Plasma (physics)

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File:Plasma-lamp 2.jpg
plasma lamp, illustrating some of the more complex phenomena of a plasma, including filamentation. The colors are a result of relaxation of electrons in excited states to lower energy states after they have recombined with ions. These processes emit light in a spectrum characteristic of the gas being excited.

In physics and chemistry, a plasma is typically an ionized gas. Plasma is considered to be a distinct state of matter, apart from gases, because of its unique properties. Ionized refers to presence of one or more free electrons, which are not bound to an atom or molecule. The free electric charges make the plasma electrically conductive so that it responds strongly to electromagnetic fields.

Plasma typically takes the form of neutral gas-like clouds (e.g. stars) or charged ion beams, but may also include dust and grains (called dusty plasmas).[1] They are typically formed by heating and ionizing a gas, stripping electrons away from atoms, thereby enabling the positive and negative charges to move more freely.

History

File:Wimshurst Plasma Arc.jpg
Plasma arcs between the probes on a Wimshurst Machine. This device, invented in the early 1880s, has long been a popular laboratory demonstration of plasma.

This state of matter was first identified in a Crookes tube, and so described by Sir William Crookes in 1879 (he called it "radiant matter").[2] The nature of the Crookes tube "cathode ray" matter was subsequently identified by British physicist Sir J.J. Thomson in 1897,[3] and dubbed "plasma" by Irving Langmuir in 1928,[4] perhaps because it reminded him of a blood plasma.[5] Langmuir wrote:

Except near the electrodes, where there are sheaths containing very few electrons, the ionized gas contains ions and electrons in about equal numbers so that the resultant space charge is very small. We shall use the name plasma to describe this region containing balanced charges of ions and electrons."[4]

Common plasmas

Plasmas are by far the most common phase of matter in the universe, both by mass and by volume.[6] All the stars are made of plasma, and even the space between the stars is filled with a plasma, albeit a very sparse one (See astrophysical plasma, interstellar medium and intergalactic space). In the solar system, the planet Jupiter accounts for most of the non-plasma, only about 0.1% of the mass and 10−15% of the volume within the orbit of Pluto. Notable plasma physicist Hannes Alfvén also noted that due to their electric charge, very small grains also behave as ions and form part of plasma (see dusty plasmas).

Common forms of plasma include
Artificially produced plasmas
Terrestrial plasmas
Space and astrophysical plasmas

Plasma properties and parameters

File:Plasma fountain.gif
The Earth's "plasma fountain", showing oxygen, helium, and hydrogen ions which gush into space from regions near the Earth's poles. The faint yellow area shown above the north pole represents gas lost from Earth into space; the green area is the aurora borealis-or plasma energy pouring back into the atmosphere.[8]

Definition of a plasma

Although a plasma is loosely described as an electrically neutral medium of positive and negative particles, a more rigorous definition requires three criteria to be satisfied:Template:Fix/category[citation needed]

  1. The plasma approximation: Charged particles must be close enough together that each particle influences many nearby charged particles, rather than just interacting with the closest particle (these collective effects are a distinguishing feature of a plasma). The plasma approximation is valid when the number of electrons within the sphere of influence (called the Debye sphere whose radius is the Debye screening length) of a particular particle is large. The average number of particles in the Debye sphere is given by the plasma parameter, "Λ" (the Greek letter Lambda).
  2. Bulk interactions: The Debye screening length (defined above) is short compared to the physical size of the plasma. This criterion means that interactions in the bulk of the plasma are more important than those at its edges, where boundary effects may take place.
  3. Plasma frequency: The electron plasma frequency (measuring plasma oscillations of the electrons) is large compared to the electron-neutral collision frequency (measuring frequency of collisions between electrons and neutral particles). When this condition is valid, plasmas act to shield charges very rapidly (quasineutrality is another defining property of plasmas).

