Existing thermonuclear reactors are very complex, expensive, large, and heavy. During the past 30 years, innovations in mini and micro -thermo nuclear reactors have been advanced by senior author of this paper. These innovations dramatically decrease the size, weight and cost of thermonuclear reactor and its installation, and can be a viable propulsion system and electric generator. The major ob stacle in thermonuclear reactors is achiev ing the Lawson criterion , sufficient temperatures and pressure . This paper proposes that ignition can be achieved by a phenomenon called the bose condensate and the fermionic condensate; that when matter is cooled down to very low temperatures all the atoms behave as a single atom to some extent. This paper shall put forward the design and computations to demonstrate that it would be possible to achieve fission with only a microgram or even a nano -gram of uranium. This reaction can then effect fusion in a mini -thermocuclear reactor. Introduction For the last sixty years, scientists conducted R&D of a thermonuclear reactor that promises a true revolution in the energy industry. Fusion power is useful energy generated by nuclear fusion reactions. In this kind of reaction two light atomic nuclei fuse together to form a heavier nucleus and release energy. An experimental reactor, ITER, [1] was designed to produce several times more fusion power than the power into the plasma over many minutes. Construction of the facility began in 20 10, and the first plasma is expected in 2019. The problems with e xisting thermonuclear reactors is that they are very complex, expensive, large, and heavy. History of failed attempts to initiate thermonuclear fus ion. One of the earliest (in the late 1970's and early 1980's) serious attempts at an ICF design was Shiva , a 20-armed neodymium laser system bui lt at the Lawrence Livermore National Laboratory (LLNL) [2] that started operation in 1978. Shiva w as a "proof of concept" design, follo wed by the NOVA design with 10 times the p ower. [3] Funding for fusion research was sev erely constr ained in the 8 0's, but N OVA nevertheless suc cessful ly gathered enough information for a next generation ma chine whose goal was ignition. Al though net energy can be released even without ignition (the b reakeven point), ignition is considered necessary for a practical power system. The resulting design, now kno wn as the National Ignition Facility (NIF), [4] was complet ed a number of years ago at a cost of $3 .5 billion. It is a huge lab, 10 sto ries hi gh and bigger than a footb all field. Its massive build ing, heavily guarded and highly classified, stands on isolat ed ground inside the Lawrence Livermore National Laboratory. Their own staff is skeptical. "The scientific and technological progress in inertial confin ement fusion h as been subs tantial during the past decade. However, many of the technologies needed for an integrated in ertial fusion energy system are still at an early stage of 2 technolo gical maturity," the committee said in a st atement. "For all approaches to inertial fusion energy there remain critical scientific and engineering challenges." Stephen Bodner, retired director of the laser-fusion program at the Naval Research Laboratory in Washington and a longtime public critic of the ignition proj ect, said he was highly skeptical of the si gnificance of the latest development. Bodner has advocated a completely different approa ch to creating the unim aginably high temp eratures and pressures required for achieving fusion. In April, 2012 their team of physicists and engineers said they fired an array of 192 laser beams, fo cused "in pe rfect unison," and created a single pulse of energy that for 23 billionths of a second generated a thous and times more power than the entire United S tates consumes in a sin gle second. The experiment March 15 delivered to the center of the facility's target chamber 1.87 m egajoules of ultraviolet light, amount ing to 100 times more energy than any other laser system in the world. [5] "Was it just a gimmick shot, achieved without any real progress ... and d one only to demonst rate some sort of program progress?" he asked in an e-mail. "It app ears that they are just flounde ring about as th ey try to solve the m any basic problems with their ignition target design." The other very expensive European failed attempt is Hi PER (High Power laser Energy Research) [6] facility which has yet to demonstr ate the scientific proof of principle, but claims that their facility will move from the s cientific proof of principle st age to a commercial fusion reactor. Many scientists have long voiced doubts that the experiments could e ver yield enou gh energy to achieve ignition, and it 's still an open question wh ether thermonuclear reactions c an ever be achieved in the laboratory. [7] Theory of Current Thermonuclear Reactor It is not as easy as scientists previously thought. Fusion reactions require a very large amount of energy to initiate a reaction in order to overcome the so -called Coulomb barrier or fusion barrier energy . In stark contrast to attempts in deriving power f rom controlled fusion reactions in electrical power plants, fusion power has been demonstrated in various configurations of thermonuclear bombs. A modern thermonuclear weapon weighing little more than 2,400 pounds (1,100 kg) can produce an explosive force comparable to the detonation of more than 1.2 million tons (1.1 million tonnes) of TNT. Thus, even a small nuclear device no larger than traditional bombs can devastate an entire city by blast, fire and radiation. The Teller – Ulam design employs hydrogen fu sion, though in most applications the bulk of its destructive energy comes from uranium fission, not hydrogen fusion. Today virtually all the nuclear weapons deployed by the five major nuclear -armed nations use the Teller –Ulam design. Its essential feature s, which officially remained secret for nearly three decades, are: 1) separation of stages into a triggering "primary" explosive and a much more powerful "secondary" explosive, 2) compression of the secondary by X -rays coming from nuclear fission in the pr imary, a process called the "radiation implosion" of the secondary, and 3) heating of the secondary, after cold compression, by a second fission explosion inside the secondary. For more than half a century, vast amount of power generated by these explosion s has fired the imagination of scientists to harness this energy for electricity power generation. In thirty years, scientists have increased the Lawson criterion of the ICF and tokamak installations by tens of times. It is the threshold of temperatures a nd pressure Lawson number – 3 lower the better. Unfortunately, all current and some new installations (ICF and totamak) have a Lawson criterion that is tens of times lower than is necessary (Figure 1). Figure 1 . Parameter space occupied by inertial fusion energy and magnetic fusion energy devices. The regime allowing thermonuclear ignition with high gain lies near the upper right corner of the plot. The key to practical fusion power is to select a fuel that requires the minimum amount of energy to start, th at is, the lowest barrier energy. The best fuel from this standpoint is a one -to- one mix of deuterium and tritium; both are heavy isotopes of hydrogen. The D -T (Deuterium and Tritium) mix has a low barrier. In order to create the required conditions, the f uel must be heated to tens of millions of degrees, and/or must be compressed to immense pressures. To accomplish this, at present, D -T is used by two main methods of fusion: inertial confinement fusion (ICF) and magnetic confinement fusion (MCF) In inertial confinement fusion (ICF), nuclear fusion reactions are initiated by heating and compressing a target. The target is a pellet that most often contains deuterium and tritium (often only micro or milligrams). Intense laser or ion beams are used for c ompression. The beams explosively detonate the outer layers of the target. That accelerates the underlying target layers inward, sending a shockwave into the center of pellet mass. If the shockwave is powerful enough and if the center has high enough densi ty, some of the fuel will be heated enough to cause fusion reactions. In a target which has been heated and compressed to the point of thermonuclear ignition, energy can then heat surrounding fuel to cause it to fuse as well, potentially releasing tremendo us amounts of energy. Magnetic confinement fusion (MCF). Since plasmas are very good electrical conductors, magnetic fields can also confine fusion fuel. A variety of magnetic configurations can be used, the basic distinction being between magnetic mirror confinement and toroidal confinement, especially tokamaks and stellarators. 