693:. The stationary potential structures that can be measured in these machines agree very well with what one would expect theoretically. An example of a laboratory double layer can be seen in the figure below, taken from Torvén and Lindberg (1980), where we can see how well-defined and confined is the potential drop of a double layer in a double plasma machine. One of the interesting aspects of the experiment by Torvén and Lindberg (1980) is that not only did they measure the potential structure in the double plasma machine but they also found high-frequency fluctuating electric fields at the high-potential side of the double layer (also shown in the figure). These fluctuations are probably due to a beam-plasma interaction outside the double layer, which excites plasma turbulence. Their observations are consistent with experiments on electromagnetic radiation emitted by double layers in a double plasma machine by Volwerk (1993), who, however, also observed radiation from the double layer itself.
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suggested, therefore, that an ordered process was responsible. It was reported in 1977 that satellites had detected the signature of double layers as electrostatic shocks in the magnetosphere. indications of electric fields parallel to the geomagnetic field lines was obtained by the Viking satellite, which measures the differential potential structures in the magnetosphere with probes mounted on 40m long booms. These probes measured the local particle density and the potential difference between two points 80m apart. Asymmetric potential excursions with respect to 0 V were measured, and interpreted as a double layer with a net potential within the region. Magnetospheric double layers typically have a strength
533:(the developer of magnetohydrodynamics from laboratory experiments) that the polar lights or Aurora Borealis are created by electrons accelerated in the magnetosphere of the Earth. He supposed that the electrons were accelerated electrostatically by an electric field localized in a small volume bounded by two charged regions, and the so-called double layer would accelerate electrons earthwards. Since then other mechanisms involving wave-particle interactions have been proposed as being feasible, from extensive spatial and temporal in situ studies of
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approximately 10 Debye lengths. It is stated that the structures moved ‘at roughly the ion acoustic speed in the direction of the accelerated electrons, i.e., anti-earthward.’ That raises a question of what role, if any, double layers might play in accelerating auroral electrons that are precipitated downwards into the atmosphere from the magnetosphere. Double layers have also been found in the Earth's magnetosphere by the space missions
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in the auroral zone are a secondary product of precipitating electrons that have been energized in other ways, such as by electrostatic waves. Some scientists have suggested a role of double layers in solar flares. Establishing such a role indirectly is even harder to verify than postulating double layers as accelerators of auroral electrons within the Earth's magnetosphere. Serious questions have been raised on their role even there.
200:
346:: For non-relativistic current carrying double layers, electrons carry most of the current. The Langmuir condition states that the ratio of the electron and the ion current across the layer is given by the square root of the mass ratio of the ions to the electrons. For relativistic double layers the current ratio is 1; i.e. the current is carried equally by electrons and ions.
407:
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666:) and are therefore weak. A series of such double layers would tend to merge, much like a string of bar magnets, and dissipate, even within a rarefied plasma. It has yet to be explained how any overall localised charge distribution in the form of double layers might provide a source of energy for auroral electrons precipitated into the atmosphere.
340:: As described under double layer classification above, there are effectively four distinct regions of a double layer where incoming charged particles will be accelerated or decelerated along their trajectory . Within the double layer the two opposing charge distributions will tend to become neutralised by internal charged particle motion.
39:, resulting in a relatively strong electric field between the layers and weaker but more extensive compensating fields outside, which restore the global potential. Ions and electrons within the double layer are accelerated, decelerated, or deflected by the electric field, depending on their direction of motion.
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Unlike experiments in the laboratory, the concept of such double layers in the magnetosphere, and any role in creating the aurora, suffers from there so far being no identified steady source of energy. The electric potential characteristic of double layers might however indicate that, those observed
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The possible role of precipitating electrons from 1-10keV themselves generating such observed double layers or electric fields has seldom been considered or analysed. Equally, the general question of how such double layers might be generated from an alternative source of energy, or what the spatial
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Many investigations of the magnetosphere and auroral regions have been made using rockets and satellites. McIlwain discovered from a rocket flight in 1960 that the energy spectrum of auroral electrons exhibited a peak that was thought then to be too sharp to be produced by a random process and which
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The power of these fluctuations has a maximum around the plasma frequency of the ambient plasma. It was later reported that the electrostatic high-frequency fluctuations near the double layer can be concentrated in a narrow region, sometimes called the hf-spike. Subsequently, both radio emissions,
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If an incident charged particle, such as a precipitating auroral electron, encounters such a static or quasistatic structure in the magnetosphere, provided that the particle energy exceeds half the electric potential difference within the double layer, it will pass through without any net change in
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A recent development in double layer experiments in the laboratory is the investigation of so-called stairstep double layers. It has been observed that a potential drop in a plasma column can be divided into different parts. Transitions from a single double layer into two-, three-, or greater-step
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These occur at the boundary between plasma regions with different plasma properties. A plasma may have a higher electron temperature, and thermal velocity, on one side of a boundary layer than on the other. The same may apply for plasma densities. Charged particles exchanged between the regions
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have postulated that plasma may spontaneously transfer magnetically stored energy into kinetic energy by electric double layers. No credible mechanism for producing such double layers has been presented, however. Ion thrusters can provide a more direct case of energy transfer from opposing
425:: Double layers can facilitate the transfer of electrical energy into kinetic energy, dW/dt=I•ΔV where I is the electric current dissipating energy into a double layer with a voltage drop of ΔV. Alfvén points out that the current may well consist exclusively of low-energy particles. Torvén
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spacecraft data proposed strong double layers in the auroral acceleration region. Strong double layers have also been reported in the downward current region by
Andersson et al. Parallel electric fields with amplitudes reaching nearly 1 V/m were inferred to be confined to a thin layer of
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characterized double layers in the laboratory and called these structures double-sheaths. In the 1950s a thorough study of double layers started in the laboratory. Many groups are still working on this topic theoretically, experimentally and numerically. It was first proposed by
448:: A double layer cannot exist under all circumstances. In order to produce an electric field that vanishes at the boundaries of the double layer, an existence criterion says that there is a maximum to the temperature of the ambient plasma. This is the so-called Bohm criterion.
