Antidynamo theorem

In

magnetic fields that may be produced by dynamo

One notable example is

axisymmetric magnetic field can be maintained through a self-sustaining dynamo action by an axially symmetric current.^[1] Similarly, the Zeldovich's antidynamo theorem states that a two-dimensional, planar flow cannot maintain the dynamo action.^[2]

Consequences

Apart from the Earth's magnetic field, some other bodies such as Jupiter and Saturn, and the Sun have significant magnetic fields whose major component is a dipole, an axisymmetric magnetic field. These magnetic fields are self-sustained through fluid motion in the Sun or planets, with the necessary non-symmetry for the planets deriving from the Coriolis force caused by their rapid rotation, and one cause of non-symmetry for the Sun being its differential rotation.^[1]

The magnetic fields of planets with slow rotation periods and/or solid cores, such as Mercury, Venus, and Mars, have dissipated to almost nothing by comparison.

The impact of the known anti-dynamo theorems is that successful dynamos do not possess a high degree of symmetry.

References

^
doi:10.1093/mnras/94.1.39
.

^ Zeldovich, Y. B. (1957). The magnetic field in the two-dimensional motion of a conducting turbulent fluid. Sov. Phys. JETP, 4, 460-462.

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[Cowling-1934-1] 
doi:10.1093/mnras/94.1.39
.

[2] Zeldovich, Y. B. (1957). The magnetic field in the two-dimensional motion of a conducting turbulent fluid. Sov. Phys. JETP, 4, 460-462.

[1]

[2]

Consequences

See also

References