receiver devices, which receive the power and convert it back to electric current which is used by an electrical load. At the transmitter the input power is converted to an oscillating electromagnetic field by an antenna. A similar antenna or coupling device at the receiver converts the oscillating fields to an AC electric current. An important parameter that determines the pattern of waves is wavelength, or length of the antenna, which determines the frequency [25] .
If an oscillating electrical current is applied to a conductive planet, electric and magnetic fields will appear in space around that planet. If those fields are some distance into space the planet can be modeled as a spherical antenna. Such an antenna can be an assemblage of conductors in the planet, rotating as an electrical motor in space. The actual values of the electromagnetic fields in space about the antenna are complicated and can change with distance from the planet in a number of ways. The oscillating electric and magnetic fields surrounding moving electric charges in a planet can be divided into two regions, depending on distance range from the planet. The boundary between the regions is not well defined. The fields have different characteristics in the near and far regions, and different approaches for transferring power.
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Electromagnetic waves are synchronized oscillations of electric and magnetic fields that propagate at the speed of light through space. The oscillations of the perpendicular fields are in the direction of energy and wave propagation, forming a transverse wave. The wave front of electromagnetic waves emitted from a point source, such as a planet, is a sphere. The position of an electromagnetic wave within the electromagnetic spectrum can be modeled by either its frequency of oscillation or its wavelength [28] . Electromagnetic waves consist of energy and angular momentum [29] . In space they impart those quantities to dark matter with which they interact.
This distance provides the limit between the near and far-field. The parameter D corresponds to the physical length of an antenna, or the diameter of the Sun. Having an antenna electromagnetically longer than one-half the dominated wavelength emitted, considerably extends the near-field effects. Additionally, a far-field region distance df must satisfy these two conditions.
In the case of the Sun we know the diameter at the equator to be 1.392 1012 meters, which is longer than the half-wavelength of the Earth or Mercury. Therefore, the Sun is treated as a long length antenna and the planets in our solar system are treated as short length, point source antennas. Having an antenna electromagnetically longer than one-half the dominated wavelength emitted considerably extends the near-field effects. When a long length antenna emits high frequency radiation, such as the Sun, it will have a near-field region larger than what would be implied by the shorter wavelength. Planets which resemble spherical rotating antennas operating at tremendously low frequency do not share the same characteristic of typical man-made antennas. Common antennas that we use on Earth usually operate at higher frequencies in the far-field range, whereas planetary antennas transmit and receive at very low frequencies in the near-field. Shown below are the Sun and Earth frequency calculations using Fraunhofer equation that extends the reactive and radiative near-field, as well as the far radiative field, to its maximum distance. Since planets are considered electrical machines the inductive reactance power transfer seems to best fit the model. The calculations below show the dominance and tremendous reach of the near-field in wireless electrical power transfer from the Sun to the Earth.
The near-field and far-field regions of the electromagnetic field around an antenna, such as the transmitting Sun or planet, are the result of radiation scattering off an object (Figure 5). Non-radiative near-field behaviors of electromagnetic fields dominate close to the antenna or scattering planets, while electromagnetic radiation far-field behaviors prevail at greater distances.
of near-field electromagnetic interaction. Thus, for cosmic power transfer the near-field is relevant as it most resembles the transformer and the flow of high power, as opposed to low power information signals we generally associate with antennas.
The far-field is the region in which the field acts as electromagnetic radiation. In this region, it is dominated by electric or magnetic fields with electric dipole characteristics. Far-field E and B field strength decreases inversely with distance from the source, resulting in an inverse-square law for the radiated power intensity of electromagnetic radiation. In the far-field region of an antenna absorption of the radiation does not feed back to the transmitter. In the far-field region, each part of the electromagnetic field is associated with a change in the other part, and the ratio of electric and magnetic field intensities is simply the wave impedance.
A simpler view of electromagnetic radiation is that the far-field is generally that part of the electromagnetic field that has traveled sufficient distance from the source, that it has become completely disconnected from any feedback to the charges and currents that were originally responsible for it. Independent of the source charges, the electromagnetic field, as it moves farther away, is dependent only upon the accelerations of the charges that produced it.
The electrostatic and reactive near-field refers to regions such as near conductors and inside atmosphere, or polarized media, where the propagation of electromagnetic waves is interfered with. The interaction with the medium can cause energy to deflect back to the source, as occurs in the reactive near-field. Or the interaction with the medium can fail to return energy back to the source but cause a distortion in the electromagnetic wave that deviates significantly from that found in a perfect vacuum, and this indicates the radiative near-field region, which is somewhat further away [37] .
In the reactive region, not only is an electromagnetic wave being radiated outward into far space but there is a reactive component to the electromagnetic field, meaning that the nature of the field around the antenna is sensitive to electromagnetic absorption in this region, and reacts to it. In contrast, this is not true for absorption far from the antenna, which has no effect on the transmitter or antenna near-field. This dipole pattern below shows a magnetic B in orange (Figure 7). The potential energy momentarily stored in this magnetic field is indicative of the reactive near-field of a sun or planet.
The near-field is remarkable for reproducing classical electromagnetic induction and electric charge effects on the electromagnetic field, which effects die-out with increasing distance from the antenna. The electrostatic field strength is proportional to the inverse-cube of the distance 1/r3 and magnetic field strength proportional to inverse-square of distance 1/r2 [40] .
More distant near-field effects also involve energy transfer effects that couple directly to receivers near the antenna, affecting the power output of the transmitter if they do couple, but not otherwise. In a sense, the near-field offers energy that is available to a receiver only if the energy is tapped, and this is sensed by the transmitter by means of responding to electromagnetic near-fields emanating from the receiver. Again, this is the same principle that applies in induction coupled devices, such as a transformer, which draws more power at the primary circuit if power is drawn from the secondary circuit (Figure 8). This is different with the far-field, which constantly draws the same energy from the transmitter, whether it is immediately received, or not.
The amplitude of other non-radiative/non-dipole components of the electromagnetic field close to the antenna may be quite powerful, but, because of more rapid fall-off with distance they do not radiate energy to infinite distances. Instead, their energies remain trapped in the region near the antenna, not drawing power from the transmitter unless they excite a receiver in the area close to the antenna. Thus, the near-fields only transfer energy to very nearby receivers, and, when they do, the result is felt as an extra power draw in the transmitter. As an example of such an effect, power is transferred across space in a common transformer by means of near-field inductive coupling, resulting in a short range of one wavelength of the signal. Our solar system performs wireless power transfer in the exact same manner using near-field inductive coupling, but on a much larger physical and wattage scale.
Extremely close to the surface of the planet, the multipole expansion is not applicable as there are too many terms needed for detailed description of the fields. In the extreme near-field, it is sometimes useful to express the contributions as a sum of radiating fields combined with evanescent fields. An evanescent field is an oscillating electromagnetic field that does not propagate as an electromagnetic wave but whose energy is spatially concentrated near the surface. Since the net flow of electromagnetic energy is given by the average Poynting vector, that means that the Poynting vector in these regions, as averaged over a complete oscillation cycle, is zero. A characteristic of an evanescent field is that there is no net energy flow in that region. In the planet itself, or as soon as one enters a region of inhomogeneous materials, the multipole expansion is no longer valid.
The electromagnetic field in the near-field region of a spherical coil antenna is predominantly magnetic. For small values of r / λ the impedance of a magnetic loop is low and inductive, at short range being asymptotic to:
The electromagnetic field in the near-field region of a rod antenna is predominantly electrostatic. For small values of r / λ the impedance is high and capacitive, at short range being asymptotic to: 2ff7e9595c
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