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Thursday, August 20, 2015

Wireless power transfer

From Wikipedia, the free encyclopedia

Inductive charging pad for LG smartphone, using the Qi (pronounced 'Chi') system, an example of near-field wireless transfer. When the phone is set on the pad, a coil in the pad creates a magnetic field which induces a current in another coil, in the phone, charging its battery.

Wireless power transfer (WPT)[1] or wireless energy transmission is the transmission of electrical power from a power source to a consuming device without using solid wires or conductors.[2][3][4][5] It is a generic term that refers to a number of different power transmission technologies that use time-varying electromagnetic fields.[1][5][6][7] Wireless transmission is useful to power electrical devices in cases where interconnecting wires are inconvenient, hazardous, or are not possible. In wireless power transfer, a transmitter device connected to a power source, such as the mains power line, transmits power by electromagnetic fields across an intervening space to one or more receiver devices, where it is converted back to electric power and utilized.[1]

Wireless power techniques fall into two categories, non-radiative and radiative.[1][6][8][9][10] In near-field or non-radiative techniques, power is transferred over short distances by magnetic fields using inductive coupling between coils of wire or in a few devices by electric fields using capacitive coupling between electrodes.[5][8] Applications of this type are electric toothbrush chargers, RFID tags, smartcards, and chargers for implantable medical devices like artificial cardiac pacemakers, and inductive powering or charging of electric vehicles like trains or buses.[9][11] A current focus is to develop wireless systems to charge mobile and handheld computing devices such as cellphones, digital music players and portable computers without being tethered to a wall plug.

In radiative or far-field techniques, also called power beaming, power is transmitted by beams of electromagnetic radiation, like microwaves or laser beams. These techniques can transport energy longer distances but must be aimed at the receiver. Proposed applications for this type are solar power satellites, and wireless powered drone aircraft.[9] An important issue associated with all wireless power systems is limiting the exposure of people and other living things to potentially injurious electromagnetic fields (see Electromagnetic radiation and health).[9]

Overview


Generic block diagram of a wireless power system

"Wireless power transmission" is a collective term that refers to a number of different technologies for transmitting power by means of time-varying electromagnetic fields.[1][5][8] The technologies, listed in the table below, differ in the distance over which they can transmit power efficiently, whether the transmitter must be aimed (directed) at the receiver, and in the type of electromagnetic energy they use: time varying electric fields, magnetic fields, radio waves, microwaves, or infrared or visible light waves.[8]

In general a wireless power system consists of a "transmitter" device connected to a source of power such as mains power lines, which converts the power to a time-varying electromagnetic field, and one or more "receiver" devices which receive the power and convert it back to DC or AC electric power which is consumed by an electrical load.[1][8] In the transmitter the input power is converted to an oscillating electromagnetic field by some type of "antenna" device. The word "antenna" is used loosely here; it may be a coil of wire which generates a magnetic field, a metal plate which generates an electric field, an antenna which radiates radio waves, or a laser which generates light. A similar antenna or coupling device in the receiver converts the oscillating fields to an electric current. An important parameter which determines the type of waves is the frequency f in hertz of the oscillations. The frequency determines the wavelength λ = c/f of the waves which carry the energy across the gap, where c is the velocity of light.

Wireless power uses the same fields and waves as wireless communication devices like radio,[6][12] another familiar technology which involves power transmitted without wires by electromagnetic fields, used in cellphones, radio and television broadcasting, and WiFi. In radio communication the goal is the transmission of information, so the amount of power reaching the receiver is unimportant as long as it is enough that the signal to noise ratio is high enough that the information can be received intelligibly.[5][6][12] In wireless communication technologies generally only tiny amounts of power reach the receiver. By contrast, in wireless power, the amount of power received is the important thing, so the efficiency (fraction of transmitted power that is received) is the more significant parameter.[5] For this reason wireless power technologies are more limited by distance than wireless communication technologies.

These are the different wireless power technologies:[1][8][9][13][14]

Technology Range[15] Directivity[8] Frequency Antenna devices Current and or possible future applications
Inductive coupling Short Low Hz – MHz Wire coils Electric tooth brush and razor battery charging, induction stovetops and industrial heaters.
Resonant inductive coupling Mid- Low MHz – GHz Tuned wire coils, lumped element resonators Charging portable devices (Qi), biomedical implants, electric vehicles, powering busses, trains, MAGLEV, RFID, smartcards.
Capacitive coupling Short Low kHz – MHz Electrodes Charging portable devices, power routing in large scale integrated circuits, Smartcards.
Magnetodynamic[13] Short N.A. Hz Rotating magnets Charging electric vehicles.
Microwaves Long High GHz Parabolic dishes, phased arrays, rectennas Solar power satellite, powering drone aircraft.
Light waves Long High ≥THz Lasers, photocells, lenses Powering drone aircraft, powering space elevator climbers.

Field regions

Electric and magnetic fields are created by charged particles in matter such as electrons. A stationary charge creates an electrostatic field in the space around it. A steady current of charges (direct current, DC) creates a static magnetic field around it. The above fields contain energy, but cannot carry power because they are static. However time-varying fields can carry power.[16] Accelerating electric charges, such as are found in an alternating current (AC) of electrons in a wire, create time-varying electric and magnetic fields in the space around them. These fields can exert oscillating forces on the electrons in a receiving "antenna", causing them to move back and forth. These represent alternating current which can be used to power a load.

