Double layer (plasma physics)

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. 541:

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 674:

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

709:

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: 407: 303: 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. 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. 513: 89: 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. 708:

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

685:

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

540:

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

696:

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,

195:

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

704:

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

163:

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

429:

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 673:

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

528:

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. 498:

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. 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

2472:

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.

382:

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.

697:

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 603: 664: 490:

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

2731:

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 366:

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".

2042: 1803: 153:

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".

686:

distribution of electric charge might be to produce net energy changes, is seldom addressed. Under laboratory conditions an external power supply is available.

1651:

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. 2910: 2458: 689:

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".

196:

energy. Incident particles with less energy than this will also experience no net change in energy but will undergo more overall deflection.

164:

may enable potential differences to be maintained between them locally. The overall charge density, as in all double layers, will be neutral.

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)".

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". 3236:

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".

306:

The prediction of a lunar double layer was confirmed in 2003. In the shadows, the Moon charges negatively in the interplanetary medium.

2043:

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000068000005000450000001&idtype=cvips&gifs=yes

1804:

http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JAPIAU000037000007002598000001&idtype=cvips&gifs=yes

1468:

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".

1022:

Ishiguro, S.; Kamimura, T.; Sato, T. (1985). "Double layer formation caused by contact between different temperature plasmas".

961: 54:

applications. Similarly, a double layer in the auroral region requires some external driver to produce electron acceleration.

3274: 3067: 2524:"Direct Observation of Acceleration and Thermalization of Beam Electrons Caused by Double Layers in the Earth's Plasma Sheet" 1086: 866: 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".

206:

Four distinct regions of a double layer can be identified, which affect charged particles passing through it, or within it:

1513:"Spontaneous formation of current-driven double layers in density depletions and its relevance to solitary Alfven waves" 544: 232:

The details of the formation mechanism depend on the environment of the plasma (e.g. double layers in the laboratory,

2117: 2088: 971: 679: 57:

Electrostatic double layers are especially common in current-carrying plasmas, and are very thin (typically tens of

608: 1761:

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".

670: 154: 1512: 739: 414: 17: 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 80:). An early review of double layers from laboratory experiment and simulations is provided by Torvén. 1425:

Lembege, B.; Dawson, J. M. (1989). "Formation of double layers within an oblique collisionless shock".

180:

conditions, charged particles may effectively originate within the double layer, by ionization at the

3322: 2647:

Gunell, H.; et al. (1996). "Bursts of high-frequency plasma waves at an electric double layer".

3237: 1602: 315: 2964:

Raadu, M. A.; Carlqvist, P. (1981). "Electrostatic double layers and a plasma evacuation process".

2523: 2474: 1300:

Lindberg, Lennart (1988). "Observations of propagating double layers in a high current discharge".

2274: 1862: 675: 2418: 1928:"Spontaneous transfer of magnetically stored energy to kinetic energy by electric double layers" 524:

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".

2867:

Bryant, D.A.,R.Bingham and U.deAngelis (1992). "Double layers are not particle accelerators".

2904: 2733:"Auroral hiss, electron beams and standing Alfvén wave currents near Saturn's moon Enceladus" 2452: 1232:"Evolution of the plasma universe. I. Double radio galaxies, quasars, and extragalactic jets" 495: 379: 359: 327: 3212: 3102: 3014: 2977: 2940: 2794: 1990: 1896: 1360: 1313: 1173: 1000: 930: 895: 764: 3252: 3208: 3171: 3142: 3098: 3047: 3010: 2973: 2936: 2876: 2833: 2790: 2747: 2703: 2656: 2613: 2570: 2430: 2391: 2356: 2321: 2286: 2247: 2210: 2142: 2063: 2025: 1986: 1939: 1892: 1828: 1770: 1727: 1660: 1617: 1567: 1524: 1477: 1434: 1399: 1356: 1309: 1282: 1243: 1204: 1169: 1142: 1111: 1066: 1031: 996: 926: 891: 846: 803: 760: 410: 374:). In one example, the region enclosed in the double layer rapidly expands and evolves. An 331: 135: 109: 3238:"Parallel electric fields in the upward current region of the aurora: Numerical solutions" 8: 1840: 1816: 1160:

Yamamoto, Takashi; Kan, J. R. (1985). "Double layer formation due to current injection".

