ew energetic product alpha particles will interact with the wall materials, producing neutrons. For the overall reaction, the atomic masses o the isotopes are: m H amu 1 ( 1 ) = m B amu 11 ( 5 ) = m He amu 4 ( 2 ) = The Q-values o the overall reactions is: MeV Q = ( ) amu = 8.682MeV amu The pb 11 reaction is reported to have a resonance with a cross section o 0.1 b (barn) at 50 kv drive and an absolute peak o 1.2 b at 200 kv nominal drive voltage that could be used to enhance its occurrence. Six low energy electrons are released rom the ionized hydrogen and boron uel atoms which loose them around 0.67 kev. They thermalize quickly and replace other electron losses. The size o an eventual reactor using this reaction is estimated at 3 m 3 compared with 1 m 3 or a reactor using DT uel. The reactor power output increases with a stronger magnetic ield and a smaller radius, and is reported to scales as: or: P α B r = 0 0 P r B P r B where B is the magnetic ield strength r is the plasma radius The power gain is reported to scale as: G α 4 B r As a reerence value, we can take a power output o P 0 = 10 MWth with r 0 = 0.15 m plasma and a B 0 = 0.5 Tesla (T) magnetic ield. With 10 times the size o the 0.15 m plasma at 1.5 m, and ten times the 0.5 T magnetic ield at 5 T, the power would be 10 times the reerence value as:

26 P = = = MWth The most commonly studied usion process today is the reaction that occurs between deuterium and tritium DT reaction that produces helium and a ast neutron. Various magnetic coninement conigurations have been designed and developed over the years to contain the high-energy DT usion reaction. The Tokamak is one such magnetic coninement vessel, 30 m across by 110 eet tall. The Stellarator, the Tandem Mirror, and the Spheromak are other conigurations [1]. lectrostatic or electrodynamic coninement can easily achieve high temperature plasmas, but low density. On the other hand, magnetic coninement devices can achieve high densities, but high temperatures are diicult to obtain. lectrostatic and electrodynamic devices are compact in size, and hence cost less compared to the larger sizes o Tokamak and Stellarator devices. In the usion process, the reacting nuclei must overcome the Coulomb barrier repulsion between them. Since the Coulomb energy barrier increases in height with increasing atomic number, usion reactions with low Z number nuclei can occur easier than with heavier nuclei. The three possible reactions with hydrogen H nuclei: H+H D+ e H + D He + γ H + T He + γ ν e (36) where ν e is an electron neutrino, are known to have reaction cross sections too small to permit a net gain o energy at the technologically attainable temperatures. Thus one has to go to the next most abundant isotope, deuterium with its DD reaction possessing a neutron and a proton branches: D + D T (1.01 MeV )+ H (3.02 MeV ) MeV D + D He (0.82 MeV )+ n (2.45 MeV ) MeV (37) For irst generation usion reactors, the DT reaction is considered as the easiest to achieve, since it requires the lower plasma temperature to be achieved: D + T He (3.52 MeV)+ n (14.1 MeV) MeV (38) The MeV energy release rom this reaction is equivalent to 94,000 [kw.hr/gm] o DT uel. The He 3 produced in the neutron branch o the DD reaction can react with deuterium in a reaction producing charged particles and no neutrons as: D + He He (3.6 MeV )+ H (14.7 MeV )+18.3 MeV (39)

27 In a usion reactor using deuterium, the our last reactions should be expected to occur simultaneously in what is designated as the Catalyzed DD reaction, where six deuterons are used with a release o energy o 43.2 MeV, or 43.2/6 = 7.2 MeV per deuteron: Tritium and He 3 act as catalysts in the overall reaction. D + D T + H MeV D + D He + n MeV D + T He + n MeV D + He He + H MeV D 2 H + 2 He + 2 n MeV (40) For kinetic reactions temperatures below 50 kev the DHe 3 reaction is not signiicant and the energy release would be = 24.9 with each o the ive deuterons contributing an energy release o 24.9/5 = 4.98 MeV. D + D T + H MeV D + D He + n MeV D + T He + n MeV D H + He + He + 2 n MeV (41) Whereas deuterium (D) occurs in the water in the oceans and can be extracted through electrolysis or distillation, tritium (T) does not appreciably occur in nature since it is radioactive with a hal lie o years. Tritium has to be produced or bred rom the isotopes o lithium through interaction o the neutrons produced in the usion reactions with lithium surrounding the usion reaction in the orm o a blanket. Lithium or its compounds could also be used as a coolant absorbing the 14.1 MeV o energy carried out by the usion neutrons. Natural lithium occurs as 7.5 percent o the 3 Li 6 and 92.5 percent as the 3 Li 7 isotope. An exothermic reaction can occur by thermal neutrons with the irst isotope and an endothermic reaction by ast neutrons with the second isotope as ollows: Li + n (thermal) Li + n (ast) He (2.05 MeV)+ T (2.73 MeV) MeV He + n + T MeV (42) The DT reaction produces neutrons that can activate the structure o the reactor, creating some radioactivity. A ast neutron rom the usion reaction can in principle produce two tritons in these two reactions, sine it is re-emitted rom the ast reaction, and is available, i not absorbed by other nuclei, to induce the second reaction at low energy.

