METHOD AND APPARATUS FOR PRODUCING NUCLEAR ENERGY
Background of the Invention
(i) Field of the Invention
This invention relates to a method and apparatus for producing nuclear energy. By "nuclear energy" is meant energy coming from the interaction of atomic nuclei.
(ii) Prior art
A coherent boson beam consists of bosons which can be either stable or unstable. The distinction, however, between stable or unstable bosons becomes blurred when bosons are coherent. Some bosons, normally regarded as stable, will become unstable when they are coherent. For example, deuterons which are normally regarded as stable become unstable and decay when they form a coherent beam.
For a beam of deuterons with a neutralizing background of electrons, the beam is normally regarded as stable because the deuterons are separated from one another by Coulomb repulsion. Classically, they cannot fuse together. However, quantum mechanically there is still some probability that the deuterons may tunnel through the Coulomb potential barrier and fuse: d+ + d+ → 3He + n + 3.27MeV
→ t + p + 4.03MeV
(1)
with the release of nuclear energy, 3.27 and 4.03 MeV respectively.
The probability can be estimated by solving the Schrodinger equation:
(2)
Hψ = Eψ
H = + V (X)
V = α = 1/137
where μ - m/2 is the reduced mass, and V is the Coulomb potential between two deuterons.
In semiclassical approximation, equation (2) can be solved to yield the probability as:
(3)
P = exp (-2 k dr)
E = kinetic energy
rc = classical turning point setting E = 0, the probability is
P = exp
~ 10-1.7x104 (4)
Hence, the likelihood of a deuteron beam decaying is extremely small and the beam is stable.
Brief Summary of the Invention
When the boson beam becomes coherent, the decay rate rm is increased by a factor of m! rm = m! r1 (4a) where r, is the normal decay rate and m is the number of coherent particles. For m=104, the decay rate of a coherent deuteron beam becomes rm= X r1
which is comparable to the tunnelling probability given by equation (4a). Hence, for a coherent beam with particles m>10
4, the beam rapidly decays.
The decay of a coherent deuteron beam according to equation (1) will yield nuclear energy. Normally, one seeks to obtain conditions conducive to inducing confined nuclear fusion, as indicated by equation (1), by increasing the kinetic energy, i.e. the value of E in equation (2) and hence decreasing the value of k in equation (3). Hence, the probability P will increase rapidly. It follows from the above, however, that there is no need to increase the kinetic energy E of each deuteron. In fact, the relative kinetic energy of the deuteron is reduced to zero in a coherent beam. The probability of fusion is increased by a completely different physical principle, namely the collective
effect of coherent bosons.
The chief difficulty of past attempts to induce production of nuclear fusion energy arises because of the difficulty in confining charged deuteron particles for a long enough time, at close enough distance, to cause them to tunnel through the Coulomb barrier. Magnetic confinement schemes such as that adopted in the well- known "Tokamak" employ strong magnetic fields to confine deuterons. in a toroidally shaped region. Inertia confinement schemes, such as employed in known laser implosion techniques, seek to reduce the distance between the deuterons.
In the above, the term "decay" is used in reference to a beam of coherent particles whereas the mechanism actually consists of the fusion of two deuterons. Normally decay refers to one particle decaying into two or more particles. It is also possible that nuclear energy is released from the decay of an atomic nucleus, e.g., 84P0 212 → 82Pb208 + α
Polomium 212 decays into lead via α- decay with 8 MeV energy released. When a coherent beam of polomium 212 is formed, it will also decay with enhanced rate given by Eq. (5). Then we have both the decay of the coherent beam and the decay of individual atomic nuclei. Generally, nuclear energy can be obtained from fusion of two light nuclei or from fission of a heavy nuclei. By making nuclei into a coherent beam, the rate of interaction is enhanced, so that energy can be released where it is needed.
In view of the foregoing, the invention broadly comprises a method of producing nuclear energy comprising generating coherent bosons and extracting nuclear energy therefrom.
In a particular form of the invention, the nuclear energy is produced by decay of the coherent bosons.
