The core plasma can also be a source of the plasma particles that originate either
from the external sources (beams, pellets) or from the neutrals penetrating the core
boundary from the edge, or from the time evolution of the core plasma density.
(In the latter case, the core boundary source of particles can become negative if the
core density grows, reflecting core fueling by the plasma influx from the edge). Here
also, specification of the particle fluxes across the core boundary is the best choice
from the physics viewpoint, since these fluxes are usually well determined by the
particle sources in the core. For the parallel momentum transport equation, either the
zero parallel velocity (no core rotation) or zero flux of the parallel momentum across
the core boundary (core rotation not related to the edge) is usually applied if no drifts
are taken into account. This should create no problem since in most cases, the
parallel velocity of all plasma components near the core boundary is low – the
flows are well subsonic. However, plasma rotation can affect the electric fields
forming there, so one may need to think some more if working with the drifts and
currents [15].
8.3.3 Boundary Conditions at the “Radial” Edges of the Grid
The boundary conditions at the grid edges facing the first wall or the PFR (lines BCD
and AFE in Fig. 8.1) have not received much attention when the grid does not reach
the wall. There is not so much power reaching there, so the conditions at these
boundaries should have no strong impact on the first target of the modeling: the
power loading of the divertor targets. Usually, one sets a third type boundary
condition here, which relates the radial energy or particle flux at the boundary to
the particle or energy density there via prescribing the convective flux with specified
velocity. Sometimes this is done through specifying the “decay length” of the
temperature and density profiles [57], sometimes by specifying the effective convective velocities directly [15]. For the parallel momentum, either the slippage (zero
radial flux) or sticking (zero flow velocity) condition is usually applied at this
boundary.
8.3.4 Fueling Constraints
The way of specifying the level of plasma density in the computational model
requires special attention. The most natural parameter to use for this purpose
would be the total, ion plus neutral, particle content outside the separatrix
[60, 61]. This quantity, N tot , can be described by the particle balance equation that
is only weakly related to the edge plasma solution and so can be considered a truly
external, controllable parameter. Typically, N tot changes slowly and smoothly by
variation of the fueling rate and it is the parameter directly affected by gas puffing
and pumping in the experiment. However, in the experiment, N tot is practically not
8.3 Selection of Constraints
213
from the external sources (beams, pellets) or from the neutrals penetrating the core
boundary from the edge, or from the time evolution of the core plasma density.
(In the latter case, the core boundary source of particles can become negative if the
core density grows, reflecting core fueling by the plasma influx from the edge). Here
also, specification of the particle fluxes across the core boundary is the best choice
from the physics viewpoint, since these fluxes are usually well determined by the
particle sources in the core. For the parallel momentum transport equation, either the
zero parallel velocity (no core rotation) or zero flux of the parallel momentum across
the core boundary (core rotation not related to the edge) is usually applied if no drifts
are taken into account. This should create no problem since in most cases, the
parallel velocity of all plasma components near the core boundary is low – the
flows are well subsonic. However, plasma rotation can affect the electric fields
forming there, so one may need to think some more if working with the drifts and
currents [15].
8.3.3 Boundary Conditions at the “Radial” Edges of the Grid
The boundary conditions at the grid edges facing the first wall or the PFR (lines BCD
and AFE in Fig. 8.1) have not received much attention when the grid does not reach
the wall. There is not so much power reaching there, so the conditions at these
boundaries should have no strong impact on the first target of the modeling: the
power loading of the divertor targets. Usually, one sets a third type boundary
condition here, which relates the radial energy or particle flux at the boundary to
the particle or energy density there via prescribing the convective flux with specified
velocity. Sometimes this is done through specifying the “decay length” of the
temperature and density profiles [57], sometimes by specifying the effective convective velocities directly [15]. For the parallel momentum, either the slippage (zero
radial flux) or sticking (zero flow velocity) condition is usually applied at this
boundary.
8.3.4 Fueling Constraints
The way of specifying the level of plasma density in the computational model
requires special attention. The most natural parameter to use for this purpose
would be the total, ion plus neutral, particle content outside the separatrix
[60, 61]. This quantity, N tot , can be described by the particle balance equation that
is only weakly related to the edge plasma solution and so can be considered a truly
external, controllable parameter. Typically, N tot changes slowly and smoothly by
variation of the fueling rate and it is the parameter directly affected by gas puffing
and pumping in the experiment. However, in the experiment, N tot is practically not
8.3 Selection of Constraints
213