Ionosphere

From Wikipedia, the free encyclopedia

 

The ionosphere (/aɪˈɒnəˌsfɪər/) is the ionized part of Earth's upper atmosphere, from about 60 km (37 mi) to 1,000 km (620 mi) altitude, a region that includes the thermosphere and parts of the mesosphere and exosphere. The ionosphere is ionized by solar radiation. It plays an important role in atmospheric electricity and forms the inner edge of the magnetosphere. It has practical importance because, among other functions, it influences radio propagation to distant places on the Earth. The region below the ionosphere is called neutral atmosphere, or neutrosphere. 

 

Relationship of the atmosphere and ionosphere

History of discovery

As early as 1839, the German mathematician and physicist Carl Friedrich Gauss postulated that an electrically conducting region of the atmosphere could account for observed variations of Earth's magnetic field. Sixty years later, Guglielmo Marconi received the first trans-Atlantic radio signal on December 12, 1901, in St. John's, Newfoundland (now in Canada) using a 152.4 m (500 ft) kite-supported antenna for reception. The transmitting station in Poldhu, Cornwall, used a spark-gap transmitter to produce a signal with a frequency of approximately 500 kHz and a power of 100 times more than any radio signal previously produced. The message received was three dits, the Morse code for the letter S. To reach Newfoundland the signal would have to bounce off the ionosphere twice. Dr. Jack Belrose has contested this, however, based on theoretical and experimental work. However, Marconi did achieve transatlantic wireless communications in Glace Bay, Nova Scotia, one year later.

In 1902, Oliver Heaviside proposed the existence of the Kennelly–Heaviside layer of the ionosphere which bears his name. Heaviside's proposal included means by which radio signals are transmitted around the Earth's curvature. Heaviside's proposal, coupled with Planck's law of black-body radiation, may have hampered the growth of radio astronomy for the detection of electromagnetic waves from celestial bodies until 1932 (and the development of high-frequency radio transceivers). Also in 1902, Arthur Edwin Kennelly discovered some of the ionosphere's radio-electrical properties.

In 1912, the U.S. Congress imposed the Radio Act of 1912 on amateur radio operators, limiting their operations to frequencies above 1.5 MHz (wavelength 200 meters or smaller).  The government thought those frequencies were useless. This led to the discovery of HF radio propagation via the ionosphere in 1923.

In 1926, Scottish physicist Robert Watson-Watt introduced the term ionosphere in a letter published only in 1969 in Nature:

We have in quite recent years seen the universal adoption of the term 'stratosphere'..and..the companion term 'troposphere'... The term 'ionosphere', for the region in which the main characteristic is large scale ionisation with considerable mean free paths, appears appropriate as an addition to this series.

In the early 1930s, test transmissions of Radio Luxembourg inadvertently provided evidence of the first radio modification of the ionosphere; HAARP ran a series of experiments in 2017 using the eponymous Luxembourg Effect.

Edward V. Appleton was awarded a Nobel Prize in 1947 for his confirmation in 1927 of the existence of the ionosphere. Lloyd Berkner first measured the height and density of the ionosphere. This permitted the first complete theory of short-wave radio propagation. Maurice V. Wilkes and J. A. Ratcliffe researched the topic of radio propagation of very long radio waves in the ionosphere. Vitaly Ginzburg has developed a theory of electromagnetic wave propagation in plasmas such as the ionosphere.

In 1962, the Canadian satellite Alouette 1 was launched to study the ionosphere. Following its success were Alouette 2 in 1965 and the two ISIS satellites in 1969 and 1971, further AEROS-A and -B in 1972 and 1975, all for measuring the ionosphere.

On July 26, 1963 the first operational geosynchronous satellite Syncom 2 was launched. The board radio beacons on this satellite (and its successors) enabled – for the first time – the measurement of total electron content (TEC) variation along a radio beam from geostationary orbit to an earth receiver. (The rotation of the plane of polarization directly measures TEC along the path.) Australian geophysicist Elizabeth Essex-Cohen from 1969 onwards was using this technique to monitor the atmosphere above Australia and Antarctica.

Geophysics

The ionosphere is a shell of electrons and electrically charged atoms and molecules that surrounds the Earth, stretching from a height of about 50 km (31 mi) to more than 1,000 km (620 mi). It exists primarily due to ultraviolet radiation from the Sun.

The lowest part of the Earth's atmosphere, the troposphere extends from the surface to about 10 km (6.2 mi). Above that is the stratosphere, followed by the mesosphere. In the stratosphere incoming solar radiation creates the ozone layer. At heights of above 80 km (50 mi), in the thermosphere, the atmosphere is so thin that free electrons can exist for short periods of time before they are captured by a nearby positive ion. The number of these free electrons is sufficient to affect radio propagation. This portion of the atmosphere is partially ionized and contains a plasma which is referred to as the ionosphere.

Ultraviolet (UV), X-ray and shorter wavelengths of solar radiation are ionizing, since photons at these frequencies contain sufficient energy to dislodge an electron from a neutral gas atom or molecule upon absorption. In this process the light electron obtains a high velocity so that the temperature of the created electronic gas is much higher (of the order of thousand K) than the one of ions and neutrals. The reverse process to ionization is recombination, in which a free electron is "captured" by a positive ion. Recombination occurs spontaneously, and causes the emission of a photon carrying away the energy produced upon recombination. As gas density increases at lower altitudes, the recombination process prevails, since the gas molecules and ions are closer together. The balance between these two processes determines the quantity of ionization present. 

Ionization depends primarily on the Sun and its activity. The amount of ionization in the ionosphere varies greatly with the amount of radiation received from the Sun. Thus there is a diurnal (time of day) effect and a seasonal effect. The local winter hemisphere is tipped away from the Sun, thus there is less received solar radiation. The activity of the Sun is associated with the sunspot cycle, with more radiation occurring with more sunspots. Radiation received also varies with geographical location (polar, auroral zones, mid-latitudes, and equatorial regions). There are also mechanisms that disturb the ionosphere and decrease the ionization. There are disturbances such as solar flares and the associated release of charged particles into the solar wind which reaches the Earth and interacts with its geomagnetic field.

Layers of ionization

Ionospheric layers.

 

At night the F layer is the only layer of significant ionization present, while the ionization in the E and D layers is extremely low. During the day, the D and E layers become much more heavily ionized, as does the F layer, which develops an additional, weaker region of ionisation known as the F₁ layer. The F₂ layer persists by day and night and is the main region responsible for the refraction and reflection of radio waves.

D layer

The D layer is the innermost layer, 60 km (37 mi) to 90 km (56 mi) above the surface of the Earth. Ionization here is due to Lyman series-alpha hydrogen radiation at a wavelength of 121.6 nanometre (nm) ionizing nitric oxide (NO). In addition, high solar activity can generate hard X-rays (wavelength < 1 nm) that ionize N₂ and O₂. Recombination rates are high in the D layer, so there are many more neutral air molecules than ions.

Medium frequency (MF) and lower high frequency (HF) radio waves are significantly attenuated within the D layer, as the passing radio waves cause electrons to move, which then collide with the neutral molecules, giving up their energy. Lower frequencies experience greater absorption because they move the electrons farther, leading to greater chance of collisions. This is the main reason for absorption of HF radio waves, particularly at 10 MHz and below, with progressively less absorption at higher frequencies. This effect peaks around noon and is reduced at night due to a decrease in the D layer's thickness; only a small part remains due to cosmic rays. A common example of the D layer in action is the disappearance of distant AM broadcast band stations in the daytime.

During solar proton events, ionization can reach unusually high levels in the D-region over high and polar latitudes. Such very rare events are known as Polar Cap Absorption (or PCA) events, because the increased ionization significantly enhances the absorption of radio signals passing through the region. In fact, absorption levels can increase by many tens of dB during intense events, which is enough to absorb most (if not all) transpolar HF radio signal transmissions. Such events typically last less than 24 to 48 hours.

E layer

The E layer is the middle layer, 90 km (56 mi) to 150 km (93 mi) above the surface of the Earth. Ionization is due to soft X-ray (1–10 nm) and far ultraviolet (UV) solar radiation ionization of molecular oxygen (O₂). Normally, at oblique incidence, this layer can only reflect radio waves having frequencies lower than about 10 MHz and may contribute a bit to absorption on frequencies above. However, during intense sporadic E events, the E_s layer can reflect frequencies up to 50 MHz and higher. The vertical structure of the E layer is primarily determined by the competing effects of ionization and recombination. At night the E layer weakens because the primary source of ionization is no longer present. After sunset an increase in the height of the E layer maximum increases the range to which radio waves can travel by reflection from the layer.

This region is also known as the Kennelly–Heaviside layer or simply the Heaviside layer. Its existence was predicted in 1902 independently and almost simultaneously by the American electrical engineer Arthur Edwin Kennelly (1861–1939) and the British physicist Oliver Heaviside (1850–1925). However, it was not until 1924 that its existence was detected by Edward V. Appleton and Miles Barnett.

E_s

The E_s layer (sporadic E-layer) is characterized by small, thin clouds of intense ionization, which can support reflection of radio waves, rarely up to 225 MHz. Sporadic-E events may last for just a few minutes to several hours. Sporadic E propagation makes VHF-operating radio amateurs very excited, as propagation paths that are generally unreachable can open up. There are multiple causes of sporadic-E that are still being pursued by researchers. This propagation occurs most frequently during the summer months when high signal levels may be reached. The skip distances are generally around 1,640 km (1,020 mi). Distances for one hop propagation can be anywhere from 900 km (560 mi) to 2,500 km (1,600 mi). Double-hop reception over 3,500 km (2,200 mi) is possible.