Ranges of plasma parameters

Plasma parameters can take on values varying by many orders of magnitude, but the properties of plasmas with apparently disparate parameters may be very similar (see plasma scaling). The following chart considers only conventional atomic plasmas and not exotic phenomena like quark gluon plasmas:

File:Ranges of Plasmas graph.png
Range of plasmas. Density increases upwards, temperature increases towards the right. The free electrons in a metal may be considered an electron plasma[9]
Typical ranges of plasma parameters: orders of magnitude (OOM)
CharacteristicTerrestrial plasmasCosmic plasmas
Size
in metres
10−6 m (lab plasmas) to
10² m (lightning) (~8 OOM)
10−6 m (spacecraft sheath) to
1025 m (intergalactic nebula) (~31 OOM)
Lifetime
in seconds
10−12 s (laser-produced plasma) to
107 s (fluorescent lights) (~19 OOM)
101 s (solar flares) to
1017 s (intergalactic plasma) (~17 OOM)
Density
in particles per
cubic metre
107 m-3 to
1032 m-3 (inertial confinement plasma)
100 (i.e., 1) m-3 (intergalactic medium) to
1030 m-3 (stellar core)
Temperature
in kelvins
~0 K (crystalline non-neutral plasma[10]) to
108 K (magnetic fusion plasma)
10² K (aurora) to
107 K (solar core)
Magnetic fields
in teslas
10−4 T (lab plasma) to
10³ T (pulsed-power plasma)
10−12 T (intergalactic medium) to
1011 T (near neutron stars)

Degree of ionization

For plasma to exist, ionization is necessary. The word "plasma density" by itself usually refers to the "electron density", that is, the number of free electrons per unit volume. The degree of ionization of a plasma is the proportion of atoms which have lost (or gained) electrons, and is controlled mostly by the temperature. Even a partially ionized gas in which as little as 1% of the particles are ionized can have the characteristics of a plasma (i.e. respond to magnetic fields and be highly electrically conductive). The degree of ionization, α is defined as α = ni/(ni + na) where ni is the number density of ions and na is the number density of neutral atoms. The electron density is related to this by the average charge state <Z> of the ions through ne=<Z> ni where ne is the number density of electrons.

Temperatures

Plasma temperature is commonly measured in kelvins or electronvolts, and is an informal measure of the thermal kinetic energy per particle. In most cases the electrons are close enough to thermal equilibrium that their temperature is relatively well-defined, even when there is a significant deviation from a Maxwellian energy distribution function, for example due to UV radiation, energetic particles, or strong electric fields. Because of the large difference in mass, the electrons come to thermodynamic equilibrium among themselves much faster than they come into equilibrium with the ions or neutral atoms. For this reason the "ion temperature" may be very different from (usually lower than) the "electron temperature". This is especially common in weakly ionized technological plasmas, where the ions are often near the ambient temperature.

Based on the relative temperatures of the electrons, ions and neutrals, plasmas are classified as "thermal" or "non-thermal". Thermal plasmas have electrons and the heavy particles at the same temperature i.e. they are in thermal equilibrium with each other. Non-thermal plasmas on the other hand have the ions and neutrals at a much lower temperature (normally room temperature) whereas electrons are much "hotter".

Temperature controls the degree of plasma ionization. In particular, plasma ionization is determined by the "electron temperature" relative to the ionization energy (and more weakly by the density) in a relationship called the Saha equation. A plasma is sometimes referred to as being "hot" if it is nearly fully ionized, or "cold" if only a small fraction (for example 1%) of the gas molecules are ionized (but other definitions of the terms "hot plasma" and "cold plasma" are common). Even in a "cold" plasma the electron temperature is still typically several thousand degrees Celsius. Plasmas utilized in "plasma technology" ("technological plasmas") are usually cold in this sense.

Potentials

File:Lightning over Oradea Romania 2.jpg
Lightning is an example of plasma present at Earth's surface. Typically, lightning discharges 30,000 amperes, at up to 100 million volts, and emits light, radio waves, x-rays and even gamma rays.[11] Plasma temperatures in lightning can approach ~28,000 kelvin (~27,700oC) and electron densities may exceed 1024/m³.

Since plasmas are very good conductors, electric potentials play an important role. The potential as it exists on average in the space between charged particles, independent of the question of how it can be measured, is called the "plasma potential" or the "space potential". If an electrode is inserted into a plasma, its potential will generally lie considerably below the plasma potential due to what is termed a Debye sheath. The good electrical conductivity of plasmas causes their electric fields to be very small. This results in the important concept of "quasineutrality", which says the density of negative charges is approximately equal to the density of positive charges over large volumes of the plasma (Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): n_e=\langle Z\rangle n_i ), but on the scale of the Debye length there can be charge imbalance. In the special case that double layers are formed, the charge separation can extend some tens of Debye lengths.