513:
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is the simplest space charge distribution that gives a potential drop in the layer and a vanishing electric field on each side of the layer. In the laboratory, double layers have been studied for half a century, but their importance in cosmic plasmas has not been generally
352:: The instantaneous voltage drop across a current-carrying double layer is proportional to the total current, and is similar to that across a resistive element (or load), which dissipates energy in an electric circuit. A double layer cannot supply net energy on its own.
89:
157:, which occurs when the streaming velocity of electrons (basically the current density divided by the electron density) exceeds the electron thermal velocity of the plasma. It occurs in collisional plasmas having a neutral component, and is driven by drift currents.
402:: While double layers are relatively thin, they will spread over the entire cross surface of a laboratory container. Likewise where adjacent plasma regions have different properties, double layers will form and tend to cellularise the different regions.
142:
energy (~512KeV) of the electron. Double layers of such energy are to be found in laboratory experiments. The charge density is low between the two opposing potential regions and the double layer is similar to the charge distribution in a
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Wang, Rongsheng; Lu, Quanming; Khotyaintsev, Yuri V.; Volwerk, Martin; Du, Aimin; Nakamura, Rumi; Gonzalez, Walter D.; Sun, Xuan; Baumjohann, Wolfgang; Li, Xing; Zhang, Tielong; Fazakerley, Andrew N.; Huang, Can; Wu, Mingyu (2014-07-28).
442:: Double layers may be modelled using kinetic computer models like particle-in-cell (PIC) simulations. In some cases the plasma is treated as essentially one- or two-dimensional to reduce the computational cost of a simulation.
223:
Double layers will tend to be transient in the magnetosphere, as any charge imbalance will become neutralised, unless there is a sustained external source of energy to maintain them as there is under laboratory conditions.
191:
The figure shows the localised perturbation of potential produced by an idealised double layer consisting of two oppositely charged discs. The perturbation is zero at a distance from the double layer in every direction.
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used in high-power direct-current transmission lines, where the voltage drop across the device was seen to increase by several orders of magnitude. Double layers may also drift, usually in the direction of the emitted
92:
Double layer formation. Formation of a double layer requires electrons to move between two adjacent regions (Diagram 1, top) causing a charge separation. An electrostatic potential imbalance may result (Diagram 2,
69:
to the magnetic field in such a way that the perpendicular electric field is much stronger than the parallel electric field, In laser physics, a double layer is sometimes called an ambipolar electric field.
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near the plasma frequency, and whistler waves at much lower frequencies were seen to emerge from this region. Similar whistler wave structures were observed together with electron beams near Saturn's moon
61:), compared to the sizes of the plasmas that contain them. Other names for a double layer are electrostatic double layer, electric double layer, plasma double layers. The term ‘electrostatic shock’ in the
454:: A model of plasma double layers has been used to investigate their applicability to understanding ion transport across biological cell membranes. Brazilian researchers have noted that "Concepts like
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In a low density plasma, localized space charge regions may build up large potential drops over distances of the order of some tens of the Debye lengths. Such regions have been called
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Gurnett, D. A.; Averkamp, T. F.; Schippers, P.; Persoon, A. M.; Hospodarsky, G. B.; Leisner, J. S.; Kurth, W. S.; Jones, G. H.; Coates, A. J.; Crary, F. J.; Dougherty, M. K. (2011).
358:: Double layers in laboratory plasmas may be stable or unstable depending on the parameter regime. Various types of instabilities may occur, often arising due to the formation of
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in the sense that they produce oscillations across a wide frequency band. A lack of plasma stability may also lead to a sudden change in configuration often referred to as an
987:
Hultqvist, Bengt (1971). "On the production of a magnetic-field-aligned electric field by the interaction between the hot magnetospheric plasma and the cold ionosphere".
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These double layers may be generated by current-driven plasma instabilities that amplify variations of the plasma density. One example of these instabilities is the
46:, where sustained energy is provided within the layer for electron acceleration by an external power source. Double layers are claimed to have been observed in the
2020:
Gimmell, Jennifer; Sriram, Aditi; Gershman, Sophia; Post-Zwicker, Andrew (2002). "Bio-plasma physics: Measuring Ion
Transport Across Cell membranes with Plasmas".
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distribution of electric charge might be to produce net energy changes, is seldom addressed. Under laboratory conditions an external power supply is available.
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Halekas, J. S.; Mitchell, D. L.; Lin, R. P.; Hood, L. L.; Acuña, M. H.; Binder, A. B. (2002). "Evidence for negative charging of the lunar surface in shadow".
1195:
Williams, A. C.; Weisskopf, M. C.; Elsner, R. F.; Darbro, W.; Sutherland, P. G. (1986). "Accretion onto
Neutron Stars with the Presence of a Double Layer".