F layer

The F layer or region, also known as the Appleton–Barnett layer, extends from about 150 km (93 mi) to more than 500 km (310 mi) above the surface of Earth. It is the layer with the highest electron density, which implies signals penetrating this layer will escape into space. Electron production is dominated by extreme ultraviolet (UV, 10–100 nm) radiation ionizing atomic oxygen. The F layer consists of one layer (F₂) at night, but during the day, a secondary peak (labelled F₁) often forms in the electron density profile. Because the F₂ layer remains by day and night, it is responsible for most skywave propagation of radio waves and long distance high frequency (HF, or shortwave) radio communications.

Above the F layer, the number of oxygen ions decreases and lighter ions such as hydrogen and helium become dominant. This region above the F layer peak and below the plasmasphere is called the topside ionosphere. 

From 1972 to 1975 NASA launched the AEROS and AEROS B satellites to study the F region.

Ionospheric model

An ionospheric model is a mathematical description of the ionosphere as a function of location, altitude, day of year, phase of the sunspot cycle and geomagnetic activity. Geophysically, the state of the ionospheric plasma may be described by four parameters: electron density, electron and ion temperature and, since several species of ions are present, ionic composition. Radio propagation depends uniquely on electron density.

Models are usually expressed as computer programs. The model may be based on basic physics of the interactions of the ions and electrons with the neutral atmosphere and sunlight, or it may be a statistical description based on a large number of observations or a combination of physics and observations. One of the most widely used models is the International Reference Ionosphere (IRI), which is based on data and specifies the four parameters just mentioned. The IRI is an international project sponsored by the Committee on Space Research (COSPAR) and the International Union of Radio Science (URSI). The major data sources are the worldwide network of ionosondes, the powerful incoherent scatter radars (Jicamarca, Arecibo, Millstone Hill, Malvern, St Santin), the ISIS and Alouette topside sounders, and in situ instruments on several satellites and rockets. IRI is updated yearly. IRI is more accurate in describing the variation of the electron density from bottom of the ionosphere to the altitude of maximum density than in describing the total electron content (TEC). Since 1999 this model is "International Standard" for the terrestrial ionosphere (standard TS16457).

Persistent anomalies to the idealized model

Ionograms allow deducing, via computation, the true shape of the different layers. Nonhomogeneous structure of the electron/ion-plasma produces rough echo traces, seen predominantly at night and at higher latitudes, and during disturbed conditions.

Winter anomaly

At mid-latitudes, the F₂ layer daytime ion production is higher in the summer, as expected, since the Sun shines more directly on the Earth. However, there are seasonal changes in the molecular-to-atomic ratio of the neutral atmosphere that cause the summer ion loss rate to be even higher. The result is that the increase in the summertime loss overwhelms the increase in summertime production, and total F₂ ionization is actually lower in the local summer months. This effect is known as the winter anomaly. The anomaly is always present in the northern hemisphere, but is usually absent in the southern hemisphere during periods of low solar activity.

Equatorial anomaly

Electric currents created in sunward ionosphere.

 

Within approximately ± 20 degrees of the magnetic equator, is the equatorial anomaly. It is the occurrence of a trough in the ionization in the F₂ layer at the equator and crests at about 17 degrees in magnetic latitude. The Earth's magnetic field lines are horizontal at the magnetic equator. Solar heating and tidal oscillations in the lower ionosphere move plasma up and across the magnetic field lines. This sets up a sheet of electric current in the E region which, with the horizontal magnetic field, forces ionization up into the F layer, concentrating at ± 20 degrees from the magnetic equator. This phenomenon is known as the equatorial fountain.

Equatorial electrojet

The worldwide solar-driven wind results in the so-called Sq (solar quiet) current system in the E region of the Earth's ionosphere (ionospheric dynamo region) (100–130 km (62–81 mi) altitude). Resulting from this current is an electrostatic field directed west–east (dawn–dusk) in the equatorial day side of the ionosphere. At the magnetic dip equator, where the geomagnetic field is horizontal, this electric field results in an enhanced eastward current flow within ± 3 degrees of the magnetic equator, known as the equatorial electrojet.

Ephemeral ionospheric perturbations

X-rays: sudden ionospheric disturbances (SID)

When the Sun is active, strong solar flares can occur that hit the sunlit side of Earth with hard X-rays. The X-rays penetrate to the D-region, releasing electrons that rapidly increase absorption, causing a high frequency (3–30 MHz) radio blackout. During this time very low frequency (3–30 kHz) signals will be reflected by the D layer instead of the E layer, where the increased atmospheric density will usually increase the absorption of the wave and thus dampen it. As soon as the X-rays end, the sudden ionospheric disturbance (SID) or radio black-out ends as the electrons in the D-region recombine rapidly and signal strengths return to normal.

Protons: polar cap absorption (PCA)

Associated with solar flares is a release of high-energy protons. These particles can hit the Earth within 15 minutes to 2 hours of the solar flare. The protons spiral around and down the magnetic field lines of the Earth and penetrate into the atmosphere near the magnetic poles increasing the ionization of the D and E layers. PCA's typically last anywhere from about an hour to several days, with an average of around 24 to 36 hours. Coronal mass ejections can also release energetic protons that enhance D-region absorption in the polar regions.

Geomagnetic storms

A geomagnetic storm is a temporary intense disturbance of the Earth's magnetosphere.

• During a geomagnetic storm the F₂ layer will become unstable, fragment, and may even disappear completely.
• In the Northern and Southern pole regions of the Earth aurorae will be observable in the sky.

Lightning

Lightning can cause ionospheric perturbations in the D-region in one of two ways. The first is through VLF (very low frequency) radio waves launched into the magnetosphere. These so-called "whistler" mode waves can interact with radiation belt particles and cause them to precipitate onto the ionosphere, adding ionization to the D-region. These disturbances are called "lightning-induced electron precipitation" (LEP) events.

Additional ionization can also occur from direct heating/ionization as a result of huge motions of charge in lightning strikes. These events are called early/fast. 

In 1925, C. T. R. Wilson proposed a mechanism by which electrical discharge from lightning storms could propagate upwards from clouds to the ionosphere. Around the same time, Robert Watson-Watt, working at the Radio Research Station in Slough, UK, suggested that the ionospheric sporadic E layer (E_s) appeared to be enhanced as a result of lightning but that more work was needed. In 2005, C. Davis and C. Johnson, working at the Rutherford Appleton Laboratory in Oxfordshire, UK, demonstrated that the E_s layer was indeed enhanced as a result of lightning activity. Their subsequent research has focused on the mechanism by which this process can occur.

Applications

Radio communication

Due to the ability of ionized atmospheric gases to refract high frequency (HF, or shortwave) radio waves, the ionosphere can reflect radio waves directed into the sky back toward the Earth. Radio waves directed at an angle into the sky can return to Earth beyond the horizon. This technique, called "skip" or "skywave" propagation, has been used since the 1920s to communicate at international or intercontinental distances. The returning radio waves can reflect off the Earth's surface into the sky again, allowing greater ranges to be achieved with multiple hops. This communication method is variable and unreliable, with reception over a given path depending on time of day or night, the seasons, weather, and the 11-year sunspot cycle. During the first half of the 20th century it was widely used for transoceanic telephone and telegraph service, and business and diplomatic communication. Due to its relative unreliability, shortwave radio communication has been mostly abandoned by the telecommunications industry, though it remains important for high-latitude communication where satellite-based radio communication is not possible. Some broadcasting stations and automated services still use shortwave radio frequencies, as do radio amateur hobbyists for private recreational contacts.

Mechanism of refraction

When a radio wave reaches the ionosphere, the electric field in the wave forces the electrons in the ionosphere into oscillation at the same frequency as the radio wave. Some of the radio-frequency energy is given up to this resonant oscillation. The oscillating electrons will then either be lost to recombination or will re-radiate the original wave energy. Total refraction can occur when the collision frequency of the ionosphere is less than the radio frequency, and if the electron density in the ionosphere is great enough.

A qualitative understanding of how an electromagnetic wave propagates through the ionosphere can be obtained by recalling geometric optics. Since the ionosphere is a plasma, it can be shown that the refractive index is less than unity. Hence, the electromagnetic "ray" is bent away from the normal rather than toward the normal as would be indicated when the refractive index is greater than unity. It can also be shown that the refractive index of a plasma, and hence the ionosphere, is frequency-dependent, see Dispersion (optics).

The critical frequency is the limiting frequency at or below which a radio wave is reflected by an ionospheric layer at vertical incidence. If the transmitted frequency is higher than the plasma frequency of the ionosphere, then the electrons cannot respond fast enough, and they are not able to re-radiate the signal. It is calculated as shown below:

${\displaystyle f_{\text{critical}}=9\times {\sqrt {N}}}$

where N = electron density per m³ and f_critical is in Hz.

The Maximum Usable Frequency (MUF) is defined as the upper frequency limit that can be used for transmission between two points at a specified time.

${\displaystyle f_{\text{muf}}={\frac {f_{\text{critical}}}{\sin \alpha }}}$

where ${\displaystyle \alpha }$ = angle of attack, the angle of the wave relative to the horizon, and sin is the sine function.