882:

Yamamoto, Takashi; Kan, J. R. (1985). "Double layer formation due to current injection".

210:

A positive potential side of the double layer where electrons are accelerated towards it;

3256: 3175: 3146: 3051: 2880: 2837: 2751: 2732: 2707: 2660: 2617: 2574: 2434: 2395: 2360: 2325: 2290: 2251: 2214: 2146: 2067: 2029: 1943: 1832: 1774: 1731: 1664: 1621: 1571: 1528: 1481: 1438: 1403: 1286: 1247: 1208: 1146: 1115: 1070: 1035: 850: 807: 3224: 3187: 3114: 3073: 3026: 2989: 2952: 2849: 2806: 2763: 2672: 2629: 2604:

Volwerk, M (1993). "Radiation from electrostatic double layers in laboratory plasmas".

2586: 2002: 1955: 1908: 1844: 1786: 1743: 1686: 1633: 1583: 1540: 1372: 1325: 1259: 942: 776: 47: 36: 2582: 1739: 293:

2003: By the incidence of plasma on the dark side of the Moon's surface. See picture.

3228: 3191: 3118: 3077: 3063: 3030: 2993: 2956: 2892: 2853: 2810: 2676: 2668: 2633: 2625: 2590: 2543: 2504: 2113: 2006: 1959: 1951: 1912: 1848: 1790: 1782: 1747: 1637: 1587: 1544: 1493: 1450: 1376: 1329: 1181: 1082: 1008: 967: 946: 903: 862: 819: 780: 469: 176:

are sustained by an external energy source. Under most laboratory situations, unlike

2767: 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: 3260: 3216: 3179: 3150: 3127: 3106: 3055: 3018: 2981: 2944: 2884: 2841: 2798: 2755: 2711: 2664: 2621: 2578: 2535: 2494: 2486: 2475:"Observation of double layer in the separatrix region during magnetic reconnection" 2438: 2399: 2364: 2329: 2312:

Bostrom, Rolf (1992). "Observations of weak double layers on auroral field lines".

2294: 2255: 2238:

McIlwain, C E (1960). "Direct Measurement of Particles Producing Visible Auroras".

2218: 2150: 1994: 1947: 1900: 1836: 1778: 1735: 1676: 1668: 1625: 1575: 1558:

Borisov, N.; Mall, U. (2002). "The structure of the double layer behind the Moon".

1532: 1485: 1442: 1407: 1364: 1317: 1251: 1212: 1177: 1137:

Thiemann, H.; Singh, N.; Schunk, R. W. (1983). "Formation of V-shaped potentials".

1119: 1074: 1039: 1004: 934: 899: 854: 811: 768: 698: 32: 3272:

Numerical modeling of low-pressure plasmas: applications to electric double layers

3271: 530: 504: 473: 3278: 2105: 2092: 525: 477: 216:

A negative potential within the double layer where electrons are decelerated; and

3059: 1446: 1078: 858: 318:

is violated. In general, quasi-neutrality can only be violated on scales of the

2298: 705:

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.

241: 113: 108:

double layers. The strength of a double layer is expressed as the ratio of the

43: 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".

1579: 517: 480:

before him, who coined the term "plasma" after its resemblance to blood cells.

219:

A negative potential side of the double layer where electrons are accelerated.

3316: 2547: 2508: 1489: 1255: 815: 476:

also noted that association of double layers with cellular structure, as had

384: 255: 213:

A positive potential within the double layer where electrons are decelerated;

66: 62: 2824:

Khan, J. I. (1989). "A model for solar flares invoking weak double layers".

