Analytical calculation of the kinetic q factor and resonant response of toroidally confined plasmas

Symmetry-breaking perturbations in axisymmetric toroidal plasma configurations have a drastic impact on particle, energy, and momentum transport in fusion devices, thereby affecting their confinement properties. The perturbative modes strongly affect particles with specific kinetic characteristics through resonant mode-particle interactions. In this work, we present an analytical calculation of the kinetic q factor, enabling the identification of particles with kinetic properties that meet the resonant conditions. This allows us to predict the locations and structures of the corresponding resonant island chains, as well as the existence of transport barriers in the particle phase space. The analytical results, derived for the case of a large aspect ratio configuration, are systematically compared to numerical simulations, and their domain of validity is thoroughly investigated and explained. Our findings demonstrate that calculating the kinetic q factor and its dependence on both particle and magnetic field characteristics provides a valuable tool for understanding and predicting the resonant plasma response to non-axisymmetric perturbations. Moreover, this approach can be semi-analytically applied to generic realistic experimental equilibria, offering a low-computational-cost method for scenario investigations under various multi-scale perturbative modes.