The cutoff frequency is the frequency below which a radio wave fails to penetrate a layer of the ionosphere at the incidence angle required for transmission between two specified points by refraction from the layer.

Other applications

The open system electrodynamic tether, which uses the ionosphere, is being researched. The space tether uses plasma contactors and the ionosphere as parts of a circuit to extract energy from the Earth's magnetic field by electromagnetic induction.

Measurements

Overview

Scientists explore the structure of the ionosphere by a wide variety of methods. They include:

• passive observations of optical and radio emissions generated in the ionosphere
• bouncing radio waves of different frequencies from it
• incoherent scatter radars such as the EISCAT, Sondre Stromfjord, Millstone Hill, Arecibo, Advanced Modular Incoherent Scatter Radar (AMISR) and Jicamarca radars
• coherent scatter radars such as the Super Dual Auroral Radar Network (SuperDARN) radars,
• special receivers to detect how the reflected waves have changed from the transmitted waves.

A variety of experiments, such as HAARP (High Frequency Active Auroral Research Program), involve high power radio transmitters to modify the properties of the ionosphere. These investigations focus on studying the properties and behavior of ionospheric plasma, with particular emphasis on being able to understand and use it to enhance communications and surveillance systems for both civilian and military purposes. HAARP was started in 1993 as a proposed twenty-year experiment, and is currently active near Gakona, Alaska.

The SuperDARN radar project researches the high- and mid-latitudes using coherent backscatter of radio waves in the 8 to 20 MHz range. Coherent backscatter is similar to Bragg scattering in crystals and involves the constructive interference of scattering from ionospheric density irregularities. The project involves more than 11 different countries and multiple radars in both hemispheres.

Scientists are also examining the ionosphere by the changes to radio waves, from satellites and stars, passing through it. The Arecibo radio telescope located in Puerto Rico, was originally intended to study Earth's ionosphere.

Ionograms

Ionograms show the virtual heights and critical frequencies of the ionospheric layers and which are measured by an ionosonde. An ionosonde sweeps a range of frequencies, usually from 0.1 to 30 MHz, transmitting at vertical incidence to the ionosphere. As the frequency increases, each wave is refracted less by the ionization in the layer, and so each penetrates further before it is reflected. Eventually, a frequency is reached that enables the wave to penetrate the layer without being reflected. For ordinary mode waves, this occurs when the transmitted frequency just exceeds the peak plasma, or critical, frequency of the layer. Tracings of the reflected high frequency radio pulses are known as ionograms. Reduction rules are given in: "URSI Handbook of Ionogram Interpretation and Reduction", edited by William Roy Piggott and Karl Rawer, Elsevier Amsterdam, 1961 (translations into Chinese, French, Japanese and Russian are available).

Incoherent scatter radars

Incoherent scatter radars operate above the critical frequencies. Therefore, the technique allows probing the ionosphere, unlike ionosondes, also above the electron density peaks. The thermal fluctuations of the electron density scattering the transmitted signals lack coherence, which gave the technique its name. Their power spectrum contains information not only on the density, but also on the ion and electron temperatures, ion masses and drift velocities.

GNSS radio occultation

Radio occultation is a remote sensing technique where a GNSS signal tangentially scrapes the Earth, passing through the atmosphere, and is received by a Low Earth Orbit (LEO) satellite. As the signal passes through the atmosphere, it is refracted, curved and delayed. An LEO satellite samples the total electron content and bending angle of many such signal paths as it watches the GNSS satellite rise or set behind the Earth. Using an Inverse Abel's transform, a radial profile of refractivity at that tangent point on earth can be reconstructed. 

Major GNSS radio occultation missions include the GRACE, CHAMP, and COSMIC.

Indices of the ionosphere

In empirical models of the ionosphere such as Nequick, the following indices are used as indirect indicators of the state of the ionosphere.

Solar intensity

F10.7 and R12 are two indices commonly used in ionospheric modelling. Both are valuable for their long historical records covering multiple solar cycles. F10.7 is a measurement of the intensity of solar radio emissions at a frequency of 2800 MHz made using a ground radio telescope. R12 is a 12 months average of daily sunspot numbers. Both indices have been shown to be correlated to each other. 

However, both indices are only indirect indicators of solar ultraviolet and X-ray emissions, which are primarily responsible for causing ionization in the Earth's upper atmosphere. We now have data from the GOES spacecraft that measures the background X-ray flux from the Sun, a parameter more closely related to the ionization levels in the ionosphere.

Geomagnetic disturbances

• The A- and K-indices are a measurement of the behavior of the horizontal component of the geomagnetic field. The K-index uses a scale from 0 to 9 to measure the change in the horizontal component of the geomagnetic field. A new K-index is determined at the Boulder Geomagnetic Observatory.
• The geomagnetic activity levels of the Earth are measured by the fluctuation of the Earth's magnetic field in SI units called teslas (or in non-SI gauss, especially in older literature). The Earth's magnetic field is measured around the planet by many observatories. The data retrieved is processed and turned into measurement indices. Daily measurements for the entire planet are made available through an estimate of the A_p-index, called the planetary A-index (PAI).

GPS/GNSS ionospheric correction

There are a number of models used to understand the effects of the ionosphere global navigation satellite systems. The Klobuchar model is currently used to compensate for ionospheric effects in GPS. This model was developed at the US Air Force Geophysical Research Laboratory circa 1974 by John (Jack) Klobuchar. The Galileo navigation system uses the NeQuick model.

Ionospheres of other planets and natural satellites

Objects in the Solar System that have appreciable atmospheres (i.e., all of the major planets and many of the larger natural satellites) generally produce ionospheres. Planets known to have ionospheres include Venus, Uranus, Mars and Jupiter. 

The atmosphere of Titan includes an ionosphere that ranges from about 1,100 km (680 mi) to 1,300 km (810 mi) in altitude and contains carbon compounds.

Atmospheric electricity

From Wikipedia, the free encyclopedia

 

Cloud to ground lightning. Typically, lightning discharges 30,000 amperes, at up to 100 million volts, and emits light, radio waves, x-rays and even gamma rays. Plasma temperatures in lightning can approach 28,000 kelvins.

 

Atmospheric electricity is the study of electrical charges in the Earth's atmosphere (or that of another planet). The movement of charge between the Earth's surface, the atmosphere, and the ionosphere is known as the global atmospheric electrical circuit. Atmospheric electricity is an interdisciplinary topic with a long history, involving concepts from electrostatics, atmospheric physics, meteorology and Earth science.

Thunderstorms act as a giant battery in the atmosphere, charging up the electrosphere to about 400,000 volts with respect to the surface. This sets up an electric field throughout the atmosphere, which decreases with increase in altitude. Atmospheric ions created by cosmic rays and natural radioactivity move in the electric field, so a very small current flows through the atmosphere, even away from thunderstorms. Near the surface of the earth, the magnitude of the field is on average around 100 V/m.

Atmospheric electricity involves both thunderstorms, which create lightning bolts to rapidly discharge huge amounts of atmospheric charge stored in storm clouds, and the continual electrification of the air due to ionization from cosmic rays and natural radioactivity, which ensure that the atmosphere is never quite neutral.

History

Sparks drawn from electrical machines and from Leyden jars suggested to the early experimenters, Hauksbee, Newton, Wall, Nollet, and Gray, that lightning was caused by electric discharges. In 1708, Dr. William Wall was one of the first to observe that spark discharges resembled miniature lightning, after observing the sparks from a charged piece of amber. 

Benjamin Franklin's experiments showed that electrical phenomena of the atmosphere were not fundamentally different from those produced in the laboratory, by listing many similarities between electricity and lightning. By 1749, Franklin observed lightning to possess almost all the properties observable in electrical machines. 

In July 1750, Franklin hypothesized that electricity could be taken from clouds via a tall metal aerial with a sharp point. Before Franklin could carry out his experiment, in 1752 Thomas-François Dalibard erected a 40-foot (12 m) iron rod at Marly-la-Ville, near Paris, drawing sparks from a passing cloud. With ground-insulated aerials, an experimenter could bring a grounded lead with an insulated wax handle close to the aerial, and observe a spark discharge from the aerial to the grounding wire. In May 1752, Dalibard affirmed that Franklin's theory was correct.

Around June 1752, Franklin reportedly performed his famous kite experiment. The kite experiment was repeated by Romas, who drew from a metallic string sparks 9 feet (2.7 m) long, and by Cavallo, who made many important observations on atmospheric electricity. Lemonnier (1752) also reproduced Franklin's experiment with an aerial, but substituted the ground wire with some dust particles (testing attraction). He went on to document the fair weather condition, the clear-day electrification of the atmosphere, and its diurnal variation. Beccaria (1775) confirmed Lemonnier's diurnal variation data and determined that the atmosphere's charge polarity was positive in fair weather. Saussure (1779) recorded data relating to a conductor's induced charge in the atmosphere. Saussure's instrument (which contained two small spheres suspended in parallel with two thin wires) was a precursor to the electrometer. Saussure found that the atmospheric electrification under clear weather conditions had an annual variation, and that it also varied with height. In 1785, Coulomb discovered the electrical conductivity of air. His discovery was contrary to the prevailing thought at the time, that the atmospheric gases were insulators (which they are to some extent, or at least not very good conductors when not ionized). Erman (1804) theorized that the Earth was negatively charged, and Peltier (1842) tested and confirmed Erman's idea.