The magnitude of the potentials and electric fields must be determined by means other than simply finding the net charge density. A common example is to assume that the electrons satisfy the "Boltzmann relation":

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): n_e \propto e^{e\Phi/k_BT_e} .

Differentiating this relation provides a means to calculate the electric field from the density:

Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \vec{E} = (k_BT_e/e)(\nabla n_e/n_e) .

It is possible to produce a plasma which is not quasineutral. An electron beam, for example, has only negative charges. The density of a non-neutral plasma must generally be very low, or it must be very small, otherwise it will be dissipated by the repulsive electrostatic force.

In astrophysical plasmas, Debye screening prevents electric fields from directly affecting the plasma over large distances (ie. greater than the Debye length). But the existence of charged particles causes the plasma to generate and be affected by magnetic fields. This can and does cause extremely complex behavior, such as the generation of plasma double layers, an object which separates charge over a few tens of Debye lengths. The dynamics of plasmas interacting with external and self-generated magnetic fields are studied in the academic discipline of magnetohydrodynamics.

Magnetization

A plasma in which the magnetic field is strong enough to influence the motion of the charged particles is said to be magnetized. A common quantitative criterion is that a particle on average completes at least one gyration around the magnetic field before making a collision (ie. Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \omega_{ce}/\nu_{coll} > 1 where Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \omega_{ce} is the "electron gyrofrequency" and Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://api.formulasearchengine.com/v1/":): \nu_{coll} is the "electron collision rate"). It is often the case that the electrons are magnetized while the ions are not. Magnetized plasmas are anisotropic, meaning that their properties in the direction parallel to the magnetic field are different from those perpendicular to it. While electric fields in plasmas are usually small due to the high conductivity, the electric field associated with a plasma moving in a magnetic field is given by E = -v x B (where E is the electric field, v is the velocity, and B is the magnetic field), and is not affected by Debye shielding.[12]

Comparison of plasma and gas phases

Plasma is often called the fourth state of matter. It is distinct from other lower-energy states of matter; most commonly solid, liquid, and gas, although it is closely related to the gas phase in that it also has no definite form or volume. Physicists consider a plasma to be more than a gasTemplate:Fix/category[citation needed] because of a number of distinct properties including the following:

Property Gas Plasma
Electrical Conductivity Very low
Air is an excellent insulator until it breaks down into plasma at electric field strengths above 30 kilovolts per centimeter.[13]
Usually very high
For many purposes the conductivity of a plasma may be treated as infinite.
Independently acting species One
All gas particles behave in a similar way, influenced by gravity, and collisions with one another
Two or three
Electrons, ions, and neutrals can be distinguished by the sign of their charge so that they behave independently in many circumstances, with different bulk velocities and temperatures, allowing phenomena such as new types of waves and instabilities
Velocity distribution Maxwellian
Collisions usually lead to a Maxwellian velocity distribution of all gas particles, with very few relatively fast particles.
Often non-Maxwellian
Collisional interactions are often weak in hot plasmas, and external forcing can drive the plasma far from local equilibrium, and lead to a significant population of unusually fast particles.
Interactions Binary
Two-particle collisions are the rule, three-body collisions extremely rare.
Collective
Waves, or organised motion of plasma, are very important because the particles can interact at long ranges through the electric and magnetic forces.

Complex plasma phenomena

File:Tycho-supernova-xray.jpg
The remnant of "Tycho's Supernova", a huge ball of expanding plasma. The blue outer shell arises from X-ray emission by high-speed electrons.

