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Plasma physics

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This article is about plasma in the sense of an ionized gas. For other uses of the term, such as blood plasma, see plasma (disambiguation).

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Plasma-lamp.jpg
Plasma ball Ph: Luc Viatour

In physics and chemistry, a plasma is an ionized gas, and is usually considered to be a distinct phase of matter. "Ionized" means that at least one electron has been removed from a significant fraction of the molecules. The free charges make the plasma electrically conductive so that it couples strongly to electromagnetic fields. This fourth state of matter was first identified by Sir William Crookes in 1879 and dubbed "plasma" by Irving Langmuir in 1928.

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Large_helical_device_shot.gif
View of a "shot" on the Large Helical Device though a side port showing hot plasma affected by magnetic fields.
Contents

Common plasmas

Plasmas are the most common phase of matter, comprising more than 99% of the visible universe. Commonly encountered forms of plasma include:

Characteristics

The term plasma is generally reserved for a system of charged particles large enough to behave collectively. Even a partially ionized gas in which as little as 1% of the particles are ionized, can behave as a plasma and have the characteristics of a plasma (ie. respond to magnetic fields, and be highly electrically conductive).

In technical terms, the typical characteristics of a plasma are:

  1. Debye screening lengths that are short compared to the physical size of the plasma.
  2. Large number of particles within a sphere with a radius of the Debye length.
  3. Mean time between collisions usually is long when compared to the period of plasma oscillations.

Plasma scaling

Plasmas and their characteristics exist over a wide range of scales (ie. they are scaleable over many orders of magnitude):

Typical Plasma Scaling Ranges: Orders of Magnitude (OOM)
CharacteristicTerrestrial PlasmasCosmic Plasmas
Size
in metres (m)
10-6m (lab plasmas) to:
102m (lightning) (~8 OOM)
10-6m (spacecraft sheath) to
1025m (intergalactic nebula) (~31 OOM)
Lifetime
in seconds (s)
10-12s (laser-produced plasma) to:
107s (flurescent lights) (~19 OOM)
101s (solar flares) to:
1017s (intergalactic plasma) (~17 OOM)
Density
particles per
cubic metre
107 to:
1021 (inertial confinement plasma)
1030 (stellar core) to:
100(ie: 1) (intergalactic medium)
Temperature
Kelvin (K)
~0K (Crystalline non-neutral plasma) to:
108 (magnetic fusion plasma)
102K (aurora) to:
107K (Solar core)
Magnetic fields
Tesla (T)
10-4T (Lab plasma) to:
103T (pulsed-power plasma)
10-12T (intergalactic medium) to:
107T (Solar core)

Temperatures

The defining characteristic of a plasma is ionization. Although ionization can be caused by UV radiation, energetic particles, or strong electric fields, processes that tend to result in a non-Maxwellian electron distribution function, it is most commonly caused by heating the electrons in such a way that they are close to thermal equilibrium so the electron temperature is relatively well-defined. Because the large mass of the ions relative to the electrons hinders energy transfer, it is possible for the ion temperature to be very different (usually lower).

The degree of ionization is determined by the electron temperature relative to the ionization energy (and more weakly by the density) in accordance with the Saha equation. If only a small fraction of the gas molecules are ionized (for example 1%), then the plasma is said to be a cold plasma, even though the electron temperature is typically several thousand degrees. The ion temperature in a cold plasma is ofter near the ambient temperature. Because the plasmas utilized in plasma technology are typically cold, they are sometimes called technological plasmas. They are often created by using a very high electric field to accelerate electrons, which then ionize the atoms. The electric field is either capacitively or inductively coupled into the gas by means of a plasma source, e.g. microwaves. Common applications of cold plasmas include plasma-enhanced chemical vapor deposition, plasma ion doping, and reactive ion etching.

A hot plasma, on the other hand, is nearly fully ionized. This is what would commonly be known as the "fourth-state of matter". The Sun is an example of a hot plasma. The electrons and ions are more likely to have equal temperatures in a hot plasma, but there can still be significant differences.

Densities

Next to the temperature, which is of fundamental importance for the very existence of a plasma, the most important property is the density. The word "plasma density" by itself usually refers to the electron density, that is, the number of free electrons per unit volume. The ion 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>. (See quasineutrality below.) The third important quantity is the density of neutrals <math>n_0<math>. In a hot plasma this is small, but may still determine important physics. The degree of ionization is <math>n_i/(n_0+n_i)<math>.

Potentials

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 the development of a Debye sheath. Due to the good electrical conductivity, the electric fields in plasmas tend to be very small, although where double layers are formed, the potential drop can be large enough to accelerate ions to relativistic velocities and produce synchrotron radiation such as x-rays and gamma rays. This results in the important concept of quasineutrality, which says that, on the one hand, it is a very good approximation to assume that the density of negative charges is equal to the density of positive charges (<math>n_e=\langle Z\rangle n_i<math>), but that, on the other hand, electric fields can be assumed to exist as needed for the physics at hand.

