We have investigated the influence of symmetry properties of toroidal magnetic configurations on the mechanisms used for determining the radial electric field such as the momentum balance and the ambipolar particle transport. Both neoclassical and anomalous transport of particles, heat and momentum in axisymmetric and nonaxisymmetric toroidal systems are taken into account. Generally, in nonaxisymmetric systems, the radial electric field is determined by the neoclassical ambipolarity condition. For axisymmetric systems with up–down symmetry and quasisymmetric systems with stellarator symmetry, it is shown using a novel parity transformation that the particle fluxes are automatically ambipolar up to and the determination of the radial electric field Es requires solving the momentum balance equations, where δ denotes the ratio of the thermal gyroradius to the characteristic equilibrium scale length. In axisymmetric systems with large E × B flows on the order of the ion thermal velocity vTi, the radial fluxes of particles, heat and toroidal momentum are dependent on Es and its radial derivative while the time evolution of the Es profile is governed by the toroidal momentum balance equation. In nonaxisymmetric systems, E × B flows of are not generally allowed even in the presence of quasisymmetry because the nonzero radial current is produced by the large flow term in the equilibrium force balance for which the Boozer and Hamada coordinates cannot be constructed.
Axisymmetric hybrid Vlasov equilibria with applications to tokamak plasmas