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Analytical Methods to Calculate Flows and Diffusions Driven by Neoclassical Viscosities in Helical Plasmas

Shin Nishimura, Hideo Sugama, Yuji Nakamura

Fusion Science and Technology / Volume 51 / Number 1 / January 2007 / Pages 61-78

Technical Paper / Stellarators /

Methods to obtain monoenergetic viscosity coefficients by combining analytical approximations of the linearized drift kinetic equation are studied for a previously formulated full neoclassical transport matrix in general nonsymmetric toroidal plasmas. A unified analytical treatment of two coefficients due to the non-bounce-averaged radial drifts of guiding centers is shown. These coefficients were previously obtained by a direct numerical calculation of the kinetic equation in the three-dimensional (3-D) phase-space (pitch-angle, poloidal and toroidal angles). In a present study, the radial drift term in the equation is divided into three parts, and then the perturbed distribution and the resulting monoenergetic coefficients are expressed by superposed components, which can be calculated by combining analytical methods. An analytical expression for the boundary layer correction to the parallel viscosity in the 1/ regime also is newly derived to complete the full matrix without a numerical calculation in 3-D phase-space. Analytical results given by adding these components approximately reproduce results of the direct numerical calculation of the kinetic equation.

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