Although the underlying equations governing plasmas are relatively simple, plasma behaviour is extraordinarily varied and subtle: the emergence of unexpected behaviour from a simple model is a typical feature of a complex system. Such systems lie in some sense on the boundary between ordered and disordered behaviour, and cannot typically be described either by simple, smooth, mathematical functions, or by pure randomness. The spontaneous formation of interesting spatial features on a wide range of length scales is one manifestation of plasma complexity. The features are interesting, for example, because they are very sharp, spatially intermittent (the distance between features is much larger than the features themselves), or have a fractal form. Many of these features were first studied in the laboratory, and have subsequently been recognised throughout the universe. Examples of complexity and complex structures in plasmas include:

Filamentation

The striations or "stringy" things,[14] seen in many plasmas, like the plasma ball (image above), the aurora,[15] lightning,[16] electric arcs, solar flares,[17] and supernova remnants[18] They are sometimes associated with larger current densities, and are also called magnetic ropes.[19] (See also Plasma pinch)

Shocks or double layers

Narrow sheets with sharp gradients, such as shocks or double layers which support rapid changes in plasma properties. Double layers involve localised charge separation, which causes a large potential difference across the layer, but does not generate an electric field outside the layer. Double layers separate adjacent plasma regions with different physical characteristics, and are often found in current carrying plasmas. They accelerate both ions and electrons.

Electric fields and circuits

Quasineutrality of a plasma requires that plasma currents close on themselves in electric circuits. Such circuits follow Kirchhoff's circuit laws, and possess a resistance and inductance. These circuits must generally be treated as a strongly coupled system, with the behaviour in each plasma region dependent on the entire circuit. It is this strong coupling between system elements, together with nonlinearity, which may lead to complex behaviour. Electrical circuits in plasmas store inductive (magnetic) energy, and should the circuit be disrupted, for example, by a plasma instability, the inductive energy will be released as plasma heating and acceleration. This is a common explanation for the heating which takes place in the solar corona. Electric currents, and in particular, magnetic-field-aligned electric currents (which are sometimes generically referred to as "Birkeland currents"), are also observed in the Earth's aurora, and in plasma filaments.

Cellular structure

Narrow sheets with sharp gradients may separate regions with different properties such as magnetization, density, and temperature, resulting in cell-like regions. Examples include the magnetosphere, heliosphere, and heliospheric current sheet. Hannes Alfvén wrote: "From the cosmological point of view, the most important new space research discovery is probably the cellular structure of space. As has been seen, in every region of space which is accessible to in situ measurements, there are a number of 'cell walls', sheets of electric currents, which divide space into compartments with different magnetization, temperature, density, etc ."[20]

Critical ionization velocity

The Critical ionization velocity is the relative velocity between an (magnetized) ionized plasma and a neutral gas above which a runaway ionization process takes place. The critical ionization process is a quite general mechanism for the conversion of the kinetic energy of a rapidly streaming gas into ionization and plasma thermal energy. Critical phenomena in general are typical of complex systems, and may lead to sharp spatial or temporal features.

Ultracold plasma

It is possible to create ultracold plasmas, by using lasers to trap and cool neutral atoms to temperatures of 1 mK or lower. Another laser then ionizes the atoms by giving each of the outermost electrons just enough energy to escape the electrical attraction of its parent ion.

The key point about ultracold plasmas is that by manipulating the atoms with lasers, the kinetic energy of the liberated electrons can be controlled. Using standard pulsed lasers, the electron energy can be made to correspond to a temperature of as low as 0.1 K,­ a limit set by the frequency bandwidth of the laser pulse. The ions, however, retain the millikelvin temperatures of the neutral atoms. This type of non-equilibrium ultracold plasma evolves rapidly, and many fundamental questions about its behaviour remain unanswered. Experiments conducted so far have revealed surprising dynamics and recombination behavior which are pushing the limits of our knowledge of plasma physics.Template:Fix/category[citation needed] One of the metastable states of strongly nonideal plasma is Rydberg matter which forms upon condensation of excited atoms.

Non-neutral plasma

The strength and range of the electric force and the good conductivity of plasmas usually ensure that the density of positive and negative charges in any sizeable region are equal ("quasineutrality"). A plasma which has a significant excess of charge density or which is, in the extreme case, composed of only a single species, is called a non-neutral plasma. In such a plasma, electric fields play a dominant role. Examples are charged particle beams, an electron cloud in a Penning trap, and positron plasmas.[21]

Dusty plasma and grain plasma

A dusty plasma is one containing tiny charged particles of dust (typically found in space) which also behaves like a plasma. A plasma containing larger particles is called a grain plasma.

