Discrete symmetries in axisymmetric toroidal plasma confinement

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Several discrete symmetry parameters characterizing axisymmetric toroidal plasmas have been introduced. For a device without up–down symmetry such parameters are S1, related to the handedness of the toroidal current, S2, related to the direction of the toroidal velocity, and S3, characterizing the handedness of the toroidal magnetic field. All these parameters can acquire values ±1, thereby making eight different combinations. For a device with up–down symmetry only the mutual orientation of the toroidal current, toroidal velocity, and toroidal magnetic field remain important. Based on the general expression for the Lagrangian for charged particles in an external magnetic field, we identify the invariance properties of this Lagrangian (and, accordingly, of plasma behavior) with respect to these transformations. Reduced plasma models, based on the Maxwell–Boltzmann equations, and on the magnetohydrodynamic equations, are also considered. An analysis of the plasma behavior in the context of the symmetry properties may be helpful in identifying the most probable theoretical models of plasma transport.