2259: 1411: 1123: 2896: 2154: 1497: 1454: 823: 512: 460: 319: 77: 58: 51: 16:

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

2759: 2716: 2691: 2539: 2490: 2223: 2198: 1672: 1629: 1536: 177: 88: 2690:

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. 3220: 3183: 3110: 3022: 2985: 2948: 2802: 1998: 1904: 1368: 1321: 938: 772: 323: 237: 233: 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: 690: 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. 388: 375: 367: 290:

2002: When magnetic field-aligned currents encounter density cavities

144: 139: 117: 73:

Double layers are conceptually related to the concept of a 'sheath' (

28: 3086: 1974: 1927: 1880: 1344: 1231: 1216: 173: 121: 260:

1983: Injection of non-neutral electron current into a cold plasma

199: 168:

Potential imbalance will be neutralised by electron (1&3) and

3040:

Unstable Current Systems and Plasma Instabilities in Astrophysics

2019: 406: 185: 1603:"Inferring the scale height of the lunar nightside double layer" 302: 244:, etc.). Proposed mechanisms for their formation have included: 2730: 605:(where the electron temperature is assumed to lie in the range 534: 387:, and in this respect are natural analogues to the smooth-bore 3162:

Raadu, Michael A. (1994). "Energy release in double layers".

2054:

Alfven, H. (1982). "On hierarchial [sic] cosmology".

1194: 181: 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. 2689: 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).

2471: 2272: 1467: 793: 278:

1988: Current-driven instabilities (strong double layers)

169: 3125: 1925: 97:

Double layers may be classified in the following ways:

1650: 611: 547: 3235: 2826:

Proceedings of the Astronomical Society of Australia

1601:

Halekas, J. S.; Lin, R. P.; Mitchell, D. L. (2003).