35:
consisting of two parallel layers of opposite electrical charge. The sheets of charge, which are not necessarily planar, produce localised excursions of
124:. A double layer is said to be strong if the potential drop within the layer is greater than the equivalent thermal energy of the plasma's components.
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In the laboratory, double layers can be created in different devices. They are investigated in double plasma machines, triple plasma machines, and
1390:
Singh, Nagendra; Hwang, K. S. (1988). "Electric potential structures and propagation of electron beams injected from a spacecraft into a plasma".
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energy. Incident particles with less energy than this will also experience no net change in energy but will undergo more overall deflection.
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may enable potential differences to be maintained between them locally. The overall charge density, as in all double layers, will be neutral.
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2927:
Block, L. P. (1978). "A Double Layer Review (Paper dedicated to
Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May 1978)".
1086:
866:
751:
Block, L. P. (1978). "A Double Layer Review (Paper dedicated to
Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May 1978)".
2347:
Ergun, R. E.; et al. (2002). "Parallel electric fields in the upward current region of the aurora: Indirect and direct observations".
2277:; Torbert, R. B.; Parady, B.; Yatteau, J.; Kelley, M. C. (1977). "Observations of paired electrostatic shocks in the polar magnetosphere".
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Ergun, R. E.; Andersson, L.; Main, D.; Su, Y.-J.; Newman, D. L.; Goldman, M. V.; Carlson, C. W.; McFadden, J. P.; Mozer, F. S. (2002).
1102:
Stenzel, R. L.; Gekelman, W.; Wild, N. (1982). "Double layer formation during current sheet disruptions in a reconnection experiment".
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The prediction of a lunar double layer was confirmed in 2003. In the shadows, the Moon charges negatively in the interplanetary medium.
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http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000068000005000450000001&idtype=cvips&gifs=yes
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http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JAPIAU000037000007002598000001&idtype=cvips&gifs=yes
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679:
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Bulgakova, Nadezhda M.; Bulgakov, Alexander V.; Bobrenok, Oleg F. (2000). "Double layer effects in laser-ablation plasma plumes".
794:
Bulgakova, Nadezhda M.; Bulgakov, Alexander V.; Bobrenok, Oleg F. (2000). "Double layer effects in laser-ablation plasma plumes".
436:: An oblique double layer has electric fields that are not parallel to the ambient magnetic field; i.e., it is not field-aligned.
2382:
Andersson, L.; et al. (2002). "Characteristics of parallel electric fields in the downward current region of the aurora".
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Ishiguro, S.; Kamimura, T.; Sato, T. (1985). "Double layer formation caused by contact between different temperature plasmas".
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applications. Similarly, a double layer in the auroral region requires some external driver to produce electron acceleration.
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2524:"Direct Observation of Acceleration and Thermalization of Beam Electrons Caused by Double Layers in the Earth's Plasma Sheet"
670:
314:: The production of a double layer requires regions with a significant excess of positive or negative charge, that is, where
3199:
Hultqvist, Bengt; Lundin, Rickard (1988). "Parallel electric fields accelerating ions and electrons in the same direction".
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Four distinct regions of a double layer can be identified, which affect charged particles passing through it, or within it:
414:
17:
1513:"Spontaneous formation of current-driven double layers in density depletions and its relevance to solitary Alfven waves"
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The details of the formation mechanism depend on the environment of the plasma (e.g. double layers in the laboratory,
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Electrostatic double layers are especially common in current-carrying plasmas, and are very thin (typically tens of
3322:
608:
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Song, B; Angelo, N D; Merlino, R L (1992). "Stability of a spherical double layer produced through ionization".
1704:
1277:
Lennartsson, W. (1987). "Some
Aspects of Double Layer Formation in a Plasma Constrained by a Magnetic Mirror".
1512:
739:
2274:
675:
2561:
Torvén, S.; Lindberg, L. (1982). "Properties of a fluctuating double layer in a magnetized plasma column".
2133:
Langmuir, Irving (1929). "The
Interaction of Electron and Positive Ion Space Charges in Cathode Sheaths".
322:. The thickness of a double layer is of the order of ten Debye lengths, which is a few centimeters in the
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495:
379:
359:
327:
80:). An early review of double layers from laboratory experiment and simulations is provided by Torvén.
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Lembege, B.; Dawson, J. M. (1989). "Formation of double layers within an oblique collisionless shock".
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conditions, charged particles may effectively originate within the double layer, by ionization at the
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Gunell, H.; et al. (1996). "Bursts of high-frequency plasma waves at an electric double layer".
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Raadu, M. A.; Carlqvist, P. (1981). "Electrostatic double layers and a plasma evacuation process".
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Lindberg, Lennart (1988). "Observations of propagating double layers in a high current discharge".
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1928:"Spontaneous transfer of magnetically stored energy to kinetic energy by electric double layers"
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It was already known in the 1920s that a plasma has a limited capacity for current maintenance,
2781:
Hasan, S. S.; Ter Haar, D. (1978). "The Alfvén-Carlquist Double-Layer Theory of Solar Flares".
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Bryant, D.A.,R.Bingham and U.deAngelis (1992). "Double layers are not particle accelerators".