The oscillating electric and magnetic fields surrounding moving electric charges in an antenna device can be divided into two regions, depending on distance Drange from the antenna.[1][4][6][8][9][10][17] The boundary between the regions is somewhat vaguely defined.[8] The fields have different characteristics in these regions, and different technologies are used for transmitting power:
  • Near-field or nonradiative region – This means the area within about 1 wavelength (λ) of the antenna.[1][4][10] In this region the oscillating electric and magnetic fields are separate[6] and power can be transferred via electric fields by capacitive coupling (electrostatic induction) between metal electrodes, or via magnetic fields by inductive coupling (electromagnetic induction) between coils of wire.[5][6][8][9] These fields are not radiative,[10] meaning the energy stays within a short distance of the transmitter.[18] If there is no receiving device or absorbing material within their limited range to "couple" to, no power leaves the transmitter.[18] The range of these fields is short, and depends on the size and shape of the "antenna" devices, which are usually coils of wire. The fields, and thus the power transmitted, decrease exponentially with distance,[4][17][19] so if the distance between the two "antennas" Drange is much larger than the diameter of the "antennas" Dant very little power will be received. Therefore, these techniques cannot be used for long distance power transmission.
Resonance, such as resonant inductive coupling, can increase the coupling between the antennas greatly, allowing efficient transmission at somewhat greater distances,[1][4][6][9][20][21] although the fields still decrease exponentially. Therefore the range of near-field devices is conventionally devided into two categories:
  • Short range – up to about one antenna diameter: Drange ≤ Dant.[18][20][22] This is the range over which ordinary nonresonant capacitive or inductive coupling can transfer practical amounts of power.
  • Mid-range – up to 10 times the antenna diameter: Drange ≤ 10 Dant.[20][21][22][23] This is the range over which resonant capacitive or inductive coupling can transfer practical amounts of power.
  • Far-field or radiative region – Beyond about 1 wavelength (λ) of the antenna, the electric and magnetic fields are perpendicular to each other and propagate as an electromagnetic wave; examples are radio waves, microwaves, or light waves.[1][4][9] This part of the energy is radiative,[10] meaning it leaves the antenna whether or not there is a receiver to absorb it. The portion of energy which does not strike the receiving antenna is dissipated and lost to the system. The amount of power emitted as electromagnetic waves by an antenna depends on the ratio of the antenna's size Dant to the wavelength of the waves λ,[24] which is determined by the frequency: λ = c/f. At low frequencies f where the antenna is much smaller than the size of the waves, Dant << λ, very little power is radiated. Therefore the near-field devices above, which use lower frequencies, radiate almost none of their energy as electromagnetic radiation. Antennas about the same size as the wavelength Dant ≈ λ such as monopole or dipole antennas, radiate power efficiently, but the electromagnetic waves are radiated in all directions (omnidirectionally), so if the receiving antenna is far away, only a small amount of the radiation will hit it.[10][20] Therefore, these can be used for short range, inefficient power transmission but not for long range transmission.[25]
However, unlike fields, electromagnetic radiation can be focused by reflection or refraction into beams. By using a high-gain antenna or optical system which concentrates the radiation into a narrow beam aimed at the receiver, it can be used for long range power transmission.[20][25] From the Rayleigh criterion, to produce the narrow beams necessary to focus a significant amount of the energy on a distant receiver, an antenna must be much larger than the wavelength of the waves used: Dant >> λ = c/f.[26][27] Practical beam power devices require wavelengths in the centimeter region or below, corresponding to frequencies above 1 GHz, in the microwave range or above.[1]

Near-field or non-radiative techniques

The near-field components of electric and magnetic fields die out quickly beyond a distance of about one diameter of the antenna (Dant). Outside very close ranges the field strength and coupling is roughly proportional to (Drange/Dant)−3[17][28] Since power is proportional to the square of the field strength, the power transferred decreases with the sixth power of the distance (Drange/Dant)−6.[6][19][29][30] or 60 dB per decade. In other words, doubling the distance between transmitter and receiver causes the power received to decrease by a factor of 26 = 64.

Inductive coupling


Generic block diagram of an inductive wireless power system.
(right) A light bulb powered wirelessly by induction, in 1910. (left)
Modern inductive power transfer, an electric toothbrush charger. A coil in the stand produces a magnetic field, inducing an AC current in a coil in the toothbrush, which is rectified to charge the batteries.

In inductive coupling (electromagnetic induction[9][31] or inductive power transfer, IPT), power is transferred between coils of wire by a magnetic field.[6] The transmitter and receiver coils together form a transformer[6][9] (see diagram). An alternating current (AC) through the transmitter coil (L1) creates an oscillating magnetic field (B) by Ampere's law. The magnetic field passes through the receiving coil (L2), where it induces an alternating EMF (voltage) by Faraday's law of induction, which creates an AC current in the receiver.[5][31] The induced alternating current may either drive the load directly, or be rectified to direct current (DC) by a rectifier in the receiver, which drives the load. A few systems, such as electric toothbrush charging stands, work at 50/60 Hz so AC mains current is applied directly to the transmitter coil, but in most systems an electronic oscillator generates a higher frequency AC current which drives the coil, because transmission efficiency improves with frequency.[31]

Inductive coupling is the oldest and most widely used wireless power technology, and virtually the only one so far which is used in commercial products. It is used in inductive charging stands for cordless appliances used in wet environments such as electric toothbrushes[9] and shavers, to reduce the risk of electric shock.[7] Another application area is "transcutaneous" recharging of biomedical prosthetic devices implanted in the human body, such as cardiac pacemakers and insulin pumps, to avoid having wires passing through the skin.[32][33] It is also used to charge electric vehicles such as cars and to either charge or power transit vehicles like buses and trains.[9][14]

However the fastest growing use is wireless charging pads to recharge mobile and handheld wireless devices such as laptop and tablet computers, cellphones, digital media players, and video game controllers.[14]

The power transferred increases with frequency[31] and the mutual inductance M between the coils,[5] which depends on their geometry and the distance Drange between them. A widely-used figure of merit is the coupling coefficient \scriptstyle k\; =\; M/\sqrt{L_1 L_2}.[31][34] This dimensionless parameter is equal to the fraction of magnetic flux through L1 that passes through L2. If the two coils are on the same axis and close together so all the magnetic flux from L1 passes through L2, k = 1 and the link efficiency approaches 100%. The greater the separation between the coils, the more of the magnetic field from the first coil misses the second, and the lower k and the link efficiency are, approaching zero at large separations.[31] The link efficiency and power transferred is roughly proportional to k2.[31] In order to achieve high efficiency, the coils must be very close together, a fraction of the coil diameter Dant,[31] usually within centimeters,[25] with the coils' axes aligned. Wide, flat coil shapes are usually used, to increase coupling.[31] Ferrite "flux confinement" cores can confine the magnetic fields, improving coupling and reducing interference to nearby electronics,[31][32] but they are heavy and bulky so small wireless devices often use air-core coils.

Ordinary inductive coupling can only achieve high efficiency when the coils are very close together, usually adjacent. In most modern inductive systems resonant inductive coupling (described below) is used, in which the efficiency is increased by using resonant circuits.[10][21][31][35] This can achieve high efficiencies at greater distances than nonresonant inductive coupling.

Prototype inductive electric car charging system at 2011 Tokyo Auto Show
Powermat inductive charging spots in a coffee shop. Customers can set their phones and computers on them to recharge.
Wireless powered access card.