4 For the D -T reaction, the physical value is about , (1) where T is temperature, [KeV], 1 eV = 1.16 104 oK; ne is matter density, [1/сm3]; n is matter density, [1/m3];  is time, [s]. Last equation is in metric system. The thermonuclear reaction of 2H + 3D realizes if L > 1020 in CI (meter, kilogram, second) units or L > 1014 in 'cgs' (centimeter, gram, second) units. This number has not yet been achieved in any reactor, although the latest generations of machines have come close. The Lawson criterion applies to inertial confinement fusion as well as to magnetic confinement fusion but is more usefully expressed in a different form. Whereas the energy confinement time in a magnetic system is very difficult to predict or even to establish empirically, in an inertial system it must be on the order of the time it take s sound waves to travel across the plasma: (2) where  is time, s; R is distance, m; k =1.38.10-23 J/K is Boltzmann constant; mi is mass of ion, kg. Following the above derivation of the limit on neτE, we see that the product of the density and the radius must be greater than a value related to the minimum of T3/2/<σv> (here  is Boltzmann constant, v is ion speed). This condition is traditionally expr essed in terms of the mass density ρ: ρR > 1 g/cm ². To satisfy this criterion at the density of solid D+T (0.2 g/cm³) would require implausibly large laser pulse energy. Assuming the energy required scales with the mass of the fusion plasma (Elaser ~ ρR3 ~ ρ-2), compressing the fuel to 103 or 104 times solid density would reduce the energy required by a factor of 106 or 108, bringing it into a realistic range. With a compression by 103, the compressed density will be 200 g/cm³, and the compressed radius can be as small as 0.05 mm. The radius of the fuel before compression would be 0.5 mm. The initial pellet will be perhaps twice as large since most of the mass will be ablated during the compression. The fusion power density is a good figure of merit to deter mine the optimum temperature for magnetic confinement, but for inertial confinement the fractional burn -up of the fuel is probably more useful. The burn -up should be proportional to the specific reaction rate ( n²<σv>) times the confinement time (which scal es as T1/2) divided by the particle density n: burn -up fraction ~ n²<σv> T-1/2 / n ~ (nT) (<σv>/ T3/2) Thus the optimum temperature for inertial confinement fusion is that which maximizes <σv>/ T3/2, which is slightly higher than the optimum temperature for magnetic confinement. Confinement refers to all the conditions necessary to keep plasma dense and hot long enough to undergo fusion: • Equilibrium: There must be no net forces on any part of the plasma, otherwise it will rapidly disassemble. The exception, of course, is inertial confinement, where the relevant physics must occur faster than the disassembly time. units CIin)10 10( orunits cgs""in)10 10( 21 2015 14 ==  nTLTnLe imkTR / 5 • Stability: The plasma must be so const ructed that small deviations are restored to the initial state, otherwise some unavoidable disturbance will occur and grow exponentially until the plasma is destroyed. • Transport: The loss of particles and heat in all channels must be sufficiently slow. The word "confinement" is often used in the restricted sense of "energy confinement". To produce self -sustaining fusion, the energy released by the reaction (or at least a fraction of it) must be used to heat new reactant nuclei and keep them hot long enough that they also undergo fusion reactions. If more than about a milligram of fuel is used, the explosion would destroy the machine, so controlled thermonuclear fusion using inertial confinement causes tiny pellets of fuel to explode several times a second. T o induce the explosion, the pellet must be compressed to about 30 times solid density with energetic beams. If the beams are focused directly on the pellet, it is called direct drive , which can in principle be very efficient, but in practice it is difficul t to obtain the needed uniformity. An alternative approach is indirect drive , in which the beams heat a shell, and the shell radiates x -rays, which then implode the pellet. The beams are commonly laser beams, but heavy and light ion beams and electron beam s have all been investigated and tried to one degree or another. They rely on fuel pellets with a "perfect" shape in order to generate a symmetrical inward shock wave to produce the high -density plasma, and in practice these have proven difficult to produc e. In fusion research, achieving a fusion energy gain factor Q = 1 is called breakeven and is considered a significant although somewhat artificial milestone . Ignition refers to an infinite Q, that is, a self -sustaining plasma where the losses are made up for by fusion power without any external input. In a practical fusion reactor, some external power will always be required for things like current drive, refueling, profile control, and burn control. A value on the order of Q = 20 will be required if the plant is to deliver much more energy than it uses internally. In a fusion power plant, the nuclear island section of a nuclear power plant where nuclear reactions happen , has a plasma chamber with an associated vacuum system, surrounded by a plasma -facing components (first wall and diverter ) maintaining the vacuum boundary and absorbing the thermal radia tion coming from the plasma, surrounded in turn by a blanket where the neutrons are absorbe d to breed tritium and heat a working fluid that transfers the power to the balance of plant. If magnetic confinement is used, a magnet system, using primarily cryogenic superconducting magnets, is needed, and usually systems for heating and refueling the plasma and for driving current. In inertial confinement, a driver (laser or accelerator) and a focusing system are needed, as well as a means for forming and positioning the pellets . Methods in Current Reactors In order to be useful as a source of energy, a fusion reaction must satisfy several criteria. It must: • be exothermic - This may be obvious, but it limits the reactants to the low Z (number of protons) side of the curve of binding energy. It also makes helium 4He the most common product because of its extraordinarily tight binding, although 3He and 3H also show up. 6 • invol ve low Z nuclei - This is because the electrostatic repulsion must be overcome before the nuclei are close enough to fuse. • have two reactants - At anything less than stellar densities, three body collisions are too improbable. It should be noted that in in ertial confinement, both stellar densities and temperatures are exceeded to compensate for the shortcomings of the third parameter of the Lawson criterion, ICF's very short confinement time. • have two or more products - This allows simultaneous conservation of energy and momentum without relying on the (weak!) electromagnetic force. • conserve both protons and neutrons - The cross sections for the weak interaction are too small. Few reactions meet these criteria. The following are those with the largest cros s-sections: Table 1. Suitable reactions for thermonuclear fusion p (protium), D (deuterium), and T (tritium) is shorthand notation for the main three isotopes of hydrogen. For reactions with two products, the energy is divided between them in inverse proportion to their masses, as shown. In most reactions with three products, the distribution of energy varies. For reactions that can result in more than one set of products, the branching ratios are given. Some reaction candidates can be eliminated at once. The D -6Li reaction has no advantage compared to p -11B because it is roughly as difficult to burn but produces substantially more neutrons through D -D side reactions. There is also a p -7Li reaction, but the cross -section is far too low except possible for Ti > 1 MeV, but at such high temperatures an endothermic, direct neutron -producing reaction also becomes very significant. Finally there is also a p -9Be reaction, which is not only difficult to burn, but 9Be can be easily induced to split into two alphas and a neutron. In addition to the fusion reactions, the following reactions with neutrons are important in order to "breed" tritium in "dry" fusion bom bs and some proposed fusion reactors: 7 n + 6Li → T + 4He, n + 7Li → T + 4He + n. To evaluate the usefulness of these reactions, in addition to the reactants, the products, and the energy released, one needs to know something about the cross section. Any giv en fusion device will have a maximum plasma pressure that it can sustain, and an economical device will always operate near this maximum. Given this pressure, the largest fusion output is obtained when the temperature is selected so that <σv>/T² is a maxim um. This is also the temperature at which the value of the triple product nTτ required for ignition is a minimum. This chosen