Generalized kinetic equation for tokamak plasma equilibrium distribution function

A generalized kinetic equation for the equilibrium distribution function in a finite beta, arbitrary tokamak plasma is derived. The equation is correct to second order in ρ / L (ρ is the particle Larmor radius and L is the system size). Resolving the finite Larmor radius length scales with no restriction on the ratio of poloidal to total equilibrium magnetic field, B ϑ / B , it generalizes the drift kinetic theory of Hazeltine [Phys. Plasmas 15, 77 (1973)] to the limit of B ϑ / B ∼ 1 (e.g., to ensure validity for spherical tokamaks). Two cases are considered. The first provides the equilibrium distribution function, consistent with the generalized gyrokinetic formalism of Dudkovskaia et al. [Plasma Phys. Controlled Fusion 65, 045010 (2023)], derived specifically to capture neoclassical equilibrium currents in the gyrokinetic stability analyses in strong gradient regions. The second assumes short length scales in the direction perpendicular to the magnetic field, which can occur as a result of small coherent magnetic structures in the plasma, such as neoclassical tearing mode magnetic islands close to threshold. This then extends the drift island equations of Dudkovskaia et al. [Nucl. Fusion 63, 016020 (2023)] for the plasma response to magnetic islands to a spherical tokamak plasma configuration. Resolving ρ ∼ ρ ϑ (or B ϑ ∼ B ), where ρ ϑ is the particle poloidal Larmor radius, is also expected to influence calculations of the magnetic island propagation frequency and the associated contributions to the island onset conditions.