Trans-ocean wireless transfer of electricity from continent to continent

Abstract

The author offers collections from his previous research of the revolutionary new ideas: wireless transfer of electric energy to a long distance – from one continent to another continent through the Earth's ionosphere and the storage of the electric energy in the ionosphere. Earlier he also suggested the use of electronic tubes as the method for transportation of electricity into outer space and the 100-km electrostatic space towers for connection to the Earth's ionosphere. Earlier a connection to the Earth's ionosphere using 100-km solid or inflatable towers was suggested. however, the technology faces difficulties. In this work, connection to the Earth's ionosphere by thin plastic tubes supported in the atmosphere by electron gas and electrostatic force is researched. Building this system is cheap and easy using the current technology. The computation allows estimating the possibility of the suggested method.

Keywords:

• transferring of electricity in space
• transfer of electricity to spaceship, Moon, Mars
• plasma MagSail
• electricity storage
• ionosphere transfer of electricity

Introduction

The production, storage and transfer of large amounts of electric energy are an enormous problem for humanity. These spheres of industry are searching for and greatly need revolutionary ideas. Although in production of energy, space launch and flight we have new ideas (Bolonkin 1982, 1983a, 1983b, 2002, 2003, 2005, 2006a, 2006b, 2007a, 2007b, 2008a, 2008b, 2009, Krinker 2009), the new revolutionary ideas in transferring and storage of energy are only in the research stage (Bolonkin 2006a, 2006b, 2007a, 2007b, 2008a, 2008b, 2009).

Efficient transfer of electric energy to long distances is an important mega problem (intranational, international and intercontinental). The consumption of electric energy strongly depends on time (day or night), weather (hot or cold) or season (summer or winter). But an electric station can operate most efficiently in a permanent base-load generation regime. We need to transfer energy to long distances to any region that requires a supply at any given moment or in the special hydro-accumulator stations. Nowadays, a large amount of loss occurs from such energy transformation. One solution to this macro-problem is to transfer energy from Europe to the USA during night-time in Europe and from the USA to Europe during night-time in the USA. Another solution is efficient energy storage, which allows people the option to save electric energy.

The storage of a large quantity of electric energy can help to solve the problem of cheap space launch. The problem of acceleration of a spaceship can be solved by the use of a new linear electrostatic engine suggested by Bolonkin (2005) or a Magnetic Space Launcher suggested by Bolonkin (2009). However, the cheap cable space launch suggested by Bolonkin (2006a, 2006b) requires the use of gigantic energy in a short time period. (It is inevitable for any launch method because we must accelerate large masses at very high speed, 8–11 km/s.) But it is impossible to turn off the whole system and connect all electric stations to one customer. The suggested electric energy storage method can help solve this mega problem for humanity.

The idea of wireless transfer of energy through the ionosphere was suggested and researched by the author in his earlier studies (Bolonkin 1982, 1983a, 1983b, 2002, 2003, 2005, 2006a, 2006b, 2007a, 2007b, 2008a, 2008b). The connection to the Earth's ionosphere by the 100-km solid, inflatable, electrostatic or kinetic towers was suggested (Bolonkin 2002, 2003, 2006a, 2006b). But all are expensive and difficult using the current technology.

Wireless transfer of electric energy in the Earth

The idea of energy transfer from one continent to another continent without wires is interesting. The concept of resistance of the conducting medium being infinity (very large) does not depend on distance, is widely used in communication. The sender and the receiver are connected by only one wire, the other wire is the Earth. The author offers to use the Earth's ionosphere as the second plasma cable. It is known that the Earth has the first ionosphere layer E at an altitude of about 100 km (Figure 1). The concentration of electrons in this layer reaches 5 × 10⁴ 1/cm³ during the daytime and 3.1 × 10³ 1/cm³ at night (Figure 1). This layer can be used as a conducting medium for transferring electric energy and for communication to any point of the Earth. We need a minimum of two space 100-km towers (Figure 2). The cheap optimal inflatable, kinetic and solid space towers are suggested and researched by Bolonkin (2002, 2003, 2006a, 2006b, 2007b). Additional innovations are a large inflatable conducting balloon at the end of the tower and large conducting plates in the sea (ocean) that would dramatically decrease the contact resistance between the electric system and conducting medium.

Figure 1 Concentration/cm³ of electrons ( = ions) in the Earth's atmosphere during the day and night in the D, E, F1 and F2 layers of ionosphere.

Figure 2 Using the ionosphere as a conducting medium for transferring a large amount of electric energy between continents and as a large storage of electric energy. Notations: 1, Earth; 2, space tower (or electron tube) about 100 km high; 3, conducting E layer of the Earth's ionosphere and; 4, back connection through the Earth.

