Double layer (plasma physics)

This article is about the structure in plasma physics. For other uses, see Double layer.

A double layer is a structure in a plasma which consists of two parallel layers of opposite electrical charge. The sheets of charge, which are not necessarily planar, produce localised excursions of electric potential, resulting in a relatively strong electric field between the layers and weaker but more extensive compensating fields outside, which restore the global potential.[1] Ions and electrons within the double layer are accelerated, decelerated, or deflected by the electric field, depending on their direction of motion.

However, the line integral of electrostatic potential across a double layer is zero.[2] because the contours of equipotential are necessarily closed. As the electrostatic potential introduced by a double layer at distances comparable to the sheet separation rapidly tends to zero, it also follows that any charged particle entering the region of a double layer will experience no net change in energy on passing right through it.

Double layers can be created in discharge tubes, 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 aurora and are invoked in astrophysical applications. For many decades, a view has been held that double layers are instrumental in accelerating auroral electrons. This interpretation treats only the double layer's internal electric field, and overlooks the fact that this is neutralised by the double layer's external fields.

Electrostatic double layers are especially common in current-carrying plasmas, and are very thin (typically ten Debye lengths), 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 magnetosphere has been applied to electric fields oriented at an oblique angle to the magnetic field in such a way that the perpendicular electric field is much stronger than the parallel electric field,[3][4] In laser physics, a double layer is sometimes called an ambipolar electric field.[5]

Double layers are conceptually related to the concept of a 'sheath' (see Debye sheath). An early review of double layers from laboratory experiment and simulations is provided by Torvén.[6]

Double layer classification

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, bottom)

Double layers may be classified in the following ways:

Potential imbalance will be neutralised by electron (1&3) and ion (2&4) migration, unless the potential gradients are sustained by an external energy source. Under most laboratory situations, unlike outer space conditions, charged particles may effectively originate within the double layer, by ionization at the anode or cathode, and be sustained.

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.[9]

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

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

  1. A positive potential side of the double layer where electrons are accelerated towards it;
  2. A positive potential within the double layer where electrons are decelerated;
  3. A negative potential within the double layer where electrons are decelerated; and
  4. A negative potential side of the double layer where electrons are accelerated.

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.

Double layer formation mechanisms

The details of the formation mechanism depend on the environment of the plasma (e.g. double layers in the laboratory, ionosphere, solar wind, nuclear fusion, etc.). Proposed mechanisms for their formation have included:

The Moon. The prediction of a lunar double layer[24] was confirmed in 2003.[25] In the shadows, the Moon charges negatively in the interplanetary medium.[26]

Features and characteristics of double layers

Hall effect thruster. The electric fields utilised in plasma thrusters (in particular the Helicon Double Layer Thruster) may be in the form of double layers.[32]

History of double layers

This brief account of the advent of double layers in research elaborates on some information in the chronological list of events provided above.

A cluster of double layers forming in an Alfvén wave, about a sixth of the distance from the left. Click for more details

It was already known in the 1920s that a plasma has a limited capacity for current maintenance, Irving Langmuir[40] 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 (e.g. Schönhuber, 1958). Many groups are still working on this topic theoretically, experimentally and numerically. It was first proposed by Hannes Alfvén (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.[41] 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 which involve wave-particle interactions have been proposed as being feasible, from extensive spatial and temporal in situ studies of auroral particle characteristics.[42]

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 which was thought then to be too sharp to be produced by a random process and which suggested, therefore, that an ordered process was responsible.[43] It was reported in 1977 that satellites had detected the signature of double layers as electrostatic shocks in the magnetosphere.[44] indications of electric fields parallel to the geomagnetic field lines was obtained by the Viking satellite,[45] 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 (where the electron temperature is assumed to lie in the range ) 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.

Interpretation of the FAST spacecraft data proposed strong double layers in the auroral acceleration region.[46] Strong double layers have also been reported in the downward current region by Andersson et al.[47] Parallel electric fields with amplitudes reaching nearly 1 V/m were inferred to be confined to a thin layer of 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.[48]

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

In the laboratory, double layers can be created in different devices. They are investigated in double plasma machines, triple plasma machines, and Q-machines. The stationary potential structures which 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)[49] 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),[50] who, however, also observed radiation from the double layer itself.

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.[51] Subsequently, both radio emissions, near the plasma frequency, and whistler waves at much lower frequencies were seen to emerge from this region.[52] Similar whistler wave structures were observed together with electron beams near Saturn's moon Enceladus,[53] suggesting the possible presence of a double layer at lower altitude.

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 double layers are strongly sensitive to the boundary conditions of the plasma (Hershkowitz, 1992).

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 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.[54][55] 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.[56]

