beams suitable for plasma heating in magnetic fusion reactors (e.g. see [9] and the
references therein).
We notice that some excited quantum states of complex atoms/ions, the so-called
“metastable” states (spontaneous transitions from these states to lower energy states
are “forbidden” by selection rules [4]), exhibit no spontaneous decay to lower states
for a time much longer than ~2Â10
À9 s that follows from Eq. (2.2) for the transition
from the first excited to the ground state in the hydrogen atom. The examples of such
metastable states in helium are the triplet electron configuration 2
3 S 1 (see Fig. 2.2),
having extremely long natural life-time ~ 10
4 s [10], and the singlet state 2
1 S 0 which
has much shorter, ~20 ms [11], natural life-time. Such long-living metastable states
(e.g. 2
3 S 1 in helium) play very important role in ionization balance of low temperature, weakly ionized plasma, by providing the so-called Penning ionization channel, A Ã + B ! A + B
+ + e, where A Ã is a particle in a metastable state with the energy
higher than the ionization potential of the particle B (e.g. see [12–14] and the
references therein).
So far, we were discussing quantum effects related to atoms/ions. However,
plasma recycling on the PFCs results partly in the formation of molecules, which
play an important and somewhat peculiar role in edge plasma processes.
Since hydrogen is the major component in fusion plasmas, we will consider
mainly the hydrogen molecules. As before, we will distinguish molecules containing
different isotopologues of hydrogen molecule (e.g. H 2 , D 2 , DT, etc.) only when it
becomes important, otherwise, we will call them just hydrogen molecules and use
the notation H 2 . Molecular hydrogen having two nuclei introduces new features in
the energy spectrum of the quantum states. Using disparity in electron and nuclei
dynamics, related to the difference in their masses, one could start with the analysis
of electronic states assuming that the separation distance, R, between the two nuclei
is fixed (e.g. see [4]). As a result, the energy of the electronic quantum states and the
corresponding electrostatic potential of the interacting nuclei, U n (R), depend on
R. Since the dynamics of nuclei, in zero-order approximation, is ignored, the
potential curves U n (R) remain the same for all isotopologues of hydrogen molecule
(e.g. H 2 , D 2 , DT, etc.). The U n (R) terms in diatomic molecules are described by the
projections of the total orbital angular momentum on the axis passing through the
two nuclei, Λ ¼ 0, 1, . . . (which are denoted with the Greek letters Σ, Π, . . .) and
the total spin of all electrons S (in the same way as in atoms). Finally, for the case
where the atoms in the molecule are the same, the Hamiltonian is invariant with
respect to the change of sign of the coordinates of all electrons and we can speak of
the parity of electron wave functions, which can be even, denoted as “g” or odd,
denoted as “u” (from corresponding German words “gerade” and “ungerade”).
Strictly speaking, we cannot apply this property for diatomic hydrogenic molecules
composed of different isotopes. But in practice, the isotopic effect produces a very
tiny impact (of the order of the electron to nucleon mass ratio [15]) on the energy
spectrum, which, in practice, affects only the line radiation transport we will consider
later. As a result, the molecular terms of all diatomic hydrogen molecules are
practically identical to that of H 2 , shown in Fig. 2.3.
2.1 Basic Quantum Mechanical Features of Atoms, Molecules, and Ions Relevant for. . .
17
references therein).
We notice that some excited quantum states of complex atoms/ions, the so-called
“metastable” states (spontaneous transitions from these states to lower energy states
are “forbidden” by selection rules [4]), exhibit no spontaneous decay to lower states
for a time much longer than ~2Â10
À9 s that follows from Eq. (2.2) for the transition
from the first excited to the ground state in the hydrogen atom. The examples of such
metastable states in helium are the triplet electron configuration 2
3 S 1 (see Fig. 2.2),
having extremely long natural life-time ~ 10
4 s [10], and the singlet state 2
1 S 0 which
has much shorter, ~20 ms [11], natural life-time. Such long-living metastable states
(e.g. 2
3 S 1 in helium) play very important role in ionization balance of low temperature, weakly ionized plasma, by providing the so-called Penning ionization channel, A Ã + B ! A + B
+ + e, where A Ã is a particle in a metastable state with the energy
higher than the ionization potential of the particle B (e.g. see [12–14] and the
references therein).
So far, we were discussing quantum effects related to atoms/ions. However,
plasma recycling on the PFCs results partly in the formation of molecules, which
play an important and somewhat peculiar role in edge plasma processes.
Since hydrogen is the major component in fusion plasmas, we will consider
mainly the hydrogen molecules. As before, we will distinguish molecules containing
different isotopologues of hydrogen molecule (e.g. H 2 , D 2 , DT, etc.) only when it
becomes important, otherwise, we will call them just hydrogen molecules and use
the notation H 2 . Molecular hydrogen having two nuclei introduces new features in
the energy spectrum of the quantum states. Using disparity in electron and nuclei
dynamics, related to the difference in their masses, one could start with the analysis
of electronic states assuming that the separation distance, R, between the two nuclei
is fixed (e.g. see [4]). As a result, the energy of the electronic quantum states and the
corresponding electrostatic potential of the interacting nuclei, U n (R), depend on
R. Since the dynamics of nuclei, in zero-order approximation, is ignored, the
potential curves U n (R) remain the same for all isotopologues of hydrogen molecule
(e.g. H 2 , D 2 , DT, etc.). The U n (R) terms in diatomic molecules are described by the
projections of the total orbital angular momentum on the axis passing through the
two nuclei, Λ ¼ 0, 1, . . . (which are denoted with the Greek letters Σ, Π, . . .) and
the total spin of all electrons S (in the same way as in atoms). Finally, for the case
where the atoms in the molecule are the same, the Hamiltonian is invariant with
respect to the change of sign of the coordinates of all electrons and we can speak of
the parity of electron wave functions, which can be even, denoted as “g” or odd,
denoted as “u” (from corresponding German words “gerade” and “ungerade”).
Strictly speaking, we cannot apply this property for diatomic hydrogenic molecules
composed of different isotopes. But in practice, the isotopic effect produces a very
tiny impact (of the order of the electron to nucleon mass ratio [15]) on the energy
spectrum, which, in practice, affects only the line radiation transport we will consider
later. As a result, the molecular terms of all diatomic hydrogen molecules are
practically identical to that of H 2 , shown in Fig. 2.3.
2.1 Basic Quantum Mechanical Features of Atoms, Molecules, and Ions Relevant for. . .
17