In evaluating neoclassical transport by radially-local simulations, the magnetic drift tangential to a flux surface is usually ignored in order to keep the phase-space volume conservation. In this paper, effect of the tangential magnetic drift on the local neoclassical transport are investigated. To retain the effect of the tangential magnetic drift in the local treatment of neoclassical transport, a new local formulation for the drift kinetic simulation is developed. The compressibility of the phase-space volume caused by the tangential magnetic drift is regarded as a source term for the drift kinetic equation, which is solved by using a two-weight δf Monte Carlo method for non-Hamiltonian system [G. Hu and J. A. Krommes, Phys. Plasmas 1, 863 (1994)]. It is demonstrated that the effect of the drift is negligible for the neoclassical transport in tokamaks. In non-axisymmetric systems, however, the tangential magnetic drift substantially changes the dependence of the neoclassical transport on the radial electric field E r . The peaked behavior of the neoclassical radial fluxes around E r = 0 observed in conventional local neoclassical transport simulations is removed by taking the tangential magnetic drift into account.

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High electron temperature plasmas with steep temperature gradient in the core are obtained in recent experiments in the Large Helical Device [A. Komori et al., Fusion Sci. Technol. 58, 1 (2010)]. Such plasmas are called core electron-root confinement (CERC) and have attracted much attention. In typical CERC plasmas, the radial electric field shows a transition phenomenon from a small negative value (ion root) to a large positive value (electron root) and the radial electric field in helical plasmas are determined dominantly by the ambipolar condition of neoclassical particle flux. To investigate such plasmas’ neoclassical transport precisely, the numerical neoclassical transport code, FORTEC-3D [S. Satake et al., J. Plasma Fusion Res. 1, 002 (2006)], which solves drift kinetic equation based on δf Monte Carlo method and has been applied for ion species so far, is extended to treat electron neoclassical transport. To check the validity of our new FORTEC-3D code, benchmark calculations are carried out with GSRAKE [C. D. Beidler et al., Plasma Phys. Controlled Fusion 43, 1131 (2001)] and DCOM/NNW [A. Wakasa et al., Jpn. J. Appl. Phys. 46, 1157 (2007)] codes which calculate neoclassical transport using certain approximations. The benchmark calculation shows a good agreement among FORTEC-3D, GSRAKE and DCOM/NNW codes for a low temperature (Te(0)=1.0 keV) plasma. It is also confirmed that finite orbit width effect included in FORTEC-3D affects little neoclassical transport even for the low collisionality plasma if the plasma is at the low temperature. However, for a higher temperature (5 keV at the core) plasma, significant difference arises among FORTEC-3D, GSRAKE, and DCOM/NNW. These results show an importance to evaluate electron neoclassical transport by solving the kinetic equation rigorously including effect of finite radial drift for high electron temperature plasmas.

The linearized model collision operator for multiple species plasmas given by H. Sugama, T.-H. Watanabe, and M. Nunami [Phys. Plasmas 16, 112503 (2009)] is improved to be properly applicable up to the highly collisional regime. The improved linearized model operator retains conservation laws of particles, momentum, and energy as well as it reproduces the same friction-flow relations as derived by the linearized Landau operator so that this model can be used to correctly evaluate neoclassical transport fluxes in all collisionality regimes. The adjointness relations and Boltzmann's H-theorem are exactly satisfied by the improved operator except in the case of collisions between unlike particle species with unequal temperatures where these relations and H-theorem still holds approximately because there is a large difference between the masses of the two species with significantly different temperatures. Even in the unequal-temperature case, the improved operator can also be modified so as to exactly satisfy the adjointness relations while it causes the values of the friction coefficients to deviate from those given by the Landau operator. In addition, for application to gyrokinetic simulations of turbulent transport, the improved operator is transformed into the gyrophase-averaged form with keeping the finite gyroradius effect.