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2733:"Auroral hiss, electron beams and standing Alfvén wave currents near Saturn's moon Enceladus"
1232:"Evolution of the plasma universe. I. Double radio galaxies, quasars, and extragalactic jets"
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374:). In one example, the region enclosed in the double layer rapidly expands and evolves. An
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3238:"Parallel electric fields in the upward current region of the aurora: Numerical solutions"
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512:
477:
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Yamamoto, Takashi; Kan, J. R. (1985). "Double layer formation due to current injection".
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Yamamoto, Takashi; Kan, J. R. (1985). "Double layer formation due to current injection".
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A positive potential side of the double layer where electrons are accelerated towards it;
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Volwerk, M (1993). "Radiation from electrostatic double layers in laboratory plasmas".
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2003: By the incidence of plasma on the dark side of the Moon's surface. See picture.
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are sustained by an external energy source. Under most laboratory situations, unlike
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62:
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2692:"Radiation from an electron beam in a magnetized plasma: Whistler mode wave packets"
2522:
Yuan, Zhigang; Dong, Yue; Huang, Shiyong; Xue, Zuxiang; Yu, Xiongdong (2022-07-16).
2199:"The roles of static and dynamic electric fields in the auroral acceleration region"
2106:"II.6. Electric Double Layers, II.6.1. General Properties of Electric Double Layers"
1866:
1690:
1263:
3127:
2475:"Observation of double layer in the separatrix region during magnetic reconnection"
2312:
Bostrom, Rolf (1992). "Observations of weak double layers on auroral field lines".
2238:
McIlwain, C E (1960). "Direct
Measurement of Particles Producing Visible Auroras".
1558:
Borisov, N.; Mall, U. (2002). "The structure of the double layer behind the Moon".
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Thiemann, H.; Singh, N.; Schunk, R. W. (1983). "Formation of V-shaped potentials".
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319:
77:
58:
51:
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Numerical modeling of low-pressure plasmas: applications to electric double layers
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A negative potential within the double layer where electrons are decelerated; and
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is violated. In general, quasi-neutrality can only be violated on scales of the
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double layers are strongly sensitive to the boundary conditions of the plasma.
430:
potentials in the form of double layers produced by an external electric field.
108:
double layers. The strength of a double layer is expressed as the ratio of the
3038:
Smith, R. A. (1985). "On the role of double layers in astrophysical plasmas".
2888:
2845:
2443:
1718:
Torvén, S (1982). "High-voltage double layers in a magnetised plasma column".
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before him, who coined the term "plasma" after its resemblance to blood cells.
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A negative potential side of the double layer where electrons are accelerated.
199:
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2508:
1489:
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also noted that association of double layers with cellular structure, as had
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A positive potential within the double layer where electrons are decelerated;
2824:
Khan, J. I. (1989). "A model for solar flares invoking weak double layers".
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This article is about the structure in plasma physics. For other uses, see
2419:"Electrostatic double layers as auroral particle accelerators - a problem"
740:
http://adsabs.harvard.edu/cgi-bin/nph-bib_query?bibcode=1987dla..conf..295
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Brenning, N.; Axnäs, I.; Raadu, M. A.; Tennfors, E.; Koepke, M. (2006).
1681:
701:, suggesting the possible presence of a double layer at lower altitude.
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2948:
2802:
1998:
1904:
1368:
1321:
938:
772:
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3264:
3001:
Carlqvist, P. (1982). "On the physics of relativistic double layers".
2499:
2403:
2368:
2333:
2085:
1057:
Torven, S (1976). "Formation of Double Layers in
Laboratory Plasmas".
917:
Carlqvist, P. (1982). "On the physics of relativistic double layers".
837:
Torvén, S (1976). "Formation of Double Layers in
Laboratory Plasmas".
413:. The electric fields utilised in plasma thrusters (in particular the
3154:
1043:
534:
520:, about a sixth of the distance from the left. Click for more details
396:: Double layers can form in both magnetised and unmagnetised plasmas.
290:
2002: When magnetic field-aligned currents encounter density cavities
73:
Double layers are conceptually related to the concept of a 'sheath' (
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1983: Injection of non-neutral electron current into a cold plasma
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Potential imbalance will be neutralised by electron (1&3) and
87:
3040:
Unstable Current Systems and Plasma Instabilities in Astrophysics
1603:"Inferring the scale height of the lunar nightside double layer"
244:, etc.). Proposed mechanisms for their formation have included:
605:(where the electron temperature is assumed to lie in the range
387:, and in this respect are natural analogues to the smooth-bore
169:
3162:
Raadu, Michael A. (1994). "Energy release in double layers".
2054:
Alfven, H. (1982). "On hierarchial [sic] cosmology".
2183:
Alfvén, H., "On the theory of magnetic storms and aurorae",
138:
if the potential drop within the layer is comparable to the
3307:
The physics of double layers and their role in astrophysics
1139:
European Rocket and Balloon Programmes and Related Research
729:. London & Glasgow: Blackie & Son Ltd. p. 271.
2112:. Vol. 82. D. Reidel Publishing Company. p. 29.
468:
are very useful to explain the electrical properties of a
3126:
Theisen, W. L.; Carpenter, R. T.; Merlino, R. L. (1994).
278:
1988: Current-driven instabilities (strong double layers)
97:
Double layers may be classified in the following ways:
611:
547:
2826:
Proceedings of the Astronomical Society of Australia
1601:
Halekas, J. S.; Lin, R. P.; Mitchell, D. L. (2003).