28 Some other potential usion reactions with their branching ratios estimated at their cross section peaks are shown in Table 6. Reactants Table 6: Fusion Reactions and their energy releases [13]. Branching Ratios [percent] Products nergy yield [MeV] nergy yield [Joule] 1D D T 3 (1.01 MeV) + 1 p 1 (3.02 MeV) x10-13 (proton branch) 1D D He 3 (0.82 MeV) + 0 n 1 (2.45 MeV) x10-13 (neutron branch) 1D T 3 2He 4 (3.54 MeV) + 0 n 1 (14.06 MeV) x D He 3 2He 4 (3.66 MeV) + 1 p 1 (14.6 MeV) x T T 3 2He n MeV x He T He 4 + p + 0 n MeV x He 4 (4.8 MeV) + 1 D 2 (9.5 MeV) x He 4 (0.5 MeV) + 0 n 1 (1.9 MeV) + 1 p x10-12 (11.9 MeV) 1p Li 6 2He 4 (1.7 MeV) + 2 He 3 (2.3 MeV) x p Li He MeV x Be n MeV x D Li He MeV x p 1 + B He MeV x He Li He 4 + p MeV n 1 (thermal)+ 3 Li 6 2He 4 (2.05 MeV) + 1 T 3 (2.73 MeV) x n 1 (ast)+ 3 Li 7 2He 4 (2.1 MeV) + 1 T 3 (2.7 MeV) x10-13 (endothermic 2He He 3 2He p p x10-12 The majority o the usion processes under investigation are expensive, costing billions o USA dollars; require giant machines; and oer no predictability. Nonetheless, we know that usion works because every star is a usion reactor. The usion reactors o the stars and the sun are held together by a direct orce ield. This works very well and eiciently. This orce ield is gravity. Gravitational orces between particles draw them directly together. Only one other orce is known to be like gravity: this is the electric ield orce or "coulomb" orce, between electrically-charged particles. Charged particles o opposite signs attract each other with direct orces; charged particles in electric ields eel orces directly along ield gradients. Thus, usion uel plasmas could be held together eiciently by electric orces and electric ields. This is called lectrostatic Inertial Coninement Fusion or lectrodynamic Inertial Coninement Fusion. Bussard was not the irst to try to create such a ield. One notable technique acted as a diode and utilized a spherical screen grid that was biased to a positive potential, thereby attracting electrons through the screen, producing a negative potential well. As the electrons passed through the screen, they slowed down as their kinetic energy was transormed into potential energy in the potential well, and ions could then be dropped into it at the edge, all down, and be recirculated back and orth. Any particles not reacting went back into the well. The only problem with this method was that the grid was not transparent. Because o the high interception rate on the grid, essentially all o the energy put into the electron acceleration went into the grid. nergy was lost and the grid melted.