The invention further provides apparatus for carrying out the method of the invention comprising two boson generators effective to produce beams of bosons and a collision chamber arranged to receive the bosons from the beams, for collision therein, to produce said nuclear energy.
According to another aspect, the invention provides a method for release of nuclear energy through the electromagnetic decay of a coherent boson beam, the bosons being the nuclei of atoms, comprising generating the coherent boson beam and permitting the bosons therein to decay according to a reaction A+ A→ B + C + E where the 'A' comprises coherent bosons; 'B' denotes the fusion product of the 'A'; 'C denotes one or more bosons; and E is the released energy.
The invention further provides apparatus for carrying out the invention comprising means for generating a coherent boson beam and allowing the beam to undergo electromagnetic decay to produce energy.
The scheme of the foregoing inventions requires neither exceptionally long interaction times nor small distances between deuterons. It is only required that the deuterons be coherent so that the m factorial (ml) factor is effective to overcome the normally extremely small probability mentioned above.
By freely expanding ions with neutral gas one may cool the ions to a temperature T close to 1. K, and by expanding the ions by the use of a vanishing magnetic field, one may further cool the ions to 10-3 .K millidegree Kelvin. Such a very cool ion beam may be utilized in conjunction with the induced scattering mechanism described in International Patent Application PCT/AU86/00212 incorporated herein by reference.
Brief Description of the Drawings The inventions are further described by way of example only with reference to the accompanying drawings in which:
Figure 1 is a diagrammatic axial section of an apparatus for carrying out the method of this invention;
Figure 2 is a diagrammatic cross section of an apparatus constructed in accordance with the invention; and
Figure 3 is a momentum conservation diagram.
Detailed Description The scheme to be described is effective to create coherent deuterons by the collision of two very cool (10-3. K) deuteron ion beams.
Figure 1 shows microwave plasma generators 10,12 which create deuteron ions at approximately 1 atmosphere pressure. These ions are expanded as deuteron-electron plasma and neutral deuterium gas in vacuum chambers 18,20 at a pressure of 10-6 torr. Resultant deuteron-electron beams 14,16 are collimated in the forward directions by respective sets of skimmers
22,24. During the expansion phase, external magnetic fields are imposed by solenoids 26,28 surrounding skimmers 22,24. The magnetic fields extend in the direction of the deuteron-electron plasma beams. The magnetic fields may be created by the described solenoids or more economically by permanent magnets, (not shown) say of 5 kilogauss. The deuteron-electron plasma beams heat up when entering into the magnetic fields. In this initial stage the plasma will be cooled down by collision with the neutral cool gas. The neutral gas background can be cooled down to about 1.K as is the plasma. The deuteron-electron plasma beams then cool down further to millidegree Kelvin expanding thereafter during passage through the strong magnetic field (of kilogauss) provided by solenoids 26,28 which fields reduce to almost zero outside the vicinities of the solenoids.
The two beams 14,16 are coaxially aligned and directed into a collision chamber 30. There are four parameters that are relevant to the creation of coherent deuterons in chamber 30, pursuant to this collision.
1) The density of deuteron ions n. The higher the density of the deuteron ions, the higher are the chances of the ions becoming coherent. Typically n, may be I012/cm3 at the microwave plasma generators 10,12 decreasing to 109/cm3 during the plasma expansion phase.
2) The kinetic energy K of the deuteron beam. The plasma in microwave plasma generators 10,12 has a temperature of 103.Ks which is equivalent to 0.1 eV kinetic energy. Hence the deuteron-electron beams have longitudinal kinetic energy of the order 0.1 eV.
3) The longitudinal temperature TL of the deuteron- electron plasma. This may be about 1°K after expansion into the vacuum chambers 18,20.
4) The transverse temperature TT of the deuteron- electron plasma. This may drop to TT~ 10-3°K (or 10-7 eV) at the collision chamber 30.