1021: 1136: 1101: 65:has been applied to electric fields oriented at an 3087:"Dynamical aspects of electrostatic double layers" 1975:"Dynamical aspects of electrostatic double layers" 1600: 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 1760: 598:{\displaystyle e\phi _{DL}/k_{B}T_{e}\approx 0.1} 3314: 2521: 1881:"Interstellar clouds and the formation of stars" 263:1985: Increasing the current density in a plasma 3198: 1926:Torvén, S; Lindberg, L; Carpenter, R T (1985). 1878: 297: 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). 3084: 2963: 2560: 1973:Raadu, Michael A.; Rasmussen, J. Juul (1988). 1972: 1817:"Paradigm transition in cosmic plasma physics" 1343:Raadu, Michael A.; Rasmussen, J. Juul (1988). 1342: 2780: 2103: 1424: 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 1557: 1276: 1159: 881: 659:{\displaystyle 2eV\leq k_{B}T_{e}\leq 20eV} 3309:, Physics Reports, 178, 25–97, 1989. 2168: 1389: 172:(2&4) migration, unless the potential 3000: 2715: 2498: 2442: 2381: 2222: 1680: 986: 916: 516:A cluster of double layers forming in an 269:1986: By pinches in cosmic plasma regions 2237: 2132: 2022:Aps Ohio Sections Fall Meeting Abstracts 1299: 511: 405: 301: 198: 87: 2603: 2417:Bryant, D.A., and G.M.Courtier (2015). 2311: 281:1988: Spacecraft-ejected electron beams 227: 3315: 2866: 2646: 2416: 2196: 2053: 1814: 1717: 1229: 1059:Astrophysics and Space Science Library 1056: 963:Acceleration in the Auroral and Beyond 959: 839:Astrophysics and Space Science Library 836: 417:) may be in the form of double layers. 3161: 3037: 2926: 2649:Journal of Physics D: Applied Physics 2606:Journal of Physics D: Applied Physics 2563:Journal of Physics D: Applied Physics 2346: 2171:Quecksilber-Niederdruck-Gasenladunger 1763:Journal of Physics D: Applied Physics 1720:Journal of Physics D: Applied Physics 1510: 750: 378:of this type was first discovered in 2823: 724: 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 13: 1879:Alfvén, H.; Carlqvist, P. (1978). 284:1989: From shock waves in a plasma 14: 3334: 3281:(2006, PDF), A. Meige, PhD thesis 2920: 2056:NASA Sti/Recon Technical Report N 1705:"1978Ap&SS..55...59B Page 60" 83: 330:, and tens of kilometers in the 275:1988: By an electrical discharge 42:Double layers can be created in 2860: 2817: 2774: 2724: 2696:Journal of Geophysical Research 2683: 2640: 2597: 2554: 2515: 2465: 2410: 2375: 2340: 2305: 2266: 2240:Journal of Geophysical Research 2231: 2203:Journal of Geophysical Research 2190: 2177: 2161: 2126: 2097: 2074: 2047: 2036: 2013: 1966: 1919: 1872: 1855: 1808: 1797: 1754: 1711: 1697: 1644: 1594: 1551: 1504: 1461: 1418: 1392:Journal of Geophysical Research 1383: 1336: 1293: 1270: 1223: 1188: 1153: 1130: 1095: 1050: 1015: 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 980: 953: 919:Astrophysics and Space Science 910: 875: 830: 787: 753:Astrophysics and Space Science 744: 733: 718: 326:, a few tens of meters in the 254:1982: Disruption of a neutral 151:Current carrying double layers 1: 3285: 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)90040-6 712: 298:Features and characteristics 116:, or in comparison with the 7: 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 10: 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. 