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, of course, 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 (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 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.

In contrast to the gas phase

Plasma is often called the fourth state of matter. It is distinct from the three lower-energy phases of matter; solid, liquid, and gas, although it is closely related to the gas phase in that it also has no definite form or volume. There is still some disagreement as to whether a plasma is a distinct state of matter or simply a type of gas. Most physicists consider a plasma to be more than a gas because of a number of distinct properties including the following:

Property Gas Plasma
Electrical Conductivity Very low
 
Very high

  1. For many purposes the electric field in a plasma may be treated as zero, although when current flows the voltage drop, though small, is finite, and density gradients are usually associated with an electric field according to the Boltzmann relation.
  2. The possibility of currents couples the plasma strongly to magnetic fields, which are responsible for a large variety of structures such as filaments, sheets, and jets.
  3. Collective phenomena are common because the electric and magnetic forces are both long-range and potentially many orders of magnitude stronger than gravitational forces.

Independently acting species One Two or three
Electrons, ions, and neutrals can be distinguished by the sign of their charge so that they behave independently in many circumstances, having different velocities or even different temperatures, leading to new types of waves and instabilities, among other things
Velocity distribution Maxwellian May be non-Maxwellian
Whereas collisional interactions always lead to a Maxwellian velocity distribution, electric fields influence the particle velocities differently. The velocity dependence of the Coulomb collision cross section can amplify these differences, resulting in phenomena like two-temperature distributions and run-away electrons.
Interactions Binary
Two-particle collisions are the rule, three-body collisions extremely rare.
Collective
Each particle interacts simultaneously with many others. These collective interactions are about ten times more important than binary collisions.

Mathematical descriptions

Plasmas may be usefully described with various levels of detail. However the plasma itself is described, if electric or magnetic fields are present, then Maxwell's equations will be needed to describe them. The coupling of the description of a conductive fluid to electromagnetic fields is known generally as magnetohydrodynamics, or simply MHD.

Fluid

The simplest possibility is to treat the plasma as a single fluid governed by the Navier Stokes Equations. A more general description is the two-fluid picture, where the ions and electrons are considered to be distinct.

Kinetic

For some cases the fluid description is not sufficient. Kinetic models include information on distortions of the velocity distribution functions with respect to a Maxwell-Boltzmann distribution. This may be important when currents flow, when waves are involved, or when gradients are very steep.

Particle-In-Cell

Particle-In-Cell models include kinetic information by following the trajectories of a large number of individual particles. Charge and current densities are determined by summing the particles in cells which are small compared to the problem at hand but still contain many particles. The electric and magnetic fields are found from the charge and current densities with appropriate boundary conditions.

Fundamental plasma parameters

All quantities are in Gaussian cgs units except temperature expressed in eV and ion mass expressed in units of the proton mass <math>\mu = m_i/m_p<math>; Z is charge state; k is Boltzmann's constant; K is wavelength; γ is the adiabatic index; ln Λ is the Coulomb logarithm.

Frequencies

  • electron gyrofrequency, the angular frequency of the circular motion of an electron in the plane perpendicular to the magnetic field:
<math>\omega_{ce} = eB/m_ec = 1.76 \times 10^7 B \mbox{rad/s}<math>
  • ion gyrofrequency, the angular frequency of the circular motion of an ion in the plane perpendicular to the magnetic field:
<math>\omega_{ci} = eB/m_ic = 9.58 \times 10^3 Z \mu^{-1} B \mbox{rad/s}<math>
  • electron plasma frequency, the frequency with which electrons oscillate when their charge density is not equal to the ion charge density (plasma oscillation):
<math>\omega_{pe} = (4\pi n_ee^2/m_e)^{1/2} = 5.64 \times 10^4 n_e^{1/2} \mbox{rad/s}<math>
  • ion plasma frequency:
<math>\omega_{pe} = (4\pi n_iZ^2e^2/m_i)^{1/2} = 1.32 \times 10^3 Z \mu^{-1/2} n_i^{1/2} \mbox{rad/s}<math>
  • electron trapping rate
<math>\nu_{Te} = (eKE/m_e)^{1/2} = 7.26 \times 10^8 K^{1/2} E^{1/2} \mbox{s}^{-1}<math>
  • ion trapping rate
<math>\nu_{Ti} = (ZeKE/m_i)^{1/2} = 1.69 \times 10^7 Z^{1/2} K^{1/2} E^{1/2} \mu^{-1/2} \mbox{s}^{-1}<math>
  • electron collision rate
<math>\nu_e = 2.91 \times 10^{-6} n_e\,\ln\Lambda\,T_e^{-3/2} \mbox{s}^{-1}<math>
  • ion collision rate
<math>\nu_i = 4.80 \times 10^{-8} Z^4 \mu^{-1/2} n_i\,\ln\Lambda\,T_i^{-3/2} \mbox{s}^{-1}<math>