Several researchers contributed to the growing body of knowledge about atmospheric electrical phenomena. Francis Ronalds began observing the potential gradient and air-earth currents around 1810, including making continuous automated recordings. He resumed his research in the 1840s as the inaugural Honorary Director of the Kew Observatory, where the first extended and comprehensive dataset of electrical and associated meteorological parameters was created. He also supplied his equipment to other facilities around the world with the goal of delineating atmospheric electricity on a global scale. Kelvin's new water dropper collector and divided-ring electrometer  were introduced at Kew Observatory in the 1860s, and atmospheric electricity remained a speciality of the observatory until its closure. For high-altitude measurements, kites were once used, and weather balloons or aerostats are still used, to lift experimental equipment into the air. Early experimenters even went aloft themselves in hot-air balloons. 

Hoffert (1888) identified individual lightning downward strokes using early cameras. Elster and Geitel, who also worked on thermionic emission, proposed a theory to explain thunderstorms' electrical structure (1885) and, later, discovered atmospheric radioactivity (1899) from the existence of positive and negative ions in the atmosphere. Pockels (1897) estimated lightning current intensity by analyzing lightning flashes in basalt (c. 1900) and studying the left-over magnetic fields caused by lightning. Discoveries about the electrification of the atmosphere via sensitive electrical instruments and ideas on how the Earth's negative charge is maintained were developed mainly in the 20th century, with CTR Wilson playing an important part. Current research on atmospheric electricity focuses mainly on lightning, particularly high-energy particles and transient luminous events, and the role of non-thunderstorm electrical processes in weather and climate.

Description

Atmospheric electricity is always present, and during fine weather away from thunderstorms, the air above the surface of Earth is positively charged, while the Earth's surface charge is negative. It can be understood in terms of a difference of potential between a point of the Earth's surface, and a point somewhere in the air above it. Because the atmospheric electric field is negatively directed in fair weather, the convention is to refer to the potential gradient, which has the opposite sign and is about 100 V/m at the surface. The potential gradient in most locations is much lower than this value because it is an average of the charge built up by every thunderstorm and atmospheric disturbance around the globe. There is a weak conduction current of atmospheric ions moving in the atmospheric electric field, about 2 picoAmperes per square metre, and the air is weakly conductive due to the presence of these atmospheric ions.

Variations

Global daily cycles in the atmospheric electric field, with a minimum around 03 UT and peaking roughly 16 hours later, were researched by the Carnegie Institution of Washington in the 20th century. This Carnegie curve variation has been described as "the fundamental electrical heartbeat of the planet".

Even away from thunderstorms, atmospheric electricity can be highly variable, but, generally, the electric field is enhanced in fogs and dust whereas the atmospheric electrical conductivity is diminished.

Links with biology

The atmospheric potential gradient leads to an ion flow from the positively charged atmosphere to the negatively charged earth surface. Over a flat field on a day with clear skies, the atmospheric potential gradient is approximately 120 V/m. Objects protruding these fields, e.g. flowers and trees, can increase the electric field strength to several kilovolts per meter. These near-surface electrostatic forces are detected by organisms such as the bumblebee to navigate to flowers and the spider to initiate dispersal by ballooning. The atmospheric potential gradient is also thought to affect sub-surface electro-chemistry and microbial processes.

Near space

The electrosphere layer (from tens of kilometers above the surface of the earth to the ionosphere) has a high electrical conductivity and is essentially at a constant electric potential. The ionosphere is the inner edge of the magnetosphere and is the part of the atmosphere that is ionized by solar radiation. (Photoionization is a physical process in which a photon is incident on an atom, ion or molecule, resulting in the ejection of one or more electrons.)

Cosmic radiation

The Earth, and almost all living things on it, are constantly bombarded by radiation from outer space. This radiation primarily consists of positively charged ions from protons to iron and larger nuclei derived sources outside our solar system. This radiation interacts with atoms in the atmosphere to create an air shower of secondary ionising radiation, including X-rays, muons, protons, alpha particles, pions, and electrons. Ionization from this secondary radiation ensures that the atmosphere is weakly conductive, and that the slight current flow from these ions over the Earth's surface balances the current flow from thunderstorms. Ions have characteristic parameters such as mobility, lifetime, and generation rate that vary with altitude.

Thunderstorms and lightning

The potential difference between the ionosphere and the Earth is maintained by thunderstorms, with lightning strikes delivering negative charges from the atmosphere to the ground. 

World map showing frequency of lightning strikes, in flashes per km² per year (equal-area projection). Lightning strikes most frequently in the Democratic Republic of the Congo. Combined 1995–2003 data from the Optical Transient Detector and 1998–2003 data from the Lightning Imaging Sensor.

 

Collisions between ice and soft hail (graupel) inside cumulonimbus clouds causes separation of positive and negative charges within the cloud, essential for the generation of lightning. How lightning initially forms is still a matter of debate: Scientists have studied root causes ranging from atmospheric perturbations (wind, humidity, and atmospheric pressure) to the impact of solar wind and energetic particles.

An average bolt of lightning carries a negative electric current of 40 kiloamperes (kA) (although some bolts can be up to 120 kA), and transfers a charge of five coulombs and energy of 500 MJ, or enough energy to power a 100-watt lightbulb for just under two months. The voltage depends on the length of the bolt, with the dielectric breakdown of air being three million volts per meter, and lightning bolts often being several hundred meters long. However, lightning leader development is not a simple matter of dielectric breakdown, and the ambient electric fields required for lightning leader propagation can be a few orders of magnitude less than dielectric breakdown strength. Further, the potential gradient inside a well-developed return-stroke channel is on the order of hundreds of volts per meter or less due to intense channel ionization, resulting in a true power output on the order of megawatts per meter for a vigorous return-stroke current of 100 kA.

If the quantity of water that is condensed in and subsequently precipitated from a cloud is known, then the total energy of a thunderstorm can be calculated. In an average thunderstorm, the energy released amounts to about 10,000,000 kilowatt-hours (3.6×10¹³ joule), which is equivalent to a 20-kiloton nuclear warhead. A large, severe thunderstorm might be 10 to 100 times more energetic.

Lightning sequence (Duration: 0.32 seconds)

Corona discharges

A depiction of atmospheric electricity in a Martian dust storm, which has been suggested as a possible explanation for enigmatic chemistry results from Mars (see also Viking lander biological experiments)

 

St. Elmo's Fire is an electrical phenomenon in which luminous plasma is created by a coronal discharge originating from a grounded object. Ball lightning is often erroneously identified as St. Elmo's Fire, whereas they are separate and distinct phenomena. Although referred to as "fire", St. Elmo's Fire is, in fact, plasma, and is observed, usually during a thunderstorm, at the tops of trees, spires or other tall objects, or on the heads of animals, as a brush or star of light. 

Corona is caused by the electric field around the object in question ionizing the air molecules, producing a faint glow easily visible in low-light conditions. Approximately 1,000 – 30,000 volts per centimetre is required to induce St. Elmo's Fire; however, this is dependent on the geometry of the object in question. Sharp points tend to require lower voltage levels to produce the same result because electric fields are more concentrated in areas of high curvature, thus discharges are more intense at the end of pointed objects. St. Elmo's Fire and normal sparks both can appear when high electrical voltage affects a gas. St. Elmo's fire is seen during thunderstorms when the ground below the storm is electrically charged, and there is high voltage in the air between the cloud and the ground. The voltage tears apart the air molecules and the gas begins to glow. The nitrogen and oxygen in the Earth's atmosphere causes St. Elmo's Fire to fluoresce with blue or violet light; this is similar to the mechanism that causes neon signs to glow.

Earth-Ionosphere cavity

The Schumann resonances are a set of spectrum peaks in the extremely low frequency (ELF) portion of the Earth's electromagnetic field spectrum. Schumann resonance is due to the space between the surface of the Earth and the conductive ionosphere acting as a waveguide. The limited dimensions of the earth cause this waveguide to act as a resonant cavity for electromagnetic waves. The cavity is naturally excited by energy from lightning strikes.

Electrical system grounding

Atmospheric charges can cause undesirable, dangerous, and potentially lethal charge potential buildup in suspended electric wire power distribution systems. Bare wires suspended in the air spanning many kilometers and isolated from the ground can collect very large stored charges at high voltage, even when there is no thunderstorm or lightning occurring. This charge will seek to discharge itself through the path of least insulation, which can occur when a person reaches out to activate a power switch or to use an electric device.

To dissipate atmospheric charge buildup, one side of the electrical distribution system is connected to the earth at many points throughout the distribution system, as often as on every support pole. The one earth-connected wire is commonly referred to as the "protective earth", and provides path for the charge potential to dissipate without causing damage, and provides redundancy in case any one of the ground paths is poor due to corrosion or poor ground conductivity. The additional electric grounding wire that carries no power serves a secondary role, providing a high-current short-circuit path to rapidly blow fuses and render a damaged device safe, rather than have an ungrounded device with damaged insulation become "electrically live" via the grid power supply, and hazardous to touch.

Each transformer in an alternating current distribution grid segments the grounding system into a new separate circuit loop. These separate grids must also be grounded on one side to prevent charge buildup within them relative to the rest of the system, and which could cause damage from charge potentials discharging across the transformer coils to the other grounded side of the distribution network.

Electrodynamic tether

From Wikipedia, the free encyclopedia

 

Medium close-up view, captured with a 70 mm camera, shows tethered satellite system deployment.