29 Bussard's invention, however, removes the diode grid and replaces it with a magnetic ield. It is known that magnetic ields do not contain neutral plasmas very well, as in the case o the Tokamak. Magnetic ields, however, contain electrons very easily because electrons are extremely light. The basic approach o electrodynamic inertial usion ollows these steps: 1. A quasi-spherical cusped magnetic ield trap is generated using circular coils or magnets. These could permanent, electrical or superconductiong magnets. 2. nergetic electrons are injected into the cusp to orm a spherical negative potential well. 3. The usion ions trapped in this spherical well are ocused through the central region and oscillate across the core until they are used. 4. The device acts like a spherical colliding beam device. 5. Fuel gas is ed at the potential well edge. The usion products escape to the system walls. Ion usion power generation occurs in the central region. The deposited ions at the periphery can lead to direct energy conversion into electricity. 6. The electron drive power is decoupled rom the usion process. 7. The power balance is aected by injected electron losses; the main losses occurring through the magnetic cusps and to the device s walls. Thus the magnetic coninement o the electrons is critical to the success o the device. The Wile Ball (WB) concept insures cusp sealing and the magnetic insulation o the walls is important. The Wile Ball is a toy consisting o perorated spherical shell with a ball bearing bouncing within it. The electrons will bounce back and orth within the magnetic ball until they ind a hole at some bounce rom which they can escape. The recirculating machine with magnetically protected coil suraces is designated as a Magnetic Grid or Magrid (MG) eect machine and reduces power losses and increases the energy gain. The cusp axis low does not need to be a loss i the device is open and the electrons can recirculate along the cusp axes to the outside o the machine. The machine itsel is thus required to be placed at the center o a containing wall or shell that is kept at a potential below that o the machine proper, by the voltage used to drive the electron injectors. In 1994, Bussard successully demonstrated a Wile Ball (WB) coniguration, achieving a beta-1 condition. In 2005, he was able to magnetically insulate the electrons rom the walls via his Magrid transporter. arly prototype experienced some losses because the original coils touched one another, resulting in intersecting magnetic ields. This made the magnetic ield lines run into the metal vessel walls resulting in electron losses. Bussard realized that all the coil containers had to be conormal to the magnetic ields they produced. I he utilized circular toroidal coils spaced at the corners, the magnetic ields could be allowed to go out between the coils. Using such a device, that oered both the Wile Ball eect and the Magrid transporter, Bussard was able to achieve 1x10 9 usions/second or 0.25 milliseconds. The Wile Ball usion reactor design uses six metal rings joined to orm a cube with one ring on each side. For a 100 MWth reactor, each ring would be about a yard in diameter. ach ring would have copper wires wound into an electromagnet. Permanent magnets using rare earths alloys such as neodymium may be possibly used i enough strength can be achieved. The whole device is emplaced inside a vacuum chamber.

30 Upon being energized, the magnets generate a cusped magnetic ield into which electrons rom an electron gun are injected. The magnetic ield squeezes the electrons into a dense ball at the core creating a highly negatively charged region. At this point either deuterons or protons and B 11 nuclei are injected into the cusped magnetic ield. Because o their positive charge they accelerate towards the negative center. Most o them traverse the center toward the other side o the reactor. However, the negative charge o the electron ball pulls them back to the center. The process repeats itsel thousands o times until the deuterons o the boron nuclei and protons collide with a large enough requency to use together releasing energy in the process. In the case o the pb 11 reaction, the resulting 3 He 4 nuclei are deposited on an electrical grid orcing electrons to low creating an electrical current. This direct energy conversion process is much more eicient than the thermal conversion process that would be used in the DT usion cycle. Inertial lectrostatic Fusion oers the ollowing advantages: 1. The ability to construct small, compact power reactors that are 1-3 percent the size o current magnetic coninement reactors. 2. Clean, neutronless usion cycles using initially the semi-catalyzed or the catalyzed DD reaction and eventually the pb 11 usion reaction. 3. With reactions producing primarily charged particles, direct energy conversion with high eiciency can be contemplated. 4. Fusion reactions with charged particles can be the basis o a usion space propulsion system with high speciic impulse I sp [4]. 5. Relatively simple engineering with commercial viability within 6-10 years. 6. Low cost per unit in the range o $ million rom program inception to demonstration o net power production. 