# Stellarator symmetry

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

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