 

Electrodynamic tethers (EDTs) are long conducting wires, such as one deployed from a tether satellite, which can operate on electromagnetic principles as generators, by converting their kinetic energy to electrical energy, or as motors, converting electrical energy to kinetic energy. Electric potential is generated across a conductive tether by its motion through a planet's magnetic field. 

A number of missions have demonstrated electrodynamic tethers in space, most notably the TSS-1, TSS-1R, and Plasma Motor Generator (PMG) experiments.

Tether propulsion

As part of a tether propulsion system, crafts can use long, strong conductors (though not all tethers are conductive) to change the orbits of spacecraft. It has the potential to make space travel significantly cheaper. When direct current is applied to the tether, it exerts a Lorentz force against the magnetic field, and the tether exerts a force on the vehicle. It can be used either to accelerate or brake an orbiting spacecraft. 

In 2012, the company Star Technology and Research was awarded a $1.9 million contract to qualify a tether propulsion system for orbital debris removal.

Uses for ED tethers

Over the years, numerous applications for electrodynamic tethers have been identified for potential use in industry, government, and scientific exploration. The table below is a summary of some of the potential applications proposed thus far. Some of these applications are general concepts, while others are well-defined systems. Many of these concepts overlap into other areas; however, they are simply placed under the most appropriate heading for the purposes of this table. All of the applications mentioned in the table are elaborated upon in the Tethers Handbook. Three fundamental concepts that tethers possess, are gravity gradients, momentum exchange, and electrodynamics. Potential tether applications can be seen below: 

ELECTRODYNAMICS
Electrodynamic power generation	Electrodynamic thrust generation
ULF/ELF/VLF communication antenna	Radiation belt remediation
SPACE STATION
Microgravity laboratory	Shuttle de-orbit from Space Station
Tethered Space Transfer Vehicle (STV) launch	Variable/low gravity laboratory
Attitude stabilization and control	ISS reboost
TRANSPORTATION
Generalized momentum scavenging spent stages	Internal forces for orbital modification
Satellite boost from orbiter	Tether Assisted Transportation System (TATS)
Tether re-boosting of decaying satellites	Upper stage boost from Orbiter

Electrodynamic tether fundamentals

Illustration of the EDT concept

 

The choice of the metal conductor to be used in an electrodynamic tether is determined by a variety of factors. Primary factors usually include high electrical conductivity, and low density. Secondary factors, depending on the application, include cost, strength, and melting point.

An electromotive force (EMF) is generated across a tether element as it moves relative to a magnetic field. The force is given by Faraday's Law of Induction:

${\displaystyle V_{\mathrm {emf} }=\int _{0}^{L}\left({\vec {v}}_{\mathrm {orb} }\times {\vec {B}}\right)d{\vec {L}}.}$

Without loss of generality, it is assumed the tether system is in Earth orbit and it moves relative to Earth's magnetic field. Similarly, if current flows in the tether element, a force can be generated in accordance with the Lorentz force equation

${\displaystyle {\vec {F}}=\int _{0}^{L}I(L)\,d{\vec {L}}\times {\vec {B}}.}$

In self-powered mode (deorbit mode), this EMF can be used by the tether system to drive the current through the tether and other electrical loads (e.g. resistors, batteries), emit electrons at the emitting end, or collect electrons at the opposite. In boost mode, on-board power supplies must overcome this motional EMF to drive current in the opposite direction, thus creating a force in the opposite direction, as seen in below figure, and boosting the system.

Take, for example, the NASA Propulsive Small Expendable Deployer System (ProSEDS) mission as seen in above figure. At 300 km altitude, the Earth's magnetic field, in the north-south direction, is approximately 0.18–0.32 gauss up to ~40° inclination, and the orbital velocity with respect to the local plasma is about 7500 m/s. This results in a V_emf range of 35–250 V/km along the 5 km length of tether. This EMF dictates the potential difference across the bare tether which controls where electrons are collected and / or repelled. Here, the ProSEDS de-boost tether system is configured to enable electron collection to the positively biased higher altitude section of the bare tether, and returned to the ionosphere at the lower altitude end. This flow of electrons through the length of the tether in the presence of the Earth's magnetic field creates a force that produces a drag thrust that helps de-orbit the system, as given by the above equation. The boost mode is similar to the de-orbit mode, except for the fact that a High Voltage Power Supply (HVPS) is also inserted in series with the tether system between the tether and the higher positive potential end. The power supply voltage must be greater than the EMF and the polar opposite. This drives the current in the opposite direction, which in turn causes the higher altitude end to be negatively charged, while the lower altitude end is positively charged(Assuming a standard east to west orbit around Earth).

To further emphasize the de-boosting phenomenon, a schematic sketch of a bare tether system with no insulation (all bare) can be seen in below figure.

Current and Voltage plots vs. distance of a bare tether operating in generator (de-boost) mode.

 

The top of the diagram, point A, represents the electron collection end. The bottom of the tether, point C, is the electron emission end. Similarly, ${\displaystyle V_{\mathrm {anode} }}$ and ${\displaystyle V_{\mathrm {cathode} }}$ represent the potential difference from their respective tether ends to the plasma, and ${\displaystyle V-V_{p}}$ is the potential anywhere along the tether with respect to the plasma. Finally, point B is the point at which the potential of the tether is equal to the plasma. The location of point B will vary depending on the equilibrium state of the tether, which is determined by the solution of Kirchhoff's voltage law (KVL)

${\displaystyle V_{\mathrm {anode} }+\int _{A}^{C}I(y)\,dR_{t}+R_{\mathrm {load} }I_{C}+V_{\mathrm {emit} }+V_{\mathrm {cathode} }=V_{\mathrm {emf} }}$

and Kirchhoff's current law (KCL)

${\displaystyle I_{AB}=I_{BC}+I_{C}}$

along the tether. Here ${\displaystyle I_{AB}}$, ${\displaystyle I_{BC}}$, and ${\displaystyle I_{C}}$ describe the current gain from point A to B, the current lost from point B to C, and the current lost at point C, respectively. 

Since the current is continuously changing along the bare length of the tether, the potential loss due to the resistive nature of the wire is represented as ${\displaystyle \textstyle \int _{A}^{C}I(y)\,dR_{t}}$. Along an infinitesimal section of tether, the resistance ${\displaystyle dR_{t}}$ multiplied by the current ${\displaystyle I(y)}$ traveling across that section is the resistive potential loss. 

After evaluating KVL & KCL for the system, the results will yield a current and potential profile along the tether, as seen in above figure. This diagram shows that, from point A of the tether down to point B, there is a positive potential bias, which increases the collected current. Below that point, the ${\displaystyle V-V_{p}}$ becomes negative and the collection of ion current begins. Since it takes a much greater potential difference to collect an equivalent amount of ion current (for a given area), the total current in the tether is reduced by a smaller amount. Then, at point C, the remaining current in the system is drawn through the resistive load (${\displaystyle R_{\mathrm {load} }}$), and emitted from an electron emissive device (${\displaystyle V_{\mathrm {emit} }}$), and finally across the plasma sheath (${\displaystyle V_{\mathrm {cathode} }}$). The KVL voltage loop is then closed in the ionosphere where the potential difference is effectively zero. 

Due to the nature of the bare EDTs, it is often not optional to have the entire tether bare. In order to maximize the thrusting capability of the system a significant portion of the bare tether should be insulated. This insulation amount depends on a number of effects, some of which are plasma density, the tether length and width, the orbiting velocity, and the Earth's magnetic flux density.

Tethers as generators

A space object, i.e. a satellite in Earth orbit, or any other space object either natural or man made, is physically connected to the tether system. The tether system comprises a deployer from which a conductive tether having a bare segment extends upward from space object. The positively biased anode end of tether collects electrons from the ionosphere as space object moves in direction across the Earth's magnetic field. These electrons flow through the conductive structure of the tether to the power system interface, where it supplies power to an associated load, not shown. The electrons then flow to the negatively biased cathode where electrons are ejected into the space plasma, thus completing the electric circuit. (source: U.S. Patent 6,116,544, "Electrodynamic Tether And Method of Use".)

 

An electrodynamic tether is attached to an object, the tether being oriented at an angle to the local vertical between the object and a planet with a magnetic field. The tether's far end can be left bare, making electrical contact with the ionosphere. When the tether intersects the planet's magnetic field, it generates a current, and thereby converts some of the orbiting body's kinetic energy to electrical energy. Functionally, electrons flow from the space plasma into the conductive tether, are passed through a resistive load in a control unit and are emitted into the space plasma by an electron emitter as free electrons. As a result of this process, an electrodynamic force acts on the tether and attached object, slowing their orbital motion. In a loose sense, the process can be likened to a conventional windmill- the drag force of a resistive medium(air or, in this case, the magnetosphere) is used to convert the kinetic energy of relative motion(wind, or the satellite's momentum) into electricity. In principle, compact high-current tether power generators are possible and, with basic hardware, tens, hundreds, and thousands of kilowatts appears to be attainable.

Voltage and current

NASA has conducted several experiments with Plasma Motor Generator (PMG) tethers in space. An early experiment used a 500-meter conducting tether. In 1996, NASA conducted an experiment with a 20,000-meter conducting tether. When the tether was fully deployed during this test, the orbiting tether generated a potential of 3,500 volts. This conducting single-line tether was severed after five hours of deployment. It is believed that the failure was caused by an electric arc generated by the conductive tether's movement through the Earth's magnetic field.

