modeling becomes a vital tool guiding the experiments and furthering the development of theoretical models.
Today one can identify two main directions in the edge plasma modeling. One of
them focuses on fast, relatively small-scale plasma instabilities and turbulence,
which govern anomalous cross-field plasma transport (see Chap. 7 for further
discussions). The other one is aimed at characterizing the large spatiotemporal
scale quasi-equilibria and flows of particles and energy in complex divertor geometries, including coupling to neutrals, sheath boundaries, atomic physics, plasmasurface interactions, etc. The codes used for this second direction, the so-called
“edge plasma transport codes”, include the effects of small-scale fluctuations by
using some “anomalous” transport coefficients. These coefficients could be provided
by the plasma turbulence codes, but most often, they are obtained by fitting the
results of experimental measurements in the edge plasma. In this chapter, we discuss
the main approaches to the edge plasma modeling with the transport codes.
Generally, the edge plasma of a tokamak or, especially, a stellarator is a 3D
object. Correspondingly, a 3D transport model would be desirable. However, even in
the transport approximation, a full 3D model becomes too complex and its numerical
realization is too slow for practical use. Therefore, 2D and even 1D plasma transport
codes are typically used for the interpretation of experimental results and comparison
with theoretical models [1]. There is significant progress in the development of the
3D codes [2] oriented primarily to the description of the plasma edge in stellarators
where the toroidal symmetry approximation is not applicable. However, we focus
here on the 2D transport models since they are most developed and widely used for
tokamak modeling.
8.1 Transport Modeling of the Plasma
In the edge plasma, where the flow patterns that determine the distribution of the
plasma parameters and wall loading form, the neutral particles, such as atoms and
molecules, are abundant and play an important role in the physical processes
occurring there. Since the neutrals, unlike the charged plasma particles, are not
magnetized, their description may require a different approach. If the distribution
functions of the plasma components are not far from Maxwellian (the assumption
used in the transport models), then the plasma state is characterized by the density,
fluid velocity and temperature of all sorts of the charged particles involved in the
model. The spatial profiles of these quantities and their time evolution are described
with a set of equations for the particle and energy densities and parallel momentum
of the different plasma species. Different forms of such transport equations are used
in different codes (see Chap. 6). One of the forms of these equations is
∂U s
∂t
þ ∇ Á Γ
!
U s ¼ S U s ,
ð8:1Þ
202
8 Computational Modeling of the Edge Plasma Transport Phenomena
Today one can identify two main directions in the edge plasma modeling. One of
them focuses on fast, relatively small-scale plasma instabilities and turbulence,
which govern anomalous cross-field plasma transport (see Chap. 7 for further
discussions). The other one is aimed at characterizing the large spatiotemporal
scale quasi-equilibria and flows of particles and energy in complex divertor geometries, including coupling to neutrals, sheath boundaries, atomic physics, plasmasurface interactions, etc. The codes used for this second direction, the so-called
“edge plasma transport codes”, include the effects of small-scale fluctuations by
using some “anomalous” transport coefficients. These coefficients could be provided
by the plasma turbulence codes, but most often, they are obtained by fitting the
results of experimental measurements in the edge plasma. In this chapter, we discuss
the main approaches to the edge plasma modeling with the transport codes.
Generally, the edge plasma of a tokamak or, especially, a stellarator is a 3D
object. Correspondingly, a 3D transport model would be desirable. However, even in
the transport approximation, a full 3D model becomes too complex and its numerical
realization is too slow for practical use. Therefore, 2D and even 1D plasma transport
codes are typically used for the interpretation of experimental results and comparison
with theoretical models [1]. There is significant progress in the development of the
3D codes [2] oriented primarily to the description of the plasma edge in stellarators
where the toroidal symmetry approximation is not applicable. However, we focus
here on the 2D transport models since they are most developed and widely used for
tokamak modeling.
8.1 Transport Modeling of the Plasma
In the edge plasma, where the flow patterns that determine the distribution of the
plasma parameters and wall loading form, the neutral particles, such as atoms and
molecules, are abundant and play an important role in the physical processes
occurring there. Since the neutrals, unlike the charged plasma particles, are not
magnetized, their description may require a different approach. If the distribution
functions of the plasma components are not far from Maxwellian (the assumption
used in the transport models), then the plasma state is characterized by the density,
fluid velocity and temperature of all sorts of the charged particles involved in the
model. The spatial profiles of these quantities and their time evolution are described
with a set of equations for the particle and energy densities and parallel momentum
of the different plasma species. Different forms of such transport equations are used
in different codes (see Chap. 6). One of the forms of these equations is
∂U s
∂t
þ ∇ Á Γ
!
U s ¼ S U s ,
ð8:1Þ
202
8 Computational Modeling of the Edge Plasma Transport Phenomena