Finding Equilibria that Minimize Poloidal Viscosity in Tokamaks via the FLOW Code

Extensive experimental evidence has shown that the presence of poloidal flow in tokamaks can dramatically improve transport properties. However, theory indicates that these flows are damped by poloidal viscosity, thus necessitating external drivers such as neutral beam injection or RF heating. In this work, ideal magnetohydrodynamic equilibria are calculated via the FORTRAN code FLOW [1] and a postprocessor is used to estimate the poloidal viscosity. A norm of the viscosity is then minimized over the input parameters of the calculation, i.e. the input free functions for FLOW, which are associated with intuitive physical quantities. To achieve this minimization, the FLOW code has been functionalized and wrapped within a Python script for easy use with an open-source parallel minimization package. Here, we present and compare equilibria with minimized poloidal viscosities for various FLOW input free functions, plasma aspect ratios, collisionality regimes, and expressions for poloidal viscosity. We also compare our numerical results to those of an analytical minimization, and find that we can further reduce the poloidal viscosity by up to an order of magnitude with respect to the analytic result.

[1] L. Guazzotto et. al., Physics of Plasmas, 11, 604 (2004).