Drift-kinetic simulation of neoclassical transport with impurities in tokamaks

Abstract

Plasmas in modern tokamak experiments contain a significant fraction of impurity ions in addition to the main deuterium background ions. A new multiple ion-species δf particle simulation capability has been developed to self-consistently study the nonlocal effects of impurities on neoclassical transport in toroidal plasmas. A new algorithm for an unlike-particle collision operator, including test-particle and conserving field-particle parts, is described. Effects of the carbon impurity on the main deuterium species heat flux as well as an ambipolar radial electric field in a National Spherical Torus Experiment (NSTX) [M. Ono, S. M. Kaye, Y.-K. M. Peng et al., Nucl. Fusion 40, 557 (2000)] configuration were studied. A difference between carbon poloidal rotation found from simulation and from conventional theoretical estimates has been investigated and was identified to be a nonlocal finite orbit effect. In the case of large-aspect ratio tokamak configurations with steep toroidal flow profiles, we propose a theoretical model to describe this nonlocal effect. The dominant mechanisms captured by the model are associated with ion parallel velocity modification due to steep toroidal flow and radial electric field profiles. We present simulation results for carbon poloidal velocity in NSTX. Comparisons with neoclassical theory are discussed.

Unlike-particle collision operator for gyrokinetic particle simulations

“…While temperature and parallel velocity profiles may be substantially different between different species, especially between ions and electrons, recent drift-kinetic simulations of realistic axisymmetric toroidal fusion devices show that this condition is well satisfied in deuterium plasmas in presence of carbon impurity [10,11].…”

Radially globalδfcomputation of neoclassical phenomena in a tokamak pedestal

“…The benchmarking paradigm used here is important and novel in that it depends centrally on the finite orbit width, as we examine departures from zero-orbit-width (local) theory. The benchmarking procedure may be useful to other kinetic simulations of edge plasma [3][4][5][6][7][8][9][10][11][12][13][14][15].…”

“…For improved pedestal neoclassical calculations, some researchers [3][4][5][6][7][8][9][10][11][12][13][14][15] have considered a model that may be termed "global full-f ", in contrast to the conventional approach [1,2,[16][17][18] which may be called "local δf ." In a full-f code, the entire distribution function f is solved for, whereas in a δf code, one only solves for the departure from a Maxwellian, with the Maxwellian constant on each flux surface.…”

Collisionality scaling of main-ion toroidal and poloidal rotation in low torque DIII-D plasmas

“…Some differences between the codes are the treatment of orbit squeezing effects and the inductive parallel electric field. Orbit squeezing modifications to the viscosity are not used in either FORCEBAL-NCLASS or NEO, but are included self-consistently in the particle-following GTC-NEO and have been shown to affect the ion poloidal rotation [39]. FORCEBAL-NCLASS by default includes an inductive parallel electric field E by assuming neoclassical resistivity for the ohmic current, whereas GTC-NEO and NEO by default have chosen to set the parallel inductive field to zero, as E is a difficult quantity to determine accurately.…”

“…Here K 1 is formed by evaluating the impurity concentration and parallel viscous matrix elements. Calculations of the coefficient K 1 can be done analytically [19], numerically [35,36], or determined from plasma simulations [37,38,39].…”