Double layer

Saturnian aurora whose reddish colour is characteristic of ionized hydrogen plasma. Powered by the Saturnian equivalent of filamentary Birkeland currents, streams of charged particles from the interplanetary medium interact with the planet's magnetic field and funnel down to the poles. Filamentary currents are associated with double layers whose electric fields accelerate the ions.

A double layer is an electric charge separation region that forms in a plasma. It consists of two oppositely charged parallel layers, resulting in a voltage drop and electric field across the layer, which accelerates the plasma's electrons and positive ions in opposite directions, producing an electric current. All electrons spiralling through a magnetic field will produce radiation, and a large potential drop across the layer may accelerate electrons to relativistic velocities (ie close to the speed of light), which may produce synchrotron radiation.

Double layers may be found anywhere that plasmas are found, from discharge tubes to space plasmas to the Birkeland currents supplying the Earth's aurora. And although plasmas are highly electrically conductive, a property that tends to neutralised charges, double layers may form when two plasma regions with different properties come into contact, or when an electric current flows through a plasma. The physics of double layers are also utilised to produce ion thrusters, such as the Helicon Double Layer Thruster [3] [4].

A double layer is also called an electrostatic double layer, electric double layer, plasma double layers electrostatic shock, and space charge layer. In the study if neutron stars, a double layer is sometimes called a "vacuum gap". In laser physics, it is sometimes called ambipolar electric field [5].

In electrochemistry, a double layer is the name of a thin charged structure formed on the interface between electrode and a solution of electrolyte.

1 Double layer features
2 Typical double layers
3 Double Layer formation
- 3.1 Boundary double layer formation
4 History of double layers
5 External links
6 References

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Double layer features

Hall effect thruster. The electric field in a double layer is so effective at accelerating ions, that electric fields are used in ion drives

Classification: Double layers may be classified in the following ways:
- Time-dependent and time-independent double layers. A time-independent double layer is an idealized steady double layer. In reality, double layers are time-dependent highly dynamical structures.
- Weak and strong double layers. A double layer is said to be strong if the potential drop across the layer is greater than the equivalent thermal potentials of all free and reflected electron and ion populations. A strong double layer is also defined as one in which the velocity of ions across the double layer, is greater than the velocity of those entering the double layer. ([6], PDF)
- Relativistic and non-relativistic double layers. A double layer is said to be relativistic if it accelerates both electrons and ions to relativistic velocities (ie. close to the speed of light). The charge distribution in a relativistic double layer is such that the "surface" charge density at the anode appears independent of the thickness of the double layer; in this respect, the double layer is similar to the charge distribution in a capacitor.
- Electric and current-free double layers. An electric double layer features a potential drop, may accelerate charged particles, and may be current-driven. A current-free double layer (sometimes called a current-free electric double layer, CFDL) may be formed without a current or voltage difference, and contains no trapped or counter-streaming ions, (i.e., the relative electron-ion drift is zero). [7] [8]
Quasi-neutrality: The production of a double layer requires regions with a significant excess of positive or negative charge, that is, where quasi-neutrality is violated.(Block, 1978, p.60; Hasan et al., 1978, p.92) Since quasi-neutrality can only be violated over a scale of the Debye length, the thickness of a double layer is of the order of several tens of Debye lengths, a few centimeters in the ionosphere, a few tens of meter in the interplanetary medium, and tens of kilometers in the intergalactic medium.
Particle acceleration: The potential drop across the double layer will accelerate electrons and positive ions in opposite directions. The magnitude of the potential drop, irrespective of the width the layer, determines the acceleration of the ions. In strong double layers, this will result in beams or jets of charged particles.
Radiation emitted: All plasmas emit radiation. If the ions and electrons in a double layer are accelerated to relativistic velocities, synchrotron radiation may be produced in the form of radio waves, x-rays and gamma rays. This mechanism has been suggested to explain some astrophysical observations.[9]
Particle populations: Four populations of charge particles make up a double layer (1) Free electrons that are accelerate across the double layer (2) Free positive ions that are accelerated in the opposite direction across the double layer (3) Reflected electrons that approach the double layer, but are reflected back and counterstream away (4) Reflected positive ions that approach the double layer, but are reflected back and counterstream away.

Our Moon in x-rays. Even the dark side of the Moon produces some x-rays. In the shadows, the Moon charges negatively in the interplanetary medium. The prediction of a lunar double layer [1] was confirmed in 2003 [2] PDF