Mathematical descriptions

File:Magnetic rope.png
The complex self-constricting magnetic field lines and current paths in a field-aligned Birkeland current which may develop in a plasma[22]

To completely describe the state of a plasma, we would need to write down all the particle locations and velocities, and describe the electromagnetic field in the plasma region. However, it is generally not practical or necessary to keep track of all the particles in a plasma. Therefore, plasma physicists commonly use less detailed descriptions known as models, of which there are two main types:

Fluid model

Fluid models describe plasmas in terms of smoothed quantities like density and averaged velocity around each position (see Plasma parameters). One simple fluid model, magnetohydrodynamics, treats the plasma as a single fluid governed by a combination of Maxwell's Equations and the Navier-Stokes Equations. A more general description is the two-fluid picture, where the ions and electrons are described separately. Fluid models are often accurate when collisionality is sufficiently high to keep the plasma velocity distribution close to a Maxwell-Boltzmann distribution. Because fluid models usually describe the plasma in terms of a single flow at a certain temperature at each spatial location, they can neither capture velocity space structures like beams or double layers nor resolve wave-particle effects.

Kinetic model

Kinetic models describe the particle velocity distribution function at each point in the plasma, and therefore do not need to assume a Maxwell-Boltzmann distribution. A kinetic description is often necessary for collisionless plasmas. There are two common approaches to kinetic description of a plasma. One is based on representing the smoothed distribution function on a grid in velocity and position. The other, known as the particle-in-cell (PIC) technique, includes kinetic information by following the trajectories of a large number of individual particles. Kinetic models are generally more computationally intensive than fluid models. The Vlasov equation may be used to describe how a system of particles evolves in an electromagnetic environment.

Common artificial plasma

Most artificial plasmas are generated by the application of electric and/or magnetic fields. Plasma generated in a laboratory setting and for industrial use can be generally categorized by:

  • The type of power source used to generate the plasma; DC, RF and microwave.
  • The pressure at which they operate; vacuum pressure (< 10 mTorr), moderate pressure (~ 1 Torr), and atmospheric pressure (760 Torr).
  • The degree of ionization within the plasma; fully ionized, partially ionized, weakly ionized.
  • The temperature relationships within the plasma; Thermal plasma (Te = Tion = Tgas), Non-Thermal or "cold" plasma (Te >> Tion = Tgas)
  • The electrode configuration used to generate the plasma.
  • The magnetization of the particles within the plasma; Magnetized (both ion and electrons are trapped in Larmor orbits by the magnetic field), partially magnetized (the electrons but not the ions are trapped by the magnetic field), non-magnetized (the magnetic field is too weak to trap the particles in orbits but may generate Lorentz forces).
  • Its application

Examples of industrial/commercial plasma

Low-pressure discharges

Glow discharge plasmas: Non-thermal plasmas generated by the application of DC or low frequency RF (<100 kHz) electric field to the gap between two metal electrodes. Probably the most common plasma; this is the type of plasma generated within fluorescent light tubes.
Capacitively coupled plasma (CCP): Similar to glow discharge plasmas, but generated with high frequency RF electric fields, typically 13.56 MHz. It differs from Glow discharges in that the sheaths are much less intense. These are widely used in the microfabrication and integrated circuit manufacturing industries for plasma etching and plasma enhanced chemical vapor deposition.
Inductively Coupled Plasmas (ICP): Similar to a CCP and with similar applications but the electrode consists of a coil wrapped around the discharge volume which inductively excites the plasma.

Atmospheric pressure

Arc discharge: This is a high power thermal discharge of very high temperature ~10,000 K. It can be generated using various power supplies. It is commonly used in metallurgical processes. For example it is used to melt rocks containing Al2O3 to produce aluminum.
Corona discharge: This is a non-thermal discharge generated by the application of high voltage to sharp electrode tips. It is commonly used in ozone generators and particle precipitators.
Dielectric Barrier Discharge (DBD): Invented by SiemensTemplate:Fix/category[citation needed], this is a non-thermal discharge generated by the application of high voltages across small gaps wherein a non-conducting coating prevents the transition of the plasma discharge into an arc. It is often mislabeled 'Corona' discharge in industry and has similar application to Corona Discharges. It is also widely used in the web treatment of fabrics. The application of the discharge to synthetic fabrics and plastics functionalizes the surface and allows for paints, glues and similar materials to adhere.