Theory and computation of these ideas are presented in the ‘Macroprojects’ section.

However, the solid 100-km space towers are very expensive. The main innovation in this work is the connection to the ionosphere by a cheap film tube filled with electron gas.

Electronic tubes

Bolonkin's (1982, 1983a, 1983b) first innovations in electrostatic applications were developed in 1982–1983.

Later, a series of articles on this topic were published by Bolonkin (2002, 2003, 2005, 2006a, 2006b, 2007a, 2007b, 2008a, 2008b, 2009). In particular, in the work of Bolonkin (2007a, 2008a), the theory of electronic gas and its application to building (without space flight!) inflatable electrostatic space tower up to the stationary orbit of the Earth's satellite geosynchronous earth orbit (GEO) was developed.

In the given work, this theory was applied to special inflatable electronic tubes made from thin insulator film. It is shown that the charged tube filled with electron gas is electrically neutral, which can have a high internal pressure on the electron gas.

The main property of the AB electronic tube is a very low electric resistance because electrons have small friction on the tube wall. (In conventional solid (metal) conductors, the electrons strike against the immobile ions located in the whole volume of the conductor.) The abnormal low electric resistance was found along the lateral axis only in nanotubes (they have a tube structure!). In theory, metallic nanotubes can have an electric current density (along the axis) more than 1000 times greater than metals such as silver and copper. Nanotubes have excellent heat conductivity along the axis up to 6000 W/m K. Copper, by contrast, has only 385 W/m K. The electronic tubes explain why there is this effect. Nanotubes have the tube structure and electrons can freely move along the axis (they have friction only on the tube wall).

Moreover, the moving electrons produce a magnetic field. The author shows that this magnetic field presses against the electron gas. When this magnetic pressure equals the electrostatic pressure, the electron gas may not remain in contact with the tube walls and their friction becomes zero. The electron tube effectively becomes a superconductor for any surrounding temperature, even higher than the room temperature! The author derives conditions for it and shows how we can significantly decrease the electric resistance.

Description, innovations and applications of electronic tubes

An electronic AB tube is a tube filled with electron gas (Figure 3). Electron gas is the lightest gas known in nature, far lighter than hydrogen. Therefore, tubes filled with this gas have the maximum possible lift force in the atmosphere (equal essentially to the lift force of the vacuum). The applications of electron gas are based on one little-known fact – the electrons located within a cylindrical tube having a positively charged cover (envelope) are in neutral-charge conditions – the total attractive force of the positive envelope plus negative contents equals zero. This means that the electrons do not adhere to the positively charged tube cover. They will freely fly into the AB tube. It is known, if the Earth (or another planet) would have, despite the massive pressures there, an empty space in the Earth's very core, any matter in this (hypothetical!) cavity would be in a state of weightlessness (free fall). All around, attractions balance, leaving no vector ‘down’.

Figure 3 Electronic vacuum AB tube. (a) Cross section of tube. (b) Side view. Notations: 1, internal part of tube filled by free electrons; 2, insulator envelope of tube; 3, positive charges on the outer surface of envelope (over this may be an additional film insulator) and 4, atmospheric pressure.

Analogously, this means that the AB tube is a conductor of electricity. Under electric tension (voltage), the electrons will collectively move without internal friction, with no vector ‘down’ to the walls, where friction might lie in contrast to the movement of electrons in metal (where moving electrons impact against a motionless ion grate). In the AB tube, we have only electron friction on the tube wall. This friction is significantly less than the friction electrons would experience against ionic structures – and, therefore, so is the electrical resistance.

When the density of electron gas equals n = 1.65 × 10¹⁶/r 1/m³ (where r is radius of tube, m), the electron gas has pressure equal to atmospheric pressure of 1 atm (see research below). In this case, the tube cover may be a very thin – though well sealed – insulator film. The outer surface of this film is charged positively by static charges equal to the electron charges and the AB tube is thus an electrically neutral body.

Moreover, when electrons move into the AB tube, the electric current produces a magnetic field (Figure 4). This magnetic field compresses the electron cord and decreases the contact (and friction and thus electric resistance) between electrons and tube walls. In the theoretical section a simple relation is given between the electric current and linear tube charge when the magnetic pressure is equal to electron gas pressure i = cτ [where i is electric current (A); c = 3 × 10⁸ m/s is the light speed; τ is tube linear electric charge (C/m)]. In this case, the electron friction equals zero and the AB tube becomes superconductive at any outer temperature. Unfortunately, this condition requires the electron speed to be equal to the light speed. However, there is no problem in setting the electron speed very close to light speed. This means that we can make the electric conductivity of AB tubes very close to superconductivity almost regardless of the outer temperature.

