Calculation of neoclassical toroidal viscosity with a particle simulation in the tokamak magnetic braking experiments

Accurate calculation of perturbed distribution function delta f and perturbed magnetic field delta B is essential to achieve prediction of non-ambipolar transport and neoclassical toroidal viscosity (NTV) in perturbed tokamaks. This paper reports a study of the NTV with a delta f particle code (POCA) and improved understanding of magnetic braking in tokamak experiments. POCA calculates the NTV by computing delta f with guiding-centre orbit motion and using delta B from the ideal perturbed equilibrium code (IPEC). Theories of NTV for magnetic field resonance, collisionality dependency, and toroidal mode coupling are tested in the simple configurations using the particle simulations. The POCA simulations are also compared with experimental estimations for NTV, which are measured from angular momentum balance (DIII-D) and toroidal rotational damping rate (NSTX). The calculation shows reasonable agreement in total NTV torque for the DIII-D discharge with weak rotational resonances in the nu(-) root nu. regime. In NSTX discharges where the bounce-harmonic resonances dominantly appear, the POCA simulation gives total NTV torques comparable to the measurements, however large discrepancies are found in the detailed damping and NTV profiles. It is discussed that a self-consistent calculation of delta B using general perturbed equilibria is eventually necessary since a non-ideal plasma response can change the perturbed field and thereby the NTV torque.