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| In [[plasma physics]], '''waves in plasmas''' are an interconnected set of particles and fields which propagates in a periodically repeating fashion. A [[Plasma (physics)|plasma]] is a [[Plasma (physics)#Potentials|quasineutral]], [[electrical conductivity|electrically conductive]] [[fluid]]. In the simplest case, it is composed of [[electron]]s and a single species of positive [[ion]]s, but it may also contain multiple ion species including negative ions as well as neutral particles. Due to its [[electrical conductivity]], a plasma couples to [[electric field|electric]] and [[magnetic field]]s. This complex of particles and fields supports a wide variety of [[wave]] phenomena.
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| == Terminology and classification ==
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| Waves in plasmas can be classified as '''electromagnetic''' or '''electrostatic''' according to whether or not there is an oscillating magnetic field. Applying [[Faraday's law of induction]] to [[plane wave]]s, we find <math>\mathbf{k}\times\tilde{\mathbf{E}}=\omega\tilde{\mathbf{B}}</math>, implying that an electrostatic wave must be purely [[longitudinal wave|longitudinal]]. An electromagnetic wave, in contrast, must have a [[transverse wave|transverse]] component, but may also be partially longitudinal.
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| Waves can be further classified by the '''oscillating species'''. In most plasmas of interest, the [[electron temperature]] is comparable to or larger than the ion temperature. This fact, coupled with the much smaller mass of the electron, implies that the electrons move much faster than the ions. An '''electron mode''' depends on the mass of the electrons, but the ions may be assumed to be infinitely massive, i.e. stationary. An '''ion mode''' depends on the ion mass, but the electrons are assumed to be massless and to redistribute themselves instantaneously according to the [[Boltzmann relation]]. Only rarely, e.g. in the [[lower hybrid oscillation]], will a mode depend on both the electron and the ion mass.
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| The various modes can also be classified according to whether they propagate in an '''[[Plasma (physics)#Magnetization|unmagnetized]]''' plasma or '''parallel''', '''perpendicular''', or '''oblique''' to the stationary magnetic field. Finally, for perpendicular electromagnetic electron waves, the perturbed electric field can be parallel or perpendicular to the stationary magnetic field.
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| {| class="wikitable"
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| |+ Summary of elementary plasma waves
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| |-
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| ! EM character !! oscillating species !! conditions !! [[dispersion relation]] !! name
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| | rowspan = 5 | electrostatic || rowspan = 2 | electrons || <math>\vec B_0=0\ {\rm or}\ \vec k\|\vec B_0</math> || <math>\omega^2=\omega_p^2+3k^2v_{th}^2</math> || [[plasma oscillation]] (or Langmuir wave)
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| | <math>\vec k\perp\vec B_0</math> || <math>\omega^2=\omega_p^2+\omega_c^2=\omega_h^2</math> || [[upper hybrid oscillation]]
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| | rowspan = 3 | ions || <math>\vec B_0=0\ {\rm or}\ \vec k\|\vec B_0</math> || <math>\omega^2=k^2v_s^2=k^2\frac{\gamma_eKT_e+\gamma_iKT_i}{M}</math> || [[ion acoustic wave]]
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| | <math>\vec k\perp\vec B_0</math> (nearly)|| <math>\omega^2=\Omega_c^2+k^2v_s^2</math> || [[electrostatic ion cyclotron wave]]
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| | <math>\vec k\perp\vec B_0</math> (exactly)|| <math>\omega^2=[(\Omega_c\omega_c)^{-1}+\omega_i^{-2}]^{-1}</math> || [[lower hybrid oscillation]]
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| | rowspan = 8 | electromagnetic || rowspan = 5 | electrons || <math>\vec B_0=0</math> || <math>\omega^2=\omega_p^2+k^2c^2</math> || [[light]] wave
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| | <math>\vec k\perp\vec B_0,\ \vec E_1\|\vec B_0</math> || <math>\frac{c^2k^2}{\omega^2}=1-\frac{\omega_p^2}{\omega^2}</math> || [[Electromagnetic electron wave#O wave|O wave]]
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| | <math>\vec k\perp\vec B_0,\ \vec E_1\perp\vec B_0</math> || <math>\frac{c^2k^2}{\omega^2}=1-\frac{\omega_p^2}{\omega^2}\,
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| \frac{\omega^2-\omega_p^2}{\omega^2-\omega_h^2}</math> || [[Electromagnetic electron wave#X wave|X wave]]
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| | <math>\vec k\|\vec B_0</math> ([[Polarization (waves)|right circ. pol.]])|| <math>\frac{c^2k^2}{\omega^2}=1-\frac{\omega_p^2/\omega^2}{1-(\omega_c/\omega)}</math> || [[Electromagnetic electron wave#R wave and L wave|R wave]] (whistler mode)
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| | <math>\vec k\|\vec B_0</math> ([[Polarization (waves)|left circ. pol.]])|| <math>\frac{c^2k^2}{\omega^2}=1-\frac{\omega_p^2/\omega^2}{1+(\omega_c/\omega)}</math> || [[Electromagnetic electron wave#R wave and L wave|L wave]]
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| | rowspan = 3 | ions || <math>\vec B_0=0</math> || || none
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| | <math>\vec k\|\vec B_0</math> || <math>\omega^2=k^2v_A^2</math> || [[Alfvén wave]]
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| | <math>\vec k\perp\vec B_0</math> || <math>\frac{\omega^2}{k^2}=c^2\,
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| \frac{v_s^2+v_A^2}{c^2+v_A^2}</math> || [[magnetosonic wave]]
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| |}
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| <math>\omega</math> - [[Frequency#Frequency_of_waves|wave frequency]],
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| <math>k</math> - [[wave number]],
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| <math>c</math> - [[speed of light]],
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| <math>\omega_p</math> - [[plasma frequency]], | |
| <math>\omega_i</math> - ion [[plasma frequency]],
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| <math>\omega_c</math> - [[Plasma parameters|electron gyrofrequency]],
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| <math>\Omega_c</math> - [[Plasma parameters|proton gyrofrequency]],
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| <math>\omega_h</math> - [[Upper hybrid oscillation|upper hybrid frequency]],
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| <math>v_s</math> - [[Speed_of_sound#Speed_in_plasma|plasma "sound" speed]],
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| <math>v_A</math> - [[Alfvén_velocity#Alfv.C3.A9n_velocity|plasma Alfvén speed]]
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| ==References==
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| *Swanson, D.G. ''Plasma Waves'' (2003). 2nd edition.
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| *[[Thomas H. Stix|Stix, Thomas Howard]]. ''Waves in Plasmas'' (1992).
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| ==See also==
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| * [[Magnetohydrodynamics#MHD waves|Magnetohydrodynamic waves]]
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| * [[Appleton-Hartree equation]]
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| * [[plasmon]]
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| * [[Surface plasmon resonance]]
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| * [[index of wave articles]]
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| * [[List of plasma (physics) applications articles]]
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| [[Category:Waves in plasmas| ]]
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