Figure 4 Electrostatic and magnetic intensities into AB tube. (a) Electrostatic intensity (pressure) via tube radius. (b) Magnetic intensity (pressure) from electric current vs. tube radius.

Theory of plasma transfer for electric energy, estimations and computations

Long-distance wireless transfer of electricity on Earth

The transfer of electric energy from one continent to another continent through ionosphere and the Earth's surface is described again. For this transfer, we need two space towers 100-km in height; the towers must have a large conducting ball at the top end and underground (better, underwater) plates for decreasing the contact electric resistance (a good Earth ground). The contacting ball is a large (up to 100–200 m diameter) inflatable gas balloon having a conductive layer (covering or coating).

Let us suggest a method which allows computation of the parameters and possibilities of this electric line.

The electric resistance and other values for a conductive medium can be estimated by the following equations:

where R is the electric resistance of a conductive medium (Ω) (for sea water ρ = 0.3 Ω m); a is the radius of the contacting (source and receiving sphere) balloon (m); λ is the electric conductivity (Ω m)^− 1 and E _a is electric intensity on the balloon surface (V/m).

The conductivity λ of the E layer of the Earth's ionosphere as a rare ionised gas can be estimated by the equations

where n = 3.1 × 10⁹–5 × 10¹¹ 1/m³ is the density of free electrons in E layer of the Earth's ionosphere; τ is the time of electrons on their track (s); L is the length traversed by electrons on their track (m); v is the average electron velocity (m/s); r _m  = 3.7 × 10¹⁰ m (for hydrogen N₂) is the diameter of gas molecule; p = 3.2 × 10³ N/m² is the gas pressure for altitude of 100 km and m _e  = 9.11 × 10³¹ kg is the mass of electrons.

The transfer power and efficiency are

where R _c is the common electric resistance of the conductive medium (Ω) and R is the total resistance of the electric system (Ω).

See the detailed computations in the ‘Macroprojects’ section.

The Earth's ionosphere as the gigantic storage of electric energy

The Earth's surface and the Earth's ionosphere are gigantic spherical condensers. The electric capacitance and electric energy stored in this condenser can be estimated by equations:

where C is the capacity of condenser (C); R ₀ = 6.369 × 10⁶ m is the radius of the Earth; H is the altitude of E layer (m); ϵ₀ = 8.85 × 10¹² F/m is the electrostatic constant and E is the electric energy (J).

The leakage current is

where i is the leakage currency (A); λ _a is the conductivity of the Earth's atmosphere (Ω m^− 1); n _a is the free electron density of the atmosphere (1/m³); μ = 1.3 × 10⁴ m²/(sV) (for N₂) is the ion mobility; R _a is the Earth's atmospheric resistance (Ω) and t is the time of discharging in times (s).

Theory and computation of electronic tube

For the interested reader, the evidence of the main equations, estimations and computations is given below.

1. Relation between the linear electric charge of the tube and electron gas pressure on the tube surface:

where p is the electron pressure (N/m²); ϵ₀ = 8.85 × 10^− 12 F/m is the electrostatic constant; k = 9 × 10⁹ Nm²/C² is the electrostatic constant; E is the electric intensity, V/m; τ is the linear charges of tube (C/m) and r is radius of tube (m).

For example, for atmospheric pressure p = 10⁵ N/m² we receive E = 1.5 × 10⁸ V/m, N/C, the linear charge τ = 0.00833r (C/m).

2. Density of electron (ion) in 1 m³ in tube.

where n is the charge (electron or ion) density (1/m³); e = 1.6 × 10^− 19 C is the charge of electron; m _e  = 9.11 × 10^− 31 kg is the mass of electron; m _p  = 1.67 × 10^− 27 kg is the mass of proton; M _e is the mass density of electron (kg/m³) and M _i is the mass density of ion (kg/m³).

For electron pressure 1 atm, the electron density (number of particles in 1 m³) is n = 1.65 × 10¹⁶/r.

3. Electric resistance of AB tube. We estimate the friction of electrons on the tube wall by gas-kinetic theory:

where F _B is the electron friction (N); η_B is the coefficient of friction; S is the friction area (m²); V is the electron speed (m/s); ρ is the density of electron gas (kg/m³); is the relative electron friction (N/m²) and j is the current density (A/m²).

4. Electric loss. The electric loss (power) in the tube is

where P _T is the electric loss (W); L is the tube length (m) and i is the electric current (A).