484: 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: 488: 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: 3034: 2997: 2960: 2915: 2914: 2908: 2900: 2864: 2858: 2857: 2821: 2815: 2814: 2778: 2772: 2771: 2737: 2728: 2722: 2721: 2719: 2687: 2681: 2680: 2644: 2638: 2637: 2612:(8): 1192–1202. 2601: 2595: 2594: 2558: 2552: 2551: 2519: 2513: 2512: 2502: 2469: 2463: 2462: 2456: 2448: 2446: 2414: 2408: 2407: 2390:(8): 3600–3609. 2379: 2373: 2372: 2355:(9): 3685–3694. 2344: 2338: 2337: 2309: 2303: 2302: 2270: 2264: 2263: 2235: 2229: 2228: 2226: 2194: 2188: 2181: 2175: 2174: 2165: 2159: 2158: 2130: 2124: 2123: 2101: 2095: 2078: 2072: 2071: 2051: 2045: 2040: 2034: 2033: 2017: 2011: 2010: 1970: 1964: 1963: 1923: 1917: 1916: 1876: 1870: 1859: 1853: 1852: 1812: 1806: 1801: 1795: 1794: 1758: 1752: 1751: 1715: 1709: 1708: 1701: 1695: 1694: 1684: 1648: 1642: 1641: 1607: 1598: 1592: 1591: 1555: 1549: 1548: 1508: 1502: 1501: 1465: 1459: 1458: 1422: 1416: 1415: 1387: 1381: 1380: 1340: 1334: 1333: 1297: 1291: 1290: 1274: 1268: 1267: 1227: 1221: 1220: 1192: 1186: 1185: 1157: 1151: 1150: 1134: 1128: 1127: 1099: 1093: 1092: 1054: 1048: 1047: 1044:10.1063/1.865390 1019: 1013: 1012: 984: 978: 977: 957: 951: 950: 914: 908: 907: 879: 873: 872: 834: 828: 827: 791: 785: 784: 748: 742: 737: 731: 730: 722: 665: 663: 662: 657: 643: 642: 633: 632: 604: 602: 601: 596: 588: 587: 578: 577: 568: 563: 562: 508: 316:quasi-neutrality 147:in that respect. 132:non-relativistic 3338: 3337: 3333: 3332: 3331: 3329: 3328: 3327: 3313: 3312: 3288: 3279:Wayback Machine 3240: 3130: 3070: 2923: 2918: 2902: 2901: 2865: 2861: 2822: 2818: 2779: 2775: 2735: 2729: 2725: 2702:(A11): A11212. 2688: 2684: 2645: 2641: 2602: 2598: 2559: 2555: 2520: 2516: 2470: 2466: 2450: 2449: 2415: 2411: 2380: 2376: 2345: 2341: 2310: 2306: 2271: 2267: 2236: 2232: 2195: 2191: 2182: 2178: 2166: 2162: 2135:Physical Review 2131: 2127: 2120: 2102: 2098: 2093:Wayback Machine 2079: 2075: 2052: 2048: 2041: 2037: 2018: 2014: 1971: 1967: 1924: 1920: 1877: 1873: 1860: 1856: 1821:Physica Scripta 1813: 1809: 1802: 1798: 1759: 1755: 1716: 1712: 1703: 1702: 1698: 1649: 1645: 1605: 1599: 1595: 1556: 1552: 1509: 1505: 1466: 1462: 1423: 1419: 1388: 1384: 1341: 1337: 1298: 1294: 1275: 1271: 1228: 1224: 1193: 1189: 1158: 1154: 1135: 1131: 1100: 1096: 1089: 1055: 1051: 1020: 1016: 985: 981: 974: 958: 954: 915: 911: 880: 876: 869: 835: 831: 792: 788: 749: 745: 738: 734: 723: 719: 715: 638: 634: 628: 624: 610: 607: 606: 583: 579: 573: 569: 564: 555: 551: 546: 543: 542: 526:Irving Langmuir 509: 503: 487: 478:Irving Langmuir 423:Energy transfer 400:Cellular nature 300: 230: 86: 44:discharge tubes 21: 12: 11: 5: 3336: 3326: 3325: 3311: 3310: 3305:Raadu, M.,A., 3303: 3296: 3287: 3284: 3283: 3282: 3269: 3233: 3196: 3170:(1–4): 29–38. 