65:has been applied to electric fields oriented at an
3087:"Dynamical aspects of electrostatic double layers"
1975:"Dynamical aspects of electrostatic double layers"
1345:"Dynamical aspects of electrostatic double layers"
658:
597:
362:of ions and electrons. Unstable double layers are
272:1987: In a plasma constrained by a magnetic mirror
2084:, vol. 19, p. 989, Dec. 1991. See extract on the
598:{\displaystyle e\phi _{DL}/k_{B}T_{e}\approx 0.1}
1881:"Interstellar clouds and the formation of stars"
263:1985: Increasing the current density in a plasma
1926:Torvén, S; Lindberg, L; Carpenter, R T (1985).
488:
266:1986: In the accretion column of a neutron star
248:1971: Between plasmas of different temperatures
3085:Raadu, Michael A.; Rasmussen, J. Juul (1988).
1973:Raadu, Michael A.; Rasmussen, J. Juul (1988).
1817:"Paradigm transition in cosmic plasma physics"
1343:Raadu, Michael A.; Rasmussen, J. Juul (1988).
8:
3293:On the theory of magnetic storms and aurorae
2909:: CS1 maint: multiple names: authors list (
2457:: CS1 maint: multiple names: authors list (
1867:ESA accelerates towards a new space thruster
134:double layers. A double layer is said to be
112:in comparison with the plasma's equivalent
659:{\displaystyle 2eV\leq k_{B}T_{e}\leq 20eV}
3309:, Physics Reports, 178, 25–97, 1989.
172:(2&4) migration, unless the potential
2715:
2498:
2442:
2222:
1680:
638:
628:
610:
583:
573:
564:
555:
546:
516:A cluster of double layers forming in an
269:1986: By pinches in cosmic plasma regions
2022:Aps Ohio Sections Fall Meeting Abstracts
2417:Bryant, D.A., and G.M.Courtier (2015).
717:
281:1988: Spacecraft-ejected electron beams
2902:
2450:
1059:Astrophysics and Space Science Library
963:Acceleration in the Auroral and Beyond
839:Astrophysics and Space Science Library
417:) may be in the form of double layers.
2649:Journal of Physics D: Applied Physics
2606:Journal of Physics D: Applied Physics
2563:Journal of Physics D: Applied Physics
2171:Quecksilber-Niederdruck-Gasenladunger
1763:Journal of Physics D: Applied Physics
1720:Journal of Physics D: Applied Physics
378:of this type was first discovered in
7:
338:Electrostatic potential distribution
2314:IEEE Transactions on Plasma Science
2082:IEEE Transactions on Plasma Science
2080:G. L. Rogoff, Ed., "Introduction",
1863:Helicon Double Layer Thruster study
1236:IEEE Transactions on Plasma Science
1879:Alfvén, H.; Carlqvist, P. (1978).
284:1989: From shock waves in a plasma
14:
3281:(2006, PDF), A. Meige, PhD thesis
2056:NASA Sti/Recon Technical Report N
1705:"1978Ap&SS..55...59B Page 60"
330:, and tens of kilometers in the
275:1988: By an electrical discharge
42:Double layers can be created in
2696:Journal of Geophysical Research
2240:Journal of Geophysical Research
2203:Journal of Geophysical Research
1392:Journal of Geophysical Research
3300:Physics of the Plasma Universe
3201:Astrophysics and Space Science
3091:Astrophysics and Space Science
3003:Astrophysics and Space Science
2966:Astrophysics and Space Science
2929:Astrophysics and Space Science
2783:Astrophysics and Space Science
2273:Mozer, F. S.; Carlson, C. W.;
1979:Astrophysics and Space Science
1885:Astrophysics and Space Science
1841:10.1088/0031-8949/1982/T2A/002
1349:Astrophysics and Space Science
1302:Astrophysics and Space Science
919:Astrophysics and Space Science
753:Astrophysics and Space Science
326:, a few tens of meters in the
254:1982: Disruption of a neutral
151:Current carrying double layers
1:
1279:Double Layers in Astrophysics
415:Helicon Double Layer Thruster
2740:Geophysical Research Letters
2528:Geophysical Research Letters
2479:Geophysical Research Letters
1932:Plasma Phys. Control. Fusion
1653:Geophysical Research Letters
1610:Geophysical Research Letters
1517:Geophysical Research Letters
1182:10.1016/0032-0633(85)90040-6
1104:Geophysical Research Letters
1009:10.1016/0032-0633(71)90033-X
904:10.1016/0032-0633(85)90040-6
298:Features and characteristics
116:, or in comparison with the
3128:"Filamentary double layers"
3060:10.1007/978-94-009-6520-1_9
2583:10.1088/0022-3727/13/12/014
1865:", European Space Agency; "
1740:10.1088/0022-3727/15/10/012
1447:10.1103/PhysRevLett.62.2683
1230:Peratt, Anthony L. (1986).
1162:Planetary and Space Science
1079:10.1007/978-94-009-9500-0_9
989:Planetary and Space Science
884:Planetary and Space Science
859:10.1007/978-94-009-9500-0_9
251:1976: In laboratory plasmas
3339:
2669:10.1088/0022-3727/29/3/025
2626:10.1088/0022-3727/26/8/007
2299:10.1103/PhysRevLett.38.292
1952:10.1088/0741-3335/27/2/005
1783:10.1088/0022-3727/25/6/006
537:particle characteristics.
