particles and in order to calculate these terms, one needs a proper model for neutral
transport. The distribution of the neutrals in the plasma edge depends, in particular,
on the plasma parameters - hence the equations describing the neutrals must be
solved together with Eqs. (8.1) and the corresponding blocks of the code realizing
the model must be coupled. From the coupling viewpoint, the fluid equations for
neutral transport similar to Eqs. (8.1) would be the most natural choice. However,
this implies short mean-free-path of neutrals with respect to neutral-ion or neutralneutral collisions, which, except for the regions of high plasma density, can be
longer than the scale length of the profiles of the plasma parameters. Furthermore,
because of the absence of interaction with the magnetic field, the neutral transport
has no preferential direction and should be described in full 3D, which is computationally demanding. Therefore, kinetic, Monte-Carlo type modeling is mostly used
in the major codes for edge plasma modeling for high fidelity simulations.
8.2.1 Fluid Description of Neutrals
Because of relative simplicity – compared with the kinetic model – the fluid-like
models for neutral transport in the divertor received considerable attention from the
developers of the edge modeling codes [35–40]. These models rely on the relaxation
of the distribution function of hydrogen isotope atoms towards the ion distribution
function in charge-exchange collisions with the plasma ions [35] since the neutralneutral collisions are usually too seldom to establish the Maxwellian distribution of
neutral species (see Sect. 4.5 for more detail). The models are of different complexity; some of them take into account wall reflection and volumetric recombination and
provide sources of particles, momentum and energy for Eq. (8.1). Their comparison
with kinetic, Monte-Carlo models shows reasonable agreement, but for restricted
Monte-Carlo models that describe the hydrogenic atoms only [41]. However, the
importance of molecule transport in the description of divertor performance was
clearly demonstrated using the full kinetic Monte-Carlo neutral model (see e.g. [42])
and the results obtained with a fluid neutral model differ, sometimes even qualitatively, from those obtained with the kinetic model [37]. Besides the lack of molecules in the fluid models, there are several other reasons for this difference. The
radial profiles of the plasma parameters outside the separatrix are quite narrow, so
the condition of smallness of the ratio of the neutral mean-free-path to the scale
length of variation of the plasma parameters, necessary for validity of the fluid
closure of the transport equations, is violated for neutrals in most of the edge plasma,
except for the dense divertor regions close to the targets. It is difficult to describe
correctly in a fluid model all the vast variety of physical processes that occur in
collisions involving the neutral particles in the plasma and on the wall, as well as the
geometry detail of the particular divertor configuration. In addition, the validity of
the assumption of charge-exchange relaxation is not obvious for the impurity atoms.
There have been efforts to produce a hybrid, fluid-kinetic model for the neutral
transport in the edge plasma [43–45], which would either apply kinetic corrections to
208
8 Computational Modeling of the Edge Plasma Transport Phenomena
transport. The distribution of the neutrals in the plasma edge depends, in particular,
on the plasma parameters - hence the equations describing the neutrals must be
solved together with Eqs. (8.1) and the corresponding blocks of the code realizing
the model must be coupled. From the coupling viewpoint, the fluid equations for
neutral transport similar to Eqs. (8.1) would be the most natural choice. However,
this implies short mean-free-path of neutrals with respect to neutral-ion or neutralneutral collisions, which, except for the regions of high plasma density, can be
longer than the scale length of the profiles of the plasma parameters. Furthermore,
because of the absence of interaction with the magnetic field, the neutral transport
has no preferential direction and should be described in full 3D, which is computationally demanding. Therefore, kinetic, Monte-Carlo type modeling is mostly used
in the major codes for edge plasma modeling for high fidelity simulations.
8.2.1 Fluid Description of Neutrals
Because of relative simplicity – compared with the kinetic model – the fluid-like
models for neutral transport in the divertor received considerable attention from the
developers of the edge modeling codes [35–40]. These models rely on the relaxation
of the distribution function of hydrogen isotope atoms towards the ion distribution
function in charge-exchange collisions with the plasma ions [35] since the neutralneutral collisions are usually too seldom to establish the Maxwellian distribution of
neutral species (see Sect. 4.5 for more detail). The models are of different complexity; some of them take into account wall reflection and volumetric recombination and
provide sources of particles, momentum and energy for Eq. (8.1). Their comparison
with kinetic, Monte-Carlo models shows reasonable agreement, but for restricted
Monte-Carlo models that describe the hydrogenic atoms only [41]. However, the
importance of molecule transport in the description of divertor performance was
clearly demonstrated using the full kinetic Monte-Carlo neutral model (see e.g. [42])
and the results obtained with a fluid neutral model differ, sometimes even qualitatively, from those obtained with the kinetic model [37]. Besides the lack of molecules in the fluid models, there are several other reasons for this difference. The
radial profiles of the plasma parameters outside the separatrix are quite narrow, so
the condition of smallness of the ratio of the neutral mean-free-path to the scale
length of variation of the plasma parameters, necessary for validity of the fluid
closure of the transport equations, is violated for neutrals in most of the edge plasma,
except for the dense divertor regions close to the targets. It is difficult to describe
correctly in a fluid model all the vast variety of physical processes that occur in
collisions involving the neutral particles in the plasma and on the wall, as well as the
geometry detail of the particular divertor configuration. In addition, the validity of
the assumption of charge-exchange relaxation is not obvious for the impurity atoms.
There have been efforts to produce a hybrid, fluid-kinetic model for the neutral
transport in the edge plasma [43–45], which would either apply kinetic corrections to
208
8 Computational Modeling of the Edge Plasma Transport Phenomena