Resonant inductive coupling


Diagram of the resonant inductive wireless power system demonstrated by Marin Soljačić's MIT team in 2007. The resonant circuits were coils of copper wire which resonated with their internal capacitance (dotted capacitors) at 10 MHz. Power was coupled into the transmitter resonator, and out of the receiver resonator into the rectifier, by small coils which also served for impedance matching.

Resonant inductive coupling (electrodynamic coupling,[9] evanescent wave coupling or strongly coupled magnetic resonance[20]) is a form of inductive coupling in which power is transferred by magnetic fields (B, green) between two resonant circuits (tuned circuits), one in the transmitter and one in the receiver (see diagram, right).[6][7][9][10][35] Each resonant circuit consists of a coil of wire connected to a capacitor, or a self-resonant coil or other resonator with internal capacitance. The two are tuned to resonate at the same resonant frequency. The resonance between the coils can greatly increase coupling and power transfer, analogously to the way a vibrating tuning fork can induce sympathetic vibration in a distant fork tuned to the same pitch. Nikola Tesla first discovered resonant coupling during his pioneering experiments in wireless power transfer around the turn of the 20th century,[36][37][38] but the possibilities of using resonant coupling to increase transmission range has only recently been explored.[39] In 2007 a team led by Marin Soljačić at MIT used two coupled tuned circuits each made of a 25 cm self-resonant coil of wire at 10 MHz to achieve the transmission of 60 W of power over a distance of 2 meters (6.6 ft) (8 times the coil diameter) at around 40% efficiency.[7][9][20][37][40]

The concept behind resonant inductive coupling is that high Q factor resonators exchange energy at a much higher rate than they lose energy due to internal damping.[20] Therefore, by using resonance, the same amount of power can be transferred at greater distances, using the much weaker magnetic fields out in the peripheral regions ("tails") of the near fields (these are sometimes called evanescent fields[20]). Resonant inductive coupling can achieve high efficiency at ranges of 4 to 10 times the coil diameter (Dant).[21][22][23] This is called "mid-range" transfer,[22] in contrast to the "short range" of nonresonant inductive transfer, which can achieve similar efficiencies only when the coils are adjacent. Another advantage is that resonant circuits interact with each other so much more strongly than they do with nonresonant objects that power losses due to absorption in stray nearby objects are negligible.[10][20] A drawback of resonant coupling is that at close ranges when the two resonant circuits are tightly coupled, the resonant frequency of the system is no longer constant but "splits" into two resonant peaks, so the maximum power transfer no longer occurs at the original resonant frequency and the oscillator frequency must be tuned to the new resonance peak.[21]

Resonant technology is currently being widely incorporated in modern inductive wireless power systems.[31] One of the possibilities envisioned for this technology is area wireless power coverage. A coil in the wall or ceiling of a room might be able to wirelessly power lights and mobile devices anywhere in the room, with reasonable efficiency.[7] An environmental and economic benefit of wirelessly powering small devices such as clocks, radios, music players and remote controls is that it could drastically reduce the 6 billion batteries disposed of each year, a large source of toxic waste and groundwater contamination.[25]

Capacitive coupling

In capacitive coupling (electrostatic induction), the dual of inductive coupling, power is transmitted by electric fields[5] between electrodes such as metal plates. The transmitter and receiver electrodes form a capacitor, with the intervening space as the dielectric.[5][6][9][32][41] An alternating voltage generated by the transmitter is applied to the transmitting plate, and the oscillating electric field induces an alternating potential on the receiver plate by electrostatic induction,[5][41] which causes an alternating current to flow in the load circuit. The amount of power transferred increases with the frequency[41] and the capacitance between the plates, which is proportional to the area of the smaller plate and (for short distances) inversely proportional to the separation.[5]
Capacitive coupling has only been used practically in a few low power applications, because the very high voltages on the electrodes required to transmit significant power can be hazardous,[6][9] and can cause unpleasant side effects such as noxious ozone production. In addition, in contrast to magnetic fields,[20] electric fields interact strongly with most materials, including the human body, due to dielectric polarization.[32] Intervening materials between or near the electrodes can absorb the energy, in the case of humans possibly causing excessive electromagnetic field exposure.[6] However capacitive coupling has a few advantages over inductive. The field is largely confined between the capacitor plates, reducing interference, which in inductive coupling requires heavy ferrite "flux confinement" cores.[5][32] Also, alignment requirements between the transmitter and receiver are less critical.[5][6][41] Capacitive coupling has recently been applied to charging battery powered portable devices[42] and is being considered as a means of transferring power between substrate layers in integrated circuits.[43]

Capacitive wireless power systems
Bipolar
Unipolar

Two types of circuit have been used:
  • Bipolar design:[44] In this type of circuit, there are two transmitter plates and two receiver plates. Each transmitter plate is coupled to a receiver plate. The transmitter oscillator drives the transmitter plates in opposite phase (180° phase difference) by a high alternating voltage, and the load is connected between the two receiver plates. The alternating electric fields induce opposite phase alternating potentials in the receiver plates, and this "push-pull" action causes current to flow back and forth between the plates through the load. A disadvantage of this configuration for wireless charging is that the two plates in the receiving device must be aligned face to face with the charger plates for the device to work.
  • Unipolar design:[5][41] In this type of circuit, the transmitter and receiver have only one active electrode, and either the ground or a large inactive capacitive electrode serves as the return path for the current. The transmitter oscillator and the load is connected between the electrodes and a ground connection, inducing an alternating potential on the nearby receiving electrode with respect to ground, causing alternating current to flow through the load connected between it and ground.
Resonance can also be used with capacitive coupling to extend the range. At the turn of the century, Nikola Tesla did the first experiments with both resonant electrostatic and magnetic coupling.

Magnetodynamic coupling 

In this method, power is transmitted between two rotating armatures, one in the transmitter and one in the receiver, which rotate synchronously, coupled together by a magnetic field generated by permanent magnets on the armatures.[13] The transmitter armature is turned either by or as the rotor of an electric motor, and its magnetic field exerts torque on the receiver armature, turning it. The magnetic field acts like a mechanical coupling between the armatures.[13] The receiver armature produces power to drive the load, either by turning a separate electric generator or by using the receiver armature itself as the rotor in a generator.