5. Relative electric loss is

Compare the relative loss of the suggested electric (tube) line and the conventional electric long-distance line, assume that the electric line has length L = 2000 km, electric voltage U = 10⁶ V, electric current i = 300 A and atmospheric pressure in the tube, and suggested line has tube r = 1 m, the relative loss equals  = 0.005. For a conventional electric line having a cross-sectional copper wire of 1 cm², the relative loss is  = 0.105, that is, 21 times more than the suggested electric line. The computation of Equation (10) for atmospheric pressure and for ratio L/U = 1 is presented in Figure 5. As you see for electric line L = 1000 km, voltage U = 1 million V, tube radius r = 2.2 m and the electric current i = 50 A, the relative loss of electric power is one/millionth (10^− 6) (only 50 W for transmitted power of 50 millions watt!). For connecting the Earth's surface with the ionosphere, we need only 100-km electronic tube or 100-km electrostatic tower (Bolonkin 2007b).

Figure 5 Relative electric loss via radius of tube for electric current i = 50–1000 A, the atmospheric pressure in the tube and ratio L/U = 1.

Moreover, the suggested electric line is many times cheaper and may be levitated into the atmosphere at high altitude. It does not need a mast and ground, does not require expensive copper and does not allow easy surface access to line tapping thieves who wish to steal the electric energy. And this levitating electric line may be suspended with equal ease over the sea as over land.

6. Lift force of tube (L _F,1, kg/m) and mass of 1 m length of tube (W ₁, kg/m) are given as

where ρ is the air density, at sea level ρ = 1.225 kg/m³; v is the volume of 1 m of tube length (m³); γ is the density of tube envelope, for most plastics γ = 1500–1800 kg/m³ and δ is the film thickness (m).

Example

For r = 10 m and δ = 0.1 mm, the lift force is 384 kg/m and cover mass is 11.3 kg/m.

7. Artificial fibre and tube (cable) properties (Kikoin 1976, Galasso 1989, Dresselhous 2000, AIP 2003). Cheap artificial fibres are currently being manufactured, which have tensile strengths of 3–5 times more than steel and densities 4–5 times less than steel. There are also experimental fibres (whiskers) that have tensile strengths 30–100 times more than steel and densities 2–5 times less than steel. For example, in Galasso (1989, p. 158), there is a fibre (whisker) C _D , which has a tensile strength of σ = 8000 kg/mm² and density (specific gravity) of γ = 3.5 g/cm³. If we use an estimated strength of 3500 kg/mm² (σ = 7·10¹⁰ N/m², γ = 3500 kg/m³), then the ratio is γ/σ = 0.1 × 10^− 6 or σ/γ = 10 × 10⁶.

Although the described (Galasso 1989) graphite fibres are strong (σ/γ = 10 × 10⁶), they are at least still 10 times weaker than what theory predicts. A steel fibre has a tensile strength of 5000 MPa (500 kg/mm²), the theoretical limit is 22,000 MPa (2200 kg/mm²) (1987); polyethylene fibre has a tensile strength of 20,000 MPa with a theoretical limit of 35,000 MPa (1987). The very high tensile strength is due to its nanotube structure (Dresselhous 2000).

Apart from unique electronic properties, the mechanical behaviour of nanotubes is also of interest because nanotubes are seen as the ultimate carbon fibre, which can be used as reinforcements in advanced composite technology. Earlier theoretical work and recent experiments on individual nanotubes (mostly multi wall nano tubes, MWNTs) have confirmed that nanotubes are one of the stiffest materials ever made. Although carbon–carbon covalent bonds are one of the strongest in nature, a structure based on a perfect arrangement of these bonds oriented along the axis of nanotubes would produce an exceedingly strong material. Traditional carbon fibres show high strength and stiffness, but fall far short of the theoretical, in-plane strength of graphite layers by an order of magnitude. Nanotubes come close to being the best fibre that can be made from graphite.

For example, whiskers of carbon nanotube (CNT) material have a tensile strength of 200 GPa and a Young's modulus over 1 TPa (1999). The theory predicts 1 TPa and a Young's modulus of 1–5 TPa. The hollow structure of nanotubes makes them very light [the specific density varies from 0.8 g/cc for single wall nano tubes (SWNTs) to 1.8 g/cc for MWNTs, compared to 2.26 g/cc for graphite or 7.8 g/cc for steel). Tensile strength of MWNTs nanotubes reaches 150 GPa.