When a tether is moved at a velocity (v) at right angles to the Earth's magnetic field (B), an electric field is observed in the tether's frame of reference. This can be stated as:

E = v * B = vB

The direction of the electric field (E) is at right angles to both the tether's velocity (v) and magnetic field (B). If the tether is a conductor, then the electric field leads to the displacement of charges along the tether. Note that the velocity used in this equation is the orbital velocity of the tether. The rate of rotation of the Earth, or of its core, is not relevant. In this regard, see also homopolar generator.

Voltage across conductor

With a long conducting wire of length L, an electric field E is generated in the wire. It produces a voltage V between the opposite ends of the wire. This can be expressed as:

${\displaystyle V=\mathbf {E} \cdot \mathbf {L} =EL\cos \tau =vBL\cos \tau }$

where the angle τ is between the length vector (L) of the tether and the electric field vector (E), assumed to be in the vertical direction at right angles to the velocity vector (v) in plane and the magnetic field vector (B) is out of the plane.

Current in conductor

An electrodynamic tether can be described as a type of thermodynamically "open system". Electrodynamic tether circuits cannot be completed by simply using another wire, since another tether will develop a similar voltage. Fortunately, the Earth's magnetosphere is not "empty", and, in near-Earth regions (especially near the Earth's atmosphere) there exist highly electrically conductive plasmas which are kept partially ionized by solar radiation or other radiant energy. The electron and ion density varies according to various factors, such as the location, altitude, season, sunspot cycle, and contamination levels. It is known that a positively charged bare conductor can readily remove free electrons out of the plasma. Thus, to complete the electrical circuit, a sufficiently large area of uninsulated conductor is needed at the upper, positively charged end of the tether, thereby permitting current to flow through the tether.

However, it is more difficult for the opposite (negative) end of the tether to eject free electrons or to collect positive ions from the plasma. It is plausible that, by using a very large collection area at one end of the tether, enough ions can be collected to permit significant current through the plasma. This was demonstrated during the Shuttle orbiter's TSS-1R mission, when the shuttle itself was used as a large plasma contactor to provide over an ampere of current. Improved methods include creating an electron emitter, such as a thermionic cathode, plasma cathode, plasma contactor, or field electron emission device. Since both ends of the tether are "open" to the surrounding plasma, electrons can flow out of one end of the tether while a corresponding flow of electrons enters the other end. In this fashion, the voltage that is electromagnetically induced within the tether can cause current to flow through the surrounding space environment, completing an electrical circuit through what appears to be, at first glance, an open circuit.

Tether current

The amount of current (I) flowing through a tether depends on various factors. One of these is the circuit's total resistance (R). The circuit's resistance consist of three components:

1. the effective resistance of the plasma,
2. the resistance of the tether, and
3. a control variable resistor.

In addition, a parasitic load is needed. The load on the current may take the form of a charging device which, in turn, charges reserve power sources such as batteries. The batteries in return will be used to control power and communication circuits, as well as drive the electron emitting devices at the negative end of the tether. As such the tether can be completely self-powered, besides the initial charge in the batteries to provide electrical power for the deployment and startup procedure.

The charging battery load can be viewed as a resistor which absorbs power, but stores this for later use (instead of immediately dissipating heat). It is included as part of the "control resistor". The charging battery load is not treated as a "base resistance" though, as the charging circuit can be turned off at any time. When off, the operations can be continued without interruption using the power stored in the batteries.

Current collection / emission for an EDT system: theory and technology

Understanding electron and ion current collection to and from the surrounding ambient plasma is critical for most EDT systems. Any exposed conducting section of the EDT system can passively ('passive' and 'active' emission refers to the use of pre-stored energy in order to achieve the desired effect) collect electron or ion current, depending on the electric potential of the spacecraft body with respect to the ambient plasma. In addition, the geometry of the conducting body plays an important role in the size of the sheath and thus the total collection capability. As a result, there are a number of theories for the varying collection techniques. 

The primary passive processes that control the electron and ion collection on an EDT system are thermal current collection, ion ram collection affects, electron photoemission, and possibly secondary electron and ion emission. In addition, the collection along a thin bare tether is described using orbital motion limited (OML) theory as well as theoretical derivations from this model depending on the physical size with respect to the plasma Debye length. These processes take place all along the exposed conducting material of the entire system. Environmental and orbital parameters can significantly influence the amount collected current. Some important parameters include plasma density, electron and ion temperature, ion molecular weight, magnetic field strength and orbital velocity relative to the surrounding plasma.

Then there is active collection and emission techniques involved in an EDT system. This occurs through devices such as a hollow cathode plasma contactors, thermionic cathodes, and field emitter arrays. The physical design of each of these structures as well as the current emission capabilities are thoroughly discussed.

Bare conductive tethers

The concept of current collection to a bare conducting tether was first formalized by Sanmartin and Martinez-Sanchez. They note that the most area efficient current collecting cylindrical surface is one that has an effective radius less than ~1 Debye length where current collection physics is known as orbital motion limited (OML) in a collisionless plasma. As the effective radius of the bare conductive tether increases past this point then there are predictable reductions in collection efficiency compared to OML theory. In addition to this theory (which has been derived for a non-flowing plasma), current collection in space occurs in a flowing plasma, which introduces another collection affect. These issues are explored in greater detail below.

Orbit motion limited (OML) theory

The electron Debye length is defined as the characteristic shielding distance in a plasma, and is described by the equation

${\displaystyle \lambda _{\mathrm {De} }\cong {\sqrt {\frac {\varepsilon _{0}T_{e}}{qn_{0}}}}.}$

This distance, where all electric fields in the plasma resulting from the conductive body have fallen off by 1/e, can be calculated. OML theory is defined with the assumption that the electron Debye length is equal to or larger than the size of the object and the plasma is not flowing. The OML regime occurs when the sheath becomes sufficiently thick such that orbital effects become important in particle collection. This theory accounts for and conserves particle energy and angular momentum. As a result, not all particles that are incident onto the surface of the thick sheath are collected. The voltage of the collecting structure with respect to the ambient plasma, as well as the ambient plasma density and temperature, determines the size of the sheath. This accelerating (or decelerating) voltage combined with the energy and momentum of the incoming particles determines the amount of current collected across the plasma sheath. 

The orbital-motion-limit regime is attained when the cylinder radius is small enough such that all incoming particle trajectories that are collected are terminated on the cylinder's surface are connected to the background plasma, regardless of their initial angular momentum (i.e., none are connected to another location on the probe's surface). Since, in a quasi-neutral collisionless plasma, the distribution function is conserved along particle orbits, having all “directions of arrival” populated corresponds to an upper limit on the collected current per unit area (not total current).

In an EDT system, the best performance for a given tether mass is for a tether diameter chosen to be smaller than an electron Debye length for typical ionospheric ambient conditions (Typical ionospheric conditions in the from 200 to 2000 km altitude range, have a T_e ranging from 0.1 eV to 0.35 eV, and n_e ranging from 10^10 m^-3 to 10^12 m^-3 ), so it is therefore within the OML regime. Tether geometries outside this dimension have been addressed. OML collection will be used as a baseline when comparing the current collection results for various sample tether geometries and sizes. 

In 1962 Gerald H. Rosen derived the equation that is now known as the OML theory of dust charging. According to Robert Merlino of the University of Iowa, Rosen seems to have arrived at the equation 30 years before anyone else.

Deviations from OML theory in a non-flowing plasma

For a variety of practical reasons, current collection to a bare EDT does not always satisfy the assumption of OML collection theory. Understanding how the predicted performance deviates from theory is important for these conditions. Two commonly proposed geometries for an EDT involve the use of a cylindrical wire and a flat tape. As long as the cylindrical tether is less than one Debye length in radius, it will collect according to the OML theory. However, once the width exceeds this distance, then the collection increasingly deviates from this theory. If the tether geometry is a flat tape, then an approximation can be used to convert the normalized tape width to an equivalent cylinder radius. This was first done by Sanmartin and Estes and more recently using the 2-Dimensional Kinetic Plasma Solver (KiPS 2-D) by Choiniere et al.

Flowing plasma effect

There is at present, no closed-form solution to account for the effects of plasma flow relative to the bare tether. However, numerical simulation has been recently developed by Choiniere et al. using KiPS-2D which can simulate flowing cases for simple geometries at high bias potentials. This flowing plasma analysis as it applies to EDTs have been discussed. This phenomenon is presently being investigated through recent work, and is not fully understood.

Endbody collection

This section discusses the plasma physics theory that explains passive current collection to a large conductive body which will be applied at the end of an ED tether. When the size of the sheath is much smaller than the radius of the collecting body then depending on the polarity of the difference between the potential of the tether and that of the ambient plasma, (V – Vp), it is assumed that all of the incoming electrons or ions that enter the plasma sheath are collected by the conductive body. This 'thin sheath' theory involving non-flowing plasmas is discussed, and then the modifications to this theory for flowing plasma is presented. Other current collection mechanisms will then be discussed. All of the theory presented is used towards developing a current collection model to account for all conditions encountered during an EDT mission.

Passive collection theory

In a non-flowing quasi-neutral plasma with no magnetic field, it can be assumed that a spherical conducting object will collect equally in all directions. The electron and ion collection at the end-body is governed by the thermal collection process, which is given by Ithe and Ithi.

Flowing plasma electron collection mode

The next step in developing a more realistic model for current collection is to include the magnetic field effects and plasma flow effects. Assuming a collisionless plasma, electrons and ions gyrate around magnetic field lines as they travel between the poles around the Earth due to magnetic mirroring forces and gradient-curvature drift. They gyrate at a particular radius and frequency dependence upon their mass, the magnetic field strength, and energy. These factors must be considered in current collection models. 