Fields of active research

File:HallThruster 2.jpg
Hall effect thruster. The electric field in a plasma double layer is so effective at accelerating ions that electric fields are used in ion drives

This is just a partial list of topics. A more complete and organized list can be found on the Web site for Plasma science and technology.[23]

Footnotes

  1. Greg Morfill et al, Focus on Complex (Dusty) Plasmas (2003) New J. Phys. 5
  2. Crookes presented a lecture to the British Association for the Advancement of Science, in Sheffield, on Friday, 22 August 1879 [1] [2]
  3. Announced in his evening lecture to the Royal Institution on Friday, 30th April 1897, and published in Philosophical Magazine, 44, 293 [3]
  4. 4.0 4.1 I. Langmuir, "Oscillations in ionized gases," Proc. Nat. Acad. Sci. U.S., vol. 14, p. 628, 1928
  5. G. L. Rogoff, Ed., IEEE Transactions on Plasma Science, vol. 19, p. 989, Dec. 1991. See extract at http://www.plasmacoalition.org/what.htm
  6. It is often stated that more than 99% of the universe is plasma. See, for example, D. A. Gurnett, A. Bhattacharjee, Introduction to Plasma Physics: With Space and Laboratory Applications (2005) (Page 2) and also K Scherer, H Fichtner, B Heber, "Space Weather: The Physics Behind a Slogan" (2005) (Page 138). Essentially all of the visible light from space comes from stars, which are plasmas with a temperature such that they radiate strongly at visible wavelengths. Most of the ordinary (or baryonic) matter in the universe, however, is found in the intergalactic medium, which is also a plasma, but much hotter, so that it radiates primarily as x-rays. The current scientific consensus is that about 96% of the total energy density in the universe is not plasma or any other form of ordinary matter, but a combination of cold dark matter and dark energy.
  7. IPPEX Glossary of Fusion Terms
  8. Plasma fountain Source, press release: Solar Wind Squeezes Some of Earth's Atmosphere into Space
  9. After Peratt, A. L., "Advances in Numerical Modeling of Astrophysical and Space Plasmas" (1966) Astrophysics and Space Science, v. 242, Issue 1/2, p. 93-163.
  10. See The Nonneutral Plasma Group at the University of California, San Diego
  11. See Flashes in the Sky: Earth's Gamma-Ray Bursts Triggered by Lightning
  12. Richard Fitzpatrick, Introduction to Plasma Physics, Magnetized plasmas
  13. Hong, Alice (2000). "Dielectric Strength of Air". The Physics Factbook. 
  14. Dickel, J. R., "The Filaments in Supernova Remnants: Sheets, Strings, Ribbons, or?" (1990) Bulletin of the American Astronomical Society, Vol. 22, p.832
  15. Grydeland, T., et al, "Interferometric observations of filamentary structures associated with plasma instability in the auroral ionosphere" (2003) Geophysical Research Letters, Volume 30, Issue 6, pp. 71-1
  16. Moss, Gregory D., et al, "Monte Carlo model for analysis of thermal runaway electrons in streamer tips in transient luminous events and streamer zones of lightning leaders" (2006) Journal of Geophysical Research, Volume 111, Issue A2, CiteID A02307
  17. Doherty, Lowell R., "Filamentary Structure in Solar Prominences." (1965) Astrophysical Journal, vol. 141, p.251
  18. Hubble views the Crab Nebula M1: The Crab Nebula Filaments
  19. Zhang, Yan-An, et al, "A rope-shaped solar filament and a IIIb flare" (2002) Chinese Astronomy and Astrophysics, Volume 26, Issue 4, p. 442-450
  20. Hannes Alfvén, Cosmic Plasma (1981) See section VI.13.1. Cellular Structure of Space.
  21. R. G. Greaves, M. D. Tinkle, and C. M. Surko, "Creation and uses of positron plasmas", Physics of Plasmas -- May 1994 -- Volume 1, Issue 5, pp. 1439-1446
  22. See Evolution of the Solar System, 1976)
  23. Web site for Plasma science and technology

See also

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