This device has been proposed as an alternative to inductive power transfer for noncontact charging of electric vehicles.[13] A rotating armature embedded in a garage floor or curb would turn a receiver armature in the underside of the vehicle to charge its batteries.[13] It is claimed that this technique can transfer power over distances of 10 to 15 cm (4 to 6 inches) with high efficiency, over 90%.[13][45] Also, the low frequency stray magnetic fields produced by the rotating magnets produce less electromagnetic interference to nearby electronic devices than the high frequency magnetic fields produced by inductive coupling systems. A prototype system charging electric vehicles has been in operation at University of British Columbia since 2012. Other researchers, however, claim that the two energy conversions (electrical to mechanical to electrical again) make the system less efficient than electrical systems like inductive coupling.[13]

Far-field or radiative techniques

Far field methods achieve longer ranges, often multiple kilometer ranges, where the distance is much greater than the diameter of the device(s). The main reason for longer ranges with radio wave and optical devices is the fact that electromagnetic radiation in the far-field can be made to match the shape of the receiving area (using high directivity antennas or well-collimated laser beams). The maximum directivity for antennas is physically limited by diffraction.

In general, visible light (from lasers) and microwaves (from purpose-designed antennas) are the forms of electromagnetic radiation best suited to energy transfer.
The dimensions of the components may be dictated by the distance from transmitter to receiver, the wavelength and the Rayleigh criterion or diffraction limit, used in standard radio frequency antenna design, which also applies to lasers. Airy's diffraction limit is also frequently used to determine an approximate spot size at an arbitrary distance from the aperture. Electromagnetic radiation experiences less diffraction at shorter wavelengths (higher frequencies); so, for example, a blue laser is diffracted less than a red one.

The Rayleigh criterion dictates that any radio wave, microwave or laser beam will spread and become weaker and diffuse over distance; the larger the transmitter antenna or laser aperture compared to the wavelength of radiation, the tighter the beam and the less it will spread as a function of distance (and vice versa). Smaller antennae also suffer from excessive losses due to side lobes. However, the concept of laser aperture considerably differs from an antenna. Typically, a laser aperture much larger than the wavelength induces multi-moded radiation and mostly collimators are used before emitted radiation couples into a fiber or into space.

Ultimately, beamwidth is physically determined by diffraction due to the dish size in relation to the wavelength of the electromagnetic radiation used to make the beam.

Microwave power beaming can be more efficient than lasers, and is less prone to atmospheric attenuation caused by dust or water vapor.

Then the power levels are calculated by combining the above parameters together, and adding in the gains and losses due to the antenna characteristics and the transparency and dispersion of the medium through which the radiation passes. That process is known as calculating a link budget.

Microwaves


An artist's depiction of a solar satellite that could send electric energy by microwaves to a space vessel or planetary surface.

Power transmission via radio waves can be made more directional, allowing longer distance power beaming, with shorter wavelengths of electromagnetic radiation, typically in the microwave range.[46] A rectenna may be used to convert the microwave energy back into electricity. Rectenna conversion efficiencies exceeding 95% have been realized. Power beaming using microwaves has been proposed for the transmission of energy from orbiting solar power satellites to Earth and the beaming of power to spacecraft leaving orbit has been considered.[47][48]

Power beaming by microwaves has the difficulty that, for most space applications, the required aperture sizes are very large due to diffraction limiting antenna directionality. For example, the 1978 NASA Study of solar power satellites required a 1-km diameter transmitting antenna and a 10 km diameter receiving rectenna for a microwave beam at 2.45 GHz.[49] These sizes can be somewhat decreased by using shorter wavelengths, although short wavelengths may have difficulties with atmospheric absorption and beam blockage by rain or water droplets. Because of the "thinned array curse," it is not possible to make a narrower beam by combining the beams of several smaller satellites.

For earthbound applications, a large-area 10 km diameter receiving array allows large total power levels to be used while operating at the low power density suggested for human electromagnetic exposure safety. A human safe power density of 1 mW/cm2 distributed across a 10 km diameter area corresponds to 750 megawatts total power level. This is the power level found in many modern electric power plants.

Following World War II, which saw the development of high-power microwave emitters known as cavity magnetrons, the idea of using microwaves to transmit power was researched. By 1964, a miniature helicopter propelled by microwave power had been demonstrated.[50]

Japanese researcher Hidetsugu Yagi also investigated wireless energy transmission using a directional array antenna that he designed. In February 1926, Yagi and his colleague Shintaro Uda published their first paper on the tuned high-gain directional array now known as the Yagi antenna. While it did not prove to be particularly useful for power transmission, this beam antenna has been widely adopted throughout the broadcasting and wireless telecommunications industries due to its excellent performance characteristics.[51]

Wireless high power transmission using microwaves is well proven. Experiments in the tens of kilowatts have been performed at Goldstone in California in 1975[52][53][54] and more recently (1997) at Grand Bassin on Reunion Island.[55] These methods achieve distances on the order of a kilometer.
Under experimental conditions, microwave conversion efficiency was measured to be around 54%.[56]

A change to 24 GHz has been suggested as microwave emitters similar to LEDs have been made with very high quantum efficiencies using negative resistance, i.e., Gunn or IMPATT diodes, and this would be viable for short range links.

Recently, researchers at the University of Washington introduced power over Wi-Fi, which trickle-charges batteries and powered battery-free cameras and temperature sensors using transmissions from Wi-Fi routers.[57]

Lasers


With a laser beam centered on its panel of photovoltaic cells, a lightweight model plane makes the first flight of an aircraft powered by a laser beam inside a building at NASA Marshall Space Flight Center.

In the case of electromagnetic radiation closer to the visible region of the spectrum (tens of micrometers to tens of nanometres), power can be transmitted by converting electricity into a laser beam that is then pointed at a photovoltaic cell.[58] This mechanism is generally known as "power beaming" because the power is beamed at a receiver that can convert it to electrical energy.

