1
Possibility of controlled nuclear fusion by means of Gravity Control Fran De Aquino Maranhao State University, Physics Department, S.Luis/MA, Brazil. Copyright © 2011 by Fran De Aquino All Rights Reserved The gravity control process described in the articles Mathematical Foundations of the Relativistic Theory of Quantum Gravity [1] and Gravity Control by means of Electromagnetic Field through Gas at Ultra-Low Pressure, [2] points to the possibility of obtaining Controlled Nuclear Fusion by means of increasing of the intensity of the gravitational interaction between the nuclei. When the gravitational forces FG = Gmgm′g r2 become greater than the
where K = 1.758× 10−27 and j rms = j 2 . Thus, the gravitational force equation can be expressed by
electrical forces FE = qq ′ 4πε 0 r 2 between the nuclei, then nuclear fusion reactions can occur. The equation of correlation between gravitational mass and inertial mass [1]
⎧ ⎡ 4 ⎤⎫⎪ qq′ 4πε μr jrms ⎪ ⎢ 0 ⎨1− 2 1+ K 2 3 −1⎥⎬ > ⎥⎪ Gmi0mi′0 σρ f ⎪⎩ ⎢⎣ ⎦⎭
⎧ ⎡ 3 ⎤⎫ μ ⎛ σ ⎞ E4 ⎥⎪ ⎪ ⎢ χ = = ⎨1 − 2 1 + 2 ⎜⎜ ⎟⎟ 2 −1 ⎬ ⎥ mi ⎪ ⎢ 4c ⎝ 4πf ⎠ ρ ⎥⎦⎪⎭ ⎩ ⎢⎣ mg
(1)
tells us that the gravitational mass can be strongly increased. Thus, if E = E m sin ωt , then the average value for 2
E is equal to
1
2
2 m
E , because E varies
sinusoidaly ( E m is the maximum value for E ). On the other hand, Erms = Em
2.
Consequently, we can replace E 4 for 4 . In addition, as j = σE (Ohm's E rms vectorial Law), then Eq. (1) can be rewritten as follows χ=
⎧ ⎡ ⎤⎫⎪ μ j4 ⎪ = ⎨1− 2⎢ 1+ K r 2rms3 −1⎥⎬ mi0 ⎪ ⎢ ⎥⎪ σρ f ⎦⎭ ⎩ ⎣ mg
(2)
FG = Gmgm′g r2 = χ2Gmi0mi′0 r2 = 2
⎧ ⎡ ⎤⎫⎪ μ j4 ⎪ = ⎨1− 2⎢ 1+ K r 2rms3 −1⎥⎬ Gmi0mi′0 r2 ⎥⎪ σρ f ⎪⎩ ⎢⎣ ⎦⎭
(3)
In order to obtain FG > FE we must have
(4)
The carbon fusion is a set of nuclear fusion reactions that take place in massive stars (at least 8M sun at birth). It requires high temperatures ( > 5×108 K ) and densities ( > 3 × 10 9 kg .m −3 ). The principal reactions are: 23
12
C + 12C →
20
Na + p + 2.24 MeV
Ne + α + 4.62 MeV
24
Mg + γ +13.93 MeV
In the case of Carbon nuclei (12C) of a thin carbon wire (carbon fiber) ( σ ≅ 4×104 S.m−1 ; ρ = 2.2 ×103 S.m−1 ) Eq. (4) becomes ⎧ ⎡ 4 ⎤⎫⎪ e2 ⎪ ⎢ −39 jrms ⎥ − + × − 1 2 1 9 . 08 10 1 > ⎨ ⎬ f 3 ⎥⎪ 16πε0Gm2p ⎪⎩ ⎢⎣ ⎦⎭
2 whence we conclude that the condition for the 12C + 12C fusion reactions occur is jrms
3 > 1.7 ×1018 f 4
(5)
If the electric current through the carbon wire has Extremely-Low Frequency (ELF), for example, if f = 1μHz , then the current density, j rms , must have the following value:
(6)
jrms > 5.4 ×1013 A.m−2
Since j rms = i rms S where S = πφ 2 4 is the area of the cross section of the wire, we can conclude that, for an ultra-thin carbon wire with 10μm -diameter, it is necessary that the current through the wire, irms , have the following intensity
irms > 42.4 A
In order to obtain an ELF current with these characteristics −6 f = 10 Hz; i rms = 42.4 A we can start from the following background: Consider an electric current I , which is the sum of a sinusoidal current iosc = i0 sin ωt 1 and the DC current I DC , i.e., I = I DC + i0 sin ωt ; ω = 2πf . If i0 << I DC then I ≅ I DC . Thus, the current I varies with the frequency f , but the variation of its intensity is quite small in comparison with I DC , i.e., I will be practically constant (Fig. 1). Thus, we obtain i rms ≅ I DC ( See Fig.2).
(
)
i0
irms > 4.24 k A
Obviously, this current will explode the carbon wire. However, this explosion becomes negligible in comparison with the very strong gravitational implosion, which occurs simultaneously due to the enormous increase in intensities of the gravitational forces among the carbon nuclei produced by means of the ELF current through the carbon wire as predicted by Eq. (3). Since, in this case, the gravitational forces among the carbon nuclei become greater than the repulsive electric forces among them the result is the production of 12C + 12C fusion reactions. Similar reactions can occur by using a lithium wire. In addition, it is important to note that j rms is directly proportional
3 4
to f (Eq.5). −8
Thus,
for
example, if f = 10 Hz , the current necessary to produce the fusion reactions will be i rms = 130 A . However, it seems that in practice is better to reduce the diameter of the wire. For a diameter of 1μm (10 −6 m) , the intensity of the current must have the following value
IDC
I = IDC + iosc
t Fig. 1 - The electric current I varies with frequency f . But the variation of I is quite small in comparison with I DC due to i o << I DC . In this way, we can consider I ≅ I DC .
1
In order to generate the ELF electric current
iosc with f = 10 −6 Hz , we can use the widelyknown Function Generator HP3325A (Op.002 High Voltage Output) that can generate sinusoidal voltages with extremely-low frequencies down to
f = 1 × 10 −6 Hz and amplitude up to 20V (40Vpp into 500Ω load). The maximum output current is 0.08 App ; output impedance <2Ω at ELF .
3
i osc
ε2
+ −
R
I DC
~
Ultra thin wire
f = 1μHz
i rms ≅ I DC
I = I DC + i osc
Fig. 2 – Electrical Circuit
REFERENCES
[1] DeAquino, F. (2002). Mathematical Foundations of the Relativistic Theory of Quantum Gravity. Physics/0212033. [2] De Aquino, F. (2007) Gravity Control by means of Electromagnetic Field through Gas at Ultra-Low Pressure. Physics/0701091.