Alfvén’s theorem in magnetohydrodynamics

E679641

physical theorem result in magnetohydrodynamics

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 NERFINISHED ⓘ frozen-in field theorem NERFINISHED ⓘ
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 NERFINISHED ⓘ
relatedConcept	ideal Ohm’s law E + v × B = 0 ⓘ magnetic flux freezing ⓘ magnetic helicity conservation in ideal MHD ⓘ
relatedTo	Alfvén waves NERFINISHED ⓘ
relates	fluid velocity field ⓘ magnetic field lines ⓘ magnetic flux conservation ⓘ
requires	Maxwell–Faraday equation NERFINISHED ⓘ 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 ⓘ

Referenced by (1)

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

Hannes Alfvén → knownFor → Alfvén’s theorem in magnetohydrodynamics ⓘ