3159: 3123: 3082: 3068: 3035: 3009:(1–2): 21–39. 2998: 2961: 2922: 2921:External links 2919: 2917: 2916: 2859: 2816: 2773: 2723: 2682: 2655:(3): 643–654. 2639: 2596: 2553: 2514: 2464: 2429:(4): 481–482. 2409: 2374: 2339: 2320:(6): 756–763. 2304: 2265: 2230: 2189: 2176: 2160: 2141:(6): 954–989. 2125: 2118: 2096: 2073: 2046: 2035: 2012: 1965: 1938:(2): 143–158. 1918: 1891:(2): 487–509. 1871: 1854: 1807: 1796: 1769:(6): 938–941. 1753: 1710: 1696: 1643: 1593: 1566:(4): 277–299. 1550: 1503: 1476:(4): 5624–35. 1460: 1417: 1382: 1335: 1292: 1269: 1222: 1217:10.1086/164289 1187: 1168:(7): 853–861. 1152: 1129: 1094: 1087: 1049: 1014: 995:(7): 749–759. 979: 972: 966:. p. 12. 952: 909: 890:(7): 853–861. 874: 867: 829: 802:(4): 5624–35. 786: 743: 732: 716: 714: 711: 655: 652: 649: 646: 641: 637: 631: 627: 623: 620: 617: 614: 594: 591: 586: 582: 576: 572: 567: 561: 558: 554: 550: 501: 494:. An electric 486: 483: 482: 481: 449: 446:Bohm Criterion 443: 437: 431: 404: 403: 397: 391: 353: 347: 341: 335: 299: 296: 295: 294: 291: 288: 285: 282: 279: 276: 273: 270: 267: 264: 261: 258: 252: 249: 242:nuclear fusion 229: 226: 221: 220: 217: 214: 211: 166: 165: 158: 148: 125: 120:energy of the 114:thermal energy 110:potential drop 85: 84:Classification 82: 9: 6: 4: 3: 2: 3335: 3324: 3321: 3320: 3318: 3308: 3304: 3301: 3297: 3294: 3290: 3289: 3280: 3276: 3273: 3270: 3266: 3262: 3258: 3254: 3250: 3246: 3239: 3234: 3230: 3226: 3222: 3218: 3214: 3210: 3206: 3202: 3197: 3193: 3189: 3185: 3181: 3177: 3173: 3169: 3165: 3160: 3156: 3152: 3148: 3144: 3140: 3136: 3129: 3124: 3120: 3116: 3112: 3108: 3104: 3100: 3096: 3092: 3088: 3083: 3079: 3075: 3071: 3065: 3061: 3057: 3053: 3049: 3045: 3041: 3036: 3032: 3028: 3024: 3020: 3016: 3012: 3008: 3004: 2999: 2995: 2991: 2987: 2983: 2979: 2975: 2971: 2967: 2962: 2958: 2954: 2950: 2946: 2942: 2938: 2934: 2930: 2925: 2924: 2912: 2906: 2898: 2894: 2890: 2886: 2882: 2878: 2874: 2870: 2863: 2855: 2851: 2847: 2843: 2839: 2835: 2831: 2827: 2820: 2812: 2808: 2804: 2800: 2796: 2792: 2788: 2784: 2777: 2769: 2765: 2761: 2757: 2753: 2749: 2746:(6): L06102. 2745: 2741: 2734: 2727: 2718: 2713: 2709: 2705: 2701: 2697: 2693: 2686: 2678: 2674: 2670: 2666: 2662: 2658: 2654: 2650: 2643: 2635: 2631: 2627: 2623: 2619: 2615: 2611: 2607: 2600: 2592: 2588: 2584: 2580: 2576: 2572: 2568: 2564: 2557: 2549: 2545: 2541: 2537: 2533: 2529: 2525: 2518: 2510: 2506: 2501: 2496: 2492: 2488: 2484: 2480: 2476: 2468: 2460: 2454: 2445: 2440: 2436: 2432: 2428: 2424: 2420: 2413: 2405: 2401: 2397: 2393: 2389: 2385: 2378: 2370: 2366: 2362: 2358: 2354: 2350: 2343: 2335: 2331: 2327: 2323: 2319: 2315: 2308: 2300: 2296: 2292: 2288: 2284: 2280: 2276: 2275:Hudson, M. K. 2269: 2261: 2257: 2253: 2249: 2245: 2241: 2234: 2225: 2220: 2216: 2212: 2208: 2204: 2200: 2193: 2186: 2180: 2172: 2164: 2156: 2152: 2148: 2144: 2140: 2136: 2129: 