Double layer (plasma physics)

A double layer is a structure in a plasma consisting 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. Ions and electrons within the double layer are accelerated, decelerated, or deflected by the electric field, depending on their direction of motion.
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. Similarly, a double layer in the auroral region requires some external driver to produce electron acceleration.
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, In laser physics, a double layer is sometimes called an ambipolar electric field.
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.
Classification.
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.
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:
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.
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:
History.
It was already known in the 1920s that a plasma has a limited capacity for current maintenance, Irving Langmuir 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 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. 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 auroral particle characteristics.
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 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 formula_1 (where the electron temperature is assumed to lie in the range formula_2) 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. 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 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.
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 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.
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, 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 Enceladus, 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.
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. 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.