Compared to other wireless methods:[59]
  • Collimated monochromatic wavefront propagation allows narrow beam cross-section area for transmission over large distances.
  • Compact size: solid state lasers fit into small products.
  • No radio-frequency interference to existing radio communication such as Wi-Fi and cell phones.
  • Access control: only receivers hit by the laser receive power.
Drawbacks include:
  • Laser radiation is hazardous. Low power levels can blind humans and other animals. High power levels can kill through localized spot heating.
  • Conversion between electricity and light is inefficient. Photovoltaic cells achieve only 40%–50% efficiency.[60] (Efficiency is higher with monochromatic light than with solar panels).
  • Atmospheric absorption, and absorption and scattering by clouds, fog, rain, etc., causes up to 100% losses.
  • Requires a direct line of sight with the target.
Laser "powerbeaming" technology has been mostly explored in military weapons[61][62][63] and aerospace[64][65] applications and is now being developed for commercial and consumer electronics. Wireless energy transfer systems using lasers for consumer space have to satisfy laser safety requirements standardized under IEC 60825.[citation needed]

Other details include propagation,[66] and the coherence and the range limitation problem.[67]

Geoffrey Landis[68][69][70] is one of the pioneers of solar power satellites[71] and laser-based transfer of energy especially for space and lunar missions. The demand for safe and frequent space missions has resulted in proposals for a laser-powered space elevator.[72][73]

NASA's Dryden Flight Research Center demonstrated a lightweight unmanned model plane powered by a laser beam.[74] This proof-of-concept demonstrates the feasibility of periodic recharging using the laser beam system.

Energy harvesting

In the context of wireless power, energy harvesting, also called power harvesting or energy scavenging, is the conversion of ambient energy from the environment to electric power, mainly to power small autonomous wireless electronic devices.[75] The ambient energy may come from stray electric or magnetic fields or radio waves from nearby electrical equipment, light, thermal energy (heat), or kinetic energy such as vibration or motion of the device.[75] Although the efficiency of conversion is usually low and the power gathered often minuscule (milliwatts or microwatts),[75] it can be adequate to run or recharge small micropower wireless devices such as remote sensors, which are proliferating in many fields.[75] This new technology is being developed to eliminate the need for battery replacement or charging of such wireless devices, allowing them to operate completely autonomously.

History

In 1826 André-Marie Ampère developed Ampère's circuital law showing that electric current produces a magnetic field.[76] Michael Faraday developed Faraday's law of induction in 1831, describing the electromagnetic force induced in a conductor by a time-varying magnetic flux. In 1862 James Clerk Maxwell synthesized these and other observations, experiments and equations of electricity, magnetism and optics into a consistent theory, deriving Maxwell's equations. This set of partial differential equations forms the basis for modern electromagnetics, including the wireless transmission of electrical energy.[14][35] Maxwell predicted the existence of electromagnetic waves in his 1873 A Treatise on Electricity and Magnetism.[77] In 1884 John Henry Poynting developed equations for the flow of power in an electromagnetic field, Poynting's theorem and the Poynting vector, which are used in the analysis of wireless energy transfer systems.[14][35] In 1888 Heinrich Rudolf Hertz discovered radio waves, confirming the prediction of electromagnetic waves by Maxwell.[77]

Tesla's experiments


Tesla demonstrating wireless power transmission in a lecture at Columbia College, New York, in 1891. The two metal sheets are connected to his Tesla coil oscillator, which applies a high radio frequency oscillating voltage. The oscillating electric field between the sheets ionizes the low pressure gas in the two long Geissler tubes he is holding, causing them to glow by fluorescence, similar to neon lights.
(left) Experiment in resonant inductive transfer by Tesla at Colorado Springs 1899. The coil is in resonance with Tesla's magnifying transmitter nearby, powering the light bulb at bottom. (right) Tesla's unsuccessful Wardenclyffe power station.

Inventor Nikola Tesla performed the first experiments in wireless power transmission at the turn of the 20th century,[35][37] and may have done more to popularize the idea than any other individual. In the period 1891 to 1904 he experimented with transmitting power by inductive and capacitive coupling using spark-excited radio frequency resonant transformers, now called Tesla coils, which generated high AC voltages.[35][37][78] With these he was able to transmit power for short distances without wires. In demonstrations before the American Institute of Electrical Engineers[78] and at the 1893 Columbian Exposition in Chicago he lit light bulbs from across a stage.[37] He found he could increase the distance by using a receiving LC circuit tuned to resonance with the transmitter's LC circuit.[36] using resonant inductive coupling.[37][38] At his Colorado Springs laboratory during 1899–1900, by using voltages of the order of 10 megavolts generated by an enormous coil, he was able to light three incandescent lamps at a distance of about one hundred feet.[79][80] The resonant inductive coupling which Tesla pioneered is now a familiar technology used throughout electronics; its use in wireless power has been recently rediscovered and it is currently being widely applied to short-range wireless power systems.[37][81]

The inductive and capacitive coupling used in Tesla's experiments is a "near-field" effect,[37] so it is not able to transmit power long distances. However, Tesla was obsessed with developing a wireless power distribution system that could transmit power directly into homes and factories, as proposed in a visionary 1900 article in Century magazine.[82][83][84][85] and believed that resonance was the key. He claimed to be able to transmit power on a worldwide scale, using a method that involved conduction through the Earth and atmosphere.[83][84][85][86] Tesla was vague about his methods. One of his ideas was to use balloons to suspend transmitting and receiving terminals in the air above 30,000 feet (9,100 m) in altitude, where the pressure is lower.[86] At this altitude, Tesla claimed, an ionized layer would allow electricity to be sent at high voltages (millions of volts) over long distances.

Resonant wireless power demonstration at the Franklin Institute, Philadelphia, 1937. Visitors could adjust the receiver's tuned circuit (right) with the two knobs. When the resonant frequency of the receiver was out of tune with the transmitter, the light would go out.

In 1901, Tesla began construction of a large high-voltage coil facility, the Wardenclyffe Tower at Shoreham, New York, intended as a prototype transmitter for a "World Wireless System" that was to transmit power worldwide, but by 1904 his investors had pulled out, and the facility was never completed.[84][87] Although Tesla claimed his ideas were proven, he had a history of failing to confirm his ideas by experiment,[88][89] and there seems to be no evidence that he ever transmitted significant power beyond the short-range demonstrations above.[14][35][36][79][89][90][91][92][93] The only report of long-distance transmission by Tesla is a claim, not found in reliable sources, that in 1899 he wirelessly lit 200 light bulbs at a distance of 26 miles (42 km).[79][90] There is no independent confirmation of this putative demonstration;[79][90][94] Tesla did not mention it,[90] and it does not appear in his meticulous laboratory notes.[94][95] It originated in 1944 from Tesla's first biographer, John J. O'Neill,[79] who said he pieced it together from "fragmentary material... in a number of publications".[96] In the 110 years since Tesla's experiments, efforts using similar equipment have failed to achieve long distance power transmission,[37][79][90][92] and the scientific consensus is his World Wireless system would not have worked.[14][35][36][84][90][97][98][99][100] Tesla's world power transmission scheme remains today what it was in Tesla's time, a fascinating dream.[14][84]

