Plasma properties and parameters

Artist's rendition of 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, where plasma energy pours back into the atmosphere.^[6]

Definition of a plasma

Although a plasma is loosely described as an electrically neutral medium of positive and negative particles, a definition can have three criteria:^[7][8]

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 are 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 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 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:

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
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 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 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 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., response to magnetic fields and high electrical conductivity). The degree of ionization, α is defined as α = n_i/(n_i + n_a) where n_i is the number density of ions and n_a is the number density of neutral atoms. The electron density is related to this by the average charge state of the ions through n_e = n_i where n_e 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 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.

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

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 and electron densities may exceed 10²⁴ m⁻³.

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 (n_e = 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":

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

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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, i.e., greater than the Debye length. But the existence of charged particles causes the plasma to generate and can 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

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, i.e., ω_ce/ν_coll > 1, where ω_ce is the "electron gyrofrequency" and ν_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]