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32-483: X-mode may refer to: The extraordinary mode , an electromagnetic wave mode for propagation in a cold magnetoplasma X-Mode , a US data broker specialized in location data X-MODE, an AWD-system from Subaru, used in the Toyota bZ4X . See also [ edit ] Mode X , an alternative video graphics display mode of IBM VGA graphics hardware Topics referred to by

64-399: A 2 = ω p a 2 + ω c a 2 {\displaystyle \omega _{a}^{2}=\omega _{pa}^{2}+\omega _{ca}^{2}} and a = e , i {\displaystyle a=e,i} . The R wave and the L wave are right-hand and left-hand circularly polarized, respectively. The R wave has a cut-off at ω R (hence

96-401: A wave vector (or wavevector ) is a vector used in describing a wave , with a typical unit being cycle per metre. It has a magnitude and direction . Its magnitude is the wavenumber of the wave (inversely proportional to the wavelength ), and its direction is perpendicular to the wavefront. In isotropic media, this is also the direction of wave propagation . A closely related vector is

128-1452: Is plane polarized with E 1 || B 0 . It has a cut-off at the plasma frequency . The X wave is the "extraordinary" wave because it has a more complicated dispersion relation: n 2 = [ ( ω + ω c i ) ( ω − ω c e ) − ω p 2 ] [ ( ω − ω c i ) ( ω + ω c e ) − ω p 2 ] ( ω 2 − ω c i 2 ) ( ω 2 − ω c e 2 ) + ω p 2 ( ω c e ω c i − ω 2 ) {\displaystyle n^{2}={\frac {[(\omega +\omega _{ci})(\omega -\omega _{ce})-\omega _{p}^{2}][(\omega -\omega _{ci})(\omega +\omega _{ce})-\omega _{p}^{2}]}{(\omega ^{2}-\omega _{ci}^{2})(\omega ^{2}-\omega _{ce}^{2})+\omega _{p}^{2}(\omega _{ce}\omega _{ci}-\omega ^{2})}}} Where ω p 2 = ω p e 2 + ω p i 2 {\displaystyle \omega _{p}^{2}=\omega _{pe}^{2}+\omega _{pi}^{2}} . It

160-527: Is a purely longitudinal wave, that is, the wave vector is in the same direction as the E-field. It is an electrostatic wave; as such, it doesn't have an oscillating magnetic field. A plasma consists of charged particles which react to electric fields, in contrast with dielectric matter. When electrons in a uniform, homogeneous plasma are perturbed from their equilibrium position, a charge separation occurs creating an electric field which acts as restoring force on

192-459: Is a vector that characterizes the wave, the four-wavevector. The four-wavevector is a wave four-vector that is defined, in Minkowski coordinates , as: where the angular frequency ω c {\displaystyle {\tfrac {\omega }{c}}} is the temporal component, and the wavenumber vector k → {\displaystyle {\vec {k}}}

224-458: Is also the direction of the Poynting vector . On the other hand, the wave vector points in the direction of phase velocity . In other words, the wave vector points in the normal direction to the surfaces of constant phase , also called wavefronts . In a lossless isotropic medium such as air, any gas, any liquid, amorphous solids (such as glass ), and cubic crystals , the direction of

256-417: Is different from Wikidata All article disambiguation pages All disambiguation pages Electromagnetic electron wave In an unmagnetized plasma, an electromagnetic electron wave is simply a light wave modified by the plasma. In a magnetized plasma, there are two modes perpendicular to the field, the O and X modes, and two modes parallel to the field, the R and L waves. The Langmuir wave

288-483: Is partly transverse (with E 1 ⊥ B 0 ) and partly longitudinal; the E-field is of the form ( E x , − j S D E x , 0 ) {\displaystyle (E_{x},-j{\frac {S}{D}}E_{x},0)} Where S , D {\displaystyle S,D} refer to the Stix notation. As the density is increased, the phase velocity rises from c until

320-486: Is related to the four-momentum as follows: The four-wavevector is related to the four-frequency as follows: The four-wavevector is related to the four-velocity as follows: Taking the Lorentz transformation of the four-wavevector is one way to derive the relativistic Doppler effect . The Lorentz matrix is defined as In the situation where light is being emitted by a fast moving source and one would like to know

