In this study, we calculate the radial transport of the toroidal angular momentum in the presence of non-axisymmetric magnetic fields. It is shown that the radial transport of the toroidal angular momentum, R2ζ·V, is proportional to the first order of gyro-radius. This implies that the neoclassical toroidal viscosity caused by asymmetric magnetic fields can change the toroidal rotation significantly.

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