# Stellarator symmetry

From FusionWiki

Stellarator symmetry is a property of typical stellarator magnetic configurations.
It is important to 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]}
Therefore, it has the same status as axisymmetry in tokamaks.

In a cylindrical coordinate system, it is expressed as follows for a scalar field:

- $ \psi(R,\phi,Z) = \psi(R,-\phi,-Z)\, $

with respect to the symmetry plane *φ = 0*. Likewise, for a vector field:

- $ \left ( B_R, B_\phi, B_Z \right )_{(R,\phi,Z)} = \left ( -B_R, B_\phi, B_Z \right )_{(R,-\phi,-Z)} $

With *N*-fold rotation symmetry around the *Z* axis, there are *2N* such planes.

## References

- ↑ R.L. Dewar, S.R. Hudson,
*Stellarator symmetry*, Physica D,**112**(1998) 275