Formation: Double layers are produced in a number of ways depending on the environment of the plasma; In general, if two plasma regions with different electron temperatures comes into contact, a double layer may form. In the laboratory, a plasma that comes into contact with a surface (eg. an electrode in a discharge tube, or the contain walls) may form the oppositely charged half of a double layer adjacent to the surface, and is called a sheath (or Debye sheath or electrostatic sheath), which tends to screen the plasma from its container. This can make it difficult to measure the properties of a plasma and double layers (see Langmuir probe).
Particle flux: For strong double layers, and in most practical cases even for rather weak double layers, the flux of electrons is greater than that of the positive ions. This is a result of quasi-neutrality inside the double layer and the fact that the less massive electrons take less time to cross the layer. (Block, 1978, p.65)
Filamentary current : Double layers are associated with current filaments or Birkeland currents. [10] ([11], PDF)
Energy supply: The voltage drop across a double layer is proportional to the total current which is supplied by the filamentary current. In this respect, Hannes Alfvén considered the double layer to be a load in part of an electric circuit. Physicist Anthony Peratt write: "Since the Double Layer acts as a load, there has to be an external source maintaining the potential difference and driving the current. In the laboratory this source is usually an electrical power supply, whereas in space it may be the magnetic energy stored in an extended current system, which responds to a change in current with an inductive voltage." (Peratt, 1991)
Stability: Double layers are usually noisy producing oscillations across a wide frequency band. They may also become unstable and explode resulting in a voltage drop that increases by several orders of magnitude, a phenomenon that was first discovered in mercury rectifiers used in high-power direct-current transmission lines.
Magnetised plasmas: Double layers can form in unmagnetised plasmas (such as in the laboratory), and also in magnetised plasmas where a magnetic field keep the plasmas away from walls of its container so that the walls play little part. The latter is more applicable to cosmic plasmas.
Cellular nature: While double layers are relatively thin, they will spread over the entire surface of a laboratory container. Likewise where adjacent plasma regions have different properties, double layers will form and tend to cellularise the different regions.
Energy transfer: Double layers fascilitate 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[12]. Torven et al also report that plasma may spontaneously transfer magnetically stored energy into kinetic energy by electric double layers [13]
Oblique double layer: This is a double layer whose electric field is not parallel to the magnetic field (ie. it is not field-aligned). The double layer may also drift, usually in the direction of the emitted electron beam, and in this respect is a natural analogue of the smooth bore magnetron.
Simulation: Double layers may be modelled with particle-in-cell (PIC) computer simulations. Mathematically, double layers are a subset of the Bernstein-Greene-Kruskal (BGK) solutions of the Poisson-Vlasov equation. To simplify calculations, they are sometimes treated as one-dimension or two-dimensional structures. However, current filaments require that they are treated as three-dimensional objects.

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Typical double layers

Location	Typical Voltage drop	Source
Ionosphere	10²- 10⁴V	Satellite
Solar	10⁹- 10¹¹V	Estimated [14]
Galactic filament	10¹⁷V	Estimated (Peratt, 1991)

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Double Layer formation

Doubler layer formation. Hotter electrons moving into a cooler plasma region (Diagram 1, top) cause a charge imbalance, resulting in a double layer that is able to accelerate electrons across it (Diagram 2, bottom).

Although the basic structure of all double layers is the same, a variety of different mechanisms have been proposed for their formation, depending on the environment of the plasma (eg. double layers in the laboratory, ionosphere, space plasmas, fusions plasma, etc). For example:

1982: Disruption of a neutral current sheet [15]
1983: Injection of non-neutral electron current into a cold plasma [16]
1985: Increasing the current density in a plasma [17]
1986: In the accretion column of a neutron star [18]
1986: By pinches in cosmic plasma regions [19]
1988: By an electrical discharge [20]
1988: Current-driven instabilities (strong double layers) [21]
1988: Spacecraft-ejected electron beams [22]
1989: From shock waves in a plasma [23]
2000: Laser radiation [24]
2002: When magnetic field-aligned currents encounter density cavities [25]
2003: By the incidence of plasma on the dark side of the Moon's surface [26]

The formation of an idealised double layer, at the boubdary between two plasma regions, is described below.

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Boundary double layer formation

The diagrams right, show two stages in the formation of a double layer. Below each diagram is a graph representing the charge distribution along the double layer.

Since a plasma generally consists of equal numbers of positively-charged protons (blue circles) and negatively-charged electrons (red circles), there is no charge imbalance (see the chart under diagram 1, right). But since protons are over 1800 times heavier than electrons, the electrons can move much faster.

The particles in a hot plasma (left side of Diagram 1) move faster than those in the cooler plasma (right side). Since the hotter electrons are moving the fastest (represented by the red arrows), they will enter the cooler plasma faster than the cooler electrons can be replenished them. This results in a negative charge build-up on the cooler side of the boundary, as represented by the chart at the bottom of diagram 2. Note also that since the hot side of the boundary is now electron-deficient, it has an excess positive charge.

The diagram shows a layer of excess negative charge in the cooler plasma, represented by the column of red circles on the right, and a corresponding layer of excess positive charge (blue circles) in the hotter plasma on the left.

In between the layers, an electric field is created which acts like a particle accelerator. A cool electron (labelled 1) entering the double layer is accelerated across it (right to left). A proton (2) entering the double layer is accelerated across it (left to right). Hot electrons (3) that move into the double layer are now decelerated (because the electric field across the double wants to accelerate electrons in the opposite direction), and are reflected by the negatively-charged layer on the cool side, and accelerated back across the double layer. Likewise, cool protons (4) that move into the double layer are decelerated, reflected, and accelerated back across the double layer.

The double layer is self-sustaining. If some of the hot electrons are still able to fully cross the double layer (ie. it is unable to decelerate them, and the negatively charge layer is not able to reflect them), then the double layer is said to be weak. Otherwise it is called a strong double layer.

If the double layer is sufficient to accelerate electrons to close to the speed of light, it is said to be a relativistic double layer.

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History of double layers

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

Double layers were first characterised in the laboratory in 1929 by Nobel Prize winning scientist Irving Langmuir [27], which he called a double-sheath. Their importance in space plasmas was first advocated by Nobel Prize winning scientist, and developer of magnetohydrodynamics, Hannes Alfvén in 1958.

Nearly 20 years later in 1977, Forrest Mozer reported that satellites had detected the signature of double layers (that he called electrostatic shocks) in the magnetosphere [28]. Several more observations and simulations followed (Coakley et al 1978; Hubbard, R. F. and Joyce, G. 1979). Some scientists have subsequently suggested a role of double layers in solar flares Refs: 1 2 3

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