Microwaves

Before World War 2, little progress was made in wireless power transmission.[91] Radio was developed for communication uses, but couldn't be used for power transmission due to the fact that the relatively low-frequency radio waves spread out in all directions and little energy reached the receiver.[14][35][91] In radio communication, at the receiver, an amplifier intensifies a weak signal using energy from another source. For power transmission, efficient transmission required transmitters that could generate higher-frequency microwaves, which can be focused in narrow beams towards a receiver.[14][35][91][98]

The development of microwave technology during World War 2, such as the klystron and magnetron tubes and parabolic antennas[91] made radiative (far-field) methods practical for the first time, and the first long-distance wireless power transmission was achieved in the 1960s by William C. Brown.[14][35] In 1964 Brown invented the rectenna which could efficiently convert microwaves to DC power, and in 1964 demonstrated it with the first wireless-powered aircraft, a model helicopter powered by microwaves beamed from the ground.[14][91] A major motivation for microwave research in the 1970s and 80s was to develop a solar power satellite.[35][91] Conceived in 1968 by Peter Glaser, this would harvest energy from sunlight using solar cells and beam it down to Earth as microwaves to huge rectennas, which would convert it to electrical energy on the electric power grid.[14][101] In landmark 1975 high power experiments, Brown demonstrated short range transmission of 475 W of microwaves at 54% DC to DC efficiency, and he and Robert Dickinson at NASA's Jet Propulsion Laboratory transmitted 30 kW DC output power across 1.5 km with 2.38 GHz microwaves from a 26 m dish to a 7.3 x 3.5 m rectenna array.[14][102] The incident-RF to DC conversion efficiency of the rectenna was 80%.[14][102] In 1983 Japan launched MINIX (Microwave Ionosphere Nonlinear Interation Experiment), a rocket experiment to test transmission of high power microwaves through the ionosphere.[14]

In recent years a focus of research has been the development of wireless-powered drone aircraft, which began in 1959 with the Dept. of Defense's RAMP (Raytheon Airborne Microwave Platform) project[91] which sponsored Brown's research. In 1987 Canada's Communications Research Center developed a small prototype airplane called Stationary High Altitude Relay Platform (SHARP) to relay telecommunication data between points on earth similar to a communication satellite. Powered by a rectenna, it could fly at 13 miles (21 km) altitude and stay aloft for months. In 1992 a team at Kyoto University built a more advanced craft called MILAX (MIcrowave Lifted Airplane eXperiment). In 2003 NASA flew the first laser powered aircraft. The small model plane's motor was powered by electricity generated by photocells from a beam of infrared light from a ground based laser, while a control system kept the laser pointed at the plane.

Near-field technologies

Inductive power transfer between nearby coils of wire is an old technology, existing since the transformer was developed in the 1800s. Induction heating has been used for 100 years. With the advent of cordless appliances, inductive charging stands were developed for appliances used in wet environments like electric toothbrushes and electric razors to reduce the hazard of electric shock.

One field to which inductive transfer has been applied is to power electric vehicles. In 1892 Maurice Hutin and Maurice Leblanc patented a wireless method of powering railroad trains using resonant coils inductively coupled to a track wire at 3 kHz.[103] The first passive RFID (Radio Frequency Identification) technologies were invented by Mario Cardullo[104] (1973) and Koelle et al.[105] (1975) and by the 1990s were being used in proximity cards and contactless smartcards.

The proliferation of portable wireless communication devices such as cellphones, tablet, and laptop computers in recent decades is currently driving the development of wireless powering and charging technology to eliminate the need for these devices to be tethered to wall plugs during charging.[106] The Wireless Power Consortium was established in 2008 to develop interoperable standards across manufacturers.[106] Its Qi inductive power standard published in August 2009 enables charging and powering of portable devices of up to 5 watts over distances of 4 cm (1.6 inches).[107] The wireless device is placed on a flat charger plate (which could be embedded in table tops at cafes, for example) and power is transferred from a flat coil in the charger to a similar one in the device.

In 2007, a team led by Marin Soljačić at MIT used coupled tuned circuits made of a 25 cm resonant coil at 10 MHz to transfer 60 W of power over a distance of 2 meters (6.6 ft) (8 times the coil diameter) at around 40% efficiency.[37][40]

Saturday, August 8, 2015

Physicists produce world’s first sample of potential wonder-material: stanene Meet graphene’s newest relative.

Image: Nature Materials (2015)
 
Physicists produce world’s first sample of potential wonder-material: stanene.
Meet graphene’s newest relative.
 
BEC CREW
7 AUG 2015
 
Scientists have been theorising about its existence since 2013, but now it’s finally here in physical form: stanene, an intriguing new material made up of a one-atom thick mesh of tin. Just like its much-hyped cousin, graphene - which is made of one-atom thick layers of carbon - computer models predict that stanene could conduct electricity without heat loss.

In fact, theories predict that stanene could be the most efficient material ever made when it comes to conducting electricity. Being two-dimensional, the material allows electrons to zoom along the edges of the mesh in a single lane, bypassing the energy-sapping collisions that occur in three-dimensional materials to achieve 100 percent efficiency. And theoretically, it should work at room temperature.

"It's surprising that it can work at such a high temperature," one of the team, physicist Shou-Cheng Zhang from Stanford University in the US, told Charles Q. Choi at Scientific American back in 2013. "Scientists have looked for dissipationless transport of electricity for many years, but usually the systems we find only work under extreme conditions, either very low temperature or strong magnetic fields."

Because stanene could potentially allow electrons to travel uninterrupted - collisions cause vibrations that generate heat and result in energy loss - wire made from this new material could carry electricity across great distances for long periods of time without energy loss. Imagine your smartphone, laptop, and chargers working for hours without ever getting hot.

If stanene lives up to the predictions that it can work at room temperature with 100 percent efficiency, it will be the perfect example of a topological insulator, overtaking graphene as the best new material to build the electronics of the future.

But that’s a big "if". So far, the team that produced the material has not been able to confirm that stanene has any of these properties at all, and the problem lies in the way that Zhang and his colleagues constructed it.

