collisions between the charged particles that follow different orbits in the magnetic
field, yields the values of the transport coefficients that are far too low to explain the
radial profiles of the plasma parameters observed experimentally. There must be
so-called “collective” effects related to some relatively small-scale turbulence, which
are responsible for cross-field transport. These effects appear in the edge plasma
models through the “anomalous” transport coefficients that are constructed to meet
some empirical expectations, mostly, the radial profiles at the mid-plane of the
plasma temperature and density or of the width of the power-carrying layer close
to the separatrix in the SOL [15, 16]. Given the lack of detailed understanding of the
processes causing the cross-field transport, the cross-field diffusivities are often set
piecewise constant in the edge plasma. There have been attempts to adjust their
profiles to reach a better match to the experimental measurements (see e.g. [17–19]).
However, such an adjustment depends on the assumptions made for the parallel
transport, the neutral transport, drifts and so on [20, 21] and is therefore not
universal. The cross-field flow of particles naturally conveys the energy and parallel
momentum.
Besides these diffusion-like flows, there are regular cross-field flows related to the
macroscopic E
! Â B
!
drifts of the charged particles [22–24] and intermittent convection [25–27]. The drift-related flows are described rather strictly in the transport
equations [15], but their inclusion in the computer models is still not routine. The
complex picture of the magnetic drifts that cause electric currents that affect the
distribution of the electric fields that cause the E
! Â B
!
drift flows requires special
effort to make the computations stable. We will discuss the drift effects in some more
detail below.
The intermittent transport is less well understood. Experimentally, it is observed
as a radial motion of some plasma structures (“blobs” or “filaments”) aligned with
the magnetic field [26–28]. There is some insight from theory into the nature of the
radial transport of such coherent structures in the magnetic field [29], which predicts
the velocity of their propagation, but no reliable model of formation of these “blobs”
is available at present (see also Chap. 7). In the transport models, the intermittency is
usually treated as time-average outward convection with a prescribed velocity
[30, 31]. However, a simple model of the outward pinch has two principal drawbacks. First, the filaments (or “blobs”) forming this flow contain the plasma with
parameters close to those at the separatrix, which are very different from those of the
background plasma in the far SOL, and this plasma does not mix with the background. On the contrary, the description of this flow by adding the convection
velocity (or with the enhancement of the diffusivity) effectively mixes the blobs
with the background. Whereas the fast-moving “blobs” can deliver a significant
amount of the hot particles, before they spread along the field line and sink to the
target, to the wall, thus forming some intermittent wall loading pattern, the slowly
diffusing, average plasma has enough time to deposit it all onto the targets. This does
also replace the heterogeneous plasma background for neutral transport with the
homogeneous, averaged one. Given the non-linear, threshold nature of the dependence of the neutral penetration depth on the background plasma parameters, such
206
8 Computational Modeling of the Edge Plasma Transport Phenomena
field, yields the values of the transport coefficients that are far too low to explain the
radial profiles of the plasma parameters observed experimentally. There must be
so-called “collective” effects related to some relatively small-scale turbulence, which
are responsible for cross-field transport. These effects appear in the edge plasma
models through the “anomalous” transport coefficients that are constructed to meet
some empirical expectations, mostly, the radial profiles at the mid-plane of the
plasma temperature and density or of the width of the power-carrying layer close
to the separatrix in the SOL [15, 16]. Given the lack of detailed understanding of the
processes causing the cross-field transport, the cross-field diffusivities are often set
piecewise constant in the edge plasma. There have been attempts to adjust their
profiles to reach a better match to the experimental measurements (see e.g. [17–19]).
However, such an adjustment depends on the assumptions made for the parallel
transport, the neutral transport, drifts and so on [20, 21] and is therefore not
universal. The cross-field flow of particles naturally conveys the energy and parallel
momentum.
Besides these diffusion-like flows, there are regular cross-field flows related to the
macroscopic E
! Â B
!
drifts of the charged particles [22–24] and intermittent convection [25–27]. The drift-related flows are described rather strictly in the transport
equations [15], but their inclusion in the computer models is still not routine. The
complex picture of the magnetic drifts that cause electric currents that affect the
distribution of the electric fields that cause the E
! Â B
!
drift flows requires special
effort to make the computations stable. We will discuss the drift effects in some more
detail below.
The intermittent transport is less well understood. Experimentally, it is observed
as a radial motion of some plasma structures (“blobs” or “filaments”) aligned with
the magnetic field [26–28]. There is some insight from theory into the nature of the
radial transport of such coherent structures in the magnetic field [29], which predicts
the velocity of their propagation, but no reliable model of formation of these “blobs”
is available at present (see also Chap. 7). In the transport models, the intermittency is
usually treated as time-average outward convection with a prescribed velocity
[30, 31]. However, a simple model of the outward pinch has two principal drawbacks. First, the filaments (or “blobs”) forming this flow contain the plasma with
parameters close to those at the separatrix, which are very different from those of the
background plasma in the far SOL, and this plasma does not mix with the background. On the contrary, the description of this flow by adding the convection
velocity (or with the enhancement of the diffusivity) effectively mixes the blobs
with the background. Whereas the fast-moving “blobs” can deliver a significant
amount of the hot particles, before they spread along the field line and sink to the
target, to the wall, thus forming some intermittent wall loading pattern, the slowly
diffusing, average plasma has enough time to deposit it all onto the targets. This does
also replace the heterogeneous plasma background for neutral transport with the
homogeneous, averaged one. Given the non-linear, threshold nature of the dependence of the neutral penetration depth on the background plasma parameters, such
206
8 Computational Modeling of the Edge Plasma Transport Phenomena