In 2000, a multi-walled CNT was tested to have a tensile strength of 63 GPa. Since CNTs have a low density for a solid of 1.3–1.4 g/cm³, its specific strength of up to 48,000 kN·m/kg is the best of known materials, compared to high-carbon steels of 154 kN·m/kg.

The theory predicts the tensile stress of different types of nanotubes such as Armchair SWNT – 120 GPa and Zigzag SWNT – 94 GPa.

Specific strength (strength/density) is important in the design of the systems presented in this paper; nanotubes have values of at least two orders of magnitude greater than steel. Traditional carbon fibres have a specific strength 40 times that of steel. Since nanotubes are made of graphitic carbon, they have good resistance to chemical attack and have high thermal stability. Oxidation studies have shown that the onset of oxidation shifts by about 100°C or higher in nanotubes compared to high modulus graphite fibres. In a vacuum, or reducing atmosphere, nanotube structures will be stable to any practical service temperature (in vacuum up to 2800°C and in air up to 750°C).

In theory, metallic nanotubes can have an electric current density (along axis) more than 1000 times greater than metals such as silver and copper. Nanotubes have excellent heat conductivity along axis up to 6000 W/m K. Copper, by contrast, has only 385 W/m K.

About 60 tons/year of nanotubes are produced now (2007). Price is about $100–50,000/kg. Experts predict the production of nanotubes on the order of 6000 tons/year and with a price of $1–100/kg to 2012.

Commercial artificial fibres are cheap and widely used in tyres and countless other applications. The authors have found only older information about textile fibre for inflatable structures (Harris 1973). This refers to DuPont textile Fibre B and Fibre PRD-49 for tyre cord. They are six times as strong as steel (psi is 400,000 or 312 kg/mm²) with a specific gravity of only 1.5 g/cm³. Minimum available yarn size (denier) is 200 ft, tensile modulus is 8.8 × 10⁶ psi (B) and 20 × 10⁶ psi (PRD-49), and ultimate elongation (%) is 4 (B) and 1.9 (PRD-49). Some data are given in Table 1.

Table 1 Material properties.

Material	Tensile strength (kg/mm^2)	Density (g/cm^3)
Whiskers
AlB12	2650	2.6
B	2500	2.3
B4C	2800	2.5
TiB2	3370	4.5
SiC	1380–4140	3.22
Other materials
Steel prestressing strands	186	7.8
Steel piano wire	220–248
Steel A514	76	7.8
Aluminium alloy	45.5	2.7
Titanium alloy	90	4.51
Polypropylene	2–8	0.91
Fibres
QC-8805	620	1.95
TM9	600	1.79
Allien 1	580	1.56
Allien 2	300	0.97
Kevlar or Twaron	362	1.44
Dynecta or Spectra	230–350	0.97
Vectran	283–334	0.97
E-Glass	347	2.57
S-Glass	471	2.48
Basalt fibre	484	2.7
Carbon fibre	565	1.75
Carbon nanotubes	6200	1.34
Source: Kikoin (1976), Galasso (1989), Dresselhous (2000), AIP (2003).

Industrial fibres have σ up to 500–600 kg/mm², γ up to 1500–1800 kg/m³ and σ/γ = 2.78 × 10⁶. But we are projecting the use of the cheapest films and cables applicable in this work (safety σ = 100–200 kg/mm²).

8. Dielectric strength of insulator. As seen above, the tube needs film that separates the positive charges located in a conductive layer from the electron gas located in the tube. This film must have a high dielectric strength. Thus material can keep a high E (see Table 2 taken from Bolonkin (2005)).

Table 2 Properties of various good insulators (re-calculated in metric system).

Insulator	Resistivity (Ω m)	Dielectric strength, E i (MV/m)	Dielectric constant, ϵ
Lexan	10^17–10^19	320–640	3
Kapton H	10^19–10^20	120–320	3
Kel-F	10^17–10^19	80–240	2–3
Mylar	10^15–10^16	160–640	3
Parylene	10^17–10^20	240–400	2–3
Polyethylene	10^18–5 × 10^18	40–680^a	2
Poly (tetrafluoroethylene)	10^15–5 × 10^19	40–280^b	2
Air (1 atm, 1 mm gap)		4	1
Vacuum (1.3 × 10^–3 Pa, 1 mm gap)		80–120	1
Sources: Encyclopedia of Science & Technology (New York, 2002, Vol. 6, p. 104, 229, 231) and Kikoin (1976). Note: Dielectric constant ϵ can reach 4.5–7.5 for mica (E is up 200 MV/m), 6–10 for glasses (E = 40 MV/m) and 900–3000 for special ceramics (marks are CM-1 and T-900; Kikoin 1976, p. 321) (E = 13–28 MV/m). Ferroelectrics have ϵ up to 10^4–10^5. Dielectric strength appreciably depends on surface roughness, thickness, purity, temperature and other conditions of materials. Very clean material without admixture (for example, quartz) can have dielectric strength up to 1000 MV/m. As seen, we have the needed dielectric material, but it is necessary to find good (and strong) resistive materials and to research conditions which increase the dielectric strength.
a For room temperature 500–700 MV/m.
b 400–500 MV/m.