optimum temperature and the value of <σv>/T² at that temperature is given for a few of these reactions in the following table 2. Table 2. Optimum temperature and the value of <σv>/T² at that temperature fuel T [keV] <σv>/T² [m³/s/keV²] D-T 13.6 1.24×10-24 D-D 15 1.28×10-26 D-3He 58 2.24×10-26 p-6Li 66 1.46×10-27 p-11B 123 3.01×10-27 Note that many of the reactions form chains. For instance, a reactor fueled with T and 3He will create some D, which is then possible to use in the D + 3He reaction if the energies are "right". An elegant idea is to combine the reactions (8) and (9). The 3He from reaction (8) can react with 6Li in reaction (9) before completely thermalizing. This produces an energetic proton which in turn undergoes reaction (8) before thermalizing. A detailed analysis shows that this idea will not really work well, but it i s a good example of a case where the usual assumption of a Maxwellian plasma is not appropriate. Any of the reactions above can, in principle, be the basis of fusion power production. In addition to the temperature and cross section discussed above, we mus t consider the total energy of the fusion products Efus, the energy of the charged fusion products Ech, and the atomic number Z of the non -hydrogenic reactant. Specification of the D -D reaction entails some difficulties, though. To begin with, one must ave rage over the two branches (2) and (3). More difficult is to decide how to treat the T and 3He products. T burns so well in a deuterium plasma that it is almost impossible to extract from the plasma. The D -3He reaction is optimized at a much higher tempera ture, so the burn -up at the optimum D -D temperature may be low, so it seems reasonable to assume the T but not the 3He gets burned up and adds its energy to the net reaction. Thus we will count the D -D fusion energy as Efus = (4.03+17.6+3.27)/2 = 12.5 MeV and the energy in charged particles as Ech = (4.03+3.5+0.82)/2 = 4.2 MeV. Another unique aspect of the D -D reaction is that there is only one reactant, which must be taken into account when calculating the reaction rate. 8 With this choice, we tabulate param eters for four of the most important reactions (table 3). Table 3. Parameters of the most important reactions Fuel Z Efus [MeV] Ech MeV] Neutronicity D-T 1 17.6 3.5 0.80 D-D 1 12.5 4.2 0.66 D-3He 2 18.3 18.3 ~ 0.05 p-11B 5 8.7 8.7 ~ 0.001 The last column is the neutronicity of the reaction, the fraction of the fusion energy released as neutrons. This is an important indicator of the magnitude of the problems associated with neutrons like radiation damage, biological shielding, remote handli ng, and safety. For the first two reactions it is calculated as ( Efus-Ech)/Efus. For the last two reactions, where this calculation would give zero, the values quoted are rough estimates based on side reactions that produce neutrons in a plasma in thermal equilibrium. Of course, the reactants should also be mixed in the optimal proportions. This is the case when each reactant ion plus its associated electrons accounts for half the pressure. Assuming that the total pressure is fixed, this means that density of the non -hydrogenic ion is smaller than that of the hydrogenic ion by a factor 2/( Z+1). Therefore the rate for these reactions is reduced by the same factor, on top of any differences in the values of <σv>/T². On the other hand, because the D-D reaction has only one reactant, the rate is twice as high as if the fuel were divided between two hydrogenic species. Thus, there is a "penalty" of (2/(Z+1)) for non -hydrogenic fuels arising from the fact that they require more electrons, which take up pressure wit hout participating in the fusion reaction. There is, at the same time, a "bonus" of a factor 2 for D -D due to the fact that each ion can react with any of the other ions, not just a fraction of them. We can now compare these reactions in the following tabl e 4. Table 4. Comparison of reactions fuel <σv>/T² penalty/ bonus reactivity Lawson criterion power density D-T 1.24×10-24 1 1 1 1 D-D 1.28×10-26 2 48 30 68 D-3He 2.24×10-26 2/3 83 16 80 p-11B 3.01×10-27 1/3 1240 500 2500 The maximum value of <σv>/T² is taken from a previous table. The "penalty/bonus" factor is that related to a non -hydrogenic reactant or a single -species reaction. The values in the column "reactivity" are found by dividing (1.24×10-24 by the product of the second and third 9 columns. It indicates the factor by which the other reactions occur more slowly than the D -T reaction under comparable conditions. The column "Lawson criterion" weights these results with Ech and gives an indication of how much more difficult it is to achieve ignition with these reactions, relative to the difficulty for the D -T reaction. The last column is labeled "power density" and weights the practical reactivity with Efus. It indicates how much lower the fusion power density of the other reactions is compa red to the D -T reaction and can be considered a measure of the economic potential. Bremsstrahlung (Brake) Losses. The phenomenon , Bremsstrahlung, was discovered by Nikola Tesla (1856 -1943) during high frequency research he conducted between 1888 and 1897. This "braking radiation", is electromagnetic radiation produced by the acceleration of a charged particle, such as an electron, when deflected by another charged particle, such as an atomic nucleus. Bremsstrahlung is free- free radiation ; radiation th at arises as a result of a charged particle that is free both before and after the deflection (acceleration) that causes the emission. Strictly speaking, bremsstrahlung refers to any radiation due to the acceleration of a charged particle, which includes s ynchrotron radiation; however, it is frequently used (even when not speaking German) in the more literal and narrow sense of radiation from electrons stopping in matter. Table 5. Rough optimum temperature and the power ratio of fusion and Bremsstrahlung radiation lost Fuel Ti (keV) Pfusion/PBremsstrahlung D-T 50 140 D-D 500 2.9 D-3He 100 5.3 3He-3He 1000 0.72 p-6Li 800 0.21 p-11B 300 0.57 The ions undergoing fusion will essentially never occur alone but will be mixed with electrons that neutralize the ions' electrical charge and form a plasma. The electrons will generally have a temperature comparable to or greater than that of the ions, so they will collide with the ions and emit Bremsstrahlung. The Sun and stars are opaque to Bremsstrahlung, but essentially any terrestrial fusion reactor will be optically thin at relevant wavelengths. Bremsstrahlung is also difficult to reflect and difficult to convert directly to e lectricity, so the ratio of fusion power produced to Bremsstrahlung radiation lost is an important figure of merit. This ratio is generally maximized at a much higher temperature than that which maximizes the power density (see the previous subsection). Th e following table shows the rough optimum temperature and the power ratio at that temperature for several reactions. The actual ratios of fusion to Bremsstrahlung power will likely be significantly lower for several reasons. For one, the calculation assume s that the energy of the fusion products is transmitted completely to the fuel ions, which then lose energy to the electrons by collisions, which in turn lose energy by Bremsstrahlung. However, because the fusion products move much 10 faster than the fuel ion s, they will give up a significant fraction of their energy directly to the electrons. Secondly, the plasma is assumed to be composed purely of fuel ions. In practice, there will be a significant proportion of impurity ions, which will lower the ratio. In particular, the fusion products themselves must remain in the plasma until they have given up their energy, and will remain some time after that in any proposed confinement scheme. Finally, all channels of energy loss other than Bremsstrahlung have been ne glected. The last two factors are related. On theoretical and experimental grounds, particle and energy confinement seem to be closely related. In a confinement scheme that does a good job of retaining energy, fusion products will build up. If the fusion p roducts are efficiently ejected, then energy confinement will be poor, too. The temperatures maximizing the fusion power compared to the Bremsstrahlung are in every case higher than the temperature that maximizes the power density and minimizes the require d value of the fusion triple product (Lawson criterion). This will not change the optimum operating point for D -T very much because the Bremsstrahlung fraction is low, but it will push the other fuels into regimes where the power density relative to D -T is even lower and the required confinement even more difficult to achieve. For D -D and D -3He, Bremsstrahlung losses will be a serious, possibly prohibitive problem. For 3He-3He, p -6Li and p -11B the