Double layer (plasma physics)

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 magnetron
• 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, ${\displaystyle \mathrm{d}W/\mathrm{d}t=I\mathrm{\Delta }V}$ 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." 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.

History

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 electric double layers. An electric double layer 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 recognized.

— Hannes Alfvén,

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 ${\displaystyle e{\varphi }_{DL}/k_B{T}_e\approx 0.1}$ (where the electron temperature is assumed to lie in the range ${\displaystyle 2eV\le k_B{T}_e\le 20eV}$) 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. Double layers have also been found in the Earth's magnetosphere by the space missions Cluster and MMS.

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.