9. Tube cover thickness. The thickness of the tube's cover may be found from equation

where p is the electron pressure minus atmospheric pressure (N/m²). If electron pressure is little more than the atmospheric pressure, the tube cover thickness may be very thin.

10. Mass of tube cover. The mass of tube cover is

where M ₁ is 1 m² cover mass (kg/m²) and M is cover mass (kg).

11. Volume V and surface of tube s are given as

where V is the tube volume (m³) and s is the tube surface (m²).

12. Relation between tube volume charge and tube liner charge for neutral tube is given as

where ρ is the tube volume charge (C/m³) and τ is the tube linear charge (C/m).

13. General charge of tube. We get the equation from

where Q is the total tube charge (C) and ϵ is the dielectric constant (see Table 2).

14. Charging energy. The charged energy is computed by the following equation:

where W is the charge energy (J) and U is the voltage (V).

15. Mass of electron gas. The mass of electron gas is

where M _e is the mass of electron gas (kg); m _e  = 9.11 × 10^− 31 kg is the mass of electron; N is number of electrons and e = 1.6 × 10¹⁹ C is the electron charge.

16. Transfer of matter (matter flow of ion gas). If we change the electron gas with ion gas, our tube transfer charged matter with very high speed is given as

where M is the mass flow (kg/s); M _i is the gas ion density (kg/m³); μ = m _i /m _p and V is the ions speed (m/s).

Example

We want to transfer to a remote location the nuclear breeder fuel – Uranium-238 (μ = 238) by line having i = 1000 A, r = 1 m, ion gas pressure 1 atm. One day contains 86,400 s.

Equation (19) gives M = 214 kg/day and speed V = 120 km/s. The AB tubes are suitable for transferring small amounts of a given matter. For transferring a large mass, the diameter of tube and electric current must be larger.

We must also have efficient devices for ionisation and utilisation of the de-ionisation (recombination) energy.

The suggested method allows direct conversion of the ionisation energy of the electron gas or ion gas to light (for example by connection between the electron and ion gases).

17. Electron gas pressure. The electron gas pressure may be computed using Equation (11). This computation is presented in Figure 6.

Figure 6 Electron pressure vs. electric intensity.

As seen, the electron pressure reaches 1 atm for an electric intensity of 150 MV/m and for negligibly small mass of the electron gas.

18. Power for support of charge. Leakage current (power) through the cover may be estimated by the following equation:

where I is the electric current (A); U is the voltage (V); R is the electric resistance (Ω); ρ is the specific resistance (Ω m) and s is the tube surface area (m²).

The estimation gives the support power a small value.

Quasi-superconductivity of AB tube

The proposed AB tube may become what we may term ‘quasi-superconductive’ when magnetic pressure equals electrostatic pressure. In this case, electrons cannot contact the tube wall, do not experience resistance friction and thus the AB tube experiences this ‘quasi-superconductivity’.

We get the following condition:

where P _e is the electronic pressure (N/m²); P _m is the magnetic pressure (N/m²); B is the magnetic intensity (T); E is the electric intensity (V/m); c is the light speed, c = 3 × 10⁸ m/s; and ϵ₀ and μ₀ = 4π × 10^− 7 are the electrostatic and magnetic constants, respectively. The relation E = cB is an important result and condition of tube superconductivity. For electron pressure of 1 atm in the tube, E = 1.5 × 10⁸ V/m (see above) and B = 0.5 T.

From Equation (21), we obtain the relation between the electric current and the tube charge for AB tube ‘quasi-superconductivity’ as

where i is the electric current (A) and τ is linear charge of tube (C/m).

For electron pressure equal to 1 atm and r = 1 m, the linear tube charge is τ = 0.00833 C/m (see above) and the required electric current is i = 2.5 × 10⁶ A (j = 0.8 A/m²). For r = 0.1 m, the current equals i = 2.5 × 10⁵ A. And for r = 0.01 m, the current equals i = 2.5 × 10⁴ A.

Unfortunately, the required electron speed (for true and full normal temperature ‘superconductivity’) equals light speed c,

This means that we cannot exactly reach the required value, but we can come very close and we can have very low electric resistance of the AB tube.