Bremsstrahlung losses appear to make a fusion reactor using these fuels impossible. In a plasma, the free electrons are constantly producing Bremsstrahlung in collisions with the ions. The power density of the Bremsstrahlung radiated is given by . (3) Te is the electron temperature, α is the fine structure constant, h is Planck's constant, and the "effective" ion charge state Z eff is given by an average over the charge states of the ions: Zeff = Σ ( Z² nZ) / ne (4) This formula is derived in "Bas ic Principles of Plasmas Physics: A Statistical Approach" by S. Ichimaru, p. 228. It applies for high enough Te that the electron deBroglie wavelength is longer than the classical Coulomb distance of closest approach. In practical units, this formula gives PPBr= = (1.69×10-32 /W cm-3) (ne/cm-3)2 (Te/eV)1/2 Zeff =, (5) = (5.34×10-37 /W m-3) (ne /m-3)2 (Te /keV)1/2 Zeff , where Wcm-3, cm-3, eV, Wm-3, m-3, keV are units of corresponding magnitudes. For very high temperatures there are relativistic corrections to this formula, that is, additional terms of order Te/mec2. Bolonkin’s Thermonuclear Reactor As early as 1983, Bolonkin [8] offer ed several innovations that he first suggested public ly for the AB multi-reflex engine, space propulsion, getting energy from plasma, etc. Over the years Bolonkin refined his design of mini and micro thermonuclear reactors for the production of electricity and for space craft propulsion. [9] [10] [11] [12] [13] [14] [15] [16]. Bolonkin’s books in which he detailed facets of is innovation incl ude [17] [8] [18] [19] and book sections include [20]. These innovations are based on Bolonkin’s early patents [21] [22] [23] eff ee eBr ZTn mhP2/12 2/323 316= 11 [24] [25] [26] [27] [28] [29] [30] [31] [32] [33] [34]; classified report [35]; and papers presented in The World Space Congress [36] [37] [38] and International Astronautical Congress [39], and American Institute of Aeronautics and Astronautics Conference and Journal [40] [41]. The components of the devices proposed in this paper have been detailed in Bolonkin’s previous papers. The configuration in the micro -thermonuclear AB- Reactor utilizes a very small fuel pellet that uses plasma confinement generated by multi -reflection of laser beam or its own magnetic field. The Lawson criterion increases by hundreds of times. Bolonkin also suggest ed a new method of heating the power - making fuel pellet by outer electric current as well as new direct method of transformation of ion kinetic energy into harvestable electricity. These offered innovations dramatically decrease the size, weight and cost of thermonuclear reactor, installation, propulsion system and electric generator. In 2006, Bolonkin researched the efficiency of these innovations for two types of the micro -thermonuclear reactors: multi -reflection reactor (ICF) and self-magnetic reactor (MCF). [42] In 2007, Bolonkin developed and researched mini -sized Micro - AB Thermonuclear Reactors for space propulsion and space power systems. [43] These small engines directly convert the high speed charged particles produced in the thermonuclear reactor into vehicle thrust or vehicle electrici ty with maximum efficienc y. The simplest AB -thermonuclear propulsion offered allows spaceships to reach spe eds of 20,000 - 50,000 km/s (1/6 of light speed) for fuel ratio 0.1 and produces a huge amount of useful electric energy. In 2008, Bolonkin offered a new kind of thermonuclear reflect reactor. [44] The remarkable feature of this new reactor is a three net AB reflector, which confines the high temperature plasma. The plasma loses part of its energy when it contacts with the net but this loss can be compensated by an additional permanent plasma heating. When the plasma is rarefied (has a small density), the heat flow to the AB reflector is not large and the temperature in the triple reflector net is lower than 2000 - 3000 K. This offered AB -reactor has significantly less power than the currently contemplated power reactors with magnetic or inertial confinemen t (hundreds -thousands of kW, not millions of kW). The author has made a number of innovations in this reactor, researched its theor y, developed methods of computation, made a sample computation of typical project. The main point of preference for the offer ed reactor is its’ likely cheapness as a power source. In 2013, Bolonkin propos ed design for a mini thermonu clear reactor [45] which uses a method bas ed upon a series of i mportant innov ations. A cumulative explosion presses a capsule with nuc lear fuel up to 100 thous ands of atmosph eres, the explosive electric generator heats the capsule/pellet up to 100 m illion d egrees and a special capsule and a special cover which keeps these pressure and temp erature in capsule up to 0.001 s ec. which is sufficient for Lawson criteria for ignition of th ermonu clear fuel. The propos ed A-B Reactor is dif ferent from pr esent magnetic confinement reactor. Th at is smaller because AB-self-magnetic reactor works using a s mall fuel capsule and do es not require las er confin ement. In present-day MCF reactor, the rare fuel gas (D+T) fills all volume of large chamber. In AB-Reactor the fuel is placed in to a sm all capsule under high pressure (or, as solid, liquid or frizzed fuel under conventional pressure). In this case the fuel densi ty can reach n = 1026 1027 1/m3 (or solid, liquid, frozen fuel may be inside condu ctive matter, n = 1028 1029 1/m3). That is enough for thermonuclear ignition and k eeping plasma under the radiation p ressure and magnetic pressure. For current M CF the m agnetic intensity is 5 T. For AB-Self-MCF the m agnetic intensi ty may be about 10 T and mor e. For AB- reactor the shaper pressure is about 1 010 1011 N/m2 (0.1 – 1 million atm). 12 Major advantages of these reactors/bombs is its very low cost, di mension, w eight and easy production, whi ch does not require a complex indust ry. The same method may be used for thermonuclear engine for electric energy plants, sh ips, aircrafts, tr acks and ro ckets. While other proprietary methods to achieve ignition may be presented in future papers, this paper proposes that ignition can be achieved by a phenomena called the bose condensate and the fermionic condensate; that when matter is cooled down to very low temperatures all the atoms behave as a single atom to some extent. This paper shall put forward the design and computations to demonstrate that it would be possible to achieve fission with only a microgram or even a nano -gram of uranium. Theory of Bolonkin’s 2013 mini thermonuclear : Estimations. The parameters of the offered installation may be estimated by the equation above and below. 1. Energy is needed for heating of plasma for nuclear reaction is computed by equation (1). For fuel D+T it is about Te = 0.34MeV. This energy nuclear has in temperature Tk = 1.16.104 Te = 4.108K. In reality this temperature is less in some times (see fig. 3). 2. Energy of nuclear explosion En , [MeV] () ,) (, 2/1 2 11 pnmAAMn nVE E+= = (6) where n is number of nuclears into unit of volume, m-3 or cm-3 (for example, 1 cm3 fuel mixture D+T contains about about 1021 nuclears in room temperature under 100 atm pressure); V is volume before nuclear reaction, m3 or cm3; E1 is energy couples of nuclear in MeV. For example, couple nuclears D+T gives E1 = 3.5+14.1 = 17.6 MeV energ y (see. Table 1, line 1). It is in 52 times more than energy needs for reaction; M is mass of the nuclear fuel in unit of volume, kg/cm3 or kg/m3 ; A is number nucleons in reactants ( A = 2 for D, A = 3 for T); mp = 1.67.10-27 kg is mass of nucleon. 2. Ma ximal pressure and energy for high speed (6 km/s) detonation explosive (for example TNT): ,2. 8314, ,  = == =u u us RRpM RvpT Ep (7) where p is gas pressure N/m2; v is gas volume, m3; T is gas temperature, K; M is explosive mass, kg; Es is specific energy of explosive, J/kg (for TNT Es = 5.4 MJ/kg); γ is specific weight of explosive, kg/m3; Ru is heat constant, J/kg.K; μ is average molar weight (for CO 2 μ = 46, for H2O μ = 18; w is outer work (energy of process, J). For example, TNT can produce in explosion p = 1010 N/m2 = 105 atm and temperature 20,000oK; E is energy, J; η is coefficient efficiency. 3. For computation of explosion extension in the impulse electric generator may be used the equations of adiabatic process in gas: , , , , , 001 211 12 21 12 21 22 11EE EpvEpp vv TT vv ppvp vpkkk k k k −==   =   =   = =−−  13 () , 11, 11,1, 111 12 111 21 2 1 12 11        −−=        −−=−−=   −−=−−kkk u u pp kvpwvv kRw TTkRwTT kvpw (8) where lower index “ 1” means the first state of gas, “ 2” means the second state of gas; k ≈ 1.4 is adiabatic constant, for very high temperature k → 1. 