161:Current-free double layers
155:Farley–Buneman instability
15:
2889:10.1103/PhysRevLett.68.37
2846:10.1017/S1323358000022840
2444:10.5194/angeo-33-481-2015
2197:Bryant, D.A (June 2002).
2169:Schonhuber, M.J. (1958).
2086:Plasma Coalition web site
1580:10.1017/s0022377802001654
1560:Journal of Plasma Physics
1197:The Astrophysical Journal
3295:, Tellus, 10, 104, 1958.
1511:Singh, Nagendra (2002).
1490:10.1103/PhysRevE.62.5624
1256:10.1109/TPS.1986.4316615
816:10.1103/PhysRevE.62.5624
3213:1988Ap&SS.144..149H
3103:1988Ap&SS.144...43R
3015:1982Ap&SS..87...21C
2978:1981Ap&SS..74..189R
2941:1978Ap&SS..55...59B
2869:Physical Review Letters
2795:1978Ap&SS..56...89H
2279:Physical Review Letters
2260:10.1029/JZ065i009p02727
2104:Hannes Alfvèn (2012) .
1991:1988Ap&SS.144...43R
1897:1978Ap&SS..55..487A
1427:Physical Review Letters
1412:10.1029/JA093iA09p10035
1361:1988Ap&SS.144...43R
1314:1988Ap&SS.144....3L
1174:1985P&SS...33..853Y
1124:10.1029/GL009i006p00680
1001:1971P&SS...19..749H
931:1982Ap&SS..87...21C
896:1985P&SS...33..853Y
765:1978Ap&SS..55...59B
2155:10.1103/physrev.33.954
669:Interpretation of the
660:
599:
521:
510:
492:electric double layers
418:
380:mercury arc rectifiers
372:exploding double layer
307:
203:
94:
3164:Space Science Reviews
960:Bryant, D.A. (1998).
661:
600:
515:
409:
328:interplanetary medium
305:
287:2000: Laser radiation
202:
91:
2760:10.1029/2011GL046854
2717:10.1029/2006JA011739
2540:10.1029/2022GL099483
2491:10.1002/2014GL061157
2224:10.1029/2001JA900162
1673:10.1029/2001GL014428
1630:10.1029/2003GL018421
1537:10.1029/2001gl014033
609:
545:
472:." Plasma physicist
452:Bio-physical analogy
434:Oblique double layer
411:Hall effect thruster
332:intergalactic medium
228:Formation mechanisms
188:, and be sustained.
3257:2002PhPl....9.3695E
3176:1994SSRv...68...29R
3147:1994PhPl....1.1345T
3052:1985IAUS..107..113S
2881:1992PhRvL..68...37B
2838:1989PASA....8...29K
2752:2011GeoRL..38.6102G
2708:2006JGRA..11111212B
2661:1996JPhD...29..643G
2618:1993JPhD...26.1192V
2575:1980pfdl.rept.....T
2435:2015AnGeo..33..481B
2423:Annales Geophysicae
2396:2002PhPl....9.3600A
2361:2002PhPl....9.3685E
2326:1992ITPS...20..756B
2291:1977PhRvL..38..292M
2252:1960JGR....65.2727M
2215:2002JGRA..107.1077B
2173:. Munchen: Lachner.
2147:1929PhRv...33..954L
2068:1982STIN...8228234A
2030:2002APS..OSF.1P017G
1944:1985PPCF...27..143T
1833:1982PhST....2...10A
1815:Alfven, H. (1982).
1775:1992JPhD...25..938S
1732:1982JPhD...15.1943T
1665:2002GeoRL..29.1435H
1622:2003GeoRL..30.2117H
1572:2002JPlPh..67..277B
1529:2002GeoRL..29.1147S
1482:2000PhRvE..62.5624B
1439:1989PhRvL..62.2683L
1404:1988JGR....9310035S
1287:1987NASCP2469..275L
1248:1986ITPS...14..639P
1209:1986ApJ...305..759W
1147:1983ESASP.183..269T
1116:1982GeoRL...9..680S
1071:1979wisp.proc..109T
1036:1985PhFl...28.2100I
851:1979wisp.proc..109T
808:2000PhRvE..62.5624B
727:Theoretical Physics
50:and are invoked in
3277:2007-08-30 at the
3245:Physics of Plasmas
3221:10.1007/BF00793178
3184:10.1007/BF00749114
3135:Physics of Plasmas
3111:10.1007/BF00793172
3023:10.1007/BF00648904
2986:10.1007/BF00642091
2949:10.1007/BF00642580
2803:10.1007/BF00643464
2384:Physics of Plasmas
2349:Physics of Plasmas
2091:2008-02-13 at the
1999:10.1007/BF00793172
1905:10.1007/BF00642272
1369:10.1007/BF00793172
1322:10.1007/BF00793169
939:10.1007/bf00648904
773:10.1007/BF00642580
656:
595:
522:
419:
394:Magnetised plasmas
308:
204:
95:
37:electric potential
3265:10.1063/1.1499121
3069:978-90-277-1887-7
2569:(12): 2285–2300.
2485:(14): 4851–4858.
2404:10.1063/1.1490134
2369:10.1063/1.1499120
2334:10.1109/27.199524
2187:, 10, 104,. 1958.
1726:(10): 1943–1949.
1470:Physical Review E
1433:(23): 2683–2686.
