Abstract
A novel radially local approximation of the drift kinetic equation is presented. The new drift kinetic equation that includes both E×B and tangential magnetic drift terms is written in the conservative form and it has favorable properties for numerical simulation that any additional terms for particle and energy sources are unnecessary for obtaining stationary solutions under the radially local approximation. These solutions satisfy the intrinsic ambipolarity condition for neoclassical particle fluxes in the presence of quasisymmetry of the magnetic field strength. Also, another radially local drift kinetic equation is presented, from which the positive definiteness of entropy production due to neoclassical transport and Onsager symmetry of neoclassical transport coefficients are derived while it sacrifices the ambipolarity condition for neoclassical particle fluxes in axisymmetric and quasi-symmetric systems.
Highlights
Represent the guiding center drift velocity, the deviation of the guiding center distribution function from the local Maxwellian equilibrium distribution, the gyroradius, and the equilibrium scale length, respectively.) in stellarator and heliotron plasmas, this vd · ∇f term is known to be influential on the resultant neoclassical transport because it significantly changes orbits of particles trapped in helical ripples
It was shown by Matsuoka et al.[13] that the neoclassical transport is significantly influenced by retaining the magnetic drift tangential to flux surfaces in vd · ∇f for the magnetic configuration of LHD especially when the radial electric field is weak
The radially local guiding center motion equations do not satisfy the conservation law of the phase-space volume while the full guiding center motion equations do. This fact causes the difficulty in obtaining the stationary solution of the local drift kinetic equation
Summary
Effects of neoclassical transport[1,2,3] on plasma confinement are more significant in stellarator and heliotron plasmas than in tokamak plasmas because, in the former, radial drift motions of trapped particles in helical ripples enhance particle and heat transport due to nonaxisymmetry of the magnetic configuration.[4,5,6] Conventional calculations of neoclassical transport fluxes are done applying radially local approximation to solving the drift kinetic equation, in which vd ·∇f are often neglected as a small term of higher order in the normalized gyroradius parameter δ ∼ ρ/L. (Here, vd , f , ρ, and L represent the guiding center drift velocity, the deviation of the guiding center distribution function from the local Maxwellian equilibrium distribution, the gyroradius, and the equilibrium scale length, respectively.) in stellarator and heliotron plasmas, this vd · ∇f term is known to be influential on the resultant neoclassical transport because it significantly changes orbits of particles trapped in helical ripples. The new local drift kinetic equation, which is written in the conservative form, has favorable properties for numerical simulation such that any additional terms for particle and energy sources are unnecessary for obtaining stationary solutions It satisfies the intrinsic ambipolarity condition for neoclassical particle fluxes in axisymmetric systems as well as in quasi-symmetric helical systems.[16,17] The present work treats interesting issues regarding the entropy production rate and Onsager symmetry[18,19] for neoclassical transport equations resulting from the new local drift kinetic model.
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