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 tens of 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: Weak and strong double layers. The strength of a double layer is expressed as the ratio of the potential drop in comparison with the plasma's equivalent thermal energy, or in comparison with the rest mass energy of the electrons. 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. Relativistic or non-relativistic double layers. A double layer is said to be relativistic if the potential drop within the layer is comparable to the rest mass 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 capacitor in that respect. Current carrying double layers 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 Farley–Buneman instability, 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. Current-free double layers 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 may enable potential differences to be maintained between them locally. The overall charge density, as in all double layers, will be neutral. 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: A positive potential side of the double layer where electrons are accelerated towards it; A positive potential within the double layer where electrons are decelerated; A negative potential within the double layer where electrons are decelerated; and 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.
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:
1971: Between plasmas of different temperatures 1976: In laboratory plasmas 1982: Disruption of a neutral current sheet 1983: Injection of non-neutral electron current into a cold plasma 1985: Increasing the current density in a plasma 1986: In the accretion column of a neutron star 1986: By pinches in cosmic plasma regions 1987: In a plasma constrained by a magnetic mirror 1988: By an electrical discharge 1988: Current-driven instabilities (strong double layers) 1988: Spacecraft-ejected electron beams 1989: From shock waves in a plasma 2000: Laser radiation 2002: When magnetic field-aligned currents encounter density cavities 2003: By the incidence of plasma on the dark side of the Moon's surface. See picture.
Features and characteristics
Thickness: The production of a double layer requires regions with a significant excess of positive or negative charge, that is, where quasi-neutrality is violated. In general, quasi-neutrality can only be violated on scales of the Debye length. The thickness of a double layer is of the order of ten Debye lengths, which is a few centimeters in the ionosphere, a few tens of meters in the interplanetary medium, and tens of kilometers in the intergalactic medium. Electrostatic potential distribution: 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. Particle flux: 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. Energy supply: 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. Stability: 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 beams of ions and electrons. Unstable double layers are noisy 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 explosion (and hence exploding double layer). In one example, the region enclosed in the double layer rapidly expands and evolves. An explosion of this type was first discovered in mercury arc rectifiers 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 electron beam, and in this respect are natural analogues to the smooth-bore magnetronhttp://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=JAPIAU000037000007002598000001&idtype=cvips&gifs=yes Magnetised plasmas: Double layers can form in both magnetised and unmagnetised plasmas. Cellular nature: 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.
Energy transfer: Double layers can facilitate the transfer of electrical energy into kinetic energy, 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 et al. 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 potentials in the form of double layers produced by an external electric field. Oblique double layer: An oblique double layer has electric fields that are not parallel to the ambient magnetic field; i.e., it is not field-aligned. Simulation: 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. Bohm criterion: 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. Bio-physical analogy: 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 charge neutrality, Debye length, and double layer are very useful to explain the electrical properties of a cellular membrane."http://scitation.aip.org/getabs/servlet/GetabsServlet?prog=normal&id=AJPIAS000068000005000450000001&idtype=cvips&gifs=yes Plasma physicist Hannes Alfvén also noted that association of double layers with cellular structure, as had Irving Langmuir before him, who coined the term "plasma" after its resemblance to blood cells.G. L. Rogoff, Ed., "Introduction", IEEE Transactions on Plasma Science, vol. 19, p. 989, Dec. 1991. See extract on the Plasma Coalition web site
History