Information about high speed of electron and ion beam is as follows. Here, is the relativistic scaling factor, β = v/c, v is relative system speed; quantities in analytical formulae are expressed in SI or cgs units, as indicated; in numerical formulae, I is in amperes (A); B is in gauss (G, 1 T = 10⁴ G); electron linear density N is in cm^− 1; temperature, voltage and energy are in K, V and MeV, β _z  = v _z /c, and k is Boltzmann's constant.

If the system is moved only along the x-axis, the Lorentz transformation is (‘ ' ’ is marked mobile system):

where t is the time (s); w is the speed in systems (m/s); v is the system speed (m/s); M is the relativistic mass (kg); p is the momentum and f is the force (N).

For computation, electrostatic and magnetic fields of light are used in the equations of relativistic theory (Lorenz's equations, in the immobile system (marked ‘₁’) the electric field is directed along the y-axis and the magnetic field is directed along the z-axis):

where ‘₁’ means the immobile system coordinate; E is the electric intensity (V/m); H is the magnetic intensity (A/m); v is the speed of the mobile system coordinate along x-axis (m/s); D is the electric displacement (C/m²) and β = v/c is relative speed of one system with respect to the other.

Relativistic electron gyroradius:

Relativistic electron energy:

Bennett pinch condition:

Alfven–Lawson limit:

The ratio of net current to I _A is given as

Here, ν = Nr _e is the Budker number, where  cm is the classical electron radius. Beam electron number density is given as

where J is the current density in A cm^− 2. For a uniform beam of radius a (in cm):

and

Child's law: Non-relativistic space-charge-limited current density between parallel plates with voltage drop V (in MV) and separation d (in cm) is given as

The condition for a longitudinal magnetic field B _z to suppress filamentation in a beam of current density J (in A cm^− 2) is

Kinetic energy necessary to accelerate a particle is

The de Broglie wavelength of particle is λ = h/p, where h = 6.6262 × 10^− 34 J s is the Planck constant and p is the particle momentum. Classical radius of electron is 2.8179 × 10^− 15 m.

Macroprojects

Wireless transfer of energy between the Earth's continents

Let us consider the following initial data: gas pressure at altitude 100 km is p = 3.2 × 10³ N/m²; temperature is 209 K; diameter of nitrogen N₂ molecule is 3.7 × 10¹⁰ m; the ion/electron density in ionosphere is n = 10¹⁰ 1/m³; radius of the conductive inflatable balloon at the top of the space tower (mast) is a = 100 m (contact area is S = 1.3 × 10⁵ m²); specific electric resistance of sea water is 0.3 Ω m; and area of the contact sea plate is 1.3 × 10³ m² (Figure 2).

The computation using Equations 1(2-17) (Bolonkin 2007a) gives: electron track in ionosphere is L = 1.5 m; electron velocity is υ = 9 × 10⁴ m/s; track time is τ = 1.67 × 10⁵ s; specific resistance of ionosphere is ρ = 4.68 × 10³ (Ω m)¹; contact resistance of top ball (balloon) is R ₁ = 0.34 Ω; contact resistance of the lower sea plates is R ₂ = 4.8 × 10³ Ω; and electric intensity on ball surface is 5 × 10⁴ V/m.

If the voltage is U = 10⁷ V, total resistance of electric system is R = 100 Ω, then electric current is I = 10⁵ A, transferred power is W = IU = 10¹² W and coefficient of efficiency is 99.66%. That is a power of 1000 powerful electric plants having power of one billion watts. In practice, we are not limited in transferring any energy in any Earth's point having the 100 km space mast and further transfer by ground-based electric lines in any geographical region of radius 1000–2000 km.

The Earth's ionosphere as the storage of electric energy

Using Equations (18) and (19) (Bolonkin 2007a), we find the Earth's ionosphere capacity C = 4.5 × 10² C. If U = 10⁸ V, the storage energy is E = 0.5CU ² = 2.25 × 10¹⁴ J. This is large energy. About 20 to 100 tons rocket may be launched into space in 100-km orbit. This energy is produced by a powerful electric plant in 1 day.

Let us now estimate the leakage of current. Cosmic rays and the Earth's radioactivity create 1.5–10.4 ions every second in 1 cm³. But as they quickly recombine to form neutral molecules, the ions concentration is small. We take the ion concentration of the lower atmosphere n = 10⁶ 1/m³. Then the specific conductivity of the Earth's atmosphere is 2.1 × 10¹⁷ (Ω m)^− 1. The leakage current is i = 10⁷ × U. The altitude of the E layer is 100 km. We consider a thickness of the atmosphere as only 10 km. Then the conductivity of the Earth's atmosphere is 10²⁴ (Ω m)^− 1, resistance is R _a  = 10²⁴ Ω and the leakage time (decrease of energy in e = 2.73 times) is 1.5 × 10⁵ years.

