Plasma (physics)

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).

Plasma ball Ph: Luc Viatour

In physics and chemistry, plasma (also called an ionized gas) is an energetic gas-phase state of matter, often referred to as "the fourth state of matter", in which some or all of the electrons in the outer atomic orbitals have become separated from the atom or molecule. The result is a collection of ions and electrons which are no longer bound to each other. Because these particles are ionized (charged), the gas behaves in a different fashion than neutral gas in, for instance, the presence of electromagnetic fields. This state of matter was first identified by Sir William Crookes in 1879, and dubbed "plasma" by Irving Langmuir in 1928.

A common fluid treatment of plasmas comes from a combination of the Navier Stokes Equations of fluid dynamics and Maxwell's equations of electromagnetism. The resulting set of equations, with appropriate approximations, is called Magnetohydrodynamics (or MHD for short).

Plasma physics is important in astrophysics in that many astronomical objects including stars, accretion disks, nebula, and the interstellar medium consist of plasma. It is also important in hypersonic aerodynamics, since at hypersonic speeds the interaction of the shock wave and the boundary layer creates enough heat to ionize the air surrounding a body. This happens, for example, upon re-entry of the Space Shuttle into Earth's atmosphere. Plasma physics is used in work studying nuclear fusion since most known fusion reactions take place in plasma.

File: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.

Characteristics

Plasma is often called the fourth state of matter. It is distinct from the three lower-energy phases of matter; solid, liquid, and gas. Plasmas are the most common form of matter, comprising more than 99% of the known visible universe. Commonly encountered forms of plasma include Fire, the Sun and other stars (which are plasmas heated by nuclear fusion), lit fluorescent lamps, lightning, the Aurora borealis, the solar wind, and interstellar nebulae. A plasma is also generated in front of a spacecraft's heat shield on reentering the atmosphere. There is still some debate as to whether plasma is an individual state of matter or simply a type of gas, but most physicists have accepted plasma as a state of matter.

In astrophysical plasmas, Debye screening prevents electric fields from affecting the plasma very much, 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. The dynamics of plasmas interacting with external and self-generated magnetic fields are studied in the academic discipline of magnetohydrodynamics.

The term plasma is generally reserved for a system of charged particles large enough to behave collectively, excluding microscopically small collections of charged particles. 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.

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 $\langle Z\rangle$ of the ions through $n_{e}=\langle Z\rangle n_{i}$. (See quasineutrality below.) The third important quantity is the density of neutrals $n_{0}$. In a hot plasma this is small, but may still determine important physics. The degree of ionization is $n_{i}/(n_{0}+n_{i})$.

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. 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 ($n_{e}=\langle Z\rangle n_{i}$), 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, $n_{e}\propto e^{e\Phi /k_{B}T_{e}}$. Differentiating this relation provides a means to calculate the electric field from the density: ${\vec {E}}=(k_{B}T_{e}/e)(\nabla n_{e}/n_{e})$.

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 $\mu =m_{i}/m_{p}$; 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:

$\omega _{ce}=eB/m_{e}c=1.76\times 10^{7}B{\mbox{rad/s}}$

• ion gyrofrequency, the angular frequency of the circular motion of an ion in the plane perpendicular to the magnetic field:

$\omega _{ci}=eB/m_{i}c=9.58\times 10^{3}Z\mu ^{-1}B{\mbox{rad/s}}$

• electron plasma frequency, the frequency with which electrons oscillate when their charge density is not equal to the ion charge density (plasma oscillation):

$\omega _{pe}=(4\pi n_{e}e^{2}/m_{e})^{1/2}=5.64\times 10^{4}n_{e}^{1/2}{\mbox{rad/s}}$

• ion plasma frequency:

$\omega _{pe}=(4\pi n_{i}Z^{2}e^{2}/m_{i})^{1/2}=1.32\times 10^{3}Z\mu ^{-1/2}n_{i}^{1/2}{\mbox{rad/s}}$

• electron trapping rate

$\nu _{Te}=(eKE/m_{e})^{1/2}=7.26\times 10^{8}K^{1/2}E^{1/2}{\mbox{s}}^{-1}$

• ion trapping rate

$\nu _{Ti}=(ZeKE/m_{i})^{1/2}=1.69\times 10^{7}Z^{1/2}K^{1/2}E^{1/2}\mu ^{-1/2}{\mbox{s}}^{-1}$

• electron collision rate

$\nu _{e}=2.91\times 10^{-6}n_{e}\,\ln \Lambda \,T_{e}^{-3/2}{\mbox{s}}^{-1}$

• ion collision rate

$\nu _{i}=4.80\times 10^{-8}Z^{4}\mu ^{-1/2}n_{i}\,\ln \Lambda \,T_{i}^{-3/2}{\mbox{s}}^{-1}$

Lengths

• electron deBroglie length, the minimum extension of an electron due to quantum mechanics:

$\lambda \!\!\!\!-=\hbar /(m_{e}kT_{e})^{1/2}=2.76\times 10^{-8}\,T_{e}^{-1/2}\,{\mbox{cm}}$

• 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:

$e^{2}/kT=1.44\times 10^{-7}\,T^{-1}\,{\mbox{cm}}$

• electron gyroradius, the radius of the circular motion of an electron in the plane perpendicular to the magnetic field:

