Approximate symmetries of guiding-centre motion

Abstract

Quasisymmetry builds a third invariant for charged-particle motion besides energy and magnetic moment. We address quasisymmetry at the level of approximate symmetries of first-order guiding-centre motion. We find that the conditions to leading order are the same as for exact quasisymmetry if one insists that the symmetry is purely spatial. We also generalise to allow for approximate phase-space symmetries, and derive weaker conditions. The latter recover "weak quasisymmetry" as a subcase, thus we prove it is spatial only to leading order, but also that it implies the existence of a wider class of independent approximate conserved quantities. Finally, we demonstrate that magnetohydrostatics imposes quasisymmetry to leading order.

References in corpus (5)

• Necessary and Sufficient Conditions for Quasisymmetry
• Near-Axis Expansion of Stellarator Equilibrium at Arbitrary Order in the Distance to the Axis
• Construction of Quasisymmetric Stellarators Using a Direct Coordinate Approach
• Differential forms for plasma physics
• General formulas for adiabatic invariants in nearly-periodic Hamiltonian systems

Cited by in corpus (7)

• Phases and phase-transitions in quasisymmetric configuration space
• Constructing the space of quasisymmetric stellarators
• Generalized Boozer coordinates: a natural coordinate system for quasisymmetry
• Islands and current singularities in quasisymmetric toroidal plasmas
• Isodrastic Magnetic fields for suppressing transitions in guiding-centre motion
• Existence of weakly quasisymmetric magnetic fields in asymmetric toroidal domains with non-tangential quasisymmetry
• Quasisymmetric magnetic fields in asymmetric toroidal domains