4. Estimation the explosive electric generator: () ,0 , , , , ,) ( ,2 0 2 1 =+ = ==−=−= = iR Lidtd lSNLslRREidtdE i WSB ss n   (9) where Ф is magnetic flux throw area S, Wb; Bn magnetic induction (intensity) perpendicular S, T; W is work of magnetic flow, J; i is electric current, A; E is electromotive force (voltage), V; R is electric resistance, Ω; ρ if specific electric resistance, for copper ρ = 1.75.10-6 Ω.cm; l is length of wire, cm; s is cross -section of wire, cm2; L is inductance of solenoid; μ0 = 4π.10-7 is magnetic constant; N is number of coils in solenoid; ls is length of solenoid, m; Ss is cross -section of solenoid, m2; t is time, s. 5. Increasing and decreasing current in the electric circuit ,2, , , exp12 0iL WRLT whereTtifi of forturnTt REi turnonFor = =   −=   −−  = (10) where io is initial current, A; W is work for state permanent current, J. 6. Ion collision rate and the mean free path ,ln1004.2 , ln 108.442 13 2/1 2/1 4 8 == =− − − ii ii i i inZT Vl T n Z  (11) where lower index “ i” means ion. 7. Safety electric current in wire: ()  5.0/   ++=tmmrTCT Cjw p pm  , (12) where j is electric current density, A/m2; γ – mass density of wire, for cupper γ = 8320 kg/m3; Cpm is heat capacity, for cupper Cpm = 0.39 kJ/kg.K; ρ is electric resistance, for cupper ρ = 1.75.10-8 Ω.m; ∆ T is safety temperature, K; Cp is heat capacity of cooling liquid, for water Cp = 4.19 kJ/kg; r is heat evaporation of the cooling liquid, for water r = 2260 kJ/kg.K; t is safety time, sec; mw/m is mass ratio of cooling liquid to wire mass. Example: for t = 0.003 sec, ∆ T = 80 oK, we get j = 3.26.103 A/mm2 without cooling. 8. Estimation of neutron penetration: , /1nn l= (13) where l is path of penetration, cm; n is density of material, cm-3; σ is cross section area of nuclear, σn ≈ 10-24 cm2. 14 9. Required thickness of the shell: ,2pd= (14) where p is pressure, N/m2; d is diameter of cylinder, m; σ is safety tensile stress, N/m2. Computations List of Main Equations Below are the main equations for estimation of benefits from the offered innovations. 1. Energy, E, is needed for Thermonuclear Reaction 2 1 031519 02 21 221 , , 10)5.12.1(, 10 625.0 1, , , 0 rrrNZA A reV JreZZkE drF ErQQkF ir +=+= == = = = −  (15) where k = 9109 constant; Z1, Z2 are charge state of 1 and 2 particles respectively; e = 1,610-19 C is charge of electron; ro = r1 + r2 is sum of radius of nuclear force, m; A is number of element; F is force, N; E is energy, J; Q is charge of particles. For example, for reaction H+H (hydrogen, Z1 = Z 2 =1, ro  210-15 m) this energy is  0.7 MeV or 0.35 MeV for every particle. This energy nuclear has in temperature Tk = 1.16.104 Te = 4.108K. The real energy is about 30 times less because part of the particles has more average speed and there is a tunnel effect. 2. Energy Needed for Ignition. Figure 3 shows a magnitude n (analog of Lawson criterion) required for ignition. 15 Fig. 3. Ration rate versus temperature in K. 3. Radiation energy from hot solid black body is (Stefan -Boltzmann Law): , (16) where E is emitted energy, W/m2;  = 5.6710-8 - Stefan -Boltzmann constant, W/m2 oK4; T is temperature in oK. 4. Wavelength corresponded of maximum energy density (Wien's Law) is (17) where b = 2.897810-3 is constant, m oK; T is temperature, oK;  is angle frequency of wave, rad/s. 5. Pressure of light for Single Full Reflection is , (18) where F - pressure, N/m2; c = 3108 is light speed, m/s, E is radiation power, W/m2. If plasma does not reflect radiation the pressure equals F = E/c . (19) 6. Pressure for Plasma Multi -Reflection [23-25] is , (20) 4T E= 002, ==Tb cE F /2=     −=q cEF12 2 16 where q is plasma reflection coefficient. For example, if q = 0.98 the radiation pressure increases by 100 times. We neglect losses of prism reflection. 7. The Bremsstrahlung (Brake) Loss energy of plasma by radiation is (T > 106 oK) (21) where PBr is power of Bremsstrahlung radiation, W/m3; ne is number of particles in m3; T is a plasma temperature, KeV; Z is charge state; Zeff is cross -section coefficient for multi -charges ions. For reactions H+D, D+T the Zeff equals 1. That loss may be very much. For some reaction they are more than useful nuclear energy and fusion nuclear reaction may be stopped. The Bremsstrahlung emission has continuous spectra. 8. Electron Frequency in Plasma is units CIin )(4.56 or units, cgs""in)(1064.5 or,4 2/12/1 42/12 nnmen pee pe ee pe ==   =  (22) where pe is electron frequency, rad/s; ne is electron density, [1/cm3]; n is electron density, [1/m3]; me = 9.1110-28 is mass of electron, g; e = 1.610-19 is electron charge, C. The plasma is reflected an electromagnet radiation if frequency of electromagnet rad iation is less than electron frequency in plasma,  < pe. That reflectivity is high. For T > 15106 oK it is more than silver and increases with plasma temperature as T3/2. The frequency of laser beam and Bremsstrahlung emission are less than electron frequency in plasma. 9. The Dep th of Penetration of outer radiation into plasma is . [cm] (23) MEAUSRE OF OPACITY For plasma density ne = 1022 1/cm3 dp = 5.3110-6 cm. 10. The Gas (Plasma) Dynamic Pressure, pk , is (24) where k = 1.3810-23 is Boltzmann constant; Te is temperature of electrons, oK; Ti is temperature of ions, oK. These temperatures may be different; n is ion density, 1/m3; pk is plasma pressure, N/m2. 11. The gas pressure , p, is = =− e z eff eff e Br nnZ Z ZTn P /) ( where, 1034.52 5.02 37 2/1 51031.5−==e pep ncd nkT p TT TTnk pk k e i e k 2 then if) ( = = += 17 , (25) Here n is gas density in 1/m3. 12. The magnetic p m and electrostatic pressure , ps, are (26) where B is electromagnetic induction, Tesla; 0 = 410-7 electromagnetic constant; 0 = 8.8510-12 , F/m, is electrostatic constant; ES is electrostatic intensity, V/m. 13. Ion thermal velocity is , (27) where  = m i /mp , mi is mass of ion, kg; mp = 1.6710-27 is mass of proton, kg. 14. Transverse Spitzer plasma resistivity , (28) where ln  = 5  15  10 is Coulomb logarithm, Z is charge state. 15. Reaction rates <v> (in cm3 s-1) averaged over Mexwellian distributions for low energy (T < 25 keV) may be represent ed by (29) where T is measured in keV. 16. The power density released in the form of charged particles is (30) Here in PDD equation it is included D + T reaction. Description of Innovation Design and Innovations If instead of the reactions of a D + T reaction detailed above, this paper proposes achieving fission using bose condensate and fermionic condensate of U233. To date the largest nkT p32= 2 0 02 21,2S s m E pBp = = cm/s 1079.92/12/1 52/1 i ii Ti TmkTv−=   =  cmTZ0.1or cm , ln 1003.13/22/3 2 =− − ⊥   T Z ,scm) 94.19 exp( 1068.3 )(,scm) 76.18 exp( 1033.2 )( 13 3/1 3/2 1213 3/1 3/2 14 − − −−− − −− − =− = T TT T DTDD  3 123 133 2 13 cmW, )( 109.2cmW,)( 106.5cmW,)( 103.3 3 3 3− −− −− − === DHe HeD DHeTD T D DTDD D DD nn Pnn Pn P  18 atom which was shown to be stable in a condensate is an isotope Er168. As these are relatively newly researched areas, it will be delineated in some detail. In quantum mechanics and particle physics, spin is an intrinsic form of angul ar momentum carried by elementary particles, composite particles (hadrons), and atomic nuclei. As the name suggests, spin was originally conceived as the rotation of a particle around some axis. This picture is correct so far as spin obeys the same mathema tical laws as quantized angular momenta do. On the other hand, spin has some peculiar properties that distinguish it from orbital angular momenta: • Spin quantum numbers may take half -integer values. • Although the direction of its spin can be changed, an elem entary particle cannot be made to spin faster or slower. • The spin of a charged particle is associated with a magnetic dipole moment with a g-factor differing from 1. This could only occur classically if the internal charge of the particle were distributed differently from its mass. The conventional definition of the spin quantum number, s, is s = n/2, where n can be any non-negative integer. Hence the allowed values of s are 0, 1/2, 1, 3/2, 2, etc. The value of s for an elementary particle depends only on t he type of particle, and cannot be altered in any known way (in contrast to the spin direction described below). The spin angular momentum, S, of any physical system is quantized. The allowed values of S are: (31) where h is the Planck constant. In contrast, orbital angular momentum can only take on integer values of s; i.e., even -numbered values of n. Fermions and bosons Those particles with half -integer spins, such as 1/2, 3/2, 5/2, are known as fermions, while those particles with integer spins, such as 0, 1, 2, are known as bosons . Properties FIGURE 4: SYMMETRIC WAVEFUNCTION FOR A (BOSONIC ) 2-PARTICLE STATE IN AN INFINITE SQUARE WELL POTENTIAL . Elementary bosons All observed elementary particles are either fermions or bosons. T he observed elementary bosons are all gauge bosons: photons, W and Z bosons, gluons, and the Higgs boson. 