352-404: Is the plasma frequency , the wave speed is the speed of light in vacuum. As the electron density increases, the phase velocity increases and the group velocity decreases until the cut-off frequency where the light frequency is equal to ω pe . This density is known as the critical density for the angular frequency ω of that wave and is given by If the critical density is exceeded,

SECTION 10

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384-506: Is the direction cosine of k 1 {\displaystyle k^{1}} with respect to k 0 , k 1 = k 0 cos ⁡ θ . {\displaystyle k^{0},k^{1}=k^{0}\cos \theta .} So As an example, to apply this to a situation where the source is moving directly away from the observer ( θ = π {\displaystyle \theta =\pi } ), this becomes: To apply this to

416-496: Is the spatial component. Alternately, the wavenumber k can be written as the angular frequency ω divided by the phase-velocity v p , or in terms of inverse period T and inverse wavelength λ . When written out explicitly its contravariant and covariant forms are: In general, the Lorentz scalar magnitude of the wave four-vector is: The four-wavevector is null for massless (photonic) particles, where

448-405: The angular wave vector (or angular wavevector ), with a typical unit being radian per metre. The wave vector and angular wave vector are related by a fixed constant of proportionality, 2 π  radians per cycle. It is common in several fields of physics to refer to the angular wave vector simply as the wave vector , in contrast to, for example, crystallography . It is also common to use

480-451: The "physics definition". See Bloch's theorem for further details. A moving wave surface in special relativity may be regarded as a hypersurface (a 3D subspace) in spacetime, formed by all the events passed by the wave surface. A wavetrain (denoted by some variable X ) can be regarded as a one-parameter family of such hypersurfaces in spacetime. This variable X is a scalar function of position in spacetime. The derivative of this scalar

512-660: The X-wave are: ω 2 = ω e 2 + ω i 2 2 ± ( ω e 2 − ω i 2 2 ) 2 + ω p e 2 ω p i 2 {\displaystyle \omega ^{2}={\frac {\omega _{e}^{2}+\omega _{i}^{2}}{2}}\pm {\sqrt {\left({\frac {\omega _{e}^{2}-\omega _{i}^{2}}{2}}\right)^{2}+\omega _{pe}^{2}\omega _{pi}^{2}}}} where ω

544-450: The cut-off at ω R {\displaystyle \omega _{R}} is reached. As the density is further increased, the wave is evanescent until the resonance at the upper hybrid frequency ω h 2 = ω p 2 + ω c 2 {\displaystyle \omega _{h}^{2}=\omega _{p}^{2}+\omega _{c}^{2}} . Then it can propagate again until

576-417: The designation of this frequency) and a resonance at ω c . The L wave has a cut-off at ω L and no resonance. R waves at frequencies below ω c /2 are also known as whistler modes . The dispersion relation can be written as an expression for the frequency (squared), but it is also common to write it as an expression for the index of refraction ck /ω (squared). Wave vector In physics ,

608-417: The electrons. Since electrons have inertia the system behaves as a harmonic oscillator, where the electrons oscillate at a frequency ω pe , called electron plasma frequency. These oscillations do not propagate—the group velocity is 0. When the thermal motion of the electrons is taken into account a shift in frequency from the electron plasma frequency ω pe occurs. Now the electron pressure gradient acts as

640-420: The equation where: The equivalent equation using the wave vector and frequency is where: The direction in which the wave vector points must be distinguished from the "direction of wave propagation ". The "direction of wave propagation" is the direction of a wave's energy flow, and the direction that a small wave packet will move, i.e. the direction of the group velocity . For light waves in vacuum, this

672-463: The frequency of light detected in an earth (lab) frame, we would apply the Lorentz transformation as follows. Note that the source is in a frame S and earth is in the observing frame, S . Applying the Lorentz transformation to the wave vector and choosing just to look at the μ = 0 {\displaystyle \mu =0} component results in where cos ⁡ θ {\displaystyle \cos \theta }

SECTION 20

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704-582: The high frequency or low electron density limit, i.e. for ω ≫ ω p e = ( n e e 2 / m e ϵ 0 ) 1 / 2 {\displaystyle \omega \gg \omega _{pe}=(n_{e}e^{2}/m_{e}\epsilon _{0})^{1/2}} or n e ≪ m e ω 2 ϵ 0 / e 2 {\displaystyle n_{e}\ll m_{e}\omega ^{2}\epsilon _{0}\,/\,e^{2}} where ω pe