A composite schematic of the complex array of physical effects and characteristics observed in the near environment of the TSS satellite.

Flowing plasma ion collection model

When the conducting body is negatively biased with respect to the plasma and traveling above the ion thermal velocity, there are additional collection mechanisms at work. For typical Low Earth Orbits (LEOs), between 200 km and 2000 km, the velocities in an inertial reference frame range from 7.8 km/s to 6.9 km/s for a circular orbit and the atmospheric molecular weights range from 25.0 amu (O+, O2+, & NO+) to 1.2 amu (mostly H+), respectively. Assuming that the electron and ion temperatures range from ~0.1 eV to 0.35 eV, the resulting ion velocity ranges from 875 m/s to 4.0 km/s from 200 km to 2000 km altitude, respectively. The electrons are traveling at approximately 188 km/s throughout LEO. This means that the orbiting body is traveling faster than the ions and slower than the electrons, or at a mesosonic speed. This results in a unique phenomenon whereby the orbiting body 'rams' through the surrounding ions in the plasma creating a beam like effect in the reference frame of the orbiting body.

Porous endbodies

Porous endbodies have been proposed as a way to reduce the drag of a collecting endbody while ideally maintaining a similar current collection. They are often modeled as solid endbodies, except they are a small percentage of the solid spheres surface area. This is, however, an extreme oversimplification of the concept. Much has to be learned about the interactions between the sheath structure, the geometry of the mesh, the size of the endbody, and its relation to current collection. This technology also has the potential to resolve a number of issues concerning EDTs. Diminishing returns with collection current and drag area have set a limit that porous tethers might be able to overcome. Work has been accomplished on current collection using porous spheres, by Stone et al. and Khazanov et al.

It has been shown that the maximum current collected by a grid sphere compared to the mass and drag reduction can be estimated. The drag per unit of collected current for a grid sphere with a transparency of 80 to 90% is approximately 1.2 – 1.4 times smaller than that of a solid sphere of the same radius. The reduction in mass per unit volume, for this same comparison, is 2.4 – 2.8 times.

Other current collection methods

In addition to the electron thermal collection, other processes that could influence the current collection in an EDT system are photoemission, secondary electron emission, and secondary ion emission. These effects pertain to all conducting surfaces on an EDT system, not just the end-body.

Space charge limits across plasma sheaths

In any application where electrons are emitted across a vacuum gap, there is a maximum allowable current for a given bias due to the self repulsion of the electron beam. This classical 1-D space charge limit (SCL) is derived for charged particles of zero initial energy, and is termed the Child-Langmuir Law. This limit depends on the emission surface area, the potential difference across the plasma gap and the distance of that gap. Further discussion of this topic can be found.

Electron emitters

There are three active electron emission technologies usually considered for EDT applications: hollow cathode plasma contactors (HCPCs), thermionic cathodes (TCs), and field emitter arrays (FEAs). System level configurations will be presented for each device, as well as the relative costs, benefits, and validation.

Thermionic cathode (TC)

Thermionic emission is the flow of electrons from a heated charged metal or metal oxide surface, caused by thermal vibrational energy overcoming the work function (electrostatic forces holding electrons to the surface). The thermionic emission current density, J, rises rapidly with increasing temperature, releasing a significant number of electrons into the vacuum near the surface. The quantitative relation is given in the equation

${\displaystyle J_{the}=A_{R}T^{2}e^{-\phi /(kt)}.}$

This equation is called the Richardson-Dushman or Richardson equation. (ф is approximately 4.54 eV and AR ~120 A/cm2 for tungsten).

Once the electrons are thermionically emitted from the TC surface they require an acceleration potential to cross a gap, or in this case, the plasma sheath. Electrons can attain this necessary energy to escape the SCL of the plasma sheath if an accelerated grid, or electron gun, is used. The equation

${\displaystyle \Delta V_{tc}=\left[{\frac {\eta \cdot I_{t}}{\rho }}\right]^{2/3}}$

shows what potential is needed across the grid in order to emit a certain current entering the device.

Here, η is the electron gun assembly (EGA) efficiency (~0.97 in TSS-1), ρ is the perveance of the EGA (7.2 micropervs in TSS-1), ΔV_tc is the voltage across the accelerating grid of the EGA, and I_t is the emitted current. The perveance defines the space charge limited current that can be emitted from a device. The figure below displays commercial examples of thermionic emitters and electron guns produced at Heatwave Labs Inc. 

Example of an electron emitting a) Thermionic Emitter and an electron accelerating b) Electron Gun Assembly.

 

TC electron emission will occur in one of two different regimes: temperature or space charge limited current flow. For temperature limited flow every electron that obtains enough energy to escape from the cathode surface is emitted, assuming the acceleration potential of the electron gun is large enough. In this case, the emission current is regulated by the thermionic emission process, given by the Richardson Dushman equation. In SCL electron current flow there are so many electrons emitted from the cathode that not all of them are accelerated enough by the electron gun to escape the space charge. In this case, the electron gun acceleration potential limits the emission current. The below chart displays the temperature limiting currents and SCL effects. As the beam energy of the electrons is increased, the total escaping electrons can be seen to increase. The curves that become horizontal are temperature limited cases.

Typical Electron Generator Assembly (EGA) current voltage characteristics as measured in a vacuum chamber.

Electron field emitter arrays (FEAs)

Field Emission

 

In field emission, electrons tunnel through a potential barrier, rather than escaping over it as in thermionic emission or photoemission. For a metal at low temperature, the process can be understood in terms of the figure below. The metal can be considered a potential box, filled with electrons to the Fermi level (which lies below the vacuum level by several electron volts). The vacuum level represents the potential energy of an electron at rest outside the metal in the absence of an external field. In the presence of a strong electric field, the potential outside the metal will be deformed along the line AB, so that a triangular barrier is formed, through which electrons can tunnel. Electrons are extracted from the conduction band with a current density given by the Fowler−Nordheim equation

${\displaystyle J_{the}=A_{FN}\cdot E_{FN}^{2}\cdot e^{-B_{FN}/E_{FN}}.}$

Energy level scheme for field emission from a metal at absolute zero temperature.

 

AFN and BFN are the constants determined by measurements of the FEA with units of A/V2 and V/m, respectively. EFN is the electric field that exists between the electron emissive tip and the positively biased structure drawing the electrons out. Typical constants for Spindt type cathodes include: AFN = 3.14 x 10-8 A/V2 and BFN = 771 V/m. (Stanford Research Institute data sheet). An accelerating structure is typically placed in close proximity with the emitting material as in the below figure. Close (micrometer scale) proximity between the emitter and gate, combined with natural or artificial focusing structures, efficiently provide the high field strengths required for emission with relatively low applied voltage and power. The following figure below displays close up visual images of a Spindt emitter.

Magnified pictures of a field emitter array (SEM photograph of an SRI Ring Cathode developed for the ARPA/NRL/NASA Vacuum Microelectronics Initiative by Capp Spindt)

 

A variety of materials have been developed for field emitter arrays, ranging from silicon to semiconductor fabricated molybdenum tips with integrated gates to a plate of randomly distributed carbon nanotubes with a separate gate structure suspended above. The advantages of field emission technologies over alternative electron emission methods are:

1. No requirement for a consumable (gas) and no resulting safety considerations for handling a pressurized vessel
2. A low-power capability
3. Having moderate power impacts due to space-charge limits in the emission of the electrons into the surrounding plasma.

One major issue to consider for field emitters is the effect of contamination. In order to achieve electron emission at low voltages, field emitter array tips are built on a micrometer-level scale sizes. Their performance depends on the precise construction of these small structures. They are also dependent on being constructed with a material possessing a low work-function. These factors can render the device extremely sensitive to contamination, especially from hydrocarbons and other large, easily polymerized molecules. Techniques for avoiding, eliminating, or operating in the presence of contaminations in ground testing and ionospheric (e.g. spacecraft outgassing) environments are critical. Research at the University of Michigan and elsewhere has focused on this outgassing issue. Protective enclosures, electron cleaning, robust coatings, and other design features are being developed as potential solutions. FEAs used for space applications still require the demonstration of long term stability, repeatability, and reliability of operation at gate potentials appropriate to the space applications.

Hollow cathode

Hollow cathodes emit a dense cloud of plasma by first ionizing a gas. This creates a high density plasma plume which makes contact with the surrounding plasma. The region between the high density plume and the surrounding plasma is termed a double sheath or double layer. This double layer is essentially two adjacent layers of charge. The first layer is a positive layer at the edge of the high potential plasma (the contactor plasma cloud). The second layer is a negative layer at the edge of the low potential plasma (the ambient plasma). Further investigation of the double layer phenomenon has been conducted by several people. One type of hollow cathode consists of a metal tube lined with a sintered barium oxide impregnated tungsten insert, capped at one end by a plate with a small orifice, as shown in the below figure. Electrons are emitted from the barium oxide impregnated insert by thermionic emission. A noble gas flows into the insert region of the HC and is partially ionized by the emitted electrons that are accelerated by an electric field near the orifice (Xenon is a common gas used for HCs as it has a low specific ionization energy (ionization potential per unit mass). For EDT purposes, a lower mass would be more beneficial because the total system mass would be less. This gas is just used for charge exchange and not propulsion.). Many of the ionized xenon atoms are accelerated into the walls where their energy maintains the thermionic emission temperature. The ionized xenon also exits out of the orifice. Electrons are accelerated from the insert region, through the orifice to the keeper, which is always at a more positive bias. 

