parallel computing, but this still requires considerable computer resources. Apart
from this, parallelization is efficient when one wants to suppress the noise by a
significant increase of the number of the test particle histories followed. However, in
the coupled fluid-kinetic calculations, the optimal strategy usually relies on keeping
the noise at a certain level, so that it does not prevent reducing its effect by reducing
the time step in the fluid code iterations. Pretty often it is the run time that determines
the level of detail set up in the model: the runs may take months [57].
The third problem is related to the different treatment of the time dependence of
the solution. Whereas Eqs.(8.1) describe the evolution of the edge plasma parameters, the standard Monte-Carlo approach assumes a steady state. It can be justified if
the evolution of the plasma parameters is much slower than the relaxation of the
neutral distribution, but this is not always the case. This inconsistency is the source
of difficulties by coupling the neutral and plasma models, which is discussed in the
next section. A modification of the Monte-Carlo algorithm that includes time
dependence in the particle tracing was proposed [58]. In some sense, it includes
the time as one more dimension in modeling [47]. However, the practical realization
of this approach [53, 58] leads to a significant increase of the numerical noise if the
particle mean-free path in this “time” direction is longer than the time step in the
iterations solving Eq. (8.1).
8.2.3 Coupling to the Plasma Model
Coupling the neutral model based on differential equations to the plasma transport
model has no principal problem. One simply adds to the system (8.1) some more
equations of a similar structure, which requires no special measures to ensure
compatibility between the two parts. However, when the Monte-Carlo approach is
in effect, a problem arises. Whereas an implicit numerical scheme is normally used
for advancing the discrete analog of Eqs. (8.1) in time, the Monte-Carlo description
is explicit. This means that the neutral-related sources in Eqs. (8.1) are consistent
with the plasma parameters before each time step, when the Monte-Carlo algorithm
is applied, but the plasma parameters consistent with these sources are only available
after the time step. Such discrepancy results in the appearance of parasitic sources in
Eqs. (8.1) [57]. These sources, at a percent level, are not very important in the energy
equations since the global energy balance in the edge plasma is sustained by
equilibration of strong terms – the power input, volumetric losses and power
delivered to the targets. They are probably not so important in the momentum
equations also. However, in particle balance, these tiny sources may become comparable with the primary players, the fueling and pumping fluxes. Indeed, in the high
recycling or detached divertor regime, see Chap. 9, the particle sources related to
recombination of plasma ions and ionization of recycling neutrals can be much
stronger than the fueling and pumping fluxes. Therefore, a percent level error in the
recycling sources can act as an order of unity error in balance of pumping and
fueling, which determines the density level or the particle content of the edge
210
8 Computational Modeling of the Edge Plasma Transport Phenomena
from this, parallelization is efficient when one wants to suppress the noise by a
significant increase of the number of the test particle histories followed. However, in
the coupled fluid-kinetic calculations, the optimal strategy usually relies on keeping
the noise at a certain level, so that it does not prevent reducing its effect by reducing
the time step in the fluid code iterations. Pretty often it is the run time that determines
the level of detail set up in the model: the runs may take months [57].
The third problem is related to the different treatment of the time dependence of
the solution. Whereas Eqs.(8.1) describe the evolution of the edge plasma parameters, the standard Monte-Carlo approach assumes a steady state. It can be justified if
the evolution of the plasma parameters is much slower than the relaxation of the
neutral distribution, but this is not always the case. This inconsistency is the source
of difficulties by coupling the neutral and plasma models, which is discussed in the
next section. A modification of the Monte-Carlo algorithm that includes time
dependence in the particle tracing was proposed [58]. In some sense, it includes
the time as one more dimension in modeling [47]. However, the practical realization
of this approach [53, 58] leads to a significant increase of the numerical noise if the
particle mean-free path in this “time” direction is longer than the time step in the
iterations solving Eq. (8.1).
8.2.3 Coupling to the Plasma Model
Coupling the neutral model based on differential equations to the plasma transport
model has no principal problem. One simply adds to the system (8.1) some more
equations of a similar structure, which requires no special measures to ensure
compatibility between the two parts. However, when the Monte-Carlo approach is
in effect, a problem arises. Whereas an implicit numerical scheme is normally used
for advancing the discrete analog of Eqs. (8.1) in time, the Monte-Carlo description
is explicit. This means that the neutral-related sources in Eqs. (8.1) are consistent
with the plasma parameters before each time step, when the Monte-Carlo algorithm
is applied, but the plasma parameters consistent with these sources are only available
after the time step. Such discrepancy results in the appearance of parasitic sources in
Eqs. (8.1) [57]. These sources, at a percent level, are not very important in the energy
equations since the global energy balance in the edge plasma is sustained by
equilibration of strong terms – the power input, volumetric losses and power
delivered to the targets. They are probably not so important in the momentum
equations also. However, in particle balance, these tiny sources may become comparable with the primary players, the fueling and pumping fluxes. Indeed, in the high
recycling or detached divertor regime, see Chap. 9, the particle sources related to
recombination of plasma ions and ionization of recycling neutrals can be much
stronger than the fueling and pumping fluxes. Therefore, a percent level error in the
recycling sources can act as an order of unity error in balance of pumping and
fueling, which determines the density level or the particle content of the edge
210
8 Computational Modeling of the Edge Plasma Transport Phenomena