19 • Photons are the force carriers of the electromagnetic field. • W and Z bosons are the force carriers which mediate the weak force. • Gluons are the fundam ental force carriers underlying the strong force. • Higgs Bosons give other particles mass via the Higgs mechanism. Their existence was confirmed by CERN on 14 March 2013. Finally, many approaches to quantum gravity postulate a force carrier for gravity, the graviton, which is a boson of spin plus or minus two. Composite bosons Composite particles (such as hadrons, nuclei, and atoms) can be bosons or fermions depending on their constituents. More precisely, because of the relation between spin and statistics, a particle containing an even number of fermions is a boson, since it has integer spin. Examples include the following: • Any meson, since mesons contain one quark and one antiquark. • The nucleus of a carbon -12 atom, which contains 6 protons and 6 neutrons. • The helium -4 atom, consisting of 2 protons, 2 neutrons and 2 electrons. The number of bosons within a composite particle made up of simple particles bound with a potential has no effect on whether it is a boson or a fermion. Bose condensate A Bose –Einstein condensate (BEC) is a state of matter of a dilute gas of bosons cooled to temperatures very close to absolute zero (that is, very near 0 K or −273.15 °C[1]). Under such conditions, a large fraction of bosons occupy the lowest quantum state, at which point macroscopic quantum phenomena become apparent. Critical Temperature This transition to BEC occurs below a critical temperature, which for a uniform three - dimensional gas consisting of non -interacting particles with no apparent internal deg rees of freedom is given by: (32) where: is the critical temperature, is the particle density, is the mass per boson, is the reduced Planck constant, is the Boltzmann constant, and is the Riemann zeta function; [9] Interactions shift the value and the corrections can be calculated by mean -field theory 20 Velocit y-distribution data graph FIGURE 5: VELOCITY -DISTRIBUTION DATA (3 VIEWS ) FOR A GAS OF RUBIDIUM ATOMS , CONFIRMING THE DISCOVERY OF A NEW PHASE OF MATTER , THE BOSE–EINSTEIN CONDENSATE . LEFT: JUST BEFORE THE APPEARANCE OF A BOSE–EINSTEIN CONDENSATE . CENTER : JUST AFTER THE APPEARANCE OF THE CONDENSATE . RIGHT: AFTER FURTHER EVAPORATION , LEAVING A SAMPLE OF NEARLY PURE CONDENSATE . In the image above Fig. 5 , the velocity -distribution data indicates the formation of a Bose – Einstein condensate o ut of a gas of rubidium atoms. The false colors indicate the number of atoms at each velocity, with red being the fewest and white being the most. The areas appearing white and light blue are at the lowest velocities. The peak is not infinitely narrow beca use of the Heisenberg uncertainty principle : spatially confined atoms have a minimum width velocity distribution. This width is given by the curvature of the magnetic potential in the given direction. More tightly confined directions have bigger widths in the ballistic velocity distribution. This anisotropy of the peak on the right is a purely quantum -mechanical effect and does not exist in the thermal distribution on the left. Quasiparticles Bose –Einstein condensation also applies to quasiparticles in sol ids. Magnons, Excitons, and Polaritons have integer spin and form condensates. • Magnons, electron spin waves, can be controlled by a magnetic field. Densities from the limit of a dilute gas to a strongly interacting Bose liquid are possible. Magnetic orderi ng is the analog of superfluidity. In 1999 condensation was demonstrated in antiferromagnetic TlCuCl3, at temperatures as large as 14 K. The high transition temperature (relative to atomic gases) is due to the magnons small mass (near an 21 electron) and grea ter achievable density. In 2006, condensation in a ferromagnetic Yttrium -iron-garnet thin film was seen even at room temperature, with optical pumping. • Excitons, electron -hole pairs, were predicted to condense at low temperature and high density by Boer et al. in 1961. Bilayer system experiments first demonstrated condensation in 2003, by Hall voltage disappearance.. Fast optical exciton creation was used to form condensates in sub -Kelvin Cu2O in 2005 on. • Polariton condensation was detected in a 5K quantum well microcavity. Attractive interactions Lithium condensates with attractive interactions could stably exist up to a critical atom number. Quench cooling the gas, the condensate grow s, then subsequently collapse as the attraction overwhelmed the zero -point energy of the confining potential, in a burst reminiscent of a supernova, with an explosion preceded by an implosion. Further work on attractive condensates had better control so they used naturally attracting atoms of rubidium -85 (having negative atom –atom scattering length). Through Feshbach resonance involving a sweep of the magnetic field causing spin flip collisions, they lowered the characteristic, discrete energies at which rubidium bonds, making their Rb -85 atoms repulsive and creating a stable co ndensate. The reversible flip from attraction to repulsion stems from quantum interference among wave -like condensate atoms. When the magnetic field strength was raised further, the condensate suddenly reverted to attraction, imploded and shrank beyond detection, then exploded, expelling about two -thirds of its 10,000 atoms. About half of the atoms in the condensate seemed to have disappeared from the experiment altogether, not seen in the cold remnant or expanding gas cloud. Under current atomic theory thi s characteristic of Bose – Einstein condensate could not be explained because the energy state of an atom near absolute zero should not be enough to cause an implosion; however, subsequent mean field theories have been proposed to explain it. Most likely the y formed molecules of two rubidium atoms, energy gained by this bond imparts velocity sufficient to leave the trap without being detected. Current research Bose –Einstein condensates composed of a wide range of isotopes have been produced. Cooling fermions to extremely low temperatures has created degenerate gases, subject to the Pauli Exclusion Principle . To exhibit Bose –Einstein condensation, the fermions must "pair up" to form bosonic compound particles (e.g. molecules or Cooper pairs). I n 1999, Lene Hau and her associates slowed a beam of light to about 17 meters per second, using a superfluid. They have since made a group of condensate atoms recoil from a light pulse such that they recorded the light's phase and amplitude, recovered by a second nearby condensate, in what they term "slow - light-mediated atomic matter -wave amplification" using Bose –Einstein condensates . Isotopes The effect has mainly been observed on alkaline atoms which have nuclear properties particularly suitable for working with traps. As of 2012, using ultra -low temperatures of 10−7 K or below, Bose –Einstein condensates had been obtained for a multitude of is otopes, mainly of alkaline , alkaline earth , and lanthanoid atoms (7Li, 23Na, 39K, 41K, 85Rb, 87Rb, 133Cs, 52Cr, 40Ca, 84Sr, 86Sr, 88Sr, 174Yb, 164Dy, and 168Er ). Research was finally successful in hydrogen with aid of special methods. In contrast, the superfluid state of 4He below 2.17 K is not a good example, 22 because the interaction between the atoms is too strong. Only 8% of atoms are in the ground state near absolute zero, rather than the 100% of a true condensate.1 Fermionic condensate A fermionic condensate is a superfluid phase formed by fermionic particles at low temperatures. It is closely relat ed to the Bose –Einstein condensate, a superfluid phase formed by bosonic atoms under similar conditions. Unlike the Bose –Einstein condensates, fermionic condensates are formed using fermions instead of bosons. The earliest recognized fermionic condensate d escribed the state of electrons in a superconductor; the physics of other examples including recent work with fermionic atoms is analogous. A chiral condensate is an example of a fermionic condensate that appears in theories of massless fermions with chira l symmetry breaking Superfluidity Fermionic condensates are attained at temperatures lower than Bose –Einstein condensates. Fermionic condensates are a type of superfluid. As the name suggests, a superfluid possesses fluid properties similar to those posses sed by ordinary liquids and gases, such as the lack of a definite shape and the ability to flow in response to applied forces. However, superfluids possess some properties that do not appear in ordinary matter. For instance, they can flow at low velocities without dissipating any energy —i.e. zero viscosity. At higher velocities, energy is dissipated by the formation of quantized vortices, which act as "holes" in the medium where superfluidity breaks down. Fermionic superfluids It is far more difficult to pr oduce a fermionic superfluid than a bosonic one, because the Pauli Exclusion Principle prohibits fermions from occupying the same quantum state. However, there is a well -known mechanism by which a superfluid may be formed from fermions. Below a certain temperature, electrons (which are fermions) can pair up to form bound pairs now known as Cooper pairs. As long as collisions with the ionic lattice of the solid do not supply enough energy to break the Cooper pairs, the electron fluid will be able to flow without dissipation. As a result, it becomes a superfluid, and the material through w hich it flows a superconductor. Creation of the first fermionic condensates Jin 2003 managed to produce a condensate out of fermionic atoms for the first time. [46] The experiment involved 500,000 potassium -40 atoms cooled to a temperature of 5×10−8 K, subjected to a time -varying magnetic field. 