Schematic of a Hollow Cathode System.

 

In electron emission mode, the ambient plasma is positively biased with respect to the keeper. In the contactor plasma, the electron density is approximately equal to the ion density. The higher energy electrons stream through the slowly expanding ion cloud, while the lower energy electrons are trapped within the cloud by the keeper potential. The high electron velocities lead to electron currents much greater than xenon ion currents. Below the electron emission saturation limit the contactor acts as a bipolar emissive probe. Each outgoing ion generated by an electron allows a number of electrons to be emitted. This number is approximately equal to the square root of the ratio of the ion mass to the electron mass. 

It can be seen in the below chart what a typical I-V curve looks like for a hollow cathode in electron emission mode. Given a certain keeper geometry (the ring in the figure above that the electrons exit through), ion flow rate, and Vp, the I-V profile can be determined.

Typical I-V Characteristic curve for a Hollow Cathode.

 

The operation of the HC in the electron collection mode is called the plasma contacting (or ignited) operating mode. The “ignited mode” is so termed because it indicates that multi-ampere current levels can be achieved by using the voltage drop at the plasma contactor. This accelerates space plasma electrons which ionize neutral expellant flow from the contactor. If electron collection currents are high and/or ambient electron densities are low, the sheath at which electron current collection is sustained simply expands or shrinks until the required current is collected. 

In addition, the geometry affects the emission of the plasma from the HC as seen in the below figure. Here it can be seen that, depending on the diameter and thickness of the keeper and the distance of it with respect to the orifice, the total emission percentage can be affected.

Typical Schematic detailing the HC emission geometry.

Plasma collection and emission summary

All of the electron emission and collection techniques can be summarized in the table following. For each method there is a description as to whether the electrons or ions in the system increased or decreased based on the potential of the spacecraft with respect to the plasma. Electrons (e-) and ions (ions+) indicates that the number of electrons or ions are being increased (↑) or reduced (↓). Also, for each method some special conditions apply (see the respective sections in this article for further clarification of when and where it applies).

Passive e− and ion emission/collection	V − Vp < 0	V − Vp > 0
Bare tether: OML	ions+ ↑	e− ↑
Ram collection	ions+ ↑	0
Thermal collection	ions+ ↑	e− ↑
Photoemmision	e− ↓	e− ↓,~0
Secondary electron emission	e− ↓	e− ↓
Secondary ion emission	ions+ ↓,~0	0
Retardation regieme	e− ↑	ions+ ↑, ~0
Active e− and ion emission	Potential does not matter
Thermionic emission	e− ↓
Field emitter arrays	e− ↓
Hollow cathodes	e− ↓	e− ↑

For use in EDT system modeling, each of the passive electron collection and emission theory models has been verified by reproducing previously published equations and results. These plots include: orbital motion limited theory, Ram collection, and thermal collection, photoemission, secondary electron emission, and secondary ion emission.

Electrodynamic tether system fundamentals

In order to integrate all the most recent electron emitters, collectors, and theory into a single model, the EDT system must first be defined and derived. Once this is accomplished it will be possible to apply this theory toward determining optimizations of system attributes. 

There are a number of derivations that solve for the potentials and currents involved in an EDT system numerically. The derivation and numerical methodology of a full EDT system that includes a bare tether section, insulating conducting tether, electron (and ion) endbody emitters, and passive electron collection is described. This is followed by the simplified, all insulated tether model. Special EDT phenomena and verification of the EDT system model using experimental mission data will then be discussed.

Bare tether system derivation

An important note concerning an EDT derivation pertains to the celestial body which the tether system orbits. For practicality, Earth will be used as the body that is orbited; however, this theory applies to any celestial body with an ionosphere and a magnetic field. 

The coordinates are the first thing that must be identified. For the purposes of this derivation, the x- and y-axis are defined as the east-west, and north-south directions with respect to the Earth's surface, respectively. The z-axis is defined as up-down from the Earth's center, as seen in the figure below. The parameters – magnetic field B, tether length L, and the orbital velocity v_orb – are vectors that can be expressed in terms of this coordinate system, as in the following equations:

${\displaystyle \mathbf {B} =B_{x}{\hat {x}}+B_{y}{\hat {y}}+B_{z}{\hat {z}}}$ 

 (the magnetic field vector),

${\displaystyle \mathbf {L} =L\cos \alpha _{\mathrm {out} }\sin \alpha _{\mathrm {in} }{\hat {x}}+L\sin \alpha _{\mathrm {out} }{\hat {y}}+L\cos \alpha _{\mathrm {out} }\cos \alpha _{\mathrm {in} }{\hat {z}}}$ 

(the tether position vector), and

${\displaystyle \mathbf {v} _{\mathrm {orb} }=v_{\mathrm {orb} }\cos \lambda _{\mathrm {out} }\sin \lambda _{\mathrm {in} }{\hat {x}}+v_{\mathrm {orb} }\sin \lambda _{\mathrm {out} }{\hat {y}}+v_{\mathrm {orb} }\cos \lambda _{\mathrm {out} }\cos \lambda _{\mathrm {in} }{\hat {z}}}$ 

(the orbital velocity vector).

The components of the magnetic field can be obtained directly from the International Geomagnetic Reference Field (IGRF) model. This model is compiled from a collaborative effort between magnetic field modelers and the institutes involved in collecting and disseminating magnetic field data from satellites and from observatories and surveys around the world. For this derivation, it is assumed that the magnetic field lines are all the same angle throughout the length of the tether, and that the tether is rigid.

Orbit velocity vector

 

Realistically, the transverse electrodynamic forces cause the tether to bow and to swing away from the local vertical. Gravity gradient forces then produce a restoring force that pulls the tether back towards the local vertical; however, this results in a pendulum-like motion (Gravity gradient forces also result in pendulus motions without ED forces). The B direction changes as the tether orbits the Earth, and thus the direction and magnitude of the ED forces also change. This pendulum motion can develop into complex librations in both the in-plane and out-of-plane directions. Then, due to coupling between the in-plane motion and longitudinal elastic oscillations, as well as coupling between in-plane and out-of-plane motions, an electrodynamic tether operated at a constant current can continually add energy to the libration motions. This effect then has a chance to cause the libration amplitudes to grow and eventually cause wild oscillations, including one such as the 'skip-rope effect', but that is beyond the scope of this derivation. In a non-rotating EDT system (A rotating system, called Momentum Exchange Electrodynamic Reboost [MXER]), the tether is predominantly in the z-direction due to the natural gravity gradient alignment with the Earth.

Derivations

The following derivation will describe the exact solution to the system accounting for all vector quantities involved, and then a second solution with the nominal condition where the magnetic field, the orbital velocity, and the tether orientation are all perpendicular to one another. The final solution of the nominal case is solved for in terms of just the electron density, n_e, the tether resistance per unit length, R_t, and the power of the high voltage power supply, P_hvps.

The below figure describes a typical EDT system in a series bias grounded gate configuration (further description of the various types of configurations analyzed have been presented) with a blow-up of an infinitesimal section of bare tether. This figure is symmetrically set up so either end can be used as the anode. This tether system is symmetrical because rotating tether systems will need to use both ends as anodes and cathodes at some point in its rotation. The V_hvps will only be used in the cathode end of the EDT system, and is turned off otherwise.

(a) A circuit diagram of a bare tether segment with (b) an equivalent EDT system circuit model showing the series bias grounded gate configuration.

 

In-plane and out-of-plane direction is determined by the orbital velocity vector of the system. An in-plane force is in the direction of travel. It will add or remove energy to the orbit, thereby increasing the altitude by changing the orbit into an elliptical one. An out-of-plane force is in the direction perpendicular to the plane of travel, which causes a change in inclination. This will be explained in the following section.

To calculate the in-plane and out-of-plane directions, the components of the velocity and magnetic field vectors must be obtained and the force values calculated. The component of the force in the direction of travel will serve to enhance the orbit raising capabilities, while the out-of-plane component of thrust will alter the inclination. In the below figure, the magnetic field vector is solely in the north (or y-axis) direction, and the resulting forces on an orbit, with some inclination, can be seen. An orbit with no inclination would have all the thrust in the in-plane direction.

Description of an in-plane and out-of-plane force.

Drag effects on an Electrodynamic Tether system.

There has been work conducted to stabilize the librations of the tether system to prevent misalignment of the tether with the gravity gradient. The below figure displays the drag effects an EDT system will encounter for a typical orbit. The in-plane angle, α_ip, and out-of-plane angle, α_op, can be reduced by increasing the endmass of the system, or by employing feedback technology. Any deviations in the gravity alignment must be understood, and accounted for in the system design.

Interstellar travel

An application of the EDT system has been considered and researched for interstellar travel by using the local interstellar medium of the Local Bubble. It has been found to be feasible to use the EDT system to supply on-board power given a crew of 50 with a requirement of 12 kilowatts per person. Energy generation is achieved at the expense of kinetic energy of the spacecraft. In reverse the EDT system could be used for acceleration. However, this has been found to be ineffective. Thrustless turning using the EDT system is possible to allow for course correction and rendezvous in interstellar space. It will not, however, allow rapid thrustless circling to allow a starship to re-enter a power beam or make numerous solar passes due to an extremely large turning radius of 3.7*10¹⁶ km (~3.7 lightyears).