As we see from Fig. 2.6, E
H
ion is around 30 eV and even higher for the transparent
and not so dense (n e < 10
14 cm
À3 ) plasma, which significantly exceeds the hydrogen
ionization potential I H ¼ 13.6 eV since the excitation rate constants exceed the
ionization ones. However, E
H
ion falls with increasing electron density above
~10
14 cm
À3 to the values close to I H ¼ 13.6 eV due to the contribution of the
multi-step processes to ionization even for transparent plasma. This effect becomes
more pronounced for the plasma opaque for the Lyman radiation.
So far, we discussed atomic processes related to atomic hydrogen. However,
hydrogen molecules, having rich internal structure due to the presence of the
rovibrational quantum states, can play an important role in high-density,
low-temperature edge plasma phenomena. At low, ~few eV, electron temperatures,
plasma cooling due to excitation of electronic states of neutrals and ions becomes
less efficient because of the reduction of corresponding rate constants. At the same
time, the cross-section of electron impact excitation of the vibrational states of
molecular hydrogen, which goes through the metastable ion H
À
ð Þ
2 having a relatively
low energy threshold [12, 17, 18], still remains large (see Fig. 2.7). As a result, the
effective “cooling” rate constant, e
K cool ¼ ΔE K ΔE , (where ΔE is the electron energy
loss due to excitation to some quantum state and K ΔE is the corresponding rate
constant) for the excitation of the first vibrational level of H 2 , e
K
vibr
cool , at small, ~1 eV,
electron temperatures exceeds the cooling rate constant for the excitation of quantum
state n ¼ 2 for atomic hydrogen, e
K
1!2
cool , (see Fig. 2.8).
The vibrational states of a Hydrogen molecule in the background electronic state
are virtually stable. Therefore, their incorporation into the CRM model (e.g. see
[31]), which assumes that the population of all excited states is settled (due to
spontaneous decay) on the time scale much shorter than the transport time scale,
cannot be justified. As a result, the population of the vibrational states should be
Fig. 2.6 Dependence of
hydrogen ionization cost
E
H
ion on electron temperature
for different plasma
densities for the case of fully
transparent plasma and
suppressed spontaneous
decay from the levels n ! 2
to the ground state, which
mimics completely opaque
condition for Lyman lines
34
2 Atomic Physics Relevant to Fusion Plasmas
H
ion is around 30 eV and even higher for the transparent
and not so dense (n e < 10
14 cm
À3 ) plasma, which significantly exceeds the hydrogen
ionization potential I H ¼ 13.6 eV since the excitation rate constants exceed the
ionization ones. However, E
H
ion falls with increasing electron density above
~10
14 cm
À3 to the values close to I H ¼ 13.6 eV due to the contribution of the
multi-step processes to ionization even for transparent plasma. This effect becomes
more pronounced for the plasma opaque for the Lyman radiation.
So far, we discussed atomic processes related to atomic hydrogen. However,
hydrogen molecules, having rich internal structure due to the presence of the
rovibrational quantum states, can play an important role in high-density,
low-temperature edge plasma phenomena. At low, ~few eV, electron temperatures,
plasma cooling due to excitation of electronic states of neutrals and ions becomes
less efficient because of the reduction of corresponding rate constants. At the same
time, the cross-section of electron impact excitation of the vibrational states of
molecular hydrogen, which goes through the metastable ion H
À
ð Þ
2 having a relatively
low energy threshold [12, 17, 18], still remains large (see Fig. 2.7). As a result, the
effective “cooling” rate constant, e
K cool ¼ ΔE K ΔE , (where ΔE is the electron energy
loss due to excitation to some quantum state and K ΔE is the corresponding rate
constant) for the excitation of the first vibrational level of H 2 , e
K
vibr
cool , at small, ~1 eV,
electron temperatures exceeds the cooling rate constant for the excitation of quantum
state n ¼ 2 for atomic hydrogen, e
K
1!2
cool , (see Fig. 2.8).
The vibrational states of a Hydrogen molecule in the background electronic state
are virtually stable. Therefore, their incorporation into the CRM model (e.g. see
[31]), which assumes that the population of all excited states is settled (due to
spontaneous decay) on the time scale much shorter than the transport time scale,
cannot be justified. As a result, the population of the vibrational states should be
Fig. 2.6 Dependence of
hydrogen ionization cost
E
H
ion on electron temperature
for different plasma
densities for the case of fully
transparent plasma and
suppressed spontaneous
decay from the levels n ! 2
to the ground state, which
mimics completely opaque
condition for Lyman lines
34
2 Atomic Physics Relevant to Fusion Plasmas