The lower the temperatures TL and TT are, the closer will be the approach to the critical condition of reaching coherence. The precise values of nl, K, TL and TT for the critical condition of coherence can be derived from the formalism of induced scattering as described in International Patent Application PCT/AU86/00212.
The following comprises an estimate of the above critical values.
Firstly, concerning the phenomenon of boson condensation, the number of states for the distribution of bosons with momentum p and energy E at a given temperature T is given by: N = gD
(5) where V is the volume and gD is the number of degeneracy for a deuteron with spin equal to one, gD=3 k being the Boltzmen constant. The density of boson particles is n
The integral can be evaluated exactly to obtain
(7)
The critical density nc at critical temperature Tc is thus set. For a given temperature T=TC if we increase the density n above the critical density nc, the extra number of bosons will condense to form coherent bosons at the lowest energy ground state. Similarly for a given density n=nc, if the temperature T drops below the critical temperature T<Tc, then there will be boson condensation. Typically, the parameters are Tc~ 1.K and nc ~ 1022 cm3. Hence for the described type of value of deuteron ions, nj=l012cm3, and there is a shortfall in the required values by ten orders of magnitude for T 1.K.
However, if one utilizes the mechanism of induced scattering the situation is different. Especially, the Coulomb scattering cross section between charged particles strongly peaks in the forward direction
(8) θ =scattered angle
If two charged beams move opposite one another, the induced scattering is of Coulomb type. The gain (g) as against ordinary S-wave scattering (or flat angular distribution) is very great.
for E=0 .lev and T
T = 10
-7eV. The critical density n
c will then drop by a factor of 10
12 from 10
22 to 10
10/cm
3. In addition, the temperature also drops. Equation (8) suggests the critical density n
c varies as temperature to the 3/2 power. So the gain (g
T) in temperature
Hence the critical density when boson condensation occurs is approximately nc ~ 107/cm3
The expected density for deuteron ions 10 /cm is larger than this critical value.
Concerning equation (1) above, it is to be noted that for a plasma beam it often happens that the temperature T in the transverse direction is different from the temperature T in the longitudinal direction. Therefore the critical condition for boson condensation needs to be modified as we show in the following.
If one associates the partition of longitudinal energy with longitudinal temperature T
L and transverse energy with transverse temperature T
T in the fashion
( 12 )
The critical condition becomes n
c = \ V P
Then we have the critical density to be nc = ! /
where boson condensation will occur. The dependence of n on transverse temperature is a linear function and that on longitudinal temperature is a square root function.
Once coherent deuterons are formed in the collision chamber 30, these will undergo nuclear fusion, and nuclear energy is released.
The mechanism of 'induced scattering' mentioned above is described particularly in International Patent Application PCT/AU86/00212 incorporated herein by reference. The mechanism is to induce a coherent state in bosons by processes such as: γ(k) + nd+ (p') + d+ (p) → (n+1) d+ (p') + γ(k') n γ + A*→ A + (n+1) γ
(14)
The number of coherent deuterons is increased by one in each scattering of photons with deuterons. This may be considered a gradual process by which the number "n" of coherent bosons such as the "d+" in the above equation increases in an exponential fashion over time (t) from an initial possibly small number no, in the following fashion: n = no λ+ where λ is a constant.
Another example of induced scattering is the following: nγc + D(p1) + D(p2) + D(pn) → nd[ + e(q1) +... e.(gzn)
(15)
Here, all the deuterium atoms initially have different momenta and in one scattering with coherent photons they all become coherent. The subscript 'c' above denotes coherence. In such a case, the coherent bosons produced are considered to be produced by forcing a substantial number of noncoherent bosons more or less instantaneously to the coherent state. Of course, in each of these examples, the d+ is exemplary only and in principle the interactions so described are applicable equally to other bosons.
