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Properties and parameters::Plasma (physics)

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Properties and parameters

Artist's rendition of the Earth's plasma fountain, showing oxygen, helium, and hydrogen ions that 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, where plasma energy pours back into the atmosphere.<ref>Plasma fountain Source, press release: Solar Wind Squeezes Some of Earth's Atmosphere into Space</ref>

Definition

Plasma is loosely described as an electrically neutral medium of unbound positive and negative particles (i.e. the overall charge of a plasma is roughly zero). It is important to note that although they are unbound, these particles are not ‘free’ in the sense of not experiencing forces. When the charges move, they generate electric currents with magnetic fields, and as a result, they are affected by each other’s fields. This governs their collective behavior with many degrees of freedom.<ref name="Sturrock">{{#invoke:citation/CS1|citation |CitationClass=book }}</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=book }} </ref> A definition can have three criteria:{{ safesubst:#invoke:Unsubst||$N=Clarify |date=__DATE__ |$B= }}<ref name="Hazeltine">{{#invoke:citation/CS1|citation |CitationClass=book }}</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=book }}</ref>

  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 charge carriers within the sphere of influence (called the Debye sphere whose radius is the Debye screening length) of a particular particle is higher than unity to provide collective behavior of the charged particles. The average number of particles in the Debye sphere is given by the plasma parameter, "Λ" (the Greek uppercase 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. When this criterion is satisfied, the plasma is quasineutral.
  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, electrostatic interactions dominate over the processes of ordinary gas kinetics.

Ranges of 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:

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Typical ranges of plasma parameters: orders of magnitude (OOM)
Characteristic Terrestrial plasmas Cosmic plasmas
Size
in meters
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) (~16 OOM)
Density
in particles per
cubic meter
107 m−3 to
1032 m−3 (inertial confinement plasma)
1 m−3 (intergalactic medium) to
1030 m−3 (stellar core)
Temperature
in Kelvin
~0 K (crystalline non-neutral plasma<ref>See The Nonneutral Plasma Group at the University of California, San Diego</ref>) 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 term "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 that 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., response to magnetic fields and high electrical conductivity). The degree of ionization, <math>\alpha</math>, is defined as <math>\alpha = \frac{n_i}{n_i + n_n}</math>, where <math>n_i</math> is the number density of ions and <math>n_n</math> is the number density of neutral atoms. The electron density is related to this by the average charge state <math>\langle Z\rangle</math> of the ions through <math>n_e = \langle Z\rangle n_i</math>, where <math>n_e</math> is the number density of electrons.

Temperatures

Plasma temperature is commonly measured in kelvins or electronvolts and is, informally, a measure of the thermal kinetic energy per particle. Very high temperatures are usually needed to sustain ionization, which is a defining feature of a plasma. The degree of 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. At low temperatures, ions and electrons tend to recombine into bound states—atoms<ref name="Nicholson">{{#invoke:citation/CS1|citation |CitationClass=book }}</ref>—and the plasma will eventually become a gas.

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 amongst 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.

Thermal vs. nonthermal plasmas

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. Nonthermal plasmas on the other hand have the ions and neutrals at a much lower temperature (sometimes room temperature), whereas electrons are much "hotter" (<math>T_e \gg T_n</math>).

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 plasmas in the sense that only a small fraction of the gas molecules are ionized.

Plasma potential

convert}} and electron densities may exceed 1024 m−3.

Since plasmas are very good electrical 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 makes their electric fields 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 (<math>n_e = \langle Z\rangle n_i</math>), 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:

<math>n_e \propto e^{e\Phi/k_BT_e}.</math>

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

<math>\vec{E} = (k_BT_e/e)(\nabla n_e/n_e).</math>

It is possible to produce a plasma that 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, i.e., greater than the Debye length. However, 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 that 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

Plasma with a magnetic field 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, i.e., <math>\omega_{\mathrm{ce}} / v_{\mathrm{coll}} > 1</math>, where <math>\omega_{\mathrm{ce}}</math> is the "electron gyrofrequency" and <math>v_{\mathrm{coll}}</math> 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 <math>\mathbf{E} = -v\times\mathbf{B}</math> (where <math>\mathbf{E}</math> is the electric field, <math>\mathbf{v}</math> is the velocity, and <math>\mathbf{B}</math> is the magnetic field), and is not affected by Debye shielding.<ref>Richard Fitzpatrick, Introduction to Plasma Physics, Magnetized plasmas</ref>

Comparison of plasma and gas phases

Plasma is often called the fourth state of matter after solid, liquids and gases.<ref>Yaffa Eliezer, Shalom Eliezer, The Fourth State of Matter: An Introduction to the Physics of Plasma, Publisher: Adam Hilger, 1989, ISBN 978-0-85274-164-1, 226 pages, page 5</ref><ref>{{#invoke:citation/CS1|citation |CitationClass=book }}</ref> It is distinct from these and other lower-energy states of matter. Although it is closely related to the gas phase in that it also has no definite form or volume, it differs in a number of ways, including the following:

Property Gas Plasma
Electrical conductivity citation CitationClass=web

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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 by collisions with one another. Two or three: Electrons, ions, protons and neutrons can be distinguished by the sign and value 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 organized motion of plasma, are very important because the particles can interact at long ranges through the electric and magnetic forces.

Plasma (physics) sections
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