Turbulent transport of the W ions in tokamak plasmas: properties derived from a test particle approach

Abstract

A detailed analysis of a special type of turbulent pinch mechanism for tungsten (W) ions is presented. It is based on the numerical simulation of ion trajectories in a complex test-particle model that contains realistic representations of the turbulence and of the confining magnetic field, plasma rotation, ion collisions, the polarization drift and the parallel stochastic acceleration. The origin of the pinch is a special type of order generated by an average poloidal velocity V p superposed on the E × B stochastic drift. It consists of a pair of radial symmetric drifts, the hidden drifts (HDs), that exactly compensate. The polarization drift and the parallel acceleration drive radial pinch velocities V x by destroying the perfect anti-symmetry of the HDs. These phenomena that were found in simplified models are theoretically validated here in a realistic model of W ion transport. The main conclusion of the paper is that this turbulent mechanism can be experimentally relevant for a large domain of parameters, which cover both existing plasmas and ITER conditions, and it can be responsible for an important amount of the W ion accumulation.

Peaking and hollowness of low-Z impurity profiles: an interplay between ITG and TEM induced turbulent transport

“…Modeling collisions with a simple time-correlated velocity field η(t) can be understood as a simplified, averaged, version of the more complex collision operators acting in the velocity space that can capture drag, scattering or diffusion. Although its frequency is barely comparable with the time scale of turbulence ν wi a/v th ∼ 10 −1 and their strength is an order of magnitude smaller than turbulent components of motion √ C(0)a/(ρ i v th ) ∼ 10 −1 , we expect collision to be important in the attenuation of convective components of transport [28].…”

“…0 ρ i ≈ 0.2 for TEM [36,44,45]. For these reasons, we choose a simple model of the turbulence spectra [28,31]:…”

“…As mentioned in the Introduction 1, the effect of impurity ions on the turbulence instabilities is small and can be neglected, thus, the trace limit is considered. This enables us to use the equations of motion (1) in the framework of a statistical testparticle approach, named in previous works 'direct numerical simulation' [27,28,31].…”

“…The latter incorporates co-existing ITG and TEM modes with appropriate spectral properties. In conjunction with a test-particle approach (coined in previous works 'direct numerical simulation' [27][28][29][30][31]) the model allows us to evaluate the relevant transport coefficients and their dependence on the plasma parameters. In particular, we show that the polarization drift convects the E × B motion leading to opposite radial pinches for TEM or ITG turbulence.…”

Scaling laws of two-dimensional incompressible turbulent transport

“…Regarding the specific numerical approach on computing the diffusion coefficients, we employ here the so-called direct numerical simulation method (DNS) [13,36,37]. DNS attempts to mimic the real trajectories {x(t)} at the numerical level.…”