More generally, then, the term 'induced scattering' as used in this application is intended to refer to any scattering process that involves any particular species of coherent particles. By way of further example, it is noted that due to boson statistics, for each n coherent bosons, there is associated an n!:
(16) akak ...ak|n(k)> =
Hence for every reaction process that involve coherent bosons, the probability is greatly enhanced by an n! factor. For two deuterons at atomic distance, the fusion rate is 10
-70/sec, a very small number indeed. However, if there are say n = 200 coherent deuterons, the rate will be increased by least by a factor 200
~10370 which amounts to almost instantaneous fusion of the 200 coherent deuterons with the release of nuclear fusion energy. Normally nuclear fusion of deuterons is enhanced by increasing the density, or reduction to distance among deuterons by high temperature and confinement scheme. However, it is clear the enhancement of nuclear fusion can come about more easily if coherent bosons such as deuterons are created first. Coherent deuterons are favorably produced at low temperature in general instead of requiring the high temperature normally associated with fusion studies. There exists some qualitative differences between the end product of normal fusion of two deuterons and the decay of a coherent deuteron beam. The two deuterons can fuse in the following ways: d+ + d+→3He + N (17)
→ t + p (18)
→ α + γ (19) Normally (17) and (18) dominates the fusion process with 50% each, while the decay into α and γ is
an electromagnetic process and is down by a factor of 1/137. However, α and γ are both bosons and can be coherent, there are additional nl factor for each coherent bosons in the decay product. Hence the dominant decay mode of a coherent deuteron beam is (19) and not (17) and (18).
The phenomenological Hamiltonian for (17) (18) (19) are
H1= h.c.
(20)
H 3 = h . c. (21)
H = h.c. (22)
with Φ stand for boson quantum field and ψ for feπnion quantum field and the indices refer to the particular particles. Using perturbation theory to calculate (19) with (2.0) first, for the decay of two coherent deuterons: (23)
where V is the normalization volume, m the mass of nucleon, and Eα the binding energy of α relative to deuterons. (=2md-mα)
For the decay of 2n coherent deuterons: (25)
the rate is
where 1/η = number of quantum states in the final state
The (2n) 1 comes from 2n coherent deuterons, (n!)2 come from two coherent bosons α and γ and the η factor is the requirement that the final state a andγ can only go into one quantum state among all available phase space in order to be coherent.
Similarly, the decay rate of two coherent deuterons into 3He and neutrons as in process (17) is
where
can be obtained from the cross section of the scattering of two deuterons (29)
with cross section given by
(30)
where is the center mass momentum of the two scattering
deuterons and E
3 is the binding energies of
3He relative to two deuterons (2m
d-m
He). The decay rate of coherent deuterons into helium plus neutrons (31)
is then given by
r
η (
3He) = (n!)(2n)! (
)
n(1-η
3) (1-2n
3)... [1-(n-1)η
3]r
1(
3He)
(32) where the (2n!) comes from the coherent character of the initial deuterons, and there is additional nl due to the commuting properties of the Hamiltonian H3 to the nth order. The fermi statistics of 3He and neutron dictates that all final particles cannot occupy the same states. This is shown up in the decrease of phase space as reflected by the (1-η3) factor for first additional fermion pair, and (1-2η3) for the second additional fermion pair to the (n-1) pair. There is no diminishing of phase space for the first pair. The η3 is again
1/η
3 = number of quantum states in the final state
As is clear from comparing (23) and (29), rn (α) is larger by at least a (n!). The other fermionic decay mode 2dt+t+p is similar to (20) by only replacing g3 by g2 and E3 by Et, the binding energy of t relative to 2d (2md-mt). Hence, the decay of coherent deuterons proceeds dominantly into bosonic channels.
It was mentioned previously that a coherent deuteron beam may decay into hadrons: d + d → 3He + n + 3.25MeV (33 ) → 3 t + p + 4MeV
via strong interaction with the release of nuclear energy. The decay products of (31) consists of odd number of nucleons, and they are all fermions. By way of illustration, a particular decay mode of the coherent deuterons in accordance with this invention is where the decay product consists of bosons such as in the following decay: d + d → 4He + γ + 23.6 MeV (34) where γ are emitted photons. Normally interaction (34) is very much weaker than interaction (33) because interaction (34) belongs to the class of electromagnetic interactions and is generally down in probability by an order of α = 1/137. So the interaction rate of (33) is very much greater than that of (34), and (34) is not important as compared with (33). However, for a coherent deuteron beam the situation is different, because the final products of (34) are bosons which may also become coherent if certain critical conditions are met and the decay rate of electromagnetic interaction (34) may then exceed that of the strong decay (33) and the electromagnetic decay may become the dominant process.