As can be seen clearly, the Earth's ionosphere may become a gigantic storage site of electricity.

The electric resistance of the electronic tube is small.

Discussion

The suggested ideas and innovations may create a jump in space and energy industries. The author has made initial basic researches that conclusively show huge industrial possibilities suggested by the methods and installations.

The suggested inflatable electrostatic AB tube has indisputably remarkable operational advantages in comparison with the conventional electric lines. The AB tube may also be used for transferring electricity to long distances without using the ionosphere.

The main innovations and applications of AB tubes are

1.	Transfer of electric energy to a long distance (up to 10,000 km) with a small electric loss.
2.	‘Quasi-superconductivity’. The suggested AB tube may have a very low electric resistance for any temperature; because, the electrons in the tube do not have ions and do not lose energy by impacts with ions. The impact of the electron with electron does not change the total impulse (momentum) of a couple of electrons and electron flow. If this idea is proved experimentally, this will be a big breakthrough in many fields of technology.
3.	Cheap electric lines suspended in high altitude (because the AB tube can have lift force in the atmosphere and does not need ground-mounted electric masts and other support structures).
4.	The big diameter AB tubes (including the electric lines for internal power) can be used as tramway for transportation.
5.	AB tubes can be used as vacuum tubes for an exit from the Earth's surface to outer space (out from the Earth's atmosphere). These may be used by an Earth telescope for the observation of the sky without atmospheric hindrances, or for sending of a plasma beam to space ships without atmospheric hindrances (Bolonkin 2006a, 2008b, Bolonkin and Cathcart 2009).
6.	Transfer of electric energy from continent to continent through the Earth's ionosphere (Bolonkin 2007a, 2008a).
7.	Inserting an anti-gravitator cable into a vacuum-enclosing AB tube for near-complete elimination of air friction (Bolonkin 2007a, 2008a). The same application for transmission of mechanical energy for long distances with minimum friction and losses (Bolonkin 2007a, 2008a).
8.	Increasing in some times the range of a conventional gun. They can shoot through the vacuum tube (up 4–6 km) and the projectile will fly in the rare atmosphere where air drag is small.
9.	Transfer of matter in a long distance with high speed (including in outer space, see author's other works).
10.	Interesting uses in nuclear and high energy physics engineering (inventions).

The suggested electronic gas may be used as filling gas for air balloons, dirigibles, energy storage, submarines and electric-charge devices (see also, Bolonkin 2007a, 2008a).

Further research and testing are necessary. As that is in science, the obstacles can slow, even stop applications of these revolutionary innovations.

Summary

This new revolutionary idea of wireless transfer of electric energy to long distance through the ionosphere or by the electronic tubes is suggested and researched. A rare plasma power cord as electric cable (wire) is used for it. It is shown that a certain minimal electric current creates a compressed force that supports the plasma cable in the compacted form. Large amounts of energy can be transferred many thousands of kilometres by this method. The requisite mass of plasma cable is merely hundreds of grams. It is computed that the macroproject: the transfer of a colossal amount of energy from one continent to another continent (for example, Europe to USA and back), using the Earth's ionosphere as a gigantic storage of electric energy (Bolonkin 1982, 1983a, 1983b, 2002, 2003, 2005, 2006a, 2006b, 2007a, 2007b, 2008a, 2008b, 2009) is possible.

The negative charged ions may also be used in the suggested current tube. See also Badescu et al. (2006), Bolonkin and Krinker (2009) and Bolonkin (2010)1,2.

Acknowledgement

The author wishes to acknowledge R.B. Cathcart (USA) for helping to correct the author's English.

Notes

1. Reader finds some of author's articles in http://Bolonkin.narod.ru/p65.htm, http://www.scribd.com and http://arxiv.org, search ‘Bolonkin’, in books ‘Non-Rocket Space Launch and Flight’, Elsevier, 2006, 488 pgs; ‘New concepts, Ideas, and Innovation in Aerospace, Technology and Human Science’, NOVA, 2008, 502 pgs.; Macro-Projects: Environment and Technology, NOVA, 2009, 536 pgs; ‘New Technologies and Revolutionary Projects’, Sbcribd, 2010, 324 pgs, Available from: http://www.scribd.com/doc/32744477.

2. Wikipedia. Space towers. Available from: http://wikipedia.org