2121: 2119:9789400983748 2115: 2111: 2110:Cosmic Plasma 2107: 2100: 2094: 2090: 2087: 2083: 2077: 2069: 2065: 2061: 2057: 2050: 2044: 2039: 2031: 2027: 2023: 2016: 2008: 2004: 2000: 1996: 1992: 1988: 1984: 1980: 1976: 1969: 1961: 1957: 1953: 1949: 1945: 1941: 1937: 1933: 1929: 1922: 1914: 1910: 1906: 1902: 1898: 1894: 1890: 1886: 1882: 1875: 1868: 1864: 1858: 1850: 1846: 1842: 1838: 1834: 1830: 1826: 1822: 1818: 1811: 1805: 1800: 1792: 1788: 1784: 1780: 1776: 1772: 1768: 1764: 1757: 1749: 1745: 1741: 1737: 1733: 1729: 1725: 1721: 1714: 1706: 1700: 1692: 1688: 1683: 1678: 1674: 1670: 1666: 1662: 1658: 1654: 1647: 1639: 1635: 1631: 1627: 1623: 1619: 1615: 1611: 1604: 1597: 1589: 1585: 1581: 1577: 1573: 1569: 1565: 1561: 1554: 1546: 1542: 1538: 1534: 1530: 1526: 1522: 1518: 1514: 1507: 1499: 1495: 1491: 1487: 1483: 1479: 1475: 1471: 1464: 1456: 1452: 1448: 1444: 1440: 1436: 1432: 1428: 1421: 1413: 1409: 1405: 1401: 1398:(A9): 10035. 1397: 1393: 1386: 1378: 1374: 1370: 1366: 1362: 1358: 1354: 1350: 1346: 1339: 1331: 1327: 1323: 1319: 1315: 1311: 1308:(1–2): 3–13. 1307: 1303: 1296: 1288: 1284: 1280: 1273: 1265: 1261: 1257: 1253: 1249: 1245: 1241: 1237: 1233: 1226: 1218: 1214: 1210: 1206: 1202: 1198: 1191: 1183: 1179: 1175: 1171: 1167: 1163: 1156: 1148: 1144: 1140: 1133: 1125: 1121: 1117: 1113: 1109: 1105: 1098: 1090: 1084: 1080: 1076: 1072: 1068: 1064: 1060: 1053: 1045: 1041: 1037: 1033: 1029: 1025: 1018: 1010: 1006: 1002: 998: 994: 990: 983: 975: 973:9780750305334 969: 965: 964: 956: 948: 944: 940: 936: 932: 928: 924: 920: 913: 905: 901: 897: 893: 889: 885: 878: 870: 864: 860: 856: 852: 848: 844: 840: 833: 825: 821: 817: 813: 809: 805: 801: 797: 790: 782: 778: 774: 770: 766: 762: 758: 754: 747: 741: 736: 728: 721: 717: 710: 706: 702: 700: 694: 692: 687: 683: 681: 677: 672: 667: 653: 650: 647: 644: 639: 635: 629: 625: 621: 618: 615: 612: 592: 589: 584: 580: 574: 570: 565: 559: 556: 552: 548: 538: 536: 532: 531:Hannes Alfvén 527: 519: 514: 506: 505:Hannes Alfvén 500: 497: 493: 479: 475: 474:Hannes Alfvén 471: 467: 463: 462: 457: 453: 450: 447: 444: 441: 438: 435: 432: 428: 424: 421: 420: 416: 412: 408: 401: 398: 395: 392: 390: 386: 385:electron beam 381: 377: 373: 369: 365: 361: 357: 354: 351: 350:Energy supply 348: 345: 344:Particle flux 342: 339: 336: 333: 329: 325: 321: 317: 313: 310: 309: 304: 292: 289: 286: 283: 280: 277: 274: 271: 268: 265: 262: 259: 257: 256:current sheet 253: 250: 247: 246: 245: 243: 239: 235: 225: 218: 215: 212: 209: 208: 207: 201: 197: 193: 189: 187: 183: 179: 175: 171: 162: 159: 156: 152: 149: 146: 141: 137: 133: 129: 126: 123: 119: 115: 111: 107: 103: 100: 99: 98: 90: 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: 2642: 2609: 2605: 2599: 2566: 2562: 2556: 2531: 2527: 2517: 2482: 2478: 2467: 2453:cite journal 2426: 2422: 2412: 2387: 2383: 2377: 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 3319:: 3259:. 3247:. 3243:. 3223:. 3215:. 3203:. 3186:. 3178:. 3168:68 3166:. 3149:. 