Stellarator symmetry: Difference between revisions
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Stellarator symmetry is a property of typical [[Stellarator|stellarator]] magnetic configurations. | Stellarator symmetry is a property of typical [[Stellarator|stellarator]] magnetic configurations. | ||
It is important be aware that it is an ''imposed'' (artificial) symmetry, | |||
reflecting the symmetry of the design of the external magnetic field coils generating the configuration, and | |||
not an ''inherent'' (natural) symmetry of stellarator plasmas. | |||
<ref>[http://dx.doi.org/10.1016/S0167-2789(97)00216-9 R.L. Dewar, S.R. Hudson, ''Stellarator symmetry'', Physica D, '''112''' (1998) 275]</ref> | |||
In a [[Toroidal coordinates|cylindrical coordinate system]], it is expressed as follows for a scalar field: | In a [[Toroidal coordinates|cylindrical coordinate system]], it is expressed as follows for a scalar field: | ||
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:<math>\left ( B_R, B_\phi, B_Z \right )_{(R,\phi,Z)} = \left ( -B_R, B_\phi, B_Z \right )_{(R,-\phi,-Z)}</math> | :<math>\left ( B_R, B_\phi, B_Z \right )_{(R,\phi,Z)} = \left ( -B_R, B_\phi, B_Z \right )_{(R,-\phi,-Z)}</math> | ||
With ''N''-fold rotation symmetry around the ''Z'' axis, there are ''2N'' such planes. | With ''N''-fold rotation symmetry around the ''Z'' axis, there are ''2N'' such planes. | ||
== References == | == References == | ||
<references/> | <references/> | ||
Revision as of 16:47, 2 February 2011
Stellarator symmetry is a property of typical stellarator magnetic configurations. It is important be aware that it is an imposed (artificial) symmetry, reflecting the symmetry of the design of the external magnetic field coils generating the configuration, and not an inherent (natural) symmetry of stellarator plasmas. [1]
In a cylindrical coordinate system, it is expressed as follows for a scalar field:
with respect to the symmetry plane φ = 0. Likewise, for a vector field:
With N-fold rotation symmetry around the Z axis, there are 2N such planes.