736-756: The plasma is called over-dense . In a magnetized plasma, except for the O wave, the cut-off relationships are more complex. The O wave is the "ordinary" wave in the sense that its dispersion relation is the same as that in an unmagnetized plasma, that is, 1 − ω p e 2 ω 2 − k 2 c 2 ω 2 = 0 → ω 2 = c 2 k 2 + ω p e 2 {\displaystyle 1-{\frac {\omega _{pe}^{2}}{\omega ^{2}}}-{\frac {k^{2}c^{2}}{\omega ^{2}}}=0\rightarrow \omega ^{2}=c^{2}k^{2}+\omega _{pe}^{2}} . It

768-427: The rest mass m o = 0 {\displaystyle m_{o}=0} An example of a null four-wavevector would be a beam of coherent, monochromatic light, which has phase-velocity v p = c {\displaystyle v_{p}=c} which would have the following relation between the frequency and the magnitude of the spatial part of the four-wavevector: The four-wavevector

800-499: The restoring force, creating a propagating wave analogous to a sound wave in non-ionized gases. Combining these two restoring forces (from the electric field and electron pressure gradient) a type of wave, named Langmuir wave, is excited. The dispersion relation is: ω 2 = ω p e 2 + 3 C e 2 k 2 {\displaystyle \omega ^{2}=\omega _{pe}^{2}+3C_{e}^{2}k^{2}} The first term on

832-905: The right-hand side of the dispersion relation is the electron plasma oscillation related to the electric field force and the second term is related to the thermal motion of the electrons, where C e is the electron thermal speed and k is the wave vector . In an unmagnetized plasma, waves above the plasma frequency propagate through the plasma according to the dispersion relation: 1 − ω p e 2 ω 2 − k 2 c 2 ω 2 = 0 → ω 2 = c 2 k 2 + ω p e 2 {\displaystyle 1-{\frac {\omega _{pe}^{2}}{\omega ^{2}}}-{\frac {k^{2}c^{2}}{\omega ^{2}}}=0\rightarrow \omega ^{2}=c^{2}k^{2}+\omega _{pe}^{2}} In an unmagnetized plasma for

864-409: The same term [REDACTED] This disambiguation page lists articles associated with the title X-mode . If an internal link led you here, you may wish to change the link to point directly to the intended article. Retrieved from " https://en.wikipedia.org/w/index.php?title=X-mode&oldid=1140299511 " Category : Disambiguation pages Hidden categories: Short description

896-421: The second cut-off at ω L {\displaystyle \omega _{L}} . The cut-off frequencies are given by where ω c {\displaystyle \omega _{c}} is the electron cyclotron resonance frequency, and ω p {\displaystyle \omega _{p}} is the electron plasma frequency . The resonant frequencies for

928-407: The symbol k for whichever is in use. In the context of special relativity , a wave four-vector can be defined, combining the (angular) wave vector and (angular) frequency. The terms wave vector and angular wave vector have distinct meanings. Here, the wave vector is denoted by ν ~ {\displaystyle {\tilde {\boldsymbol {\nu }}}} and

960-447: The wave vector may not point exactly in the direction of wave propagation. In solid-state physics , the "wavevector" (also called k-vector ) of an electron or hole in a crystal is the wavevector of its quantum-mechanical wavefunction . These electron waves are not ordinary sinusoidal waves, but they do have a kind of envelope function which is sinusoidal, and the wavevector is defined via that envelope wave, usually using

992-533: The wavenumber by ν ~ = | ν ~ | {\displaystyle {\tilde {\nu }}=\left|{\tilde {\boldsymbol {\nu }}}\right|} . The angular wave vector is denoted by k and the angular wavenumber by k = | k | . These are related by k = 2 π ν ~ {\displaystyle \mathbf {k} =2\pi {\tilde {\boldsymbol {\nu }}}} . A sinusoidal traveling wave follows

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1024-419: The wavevector is the same as the direction of wave propagation. If the medium is anisotropic, the wave vector in general points in directions other than that of the wave propagation. The wave vector is always perpendicular to surfaces of constant phase. For example, when a wave travels through an anisotropic medium , such as light waves through an asymmetric crystal or sound waves through a sedimentary rock ,

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