rates of different atomic processes. We will also consider some important examples
of the application of the CRM to atoms, molecules and ions for edge plasma
conditions, as well as line radiation transport in edge plasma and its implication
for relevant atomic processes.
2.1 Basic Quantum Mechanical Features of Atoms,
Molecules, and Ions Relevant for Magnetic Fusion
Research
As known from quantum mechanics (e.g. see [4]), atoms, molecules and their ions
can only occupy some particular quantum energy states bounded between the
so-called ground state and ionization (or dissociation) continuum of the
corresponding neutral/ion (or the molecule/molecular ion), which represents a free
electron and the remaining ion (or separated neutrals and ions). Such states can be
related to different electronic configurations and also, in the case of molecules, to
different rotationally and vibrationally excited states. It appears that the neutrals and
ions occupying excited states (situated in energy space above the ground state) play
important roles in virtually all atomic physics-related processes in edge plasmas even
though the relative fraction of such particles is often small. The situation with excited
particles is somewhat similar to that with free chemical radicals, which have low
concentrations but are important in many chemical reactions (e.g. see [5, 6]).
In this sub-section, we just review the main features of quantum states in the
atoms, molecules, and ions relevant for edge plasma (for more details one can refer
to [4] and special literature).
We start with quantum states in a hydrogen-like ion having one bound electron
and the charge number of nucleus Z (the case Z ¼ 1 corresponds to the hydrogen
atom). Omitting all relativistic effects, we find [4] that the energy levels, E n , depend
only on the principal quantum number n (1 n < 1) and
E
H Z
n ¼ À
m e Z
2 e
4
2ħ
2
1
n 2 ,
ð2:1Þ
where zero energy corresponds to the free electron (continuum), m e and e are the
electron mass and charge, and ħ is the reduced Planck constant (we neglect here the
terms of the order of the ratio of m e to the nucleon mass M nucl ). From Eq. (2.1) it
follows that the ionization potential of this hydrogen-like ion from the ground state
n ¼ 1 is I H Z ¼ m e Z
2 e
4
=2ħ
2 . However, it appears that the quantum states with n > 1
are not stable and decay rather quickly into states having lower principal quantum
numbers. The decay time from the level n to level k (k < n) is determined by the
Einstein coefficients, A
H Z
n!k , which in the quasi-classical Kramers approximation can
be written as [3]:
14
2 Atomic Physics Relevant to Fusion Plasmas
of the application of the CRM to atoms, molecules and ions for edge plasma
conditions, as well as line radiation transport in edge plasma and its implication
for relevant atomic processes.
2.1 Basic Quantum Mechanical Features of Atoms,
Molecules, and Ions Relevant for Magnetic Fusion
Research
As known from quantum mechanics (e.g. see [4]), atoms, molecules and their ions
can only occupy some particular quantum energy states bounded between the
so-called ground state and ionization (or dissociation) continuum of the
corresponding neutral/ion (or the molecule/molecular ion), which represents a free
electron and the remaining ion (or separated neutrals and ions). Such states can be
related to different electronic configurations and also, in the case of molecules, to
different rotationally and vibrationally excited states. It appears that the neutrals and
ions occupying excited states (situated in energy space above the ground state) play
important roles in virtually all atomic physics-related processes in edge plasmas even
though the relative fraction of such particles is often small. The situation with excited
particles is somewhat similar to that with free chemical radicals, which have low
concentrations but are important in many chemical reactions (e.g. see [5, 6]).
In this sub-section, we just review the main features of quantum states in the
atoms, molecules, and ions relevant for edge plasma (for more details one can refer
to [4] and special literature).
We start with quantum states in a hydrogen-like ion having one bound electron
and the charge number of nucleus Z (the case Z ¼ 1 corresponds to the hydrogen
atom). Omitting all relativistic effects, we find [4] that the energy levels, E n , depend
only on the principal quantum number n (1 n < 1) and
E
H Z
n ¼ À
m e Z
2 e
4
2ħ
2
1
n 2 ,
ð2:1Þ
where zero energy corresponds to the free electron (continuum), m e and e are the
electron mass and charge, and ħ is the reduced Planck constant (we neglect here the
terms of the order of the ratio of m e to the nucleon mass M nucl ). From Eq. (2.1) it
follows that the ionization potential of this hydrogen-like ion from the ground state
n ¼ 1 is I H Z ¼ m e Z
2 e
4
=2ħ
2 . However, it appears that the quantum states with n > 1
are not stable and decay rather quickly into states having lower principal quantum
numbers. The decay time from the level n to level k (k < n) is determined by the
Einstein coefficients, A
H Z
n!k , which in the quasi-classical Kramers approximation can
be written as [3]:
14
2 Atomic Physics Relevant to Fusion Plasmas