The electromagnetic decay of deuteron beam is particularly useful for the following reasons:
(a) Of all decays the electromagnetic decay of interaction (34) releases the maximum energy. Because the helium nucleus 4He is more tightly bound than ^He or tritium t, the amount of energy converted to kinetic energy of the final decay products in electromagnetic decay is more than that from the strong decay (33). The decay 4He + γ releases six to eight times more energy than the decay of t+H or 3He+n.
(b) The electromagnetic decay product consists of photon and He without neutron. Neutrons are released in strong decays. Because of the strong penetrating power of neutrons through matter, it is difficult to provide adequate shielding and the utilization of these in nuclear energy devices may nuclear energy more costly and complicated. On the contrary, the energy released in electromagnetic decay is mainly endowed in high energy coherent gamma rays, and the rest in charged particles 4He. The high energy gamma rays can easily be converted into an electron shower by lead plates.
The energy of the photon is given by ω = (4 -m2He)/4m = 23.6MeV
The α particle (Helium nucleus) only takes away 0.3% of the total energy.
(c) The electromagnetic decay of a coherent deuteron beam is a source of a coherent helium nuclei (or α) beam and coherent high energy gamma rays, A 23.6 MeV gamma ray laser beam may be provided by the interaction.
Referring now to Figure 2, there is shown therein a cross sectional view of a fusion device for producing nuclear energy by the described process.
The device 10 shown comprises a cryostat 12 containing liquid helium in an interior chamber 14 surrounded by a liquid nitrogen containing jacket 16. At a lower part of the cryostat, there is provided a vacuum chamber 18 having therein a container 20 containing deuterium pellets which are maintained at liquid helium temperature by virtue of being adjacent the liquid helium in chamber 14. A gate 22 is provided in a floor of the container 20 to permit release of deuterium pellets one at a time from the gate to fall within the vacuum chamber 18. The vacuum chamber 18 has a window 26 formed in a side wall thereof and laser light from a source 30 is directed via a focusing lens 32 through the window to be brought to a focus at a location 36 within the vacuum chamber.
The deuteron pellets as they fall within the chamber 18 remain at low temperature and pass to the location 36 where upon the laser light is directed thereto whereby to generate energy and gamma rays by the process above described. The location 36 is surrounded by lead shielding to absorb the gamma rays and other radiation which may be generated. At various locations as desired, the lead shielding, which may be in the form of sheeting is interfaced with one or more silicon cell layers whereby the gamma rays directed thereto through the lead shielding are converted to electric energy directly by photo electric effects. Thus, output electricity may be generated directly from the silicon cells such as at the terminals 42, 44 shown. The lead shielding is illustrated at, for example, 52 in the drawing and the silicon cells at 54. The incidence of the released photons on the lead releases showers of particles such as electrons, positrons and further
photons, the particles so produced being effective to produce the output voltage for the silicon cells 54.
The deuterons in the described pellets are rendered coherent by the incidence of the laser beam thereon, and it is the so-coherent deuterons which decay as above described to give off the gamma rays.
In this case the boson beam which decays to give out gamma rays is generated by one particular process. Particularly if coherent light is focused on deuterium solid at, say, liquid helium temperature there are three competing processes: γ + D2→ γ + (D2)c (35) γ + D→ (d+)c + e- (36)
Y + D → (γ)c + D (37) (where subscript c implies coherence).