1 Note: This should be explained in layman’s terms to be comprehensible. Does a fused atom in one quantum state remain after “defrosted”? Fusing different atoms to say make gold in condensate remains gold or comes apart when “defrosted”? In other words, if different atoms take the same space do they still keep their own identity or fuse giving a new meaning to cold fusion vs. super cold fusion. When this happens, is there the same energy exploded or is E near zero no this fusion will be without explosive force? What happens to gravitational pull? The denser the more gravitational pull. Any implications of this to theoretical temperature in a black hole? 23 Innovation: Nuclear Reactions in Energy Charge Bolonkin (2013) proposed a method for obtaining very cheap electric ener gy, liquid fuel, thermal energy, and cheap nuclear fuel using deuterium underground thermonuclear explosions. He shows the installation for generating energy is on the order of a thousand times cheaper than surface steel boiler designs offered by Russian scientists and safe r because in case of any damage , the radiation is in a deep underground cavity. In this design, t he nuclear Energy charge contains the nuclear detonator, the deuterium as explosive and cheap Uranium -238 for production the nuclear fuel for next nuclear detonator and fuel for the nuclear electric stations and nuclear weapon. The main fuel is deuterium which is abundant in sea water. Its price is about $700/kg (2012). The fuel charge may also contain the cheap lithium and beryllium because they help to produce the energy and tritium – important and expensive fuel for thermonuclear reactors. Nuclear Reactors can use the isotopes Uranium - 233, 235, 238; isotopes Plutonium -239-242; isotopes Thorium: Th -232. 2 Fig.8 . Energy charge. Notations: 1 – Nuclear charge/initiator (Uranium -233 or Plutonium -239); 2 – neutron reflector; 3 – deuterium; 4 – Uranium -238 or T horium -232. Diameter is about 1 m, mass is about 1 ton. The nuclear detonator 1 (fig.8) may use Uranium -233 or Plutonium -239. For Uranium -233 reaction is MeV2001 2 1233+++→+ n X X nU  , (33) where U-233 is uranium, n is neutron, 2 1,XX are fission fragments, 1 is multiplication factor (one is ≈ 2.7 - 3 for U-233), MeV is unit of energy (1 MeV = J13106.1− ). For Plutonium -239 the reaction is 2 What is the cost of superfluid liquid helium? Is there a way to find out ? 1 2 3 4 ENE-F3 24 MeV2002 4 3239+++→+ n X X n Pu  , (34) Where Pu -239 is plutonium; n is neutron, 4 3,XX are fission fragments; 2 is multiplication factor (one is ≈ 3.5). The high temperature produces the chain reactions in deuterium (layer 2 of fig.8.). We can succinctly write the thermonuclear reaction in deuterium as: MeV n p He D 41 3 3 2 74 2 +++→ , (35) where D is deuterium; p is proton; He-4 is helium -4 (stable isotope) The neutrons from (3) go to the layer 4 (fig .8). The layer 4 contains the cheap Uran ium- 238 or cheap Thorium -232. Protons convert them into very expensive Plutonium -239 or Uranium -233. Short (simplify) final reactions are: U n Th Pu nU233 232 239 238, →+ →+ . (36) As you see the cycle is closed -loop. Both products (Plutonium -239 and Uranium -233) may be used as nuclear fuel in production the very cheap energy for the new energy -charges (see equation (1) -(2)) or for thermonuclear weapon. We get several times more nuclear fuel in every cycle than spe nt in the energy -charge. The cost of U -238 and Th -232 is about 700$/kg (2012)3 deuteri um about 3500$/kg. The cost of Pu -239 and U -233 is about 60 Million $/kg in black market. The Russia offers the USA the pri ce 16 Millions $/kg.4 This chain reaction may be presented as: . 6.43 2 2 2 64 24 22 1 MeV n He He D +++→ (37) If we add the reaction D + n → p + 2n -2.2MeV, we receive the final reaction (3). Neutrons are very useful for getting the nuclear fuel. For increasing the production of nuclear fuel we can add into the energy -charge the Berillium -9: n He n Ben Be 2 2 24 8 9+→+→+ . (38) But for this r eaction the energy of n must be more >1.85 MeV. For this the lithium also may be used. The list of possible reactions is in table 1 above . Critical mass of uranium depends upon its density . That may be computed the equation: 6 3 26104 − = cmg Mc , (39) For ρ = 20 g/cm ; 10 mass critical3kg Mc= for ρ = 40 g/cm ;5.2 mass critical3kg Mc= for ρ = 80 g/cm g Mc625 mass critical3= . Using the neutron deflector significantly decreases the critical mass. If water neutron reflector is used , the critical mass of U -235 is 0.8 kg, of Pu -239 is 0.5 kg. In theory the Cf -251 has the minimal critical mass 10 grams.5 3 Please double check – perhaps U should be cheaper than Th 4 please double check 5 please check these numbers if still true 25 Because critical mass o f uranium depends upon its density a bose condensate and fermionic condensate has greater density. Discussion The thrust of this paper was advancing a mathematical model more in theoretical physics than experimental physics. There are however a number of empirical questions that require answers to complete this theoretical model. Since critical mass of uranium de pends upon its density, a ssuming even small U ranium condensate can be routinely achieved; t here are two empirical questions. 1. Does one neutron fission one U atom or the entire condensate? Theoretically, it is expected that surface layers would evaporate for ming opacity globe around core condensate but remaining core --if belief correct -- should fission as one.6 If antimatter particles sufficient to annihilate just one U nucleus directed to core condensate --will just one be annihilated or entire core condensate? If entire core condensate is annihilated, then contemporary views on the nature of matter is incomplete leaving the question : How deep does entangled state go? Tests of t his theoretical problem can be divided into tests of multiple sub -problems : Firstly, assuming that one neutron hitting a fissionable condensation transition (Bose, Fermionic or other condensate) will result in EVERY nucleus in the condensate simultaneously firing ; then using neutron bombardment can test the problem of the right kind of quantumly entangled state for a given very small and dense unit of fissionable material to be able to reach a very high power density upon neutron pe netration as they have a superimposed quantum state. [47] It is known that Bose -Einstein condensation can occur in quasiparticles and can be expected to obey Bose -Einstein statistics like traditional particles ; to form when low temperatures cause nearly a ll particles to occupy the lowest quantum state ; and occur in ultracold gases and materials. The calculations that lead to the conclusion that t he lower masses of material quasiparticles relative to atoms lead to higher BEC temperatures is as follows: An ideal Bose gas has a phase transitions when inter -particle spacing approaches the thermal wavelength: kBT = h2n2/3/M. The critical concentration is: N  (T/2)31/2P/h3, leading to a critical temperature: Tc < 323h6Vu0P2. The particles obey the Bose -Einstein distribution and all occupy the ground state: n(S) = ( e(Es-u)/kT - 1)-1. The bose gas can be considered in a harmonic trap, V (r) = M2/2, with the ground state occupancy fraction as a function of temperature: f(0) = N0(t)/N = 1 – (T/T c)3. In 1998, Fetter [48] further detailed expected properties of b ose concentrate quasi -particles which lends support to the notion that destruction of one BEC quasiparticle would destroy the others in the same quantum space. 