3137:. 3133:. 3113:. 3105:. 3093:. 3089:. 3072:. 3062:. 3054:. 3042:. 3025:. 3017:. 3007:87 3005:. 2988:. 2980:. 2970:74 2968:. 2951:. 2943:. 2933:55 2931:. 2907:}} 2903:{{ 2891:. 2883:. 2873:68 2871:. 2848:. 2840:. 2828:. 2805:. 2797:. 2787:56 2785:. 2762:. 2754:. 2744:38 2742:. 2738:. 2710:. 2698:. 2694:. 2671:. 2663:. 2653:29 2651:. 2628:. 2620:. 2610:26 2608:. 2585:. 2577:. 2567:13 2565:. 2542:. 2532:49 2530:. 2526:. 2503:. 2493:. 2483:41 2481:. 2477:. 2455:}} 2451:{{ 2437:. 2427:33 2425:. 2421:. 2398:. 2386:. 2363:. 2351:. 2328:. 2318:20 2316:. 2293:. 2283:38 2281:. 2254:. 2244:65 2242:. 2217:. 2205:. 2201:. 2149:. 2139:33 2137:. 2108:. 2060:82 2058:. 2001:. 1993:. 1981:. 1977:. 1954:. 1946:. 1936:27 1934:. 1930:. 1907:. 1899:. 1889:55 1887:. 1883:. 1843:. 1835:. 1823:. 1819:. 1785:. 1777:. 1767:25 1765:. 1742:. 1734:. 1724:15 1722:. 1685:. 1675:. 1667:. 1657:29 1655:. 1632:. 1624:. 1614:30 1612:. 1608:. 1582:. 1574:. 1564:67 1562:. 1539:. 1531:. 1521:29 1519:. 1515:. 1492:. 1484:. 1474:62 1472:. 1449:. 1441:. 1431:62 1429:. 1406:. 1396:93 1394:. 1371:. 1363:. 1351:. 1347:. 1324:. 1316:. 1304:. 1258:. 1250:. 1240:14 1238:. 1234:. 1211:. 1199:. 1176:. 1166:33 1164:. 1118:. 1106:. 1081:. 1073:. 1063:74 1061:. 1038:. 1028:28 1026:. 1003:. 993:19 991:. 941:. 933:. 923:87 921:. 898:. 888:33 886:. 861:. 853:. 843:74 841:. 818:. 810:. 800:62 798:. 775:. 767:. 757:55 755:. 682:. 648:20 507:, 458:, 334:. 240:, 236:, 23:A 3267:. 3263:: 3255:: 3249:9 3231:. 3219:: 3211:: 3194:. 3182:: 3174:: 3157:. 3153:: 3145:: 3139:1 3121:. 3109:: 3101:: 3080:. 3058:: 3050:: 3033:. 3021:: 3013:: 2996:. 2984:: 2976:: 2959:. 2947:: 2939:: 2913:) 2899:. 2887:: 2879:: 2856:. 2844:: 2836:: 2830:8 2813:. 2801:: 2793:: 2770:. 2758:: 2750:: 2720:. 2714:: 2706:: 2679:. 2667:: 2659:: 2636:. 2624:: 2616:: 2593:. 2581:: 2573:: 2550:. 2538:: 2511:. 2497:: 2489:: 2461:) 2447:. 2441:: 2433:: 2406:. 2402:: 2394:: 2388:9 2371:. 2367:: 2359:: 2353:9 2336:. 2332:: 2324:: 2301:. 2297:: 2289:: 2262:. 2258:: 2250:: 2227:. 2221:: 2213:: 2157:. 2153:: 2145:: 2122:. 2070:. 2066:: 2032:. 2028:: 2009:. 1997:: 1989:: 1962:. 1950:: 1942:: 1915:. 1903:: 1895:: 1851:. 1839:: 1831:: 1825:2 1793:. 1781:: 1773:: 1750:. 1738:: 1730:: 1707:. 1693:. 1679:: 1671:: 1663:: 1640:. 1628:: 1620:: 1590:. 1578:: 1570:: 1547:. 1535:: 1527:: 1500:. 1488:: 1480:: 1457:. 1445:: 1437:: 1414:. 1410:: 1402:: 1379:. 1367:: 1359:: 1332:. 1320:: 1312:: 1289:. 1285:: 1266:. 1254:: 1246:: 1219:. 1215:: 1207:: 1184:. 1180:: 1172:: 1149:. 1145:: 1126:. 1122:: 1114:: 1108:9 1091:. 1077:: 1069:: 1046:. 1042:: 1034:: 1011:. 1007:: 999:: 976:. 949:. 937:: 929:: 906:. 902:: 894:: 871:. 857:: 849:: 826:. 814:: 806:: 783:. 771:: 763:: 654:V 651:e 640:e 636:T 630:B 626:k 619:V 616:e 613:2 585:e 581:T 575:B 571:k 566:/ 560:L 557:D 549:e 20:.

Text is available under the Creative Commons Attribution-ShareAlike License. Additional terms may apply.

Knowledge

Double layer (plasma physics)

Index