$r_{e}=v_{Te}/\omega _{ce}=2.38\,T_{e}^{1/2}B^{-1}\,{\mbox{cm}}$

• ion gyroradius, the radius of the circular motion of an ion in the plane perpendicular to the magnetic field:

$r_{i}=v_{Ti}/\omega _{ci}=1.02\times 10^{2}\,\mu ^{1/2}Z^{-1}T_{i}^{1/2}B^{-1}\,{\mbox{cm}}$

• plasma skin depth, the depth in a plasma to which electromagnetic radiation can penetrate:

$c/\omega _{pe}=5.31\times 10^{5}\,n_{e}^{-1/2}\,{\mbox{cm}}$

• Debye length, the scale over which electric fields are screened out by a redistribution of the electrons:

$\lambda _{D}=(kT/4\pi ne^{2})^{1/2}=7.43\times 10^{2}\,T^{1/2}n^{-1/2}\,{\mbox{cm}}$

Velocities

• electron thermal velocity, typical velocity of an electron in a Maxwell-Boltzmann distribution:

$v_{Te}=(kT_{e}/m_{e})^{1/2}=4.19\times 10^{7}\,T_{e}^{1/2}\,{\mbox{cm/s}}$

• ion thermal velocity, typical velocity of an ion in a Maxwell-Boltzmann distribution:

$v_{Ti}=(kT_{i}/m_{i})^{1/2}=9.79\times 10^{5}\,\mu ^{-1/2}T_{i}^{1/2}\,{\mbox{cm/s}}$

• ion sound velocity, the speed of the longitudinal waves resulting from the mass of the ions and the pressure of the electrons:

$c_{s}=(\gamma ZkT_{e}/m_{i})^{1/2}=9.79\times 10^{5}\,(\gamma ZT_{e}/\mu )^{1/2}\,{\mbox{cm/s}}$

• Alfven velocity, the speed of the waves resulting from the mass of the ions and the restoring force of the magnetic field:

$v_{A}=B/(4\pi n_{i}m_{i})^{1/2}=2.18\times 10^{11}\,\mu ^{-1/2}n_{i}^{-1/2}B\,{\mbox{cm/s}}$

Dimensionless

• square root of electron/proton mass ratio

$(m_{e}/m_{p})^{1/2}=2.33\times 10^{-2}=1/42.9$

• number of particles in a Debye sphere

$(4\pi /3)n\lambda _{D}^{3}=1.72\times 10^{9}\,T^{3/2}n^{-1/2}$

• Alven velocity/speed of light

$v_{A}/c=7.28\,\mu ^{-1/2}n_{i}^{-1/2}B$

• electron plasma/gyrofrequency ratio

$\omega _{pe}/\omega _{ce}=3.21\times 10^{-3}\,n_{e}^{1/2}B^{-1}$

• ion plasma/gyrofrequency ratio

$\omega _{pi}/\omega _{ci}=0.137\,\mu ^{1/2}n_{i}^{1/2}B^{-1}$

• thermal/magnetic energy ratio

$\beta =8\pi nkT/B^{2}=4.03\times 10^{-11}\,nTB^{-2}$

• magnetic/ion rest energy ratio

$B^{2}/8\pi n_{i}m_{i}c^{2}=26.5\,\mu ^{-1}n_{i}^{-1}B^{2}$

Miscellaneous

• Bohm diffusion coefficient

$D_{B}=(ckT/16eB)=6.25\times 10^{6}\,TB^{-1}\,{\mbox{cm}}^{2}/{\mbox{s}}$

• transverse Spitzer resistivity

$\eta _{\perp }=1.15\times 10^{-14}\,Z\,\ln \Lambda \,T^{-3/2}\,{\mbox{s}}=1.03\times 10^{-2}\,Z\,\ln \Lambda \,T^{-3/2}\,\Omega \,{\mbox{cm}}$

Fields of active research

• Plasma theory
  • Plasma equilibria and stability
  • Plasma interactions with waves and beams
  • guiding center
  • adiabatic invariant
  • Debye sheath
  • Coulomb collision
• Plasmas in nature
  • Space plasmas, e.g. Earth's plasmasphere (an inner portion of the magnetosphere dense with plasma)
  • plasma cosmology
• Plasma sources
• Plasma diagnostics
  • Thomson scattering
  • Langmuir probe
  • Spectroscopy
  • Interferometry
• Plasma applications
  • Fusion power
    • Magnetic fusion energy (MFE) -- tokamak, stellarator, reversed field pinch, magnetic mirror
    • Inertial fusion energy (IFE) (also Inertial confinement fusion - ICF)
  • Industrial plasmas
    • plasma chemistry
    • plasma processing
    • plasma display

See also

• List of plasma physicists
• Important publications in plasma physics
• Magnetohydrodynamic generator

External links

• Plasmas: the Fourth State of Matter
• Plasma Science and Technology
• Plasma on the Internet comprehensive list of plasma related links.
• Introduction to Plasma Physics: a graduate level lecture course given by Richard Fitzpatrick
• An overview of plasma links and applications
• NRL Plasma Formulary online (or an html version)
• Plasma Coalition page
• Plasma Material Interaction