1088:978-94-009-9502-4
1024:Physics of Fluids
868:978-94-009-9502-4
796:Physical Review E
725:Joos, G. (1951).
470:cellular membrane
456:charge neutrality
3330:
3323:Plasma phenomena
3268:
3251:(9): 3695–3704.
3242:
3232:
3195:
3158:
3155:10.1063/1.870733
3141:(5): 1345–1348.
3132:
3122:
3081:
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2914:
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2644:
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2637:
2612:(8): 1192–1202.
2601:
2595:
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2513:
2512:
2502:
2469:
2463:
2462:
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2448:
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2414:
2408:
2407:
2390:(8): 3600–3609.
2379:
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2355:(9): 3685–3694.
2344:
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1044:10.1063/1.865390
1019:
1013:
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984:
978:
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879:
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316:quasi-neutrality
147:in that respect.
132:non-relativistic
3338:
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2135:Physical Review
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2093:Wayback Machine
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423:Energy transfer
400:Cellular nature
300:
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44:discharge tubes
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2148:
2144:
2140:
2136:
2129:
2126:
2121:
2119:9789400983748
2115:
2111:
2110:Cosmic Plasma
2107:
2100:
2097:
2094:
2090:
2087:
2083:
2077:
2074:
2069:
2065:
2061:
2057:
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2016:
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1933:
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1432:
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1421:
1418:
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1409:
1405:
1401:
1398:(A9): 10035.
1397:
1393:
1386:
1383:
1378:
1374:
1370:
1366:
1362:
1358:
1354:
1350:
1346:
1339:
1336:
1331:
1327:
1323:
1319:
1315:
1311:
1308:(1–2): 3–13.
1307:
1303:
1296:
1293:
1288:
1284:
1280:
1273:
1270:
1265:
1261:
1257:
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969:
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797:
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584:
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559:
556:
552:
548:
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536:
532:
531:Hannes Alfvén
527:
519:
514:
506:
505:Hannes Alfvén
500:
497:
493:
484:
479:
475:
474:Hannes Alfvén
471:
467:
463:
462:
457:
453:
450:
447:
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438:
435:
432:
428:
424:
421:
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398:
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390:
386:
385:electron beam
381:
377:
373:
369:
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351:
350:Energy supply
348:
345:
344:Particle flux
342:
339:
336:
333:
329:
325:
321:
317:
313:
310:
309:
304:
297:
292:
289:
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280:
277:
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256:current sheet
253:
250:
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246:
245:
243:
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227:
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208:
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137:
133:
129:
126:
123:
119:
115:
111:
107:
103:
100:
99:
98:
90:
83:
81:
79:
76:
71:
68:
67:oblique angle
64:
63:magnetosphere
60:
59:Debye lengths
55:
53:
52:astrophysical
49:
45:
40:
38:
34:
30:
26:
19:
3306:
3299:
3298:Peratt, A.,
3292:
3291:Alfvén, H.,
3248:
3244:
3207:(1–2): 149.
3204:
3200:
3167:
3163:
3138:
3134:
3094:
3090:
3043:
3039:
3006:
3002:
2969:
2965:
2932:
2928:
2905:cite journal
2875:(1): 37–39.
2872:
2868:
2862:
2832:(1): 29–31.
2829:
2825:
2819:
2786:
2782:
2776:
2743:
2739:
2726:
2699:
2695:
2685:
2652:
2648:
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2453:cite journal
2426:
2422:
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2352:
2348:
2342:
2317:
2313:
2307:
2282:
2278:
2268:
2243:
2239:
2233:
2209:(A6): 1077.
2206:
2202:
2192:
2184:
2179:
2170:
2163:
2138:
2134:
2128:
2109:
2099:
2081:
2076:
2059:
2055:
2049:
2038:
2021:
2015:
1982:
1978:
1968:
1935:
1931:
1921:
1888:
1884:
1874:
1857:
1824:
1820:
1810:
1799:
1766:
1762:
1756:
1723:
1719:
1713:
1699:
1682:10150/623417
1659:(10): 1435.
1656:
1652:
1646:
1616:(21): 2117.
1613:
1609:
1596:
1563:
1559:
1553:
1520:
1516:
1506:
1473:
1469:
1463:
1430:
1426:
1420:
1395:
1391:
1385:
1352:
1348:
1338:
1305:
1301:
1295:
1278:
1272:
1239:
1235:
1225:
1200:
1196:
1190:
1165:
1161:
1155:
1138:
1132:
1107:
1103:
1097:
1062:
1058:
1052:
1027:
1023:
1017:
992:
988:
982:
962:
955:
922:
918:
912:
887:
883:
877:
842:
838:
832:
799:
795:
789:
756:
752:
746:
735:
726:
720:
707:
703:
695:
688:
684:
668:
539:
523:
496:double layer
491:
489:
466:double layer
465:
461:Debye length
459:
455:
451:
445:
439:
433:
426:
422:
399:
393:
371:
363:
355:
349:
343:
337:
320:Debye length
311:
231:
222:
205:
194:
190:
167:
160:
150:
136:relativistic
131:
128:Relativistic
127:
105:
101:
96:
78:Debye sheath
74:
72:
56:
41:
25:double layer
24:
22:
18:Double layer
3097:(1–2): 43.
3046:: 113–123.
2246:(9): 2727.
1985:(1–2): 43.
1355:(1–2): 43.
1030:(7): 2100.
925:(1–2): 21.