7. The use o sustainable abundant uel supplies as deuterium or boron in a pure usion device, in addition to thorium in a hybrid usion-ission device. Boron is one o the arth s most common and elements occurring with a natural abundance o 80.1 a/0 B 11 and 19.9 a/0 B 10 in boron. It occurs in the Mojave Desert in Caliornia and is used in the production o lame retardants, eye drops and lat panel displays. Thorium is a byproduct o the production o the rare earth elements and is 4 times as abundant as uranium in the arth s crust. XPRINC WITH CUSPD CONFIGURATIONS A characteristic problem with the cusped conigurations is that too many electrons escape rom the system. The cause is that the magnetic ield that created the electron ball at the center o the device also directed some electrons into the metallic walls o the electromagnetic coil containers and support structures. For viable cusped systems, the electron loss problems must be solved. It is easier to work with DD usion which requires 20 kev ions compared with pb 11 usion which requires ten times as much ion energy at 200 kev. Larger reactors would require larger high voltage power supplies, transormers and switches, as well as larger heat rejection and cooling systems. It must be admitted that no closed-box machine can ever yield net usion power. Open recirculating Magrid machines and systems are required. This is an immutable result o the

31 determination o losses o electrons in experiments, that show that losses to suraces that are not magnetically shielded must be kept to less than 10-5 or so o the cusp axis low o electrons in the WB eect at β = 1. This is impossible or two reasons: 1. It is not practically possible to cover all but 10-5 o the entire surace o a box containing the interior plasma, with magnetic oils that protect all o this surace, and 2. ven i this were possible, it is not possible to protect against losses directly along the cusp axes to the end plates that bound each cusp. These intrinsic losses are inherent in the magnetic topology o a closed box system and orever prevent this rom operating at small losses. The inescapable conclusion is that all polyhedral Polywell machines must operate as open recirculating devices, and that all such systems must have essentially no B-ield unshielded surace area available to electrons in the machine, itsel. This means that all structure containing B ield-generating coils must be conormal to the ields so produced, thus coil containers must have elliptical or circular cross-sections. I not, there will be large regions in which the B ields go into the metal suraces at an angle rather than circulate around such suraces. The electrons will simply drive along these intersecting B ields, directly into the metal, to yield excessive losses. Because o this, it is also evident that no matter their individual plan orm shape (i.e. circles, squares, triangles, polygons etc.) magnet coils must not touch at their adjacent corners, but must be spaced suiciently ar apart to ensure that no B ields intersect their containers. In this way, electrons can recirculate reely around all parts o each coil, and thus operate with minimal losses. These corner spacing line-like-cusps give local current lows that reduce the eective e- trapping actor (Gmj) in the machine interior rom that or pure Wile Ball (WB) behavior alone. However, the reduction is not suicient to prevent ready attainment o the e- density ratios inside/outside, required or avoidance o external arcing. Operating as recirculating (Magrid) machines means that there will be an external region between the machine and its containing exterior wall, in which Paschen arc breakdown can occur, unless both external electron and neutral gas density can be kept below some critical level. To do so requires large scale vacuum pumping in this exterior region. However, this level is so low that it cannot produce signiicant usion rates inside the machine, i the densities are allowed to be the same across the system. Thus, some means must be ound to ensure large electron density within the machine, while maintaining it at small levels outside. This requires that the ionization o neutral gas density within the machine be very large relative to that outside; and this can be attained only by neutral gas injection directly into the machine, ollowed by subsequent very rapid ionization o this gas, beore it can escape into the exterior region. In small machines this is diicult, as time scales or neutral transport to the exterior are measured in ractions o a millisecond, and dimensions within the machines are not suicient to allow rapid ionization at the limited electron currents and densities attainable. In large machines, such as power reactors, typically 2-3 m in diameter, with high power electron drives (e.g Amps at kv or DD and kv or pb 11 ), it is easy to show that almost total ionization o the inlowing neutral gas can be achieved in a ew centimeters o electron path length at the system edge, but small devices cannot reach this condition. Thus, in small systems there is a big incentive to attempt to uel the machine with ions injected rom ion guns placed on the cusp axes. This, however, poses the problem that the ion