Lengths

  • electron deBroglie length, the minimum extension of an electron due to quantum mechanics:
<math>\lambda\!\!\!\!- = \hbar/(m_ekT_e)^{1/2} = 2.76\times10^{-8}\,T_e^{-1/2}\,\mbox{cm}<math>
  • classical distance of closest approach, the closest that two particles with the elementary charge come to each other if they approach head-on and each have a velocity typical of the temperature, ignoring quantum-mechanical effects:
<math>e^2/kT=1.44\times10^{-7}\,T^{-1}\,\mbox{cm}<math>
  • electron gyroradius, the radius of the circular motion of an electron in the plane perpendicular to the magnetic field:
<math>r_e = v_{Te}/\omega_{ce} = 2.38\,T_e^{1/2}B^{-1}\,\mbox{cm}<math>
  • ion gyroradius, the radius of the circular motion of an ion in the plane perpendicular to the magnetic field:
<math>r_i = v_{Ti}/\omega_{ci} = 1.02\times10^2\,\mu^{1/2}Z^{-1}T_i^{1/2}B^{-1}\,\mbox{cm}<math>
  • plasma skin depth, the depth in a plasma to which electromagnetic radiation can penetrate:
<math>c/\omega_{pe} = 5.31\times10^5\,n_e^{-1/2}\,\mbox{cm}<math>
  • Debye length, the scale over which electric fields are screened out by a redistribution of the electrons:
<math>\lambda_D = (kT/4\pi ne^2)^{1/2} = 7.43\times10^2\,T^{1/2}n^{-1/2}\,\mbox{cm}<math>

Velocities

<math>v_{Te} = (kT_e/m_e)^{1/2} = 4.19\times10^7\,T_e^{1/2}\,\mbox{cm/s}<math>
<math>v_{Ti} = (kT_i/m_i)^{1/2} = 9.79\times10^5\,\mu^{-1/2}T_i^{1/2}\,\mbox{cm/s}<math>
  • ion sound velocity, the speed of the longitudinal waves resulting from the mass of the ions and the pressure of the electrons:
<math>c_s = (\gamma ZkT_e/m_i)^{1/2} = 9.79\times10^5\,(\gamma ZT_e/\mu)^{1/2}\,\mbox{cm/s}<math>
  • Alfven velocity, the speed of the waves resulting from the mass of the ions and the restoring force of the magnetic field:
<math>v_A = B/(4\pi n_im_i)^{1/2} = 2.18\times10^{11}\,\mu^{-1/2}n_i^{-1/2}B\,\mbox{cm/s}<math>

Dimensionless

  • square root of electron/proton mass ratio
<math>(m_e/m_p)^{1/2} = 2.33\times10^{-2} = 1/42.9<math>
  • number of particles in a Debye sphere
<math>(4\pi/3)n\lambda_D^3 = 1.72\times10^9\,T^{3/2}n^{-1/2}<math>
  • Alven velocity/speed of light
<math>v_A/c = 7.28\,\mu^{-1/2}n_i^{-1/2}B<math>
  • electron plasma/gyrofrequency ratio
<math>\omega_{pe}/\omega_{ce} = 3.21\times10^{-3}\,n_e^{1/2}B^{-1}<math>
  • ion plasma/gyrofrequency ratio
<math>\omega_{pi}/\omega_{ci} = 0.137\,\mu^{1/2}n_i^{1/2}B^{-1}<math>
  • thermal/magnetic energy ratio
<math>\beta = 8\pi nkT/B^2 = 4.03\times10^{-11}\,nTB^{-2}<math>
  • magnetic/ion rest energy ratio
<math>B^2/8\pi n_im_ic^2 = 26.5\,\mu^{-1}n_i^{-1}B^2<math>

Miscellaneous

  • Bohm diffusion coefficient
<math>D_B = (ckT/16eB) = 6.25\times10^6\,TB^{-1}\,\mbox{cm}^2/\mbox{s}<math>
  • transverse Spitzer resistivity
<math>\eta_\perp = 1.15\times10^{-14}\,Z\,\ln\Lambda\,T^{-3/2}\,\mbox{s} = 1.03\times10^{-2}\,Z\,\ln\Lambda\,T^{-3/2}\,\Omega\,\mbox{cm}<math>

Fields of active research

See also

External links

bg:Плазма ca:Plasma da:Plasma de:Plasmaphysik el:Φυσική Πλάσματος es:Plasma (estado de la materia) fr:Physique des plasmas ia:Plasma id:Fisika plasma it:Plasma (fisica) nl:Plasmafysica no:Plasma ja:プラズマ pl:Plazma pt:Plasma ru:Физика плазмы sr:Плазма fi:Plasma sv:Plasma zh:等离子物理学

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