518:Alfvén wave
499:recognized.
370:(and hence
178:outer space
3286:References
2972:(1): 189.
2500:2160/14316
2285:(6): 292.
2024:: 1P.017.
1110:(6): 680.
691:Q-machines
440:Simulation
324:ionosphere
238:solar wind
234:ionosphere
3229:122972346
3192:189777772
3119:120316850
3078:117173000
3031:123205274
2994:123134001
2957:122977170
2935:(1): 59.
2854:117844249
2811:122003016
2789:(1): 89.
2677:250753554
2634:250871682
2591:250837586
2548:0094-8276
2509:0094-8276
2062:: 28234.
2007:120316850
1960:250863148
1913:122687137
1849:250752052
1827:: 10–19.
1791:250845364
1748:250874820
1638:121743325
1588:124908517
1545:119750076
1523:(7): 51.
1377:120316850
1330:117060217
947:123205274
781:122977170
759:(1): 59.
713:Footnotes
699:Enceladus
645:≤
622:≤
590:≈
553:ϕ
389:magnetron
376:explosion
368:explosion
356:Stability
312:Thickness
174:gradients
145:capacitor
140:rest mass
122:electrons
118:rest mass
29:structure
3317:Category
3275:Archived
2897:10045106
2768:54539728
2089:Archived
1869:" (2005)
1691:54753205
1498:11089121
1455:10040061
1264:30767626
824:11089121
502:—
3253:Bibcode
3209:Bibcode
3172:Bibcode
3143:Bibcode
3099:Bibcode
3048:Bibcode
3011:Bibcode
2974:Bibcode
2937:Bibcode
2877:Bibcode
2834:Bibcode
2791:Bibcode
2748:Bibcode
2704:Bibcode
2657:Bibcode
2614:Bibcode
2571:Bibcode
2431:Bibcode
2392:Bibcode
2357:Bibcode
2322:Bibcode
2287:Bibcode
2248:Bibcode
2211:Bibcode
2143:Bibcode
2064:Bibcode
2026:Bibcode
1987:Bibcode
1940:Bibcode
1893:Bibcode
1829:Bibcode
1771:Bibcode
1728:Bibcode
1661:Bibcode
1618:Bibcode
1568:Bibcode
1525:Bibcode
1478:Bibcode
1435:Bibcode
1400:Bibcode
1357:Bibcode
1310:Bibcode
1283:Bibcode
1281:: 275.
1244:Bibcode
1242:: 639.
1205:Bibcode
1203:: 759.
1170:Bibcode
1143:Bibcode
1141:: 269.
1112:Bibcode
1067:Bibcode
1065:: 109.
1032:Bibcode
997:Bibcode
927:Bibcode
892:Bibcode
847:Bibcode
845:: 109.
804:Bibcode
761:Bibcode
676:Cluster
535:auroral
485:History
186:cathode
93:bottom)
3302:, 1991
3227:
3190:
3117:
3076:
3066:
3029:
2992:
2955:
2895:
2852:
2809:
2766:
2675:
2632:
2589:
2546:
2534:(13).
2507:
2185:Tellus
2116:
2005:
1958:
1911:
1847:
1789:
1746:
1689:
1636:
1586:
1543:
1496:
1453:
1375:
1328:
1262:
1085:
970:
945:
865:
822:
779:
464:, and
427:et al.
106:strong
48:aurora
33:plasma
3241:(PDF)
3225:S2CID
3188:S2CID
3131:(PDF)
3115:S2CID
3074:S2CID
3027:S2CID
2990:S2CID
2953:S2CID
2850:S2CID
2807:S2CID
2764:S2CID
2736:(PDF)
2673:S2CID
2630:S2CID
2587:S2CID
2167:e.g.
2003:S2CID
1956:S2CID
1909:S2CID
1861:See "
1845:S2CID
1787:S2CID
1744:S2CID
1687:S2CID
1634:S2CID
1606:(PDF)
1584:S2CID
1541:S2CID
1373:S2CID
1326:S2CID
1260:S2CID
943:S2CID
777:S2CID
364:noisy
360:beams
182:anode
31:in a
27:is a
3064:ISBN
2911:link
2893:PMID
2544:ISSN
2505:ISSN
2459:link
2114:ISBN
1494:PMID
1451:PMID
1083:ISBN
968:ISBN
863:ISBN
820:PMID
678:and
671:FAST
104:and
102:Weak
3261:doi
3217:doi
3205:144
3180:doi
3151:doi
3107:doi
3095:144
3056:doi
3044:107
3019:doi
2982:doi
2945:doi
2885:doi
2842:doi
2799:doi
2756:doi
2712:doi
2700:111
2665:doi
2622:doi
2579:doi
2536:doi
2495:hdl
2487:doi
2439:doi
2400:doi
2365:doi
2330:doi
2295:doi
2256:doi
2219:doi
2207:107
2151:doi
1995:doi
1983:144
1948:doi
1901:doi
1837:doi
1779:doi
1736:doi
1677:hdl
1669:doi
1626:doi
1576:doi
1533:doi
1486:doi
1443:doi
1408:doi
1365:doi
1353:144
1318:doi
1306:144
1252:doi
1213:doi
1201:305
1178:doi
1120:doi
1075:doi
1040:doi
1005:doi
935:doi
900:doi
855:doi
812:doi
769:doi
680:MMS
593:0.1
184:or
170:ion
130:or
75:see
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