Parallel viscosity ⟨B⋅∇⋅Πi⟩ as a function of radial electric field Er (or, equivalently, nonequilibrium poloidal rotation) in a tokamak is studied using a five-dimensional (5D) (3D in configuration space and 2D in velocity space) Monte Carlo particle following code. It is shown that including the poloidal density variation changes the qualitative behavior of the solution causing the parallel viscosity to change sign when the Mach number Mp=|Er/vtBθ| is of the order of unity. Here, vt is the thermal velocity and Bθ is the poloidal magnetic field.
Kiviniemi, T., Heikkinen, J., & Peeters, A. G. (2000). Effect of poloidal density variation on parallel viscosity for large Mach numbers. Physics of Plasmas, 7, 5255-5258. https://doi.org/10.1063/1.1321014