"The researchers vaporised a bit of tin inside of a vacuum chamber, allowing it to form its characteristic mesh on a bismuth telluride surface," a university press release explains. "The team was able to see only the top ridges of the structure with a scanning tunneling microscope, however, and believe the substrate interacted with the mesh, preventing conductivity testing."

Physicist Ralph Claessen from the University of Würzburg in Germany, who was not involved in the study, told Chris Cesare at Nature Magazine that he’s not even sure that what Zhang and his colleagues produced is actually stanene, because the entire structure of the tiny sample can’t be seen in its entirety. 

Back in 2013, theories predicted that stanene’s two-dimensional tin lattice would form what’s known as a buckled honeycomb structure, which must include "alternate atoms folding upwards to form corrugated ridges", says Cesare. Right now, Zhang and his team can only see the upper ridge of these alternating atom, which means they cannot confirm that it is a true buckled honeycomb structure, but they told Nature Magazine  that the distance between the ridges they can see correspond to what a buckled honeycomb structure should look like.

There are a couple of options going forward, the team can work with the tiny sample they have now, and try confirming its structure using X-ray diffraction. Or they can work on producing a larger sample so the arrangement can be more easily seen. Then they will have to figure out which materials can be used instead of bismuth telluride so they can actually perform conductivity testing. The team has summarised the findings in Nature Materials.

We’re not there yet, but it’s a start, and that’s exciting enough in itself, says graphene expert, Guy Le Lay, from Aix-Marseille University in France: "It's like going to the Moon. The first step is the crucial step."

Friday, August 7, 2015

Dendroclimatology


From Wikipedia, the free encyclopedia



Variation of tree ring width translated into summer temperature anomalies for the past 7000 years, based on samples from holocene deposits on Yamal Peninsula and Siberian now living conifers.[1]

Dendroclimatology is the science of determining past climates from trees (primarily properties of the annual tree rings). Tree rings are wider when conditions favor growth, narrower when times are difficult. Other properties of the annual rings, such as maximum latewood density (MXD) have been shown to be better proxies than simple ring width. Using tree rings, scientists have estimated many local climates for hundreds to thousands of years previous. By combining multiple tree-ring studies (sometimes with other climate proxy records), scientists have estimated past regional and global climates (see Temperature record of the past 1000 years).

Advantages

Tree rings are especially useful as climate proxies in that they can be well-dated (via matching of the rings from sample to sample, i.e. dendrochronology). This allows extension backwards in time using deceased tree samples, even using samples from buildings or from archeological digs. Another advantage of tree rings is that they are clearly demarked in annual increments, as opposed to other proxy methods such as boreholes. Furthermore, tree rings respond to multiple climatic effects (temperature, moisture, cloudiness), so that various aspects of climate (not just temperature) can be studied. However, this can be a double-edged sword as discussed in Climate factors.

Limitations

Along with the advantages of dendroclimatology are some limitations: confounding factors, geographic coverage, annular resolution, and collection difficulties. The field has developed various methods to partially adjust for these challenges.

Confounding factors

There are multiple climate and non-climate factors as well as nonlinear effects that impact tree ring width. Methods to isolate single factors (of interest) include botanical studies to calibrate growth influences and sampling of "limiting stands" (those expected to respond mostly to the variable of interest).

Climate factors

Climate factors that affect trees include temperature, precipitation, sunlight, and wind. To differentiate among these factors, scientists collect information from "limiting stands". An example of a limiting stand is the upper elevation treeline: here, trees are expected to be more affected by temperature variation (which is "limited") than precipitation variation (which is in excess). Conversely, lower elevation treelines are expected to be more affected by precipitation changes than temperature variation. This is not a perfect work-around as multiple factors still impact trees even at the "limiting stand", but it helps. In theory, collection of samples from nearby limiting stands of different types (e.g. upper and lower treelines on the same mountain) should allow mathematical solution for multiple climate factors. However, this method is rarely used.

Non-climate factors

Non-climate factors include soil, tree age, fire, tree-to-tree competition, genetic differences, logging or other human disturbance, herbivore impact (particularly sheep grazing), pest outbreaks, disease, and CO2 concentration. For factors which vary randomly over space (tree to tree or stand to stand), the best solution is to collect sufficient data (more samples) to compensate for confounding noise. Tree age is corrected for with various statistical methods: either fitting spline curves to the overall tree record or using similar aged trees for comparison over different periods (regional curve standardization). Careful examination and site selection helps to limit some confounding effects, for example picking sites undisturbed by modern man.

Non-linear effects

In general, climatologists assume a linear dependence of ring width on the variable of interest (e.g. moisture). However, if the variable changes enough, response may level off or even turn opposite. The home gardener knows that one can underwater or overwater a house plant. In addition, it is possible that interaction effects may occur (for example "temperature times precipitation" may affect growth as well as temperature and precipitation on their own. Here, also, the "limiting stand" helps somewhat to isolate the variable of interest. For instance, at the upper treeline, where the tree is "cold limited", it's unlikely that nonlinear effects of high temperature ("inverted quadratic") will have numerically significant impact on ring width over the course of a growing season.

Botanical inferences to correct for confounding factors

Botanical studies can help to estimate the impact of confounding variables and in some cases guide corrections for them. These experiments may be either ones where growth variables are all controlled (e.g. in a greenhouse[citation needed]), partially controlled (e.g. FACE [Free Airborne Concentration Enhancement] experiments—add ref), or where conditions in nature are monitored. In any case, the important thing is that multiple growth factors are carefully recorded to determine what impacts growth. (Insert Fennoscandanavia paper reference). With this information, ring width response can be more accurately understood and inferences from historic (unmonitored) tree rings become more certain. In concept, this is like the limiting stand principle, but it is more quantitative—like a calibration.

Divergence problem

The divergence problem is the disagreement between the temperatures measured by the thermometers (instrumental temperatures) on one side, and the temperatures reconstructed from the latewood density or width of tree rings on the other side, at many treeline sites in northern forests.

