Theory verification and numerical benchmarking on neoclassical toroidal viscosity

Systematic verification and numerical benchmarking has been successfully carried out among three different approaches of neoclassical toroidal viscosity (NTV) theory and the corresponding codes: IPEC-PENT is developed based on the combined NTV theory but without geometric simplifications [1]; MARS-K originally calculating the kinetic energy is upgraded to calculate the NTV torque based on the equivalence between kinetic energy and NTV torque [2]; MARS-Q includes smoothly connected NTV formula [3]. The derivation and numerical results both indicate that the imaginary part of kinetic energy calculated by MARS-K is equivalent to the NTV torque in IPEC-PENT. In the benchmark of precession resonance between MARS-Q and MARS-K/IPEC-PENT, it is first time to show the agreement and the correlation between the connected NTV formula and the combined NTV theory in different collisional region. Additionally, both IPEC-PENT and MARS-K indicates the importance of the bounce harmonic resonance which could greatly enhance the NTV torque when E cross B drift frequency reaches the bounce resonance condition. Since MARS-K also has the capability to calculate the plasma response including the kinetic effect self-consistently, the self-consistent NTV torque calculations have also been tested. [1] J.-K. Park et al Phys. Rev. Lett 065002 (2009) [2] J.-K. Park, Phys. Plasmas 18 110702 (2011) [3] K.C. Shaing et al Nucl. Fusion 50 025022 (2010)