The first of these processes creates a coherent molecular deuterium beam. The second one creates a coherent deuteron beam. The third one is effective to scatter coherent light off deuterium atom. It is important to have coherent particles in the final states so that the transition rate is enhanced by boson statistics. Otherwise, focusing laser light on deuterium will only heat up the target and produce hot plasma. The final bosonic products that can become coherent are: positively charged deuterons, molecular deuterium and light. To enhance the chances of coherence one needs to cool a target to low temperature so that the momentum spread of the initial deuterium is small. The apparatus of Figure 2 uses process (
36) above for creating coherent
deuterons. Momentum conservation requires
(38)
Where
are the moments of the deuterium, the photon in the initial state and the deuteron, and the electron in the final state. The momentum k of the incoming coherent photon is fixed, and for a coherent deuteron there is a fixed value of p'. The difference between the momenta of electron and deuterium:
p-k' = p'-k = const is fixed. Figure 3 shows the momentum conservation diagram in the number of deuterium atoms with different p which can contribute to coherent deuteron with momentum p' is now considered:
At T=1.K, the spread of p is ±620eV:
The energy of the produced electron ω' is given by ω' = E + ω - E' + E B (40) where E, ω, are energies of deuterium, photon in the initial state E' that of the deuteron, and EB = -13.6eV is the binding energy of the electron in the deuterium atom. Due to the fact that electron is much lighter than deuteron (me/mα = 2.5X10-4) electron has the most energy ω'»E'. The possible spread of electron energy due to thermal energy of the deuterium target is then, for eq. (38)
Δω' ~ ΔE ~kBT ~ 10-4eV
(41) where kB is Boltzman's constant.
The spread of electron momentum Δk' is
10
-4 (42)
if ω' is of the order of lev. For a given ω', there can only be a definite p. The spread of p is only due to uncertainty principle in the volume 2x10
-2eV for L = 10μm
Hence of all the deuterium in the initial state, only a fraction rc is capable of producing coherent deuterons with momentum p', with rc given by the ratio of phase space rc = ~ 10-9
Referring to Figure 3, one may picture a hollow spherical shell with length and thickness |Δk' | with center
at C. All the p vector that can reach this spherical shell from A will be able to contribute to the coherent deuteron production. The total p available is a sphere with length op= and center at A.
For a deuterium pellet of volume V=10μm x 10μm x 10μm, the total number of deuterium atoms is 10
13, and the number of coherent deuteron m is m = r
cρV
= 104, for p = 1022/cm3. (44)
The rate of producing coherent deuterons is
w ~ (nγ)m m! (P2η2) m-1 w1 (45)
Where nγ is the number of photons, P2 is the probability that interaction (36) occurs, 1/η is the number of final states available in the scattering, and w is the rate for one photon ionization (interaction (36)). The critical condition is nγm P2 η2 > 1 (46)
The value of P2 is of the order
For one photon ionization cross section
σ2 ~ 10-19cm2, A=10μm x 10μm,
P2 ~ 10-13. For a one joule pulse from a laser,
nγ ~ 1019. Hence the critical condition is able to be satisfied.
One photon ionization is required so that the cross-section for producing deuterons is large compared with elastic photon-deuterion scattering where the cross section is ~ 10-26cm2. For multiphoton ionization, the cross section drops very rapidly with more than one photon.
The rate for multiphoton (N«no. of photons needed) ionization is
σ1=10 -19cm2
I intensity (watt/cm
2) (48)
To require one photon with energy greater than
13.6eV, a wave length less than 92.4 nm is needed.
The laser 30 may be operated in pulsed fashion, whereby to direct pulses of light at ones of the pellets of deuterium as they fall to location 36. Thus, the pulsings may be synchronized with the operation of door
22.
The deuteron pellets used in apparatus 10 may be of any form known in the art such as in the form of deuterium oxide, or may simply comprise cold (is solidified) deuterium.
Of course, although the apparatus 10 is shown as utilizing released photons to directly produce electricity by photo-electric interaction, this is not essential and energy released may be otherwise applied such as to produce heated liquid (for example steam) which is for example used to produce electricity by conventional means such as turbines.
Usually, it is to be understood that the coherent bosons from which energy is extracted by decay in accordance with this invention will be bosons having mass, or at least bosons not being photons.