See also

Footnotes

  1. Joos, G. (1951). Theoretical Physics. London & Glasgow: Blackie & Son Ltd. p. 271.
  2. Harnwell, G.P. (1949). Principles of Electricity and Magnetism. New York Toronto London: McGraw-Hill Book Company, Inc. p. 14.
  3. Temerin, M.; Mozer, F. S., "Double Layers Above the Aurora" (1987) NASA Conference Publication, #2469
  4. Block, L. P. "A double layer review" (1978) Astrophysics and Space Science, vol. 55, no. 1, May 1978, pp. 5983
  5. Bulgakova, Nadezhda M. et al., "Double layer effects in laser-ablation plasma plumes", Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics), Volume 62, Issue 4, October 2000, pp. 56245635
  6. Torvén, S. ""Formation of Double Layers in Laboratory Plasmas (1976) Astrophysics and Space Science Library, Vol. 74, p.109
  7. Yamamoto, Takashi; Kan, J. R. "Double layer formation due to current injection" (1985) Planetary and Space Science, Volume 33, Issue 7, pp. 853861.
  8. Carlqvist, P. (1982). "On the physics of relativistic double layers". Astrophysics and Space Science. 82: 21.
  9. Bryant, D.A. (1998). Acceleration in the Auroral and Beyond. p. 12. ISBN 9780750305334.
  10. Hultqvist, Bengt, "On the production of a magnetic-field-aligned electric field by the interaction between the hot magnetospheric plasma and the cold ionosphere" (1971) Planetary and Space Science, Vol. 19, p.749. See also: Ishiguro, S.; Kamimura, T.; Sato, T., "Double layer formation caused by contact between different temperature plasmas" (1985) Physics of Fluids (ISSN 0031-9171), vol. 28, July 1985, p. 21002105.
  11. Torven, S. ""Formation of Double Layers in Laboratory Plasmas (1976) Astrophysics and Space Science Library, Vol. 74, p.109
  12. Stenzel, R. L., "Double layer formation during current sheet disruptions in a reconnection experiment" (1982) Geophysical Research Letters, vol. 9, June 1982, pp. 680683.
  13. Thiemann, H.; Singh, N.; Schunk, R. W. "Formation of v-shaped potentials" (1983) In ESA Sixth ESA Symp. on European Rocket and Balloon Programs and Related Res. pp 269275
  14. Yamamoto, Takashi; Kan, J. R. "Double layer formation due to current injection" (1985) Planetary and Space Science, Volume 33, Issue 7, pp. 853861.
  15. Williams, A. C. et al. "Accretion onto neutron stars with the presence of a double layer" (1986) Astrophysical Journal, Part 1 (ISSN 0004-637X), vol. 305, June 15, 1986, pp. 759766.
  16. Peratt, Anthony L. "Evolution of the plasma universe. I Double radio galaxies, quasars, and extragalactic jets" (1986) IEEE Transactions on Plasma Science (ISSN 0093-3813), vol. PS-14, Dec. 1986, pp. 639660.
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  20. Singh, Nagendra; Hwang, K. S. "Electric potential structures and propagation of electron beams injected from a spacecraft into a plasma" (1988) Journal of Geophysical Research (ISSN 0148-0227), vol. 93, September 1, 1988, pp. 1003510040.
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  22. Bulgakova, Nadezhda M. et al. "Double layer effects in laser-ablation plasma plumes" (2000) Physical Review E (Statistical Physics, Plasmas, Fluids, and Related Interdisciplinary Topics), Volume 62, Issue 4, October 2000, pp. 56245635
  23. Singh, Nagendra "Spontaneous formation of current-driven double layers in density depletions and its relevance to solitary Alfven waves" (2002) Geophysical Research Letters, Volume 29, Issue 7, pp. 51
  24. Borisov, N.; Mall, U. "The structure of the double layer behind the Moon" (2002) Journal of Plasma Physics, vol. 67, Issue 04, pp. 277299
  25. Halekas, J. S.; Lin, R. P.; Mitchell, D. L. "Inferring the scale height of the lunar nightside double layer" (2003) Geophysical Research Letters, Volume 30, Issue 21, pp. PLA 1-1. (PDF)
  26. Halekas, J. S et al. "Evidence for negative charging of the lunar surface in shadow" (2002)
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  41. Alfvén, H., "On the theory of magnetic storms and aurorae", Tellus, 10, 104,. 1958.
  42. Bryant, D.A (June 2002). "The roles of static and dynamic electric fields in the auroral acceleration region". Journal of Geophysical Research. 107. doi:10.1029/2001JA900162.
  43. McIlwain, C E (1960). "Direct Measurement of Particles Producing Visible Auroras". Journal of Geophysical Research. 65: 2727. Bibcode:1960JGR....65.2727M. doi:10.1029/JZ065i009p02727.
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  45. Boström, Rolf "Observations of weak double layers on auroral field lines" (1992) IEEE Transactions on Plasma Science (ISSN 0093-3813), vol. 20, no. 6, pp. 756763
  46. Ergun, R. E., et al. "Parallel electric fields in the upward current region of the aurora: Indirect and direct observations" (2002) Physics of Plasmas, Volume 9, Issue 9, pp. 36853694
  47. Andersson, L., et al. "Characteristics of parallel electric fields in the downward current region of the aurora" (2002) Physics of Plasmas, Volume 9, Issue 8, pp. 36003609
  48. Bryant, D.A., and G.M.Courtier (2015). "Electrostatic double layers as auroral particle accelerators - a problem". AnGeo Comm. 33: 481–482. doi:10.5194/angeo-33-481-2015.
  49. Torvén, S.; Lindberg, L. "Properties of a fluctuating double layer in a magnetized plasma column" (1982) Journal of Physics D: Applied Physics, Volume 13, Issue 12, pp. 22852300
  50. Volwerk, M. "Radiation from electrostatic double layers in laboratory plasmas" (1993) Journal of Physics D: Applied Physics, Volume 26, Issue 8, pp. 11921202
  51. Gunell, H., et al. "Bursts of high-frequency plasma waves at an electric double layer" (1996) Journal of Physics D: Applied Physics, Volume 29, Issue 3, pp. 643654
  52. Brenning, N., et al. "Radiation from an electron beam in a magnetized plasma: Whistler mode wave packets" (2006) Journal of Geophysical Research, Volume 111, Volume 111, Issue A11, CiteID A11212
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  56. Bryant, D.A.,R.Bingham and U.deAngelis (1992). "Double layers are not particle accelerators". Physical Review Letters. 68: 37–39. doi:10.1103/PhysRevLett.68.37.

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References

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