While the thermometer records indicate a substantial warming trend, tree rings from these particular sites do not display a corresponding change in their maximum latewood density or, in some cases, their width. This does not apply to all such studies.[2] Where this applies, a temperature trend extracted from tree rings alone would not show any substantial warming. The temperature graphs calculated from instrumental temperatures and from these tree ring proxies thus "diverge" from one another since the 1950s, which is the origin of the term. This divergence raises obvious questions of whether other, unrecognized divergences have occurred in the past, prior to the era of thermometers. [3] There is evidence suggesting that the divergence is caused by human activities, and so confined to the recent past, but use of affected proxies can lead to overestimation of past temperatures, understating the current warming trend. There is continuing research into explanations and ways to avoid this problem with tree ring proxies.[2]

Geographic coverage

Trees do not cover the Earth. Polar and marine climates cannot be estimated from tree rings. In perhumid tropical regions, Australia and southern Africa, trees generally grow all year round and don't show clear annual rings. In some forest areas, the tree growth is too much influenced by multiple factors (no "limiting stand") to allow clear climate reconstruction[examples needed]. The coverage difficulty is dealt with by acknowledging it and by using other proxies (e.g. ice cores, corals) in difficult areas. In some cases it can be shown that the parameter of interest (temperature, precipitation, etc.) varies similarly from area to area, for example by looking at patterns in the instrumental record. Then one is justified in extending the dendroclimatology inferences to areas where no suitable tree ring samples are obtainable.

Annular resolution

Tree rings show the impact on growth over an entire growing season. Climate changes deep in the dormant season (winter) will not be recorded. In addition, different times of the growing season may be more important than others (i.e. May versus September) for ring width. However, in general the ring width is used to infer the overall climate change during the corresponding year (an approximation). Another problem is "memory" or autocorrelation. A stressed tree may take a year or two to recover from a hard season. This problem can be dealt with by more complex modeling (a "lag" term in the regression) or by reducing the skill estimates of chronologies.

Collection difficulties

Tree rings must be obtained from nature, frequently from remote regions. This means that special efforts are needed to map sites properly. In addition, samples must be collected in difficult (often sloping terrain) conditions. Generally, tree rings are collected using a hand-held borer device, that requires skill to get a good sample. The best samples come from felling a tree and sectioning it. However, this requires more danger and does damage to the forest. It may not be allowed in certain areas, particularly with the oldest trees in undisturbed sites (which are the most interesting scientifically). As with all experimentalists, dendroclimatologists must, at times, decide to make the best of imperfect data, rather than resample. This tradeoff is made more difficult, because sample collection (in the field) and analysis (in the lab) may be separated significantly in time and space. These collection challenges mean that data gathering is not as simple or cheap as conventional laboratory science. However, they also give the field's practitioners much enjoyment, working out of doors, with hands on trees and tools.

Other measurements

Initial work focused on measuring the tree ring width—this is simple to measure and can be related to climate parameters. But the annual growth of the tree leaves other traces. In particular maximum latewood density (MXD) is another metric used for estimating environmental variables.[4] It is, however, harder to measure. Other properties (e.g. isotope or chemical trace analysis) have also been tried most notably by L. M. Libby in her 1974 paper "Temperature Dependence of Isotope Ratios in Tree Rings".[5] In theory, multiple measurements on the same ring will allow differentiation of confounding factors (e.g. precipitation and temperature). However, most studies are still based on ring widths at limiting stands.

Measuring radiocarbon concentrations in tree rings has proven to be useful in recreating past sunspot activity, with data now extending back over 11,000 years.[6]

Origin-of-Life Story May Have Found Its Missing Link


Jesse Emspak
.

Thursday, August 6, 2015

Post-attack casualties of atomic bombings

From Wikipedia, the free encyclopedia

Film footage taken in Hiroshima in March 1946 showing victims with severe burns

In the spring of 1948, the Atomic Bomb Casualty Commission (ABCC) was established in accordance with a presidential directive from Truman to the National Academy of SciencesNational Research Council to conduct investigations of the late effects of radiation among the survivors in Hiroshima and Nagasaki.[236] One of the early studies conducted by the ABCC was on the outcome of pregnancies occurring in Hiroshima and Nagasaki, and in a control city, Kure, located 18 mi (29 km) south of Hiroshima, in order to discern the conditions and outcomes related to radiation exposure.[237] Dr. James V. Neel led the study which found that the number of birth defects was not significantly higher among the children of survivors who were pregnant at the time of the bombings.[238] The National Academy of Sciences questioned Neel's procedure which did not filter the Kure population for possible radiation exposure.[239] Among the observed birth defects there was a higher incidence of brain malformation in Nagasaki and Hiroshima, including microencephaly and anencephaly, about 2.75 times the rate seen in Kure.[240][241]

In 1985, Johns Hopkins University human geneticist James F. Crow examined Neel's research and confirmed that the number of birth defects was not significantly higher in Hiroshima and Nagasaki.[242] Many members of the ABCC and its successor Radiation Effects Research Foundation (RERF) were still looking for possible birth defects or other causes among the survivors decades later, but found no evidence that they were common among the survivors.[243][244] Despite the insignificance of birth defects found in Neel's study, historian Ronald E. Powaski wrote that Hiroshima experienced "an increase in stillbirths, birth defects, and infant mortality" following the atomic bomb.[245] Neel also studied the longevity of the children who survived the bombings of Hiroshima and Nagasaki, reporting that between 90 and 95 percent were still living 50 years later.[243]

Around 1,900 cancer deaths can be attributed to the after-effects of the bombs. An epidemiology study by the RERF states that from 1950 to 2000, 46% of leukemia deaths and 11% of solid cancer deaths among the bomb survivors were due to radiation from the bombs, the statistical excess being estimated at 200 leukemia and 1,700 solid cancers.[246]

References:

236. Putnam, Frank W. "The Atomic Bomb Casualty Commission in Retrospect". National Academy of Sciences. Retrieved January 31, 2014.

237. "The Radiation Effects Research Foundation Website". Rerf.or.jp. Archived from the original on March 8, 2009. Retrieved March 25, 2009.

238. Voosen, Paul (April 11, 2011). "Nuclear Crisis: Hiroshima and Nagasaki cast  long shadows over radiation science". E&E News. Retrieved December 22, 2013.

239.Johnston 2008, p. 143.

240.McCormack 2008, p. 56.

241."Birth defects among the children of atomic-bomb survivors (1948–1954)". Radiation Effects Research Foundation. Retrieved December 22, 2013.

242. Krimsky & Shorett 2005, p. 118.

243. "The American Spectator, Volume 35". Saturday Evening Club. 2002. p. 57.

244. "Data India". Press Institute of India. 2008. p. 697.

245. Powaski 1987, p. 27.

246."Frequently Asked Questions #2". Radiation Effects Research Foundation. Retrieved March 2, 2014.

Hate speech

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