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

Abstract

Accurate calculation of perturbed distribution function δf and perturbed magnetic field δB 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 δf particle code (POCA) and improved understanding of magnetic braking in tokamak experiments. POCA calculates the NTV by computing δf with guiding-center orbit motion and using δB from the ideal perturbed equilibrium code (IPEC). POCA simulations are compared with experimental estimations for NTV, which are measured from angular momentum balance (DIII-D) and toroidal rotational damping rate (NSTX). The calculation shows good agreement in total NTV torque for the DIII-D discharge, where an analytic neoclassical theory also gives a consistent result thanks to relatively large aspect-ratio and slow toroidal rotations. In NSTX discharges, where the aspect-ratio is small and the rotation is fast, the theory only gives a qualitative guide for predicting NTV. However, the POCA simulation largely improves the quantitative NTV prediction for NSTX. It is discussed that a selfconsistent calculation of δB using general perturbed equilibria is eventually necessary since a non-ideal plasma response can change the perturbed field and thereby the NTV torque.

Summary of the 6th asia-pacific transport working group (APTWG) meeting

“…He showed that the particle orbit code for anisotropic pressure (POCA) code, which resolves complexities of guiding-center particle motions [51], may provide a first-principles solution to NTV beyond the semi-analytic approximation. Moreover, the IPEC code may provide a 3D perturbed equilibrium and magnetic field structure based on the ideal plasma response [52]. He showed from simulations that a realistic tracking of guiding-center particle orbits and the 3D equilibrium with plasma responses are of importance for an accurate description of toroidal momentum transport in the presence of 3D fields.…”

An overview of recent physics results from NSTX

“…In one approach [49], the POCA (Particle Orbit Code for Anisotropic Pressure) code was developed to follow guiding centre orbits of particles for precisely calculating δf , the perturbed distribution function, in a non-axisymmetric ideal MHD equilibrium determined by IPEC [50]. POCA simulations show the importance of collisionality and particle resonances with the toroidal rotation, similar to that found for RWMs.…”

Extension of the flow-rate-of-strain tensor formulation of plasma rotation theory to non-axisymmetric tokamaks

“…Such further development can build upon the significant existing literature on NTV (e.g., Refs. [16][17][18][19][20][21][22][23][24][25][26][27][28] to represent the radial magnetic fields produced by field ripple, instabilities, field error, etc., and to model various mechanisms for producing parallel viscosity (i.e., for modeling g 0 ).…”

“…16,[21][22][23][24] Various specific axisymmetric and nonaxisymmetric coordinate systems can be found in the literature. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28]…”