6 Unknown how thick the opacity globe is – if the outer layer is too big and actual net reaction (core) is too small then the efficiency is too small to pay 26 But would it really be a Bose or, Fermionic condensate or some other form is for example the superimposition in a Tonks -Girardeau gas? A Tonks –Girardeau gas [49] is a Bose gas in which the repulsive interactions between bosonic particles confined to one dimension predominate so that s trictly speaking this is not a Bose –Einstein condensate as it does not demonstrate any of the characteristics, such as off diagonal long range order or a unitary two body correlation function, even in a thermodynamic limit and as such cannot be described by a macroscopically occupied orbital (order parameter) in the Gross Pitaevskii formulation. A row of bosons all confined to a one -dimensional line cannot pass each other and therefore cannot exchange places. Because the particles cannot exchange places, one might expect their behavior to be fermionic, but it turns out that their behavior differs f rom that of fermions in several important ways: the particles can all occupy the same momentum state which corresponds to neither Bose –Einstein nor Fermi –Dirac statistics. The fermionic exchange rule implies more than the exclusion of two particles from th e same point: in addition, the momentum of two identical fermions can never be the same, wherever they are located. Mathematically, there is an exact one -to-one mapping of impenetrable bosons (in a one -dimensional system) onto a system of fermions that do not interact at all. Tonks –Girardeau gas coincide with quantum Nonlinear Schrödinger equation for infinite repulsion, which can be efficiently analyzed by Quantum inverse scattering method. Or would this be Super T onks -Girardeau gas ? Super Tonks –Girardea u gas [50] represents an excited quantum gas phase with strong attractive interactions in a one -dimensional spatial geometry. Usually, strongly attractive quantum gases are expected to form dense particle clusters and lose all gas -like properties. This lowest gas -like state should be stable and show new quantum mechanical properties. Particles in a Super Tonks gas should be strongly correlated and show long range order with a Luttinger Liquid parameter K<1. Since each particle occupies a certain volume, the gas properties are similar to a classical gas of hard rods. Despite the mutual attraction, the single particle wave functions separate and the bosons behave similar to fermions with repulsive, long range interaction. To prepare the Super Tonks –Girardeau p hase it is necessary to increase the repulsive interaction strength all the way through the Tonks –Girardeau regime up to infinity. Sudden switching from infinitely strong repulsive to infinitely attractive interactions stabilizes the gas against collapse a nd connects the ground state of the Tonks gas to the excite d state of the Super Tonks gas.7 2) The problem of the cryogenic requirement for the fuze. It is also not necessarily so that the production of a condensate requires cryogenic temperatures . Using optical pumping, co ndensation in a ferromagnetic Yttrium -iron-garnet thin 7 For targeting purposes, one can speculate if this acts like a long chain – almost like an ab matter chain of particles – if rigid is it a perfect target in the long axis. Could it have applications to build a n AB matter chain. Is the ideal geometry a condensate ball for ease of targeting followed by super tonks –girardeau gas which catalysises – consider combi nation of bose and super tonks –girardeau gas 27 film was produced even at room temper ature . [51] But even if near zero Kelvin temperatures are required for this condensate in order to effect fission, this does NOT stop practical design 3) The problem of a portable mechanism to produce a condensate state The problem of achieving a portable mechanism to produce a condensate state is another problem . If you can induce a working condensate fuze in a national lab like facility a few minutes away and a few kilom eters away from point of use , some mechanism needs to be found to contain and maintain the fuze for use in the fusion device. The practical equivalent be achieved in something analogous to a specialized design of quantum dot . In a quantum dot [52], its excitons are confined in all three spatial dimensions. The exciton confinement energy can be modeled using the particle in the box. The electron and the hole can be seen as hydrogen in the Bohr model with the hydrogen nucleus replaced by the hole of positive charge and negative electron mass. Then the energy levels of the exciton can be represented as the solution to the particle in a box at the ground level (n = 1) with the mass replaced by the reduced mass. Thus by varying the size of the quantum do t, the confinement energy of the exciton can be controlled. Quantum dot b ound exciton energy is determined by the Coulomb attraction between the negatively charged electron and the positively charged hole.. When the size of the semiconductor crystal is sma ller than the Exciton Bohr radius, the Coulomb interaction must be modified to fit the situation. Being zero -dimensional, quantum dots have a sharper density of states than higher - dimensional structures. Hypothetical design s exist for such a portable devic e [53] [54] [55]. 4. The problem of achieving a large amount of condensate . One would assum e that Fuse needs in some grams of condensate. How to get, save, use it? but in fact far fewer than grams, or even micrograms might be enough to ignite a properly designed special trigger mechanism. The key property is the energy density and sharpness of the power spike. Assuming that even very small fusion ignition conditions are achieved (and the leakage from a tiny fusion ignition is not too great) ther e are various design possibilities to scale up the spark to ignite kiloton yields (and from there, much more) Related question? The mass of all the rubidium atoms in the largest condensate to date is how much ? [56] 1 mol of rubidium is 85.468 grams. 1 mo l is 6.022x10^23 atoms. Therefore, 1 atom of rubidium is 1.419x10^( -22) grams. Even allowing say 10000 rubidium atoms as the largest condensate to date that is a millionth of a nanogram, or a billionth of a microgram. But if this idea is not nonsense that could be an advantage not a disadvantage (a feature not a bug) because fission product contamination would be utterly negligible --if reliable fusion could be achieved and scaled up . 28 5. The problem of achieving the right species of fissionable material feed. Even strange isotopes like Plutonium 240 might be good 'starter' fission fuel because there is no pre-detonation problem at this scale . I am assuming U 235 because easily turned to gas as UF6 but that is only assumption. The Uranium may need to be elemental. 6. The problem of achieving scale up from reliable tiny fission detonation/fusion ignition. An ideal gas is a theoretical gas compo sed of many randomly moving point particles that do not interact except when they collide elastically. At normal conditions such as standard temperature and pressure , most real gases behave qualitatively like an ideal gas. The ideal gas model tends to fail at lower temperatures or higher pressures, when intermolecular forces and molecular size become important. As the temperature approaches zero, the entropy approaches negative infinity, in contradiction to the third law of thermodynamics . In the above "ide al" development, there is a critical point, not at absolute zero, at which the argument of the logarithm becomes unity, and the entropy be comes zero. This is unphysical. Ideal Bose and Fermi gases An ideal gas of bosons (e.g. a photon gas ) will be governed by Bose –Einstein statistics and the distribution of energy will be in the form of a Bose –Einstein distribution . An ideal gas of fermions will be governed by Fermi –Dirac statistics and the distribution of energy will be in the form of a Fermi –Dirac distribution . [57] Ideal Bose equation of state The equation of state for an ideal Bose gas [58] is where α is an exponent specific to the system (e.g. in the absence of a potential fi eld, α=3/2), z is exp(μ/kT) where μ is the chemical potential , Li is the polylogarithm , ζ is the Riemann zeta function , and Tc is the critical temperature at which a Bose –Einstein condensate begins to form. Conclusion The major obstacle in thermonuclear reactors is achieving the Lawson criterion, sufficient temperatures and pressure. During the past 30 years, innovations in mini and micro - thermonuclear reactors have been advanced by senior author of this paper. This paper proposes that ignition can be achieved by a phenomenon called the bose condensate and the fermionic condensate; that when matter is cooled down to very low temperatures all the atoms behave as a single atom to some extent. This paper put forward the design and computations to demonstrate that it would be possible to achieve fission with only a microgram or even a nano -gram of uranium. This reaction can then effect fusion in the Bolonkin micro -thermocuclear reactor. 29 Acknowledgement The author s wish to acknowledge Zarek Newman for editing this paper and offering useful advice and suggestions.