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Area Electromagnetism

IEV ref 121-14-07

en
magnetosonic wave
magnetoacoustic wave
longitudinal magnetohydrodynamic wave

Note 1 to entry: The movement of the particles of the fluid is parallel to the direction of propagation of the magnetosonic wave; its wave vector k is orthogonal to the magnetic flux density.

The phase velocity of magnetosonic waves is

c φ = c 0 ( v s 2 + v A 2 ) ( c 0 2 + v A 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yamaaBa aaleaacqaHvpGzaeqaaOGaeyypa0Jaam4yamaaDaaaleaacaaIWaaa baaaaOWaaOaaaeaadaWcaaqaamaabmaabaGaamODamaaDaaaleaaca WGZbaabaGaaGOmaaaakiabgUcaRiaadAhadaqhaaWcbaGaamyqaaqa aiaaikdaaaaakiaawIcacaGLPaaaaeaadaqadaqaaiaadogadaqhaa WcbaGaaGimaaqaaiaaikdaaaGccqGHRaWkcaWG2bWaa0baaSqaaiaa dgeaaeaacaaIYaaaaaGccaGLOaGaayzkaaaaaaWcbeaaaaa@4B80@

where

v s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaBa aaleaacaGGbbaabeaaaaa@37C3@ is the sound wave velocity (in a gas, v s = κp/ρ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaDa aaleaacaWGZbaabaaaaOGaeyypa0ZaaOaaaeaacqaH6oWAcaWGWbGa ai4laiabeg8aYbWcbeaaaaa@3E3C@ )

v A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaBa aaleaacaGGbbaabeaaaaa@37C3@ is the Alfvén wave velocity

c 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabmqaamaabaabaaGcbaGaam4yamaaBa aaleaacaaIWaaabeaaaaa@37A5@ is the speed of light in vacuum

Note 2 to entry: For low magnetic fields, the phase velocity of the magnetosonic wave approaches sound wave velocity.


fr
onde magnétoacoustique, f
onde magnétohydrodynamique longitudinale

Note 1 à l’article: Le mouvement des particules du fluide est parallèle à la direction de la propagation de l’onde magnétoacoustique; son vecteur d’onde k est orthogonal à l’induction magnétique.

La vitesse de phase des ondes magnétoacoustiques est

c φ = c 0 ( v s 2 + v A 2 ) ( c 0 2 + v A 2 ) MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaam4yamaaBa aaleaacqaHvpGzaeqaaOGaeyypa0Jaam4yamaaDaaaleaacaaIWaaa baaaaOWaaOaaaeaadaWcaaqaamaabmaabaGaamODamaaDaaaleaaca WGZbaabaGaaGOmaaaakiabgUcaRiaadAhadaqhaaWcbaGaamyqaaqa aiaaikdaaaaakiaawIcacaGLPaaaaeaadaqadaqaaiaadogadaqhaa WcbaGaaGimaaqaaiaaikdaaaGccqGHRaWkcaWG2bWaa0baaSqaaiaa dgeaaeaacaaIYaaaaaGccaGLOaGaayzkaaaaaaWcbeaaaaa@4B80@


v s MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaBa aaleaacaGGbbaabeaaaaa@37C3@ est la vitesse d'onde acoustique (dans un gaz, v s = κp/ρ MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaDa aaleaacaWGZbaabaaaaOGaeyypa0ZaaOaaaeaacqaH6oWAcaWGWbGa ai4laiabeg8aYbWcbeaaaaa@3E3C@ )

v A MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGaciGaaiaabeqaamaabaabaaGcbaGaamODamaaBa aaleaacaGGbbaabeaaaaa@37C3@ est la vitesse d'Alfvén

c 0 MathType@MTEF@5@5@+= feaagKart1ev2aqatCvAUfeBSjuyZL2yd9gzLbvyNv2CaerbuLwBLn hiov2DGi1BTfMBaeXatLxBI9gBaerbd9wDYLwzYbItLDharqqtubsr 4rNCHbGeaGqipu0Je9sqqrpepC0xbbL8F4rqqrFfpeea0xe9Lq=Jc9 vqaqpepm0xbba9pwe9Q8fs0=yqaqpepae9pg0FirpepeKkFr0xfr=x fr=xb9adbaqaaeGacaGaaiaabmqaamaabaabaaGcbaGaam4yamaaBa aaleaacaaIWaaabeaaaaa@37A5@ est la vitesse de la lumière dans le vide

Note 2 à l’article: Pour les champs magnétiques faibles, la vitesse de phase de l'onde magnétoacoustique approche la vitesse d'onde acoustique.


Publication date: 2021-03
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