Alfvén’s theorem in magnetohydrodynamics

E679641

Alfvén’s theorem in magnetohydrodynamics is a fundamental result stating that in a perfectly conducting fluid, magnetic field lines are “frozen” into the plasma and move with it, preserving their topology over time.

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Statements (47)

Predicate Object
instanceOf physical theorem ⓘ
result in magnetohydrodynamics ⓘ
alsoKnownAs Alfvén’s frozen-in flux theorem ⓘ
frozen-in field theorem ⓘ
appliesTo ideal magnetohydrodynamics ⓘ
perfectly conducting fluid ⓘ
plasma ⓘ
assumes infinite electrical conductivity ⓘ
negligible resistivity ⓘ
non-relativistic MHD in its standard form ⓘ
single-fluid MHD description ⓘ
validity of ideal Ohm’s law ⓘ
basedOn ideal induction equation of MHD ⓘ
consequence magnetic field lines are advected with the fluid flow ⓘ
topological invariants of magnetic field lines are conserved in ideal MHD ⓘ
contrastsWith magnetic reconnection in resistive MHD ⓘ
describes frozen-in behavior of magnetic field lines in a conducting fluid ⓘ
domain classical plasma physics ⓘ
continuum electrodynamics ⓘ
field magnetohydrodynamics ⓘ
historicalContext introduced in the development of magnetohydrodynamics in the 20th century ⓘ
holdsWhen magnetic Reynolds number is very large ⓘ
implies magnetic flux through any material surface comoving with the fluid is conserved ⓘ
no reconnection of magnetic field lines in ideal MHD ⓘ
mathematicallyExpressedAs dΦ_B/dt = 0 for a surface moving with the fluid ⓘ
∂B/∂t = ∇ × (v × B) in ideal MHD ⓘ
namedAfter Hannes Alfvén ⓘ
relatedConcept ideal Ohm’s law E + v × B = 0 ⓘ
magnetic flux freezing ⓘ
magnetic helicity conservation in ideal MHD ⓘ
relatedTo Alfvén waves ⓘ
relates fluid velocity field ⓘ
magnetic field lines ⓘ
magnetic flux conservation ⓘ
requires Maxwell–Faraday equation ⓘ
magnetostatic approximation for displacement current in MHD ⓘ
statesThat magnetic field line topology is preserved in time in ideal MHD ⓘ
magnetic field lines are frozen into the plasma in ideal MHD ⓘ
magnetic field lines move with the fluid in a perfectly conducting plasma ⓘ
usedIn astrophysical plasma physics ⓘ
fusion plasma confinement theory ⓘ
solar physics ⓘ
space plasma physics ⓘ
theory of magnetic field line topology ⓘ
theory of magnetic flux tubes ⓘ
violatedWhen finite resistivity is present ⓘ
non-ideal MHD effects are important ⓘ

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Referenced by (3)

Full triples — surface form annotated when it differs from this entity's canonical label.

Hannes Alfvén → knownFor → Alfvén’s theorem in magnetohydrodynamics ⓘ
Kelvin–Helmholtz instability → describedBy → magnetohydrodynamics ⓘ
linked to: Alfvén’s theorem in magnetohydrodynamics
Alfvén’s theorem in magnetohydrodynamics → alsoKnownAs → Alfvén’s frozen-in flux theorem ⓘ
linked to: Alfvén’s theorem in magnetohydrodynamics