line, such that Δω ) Γ, results in a strong reduction of σ abs (ω 0 ), which now becomes
~(c/ω 0 )
2 (Γ/Δω). For example, for the case where the Doppler effect dominates the
line broadening, the characteristic absorption length of the line corresponding to the
transition between the n-th excited state and the ground one in a hydrogen atom,
ℓ abs ~ 1/σ abs (ω 0 )[H], can be found from the following expression [20]
ℓ abs ¼ π
3=2 c=ω 1n
ð
Þ
2 n
2 A
H
n!1 =Δω D
À
Á
H
½
n
o À1
,
ð2:22Þ
where ω 1n ¼ ΔE 1n /ħ, Δω D ¼ ω 1n (2T [H] /M nucl )
1/2 /c, and T [H] is the temperature of
the hydrogen atoms. For [H] ¼ 10
14 cm
À3 and T [H] ¼ 3 eV, which are rather typical
for dense divertor plasma, from Eq. (2.22) we find the absorption lengths of
Ly α ~ 0.2 cm and Ly β ~ 2 cm, which is shorter than the characteristic scale-length
of the variation of the neutral gas density and one can expect trapping of both Ly α
and Ly β radiation.
The radiation trapping alters the partition of radiation in different line series
(e.g. Lyman and Balmer series). For example, in a transparent plasma, the partition
of Ly β (transition 3 ! 1) and H α (transition 3 ! 2) intensities depends only on the
corresponding spontaneous emission coefficients and their ratio should remain
constant. However, if Ly β is trapped (H α is not trapped in the edge plasma due to
a very small ratio [H n¼2 ]/[H]), this partition will change, which exhibits a clear
signature of the radiation trapping effects. Such a change in Ly β and H α partition
was, in particular, observed in the experiments on Alcator-C-Mod tokamak [48] and
can be seen in Fig. 2.4a, where the Ly β intensity decreases with increasing D α
intensity (D α is the line 3 ! 2 in deuterium). We note that the increase of the D α
Fig. 2.4 The dependences of the Ly β transmission (a) and the intensity of Ly α (b) on the intensity
of D α . (Reproduced with permission from [48], © AIP Publishing 1998)
2.3 Line Radiation Transport in Edge Plasma
29
~(c/ω 0 )
2 (Γ/Δω). For example, for the case where the Doppler effect dominates the
line broadening, the characteristic absorption length of the line corresponding to the
transition between the n-th excited state and the ground one in a hydrogen atom,
ℓ abs ~ 1/σ abs (ω 0 )[H], can be found from the following expression [20]
ℓ abs ¼ π
3=2 c=ω 1n
ð
Þ
2 n
2 A
H
n!1 =Δω D
À
Á
H
½
n
o À1
,
ð2:22Þ
where ω 1n ¼ ΔE 1n /ħ, Δω D ¼ ω 1n (2T [H] /M nucl )
1/2 /c, and T [H] is the temperature of
the hydrogen atoms. For [H] ¼ 10
14 cm
À3 and T [H] ¼ 3 eV, which are rather typical
for dense divertor plasma, from Eq. (2.22) we find the absorption lengths of
Ly α ~ 0.2 cm and Ly β ~ 2 cm, which is shorter than the characteristic scale-length
of the variation of the neutral gas density and one can expect trapping of both Ly α
and Ly β radiation.
The radiation trapping alters the partition of radiation in different line series
(e.g. Lyman and Balmer series). For example, in a transparent plasma, the partition
of Ly β (transition 3 ! 1) and H α (transition 3 ! 2) intensities depends only on the
corresponding spontaneous emission coefficients and their ratio should remain
constant. However, if Ly β is trapped (H α is not trapped in the edge plasma due to
a very small ratio [H n¼2 ]/[H]), this partition will change, which exhibits a clear
signature of the radiation trapping effects. Such a change in Ly β and H α partition
was, in particular, observed in the experiments on Alcator-C-Mod tokamak [48] and
can be seen in Fig. 2.4a, where the Ly β intensity decreases with increasing D α
intensity (D α is the line 3 ! 2 in deuterium). We note that the increase of the D α
Fig. 2.4 The dependences of the Ly β transmission (a) and the intensity of Ly α (b) on the intensity
of D α . (Reproduced with permission from [48], © AIP Publishing 1998)
2.3 Line Radiation Transport in Edge Plasma
29