impurity atoms in the ionization state Z and the excited level of the ionization state
Z) [21]; (iv) the so-called dielectronic recombination process (accompanied by
excitation of an ion’s electron and formation of a doubly excited atom/ion with
subsequent emission of the photon, A
Z+1 + e ! A
Z (n, n
0
) ! A
Z + ħω) should be
considered (e.g. see [38, 39] and the references therein); and v) some excited
quantum states of complex atoms/ions are “metastable” or just stable (e.g. the
ro-vibrational states of hydrogenic molecules).
To take into account such processes, one needs to modify the rate Eq. (2.12),
adding some new terms (for example, quenching of metastable states on the vacuum
chamber walls, which becomes important in weakly ionized plasma (e.g. see [13]).
This means that in such plasmas, one should consider the transport terms for the
particle density not only in the ground state but also in the metastable states.
However, in relatively high density and rather hot fusion plasma, the effective
lifetime of the metastable states is determined largely by the interactions of the
metastable atoms/ions with electrons and is strongly reduced in comparison to their
natural lifetime. In addition, the natural lifetime of ionic metastable states is decreasing as Z
À8 with increasing the ion charge Z. We also remind that some quantum
states within the “thin structure” of the hydrogen energy levels, caused by relativistic
effects, are also metastable. But due to the strong “mixing” of these levels in a fusion
plasma environment, these metastable states play no significant role. As a result, in
fusion research, the transport of metastable states is usually ignored and their
populations (as well as ionization/recombination balance and radiation loss) are
considered in a quasi-equilibrium approximation (recall Eq. (2.13)) on the equal
footage with other excited states (e.g. for details see [30] and the references therein).
The results of comprehensive numerical modeling show that for the edge plasma
conditions, even the metastable state 2
3 S 1 of helium, having the lifetime ~10
4 s, can
be treated in quasi-equilibrium approximation [40]. The presently most advanced
database providing the fusion-relevant impurity radiation loss, the contribution of
different lines, the rate constants, etc., is the ADAS database [41]. The divertor
modeling codes whose development had started before the ADAS database became
the de-facto standard can use some other data sources (for example, the AMJUEL,
HYDHEL and METHANE data sets [42] in SOLPS).
2.3 Line Radiation Transport in Edge Plasma
As we have seen in the previous sub-section, the populations of excited states are
determined by the competition between the processes involving interactions with
electrons and, playing important role, radiative decays (e.g. from level n to level k),
which are accompanied by the emission of photons having the energy ħω 0 % ΔE nk ,
where ω 0 is the photon frequency corresponding to the decay n ! k. This is the
so-called “line radiation”, which dominates in edge plasmas. However, in our
simplified analysis of the CRM for hydrogen atoms (recall Eq. (2.13)), we neglected
2.3 Line Radiation Transport in Edge Plasma
27
Z) [21]; (iv) the so-called dielectronic recombination process (accompanied by
excitation of an ion’s electron and formation of a doubly excited atom/ion with
subsequent emission of the photon, A
Z+1 + e ! A
Z (n, n
0
) ! A
Z + ħω) should be
considered (e.g. see [38, 39] and the references therein); and v) some excited
quantum states of complex atoms/ions are “metastable” or just stable (e.g. the
ro-vibrational states of hydrogenic molecules).
To take into account such processes, one needs to modify the rate Eq. (2.12),
adding some new terms (for example, quenching of metastable states on the vacuum
chamber walls, which becomes important in weakly ionized plasma (e.g. see [13]).
This means that in such plasmas, one should consider the transport terms for the
particle density not only in the ground state but also in the metastable states.
However, in relatively high density and rather hot fusion plasma, the effective
lifetime of the metastable states is determined largely by the interactions of the
metastable atoms/ions with electrons and is strongly reduced in comparison to their
natural lifetime. In addition, the natural lifetime of ionic metastable states is decreasing as Z
À8 with increasing the ion charge Z. We also remind that some quantum
states within the “thin structure” of the hydrogen energy levels, caused by relativistic
effects, are also metastable. But due to the strong “mixing” of these levels in a fusion
plasma environment, these metastable states play no significant role. As a result, in
fusion research, the transport of metastable states is usually ignored and their
populations (as well as ionization/recombination balance and radiation loss) are
considered in a quasi-equilibrium approximation (recall Eq. (2.13)) on the equal
footage with other excited states (e.g. for details see [30] and the references therein).
The results of comprehensive numerical modeling show that for the edge plasma
conditions, even the metastable state 2
3 S 1 of helium, having the lifetime ~10
4 s, can
be treated in quasi-equilibrium approximation [40]. The presently most advanced
database providing the fusion-relevant impurity radiation loss, the contribution of
different lines, the rate constants, etc., is the ADAS database [41]. The divertor
modeling codes whose development had started before the ADAS database became
the de-facto standard can use some other data sources (for example, the AMJUEL,
HYDHEL and METHANE data sets [42] in SOLPS).
2.3 Line Radiation Transport in Edge Plasma
As we have seen in the previous sub-section, the populations of excited states are
determined by the competition between the processes involving interactions with
electrons and, playing important role, radiative decays (e.g. from level n to level k),
which are accompanied by the emission of photons having the energy ħω 0 % ΔE nk ,
where ω 0 is the photon frequency corresponding to the decay n ! k. This is the
so-called “line radiation”, which dominates in edge plasmas. However, in our
simplified analysis of the CRM for hydrogen atoms (recall Eq. (2.13)), we neglected
2.3 Line Radiation Transport in Edge Plasma
27