Fig. 3.3.2: Effective atom density N0 (u) behind a normal shock into argon at initial pressures p, =0.1, 0.2, 0.5, 1, 2, 5, 10, 20 and 30 torr. The small numbers give the maximum value of
100 x a± x (N^ + N ® _ 1)/ (a0 x N 0etf) for Ar II (i = l), Ar III and Ar IV, the regions of which are indicated by .
CC
UJ
CU cc oo
DC
CO
LU cd z *—■«CC
ÜL.
CD
o _IH T T
n i,,,r ,rT-rnrrT
t h t ti I i I I I i I r
30 20
I I I t i t » I I t I t t IS H O C K S P E E D IN K M / S E C
I i I I I I I I I I I i i I I I » t t I I » I i I I I I I I I I I t I 1 I I I I I t I I I I15
20
25
30
35
40
45
50
55
60
M A C H N U M B E R
0
with 6 (X) as defined in equation (3.3.3). Based on the sum rule
approximation and using formula (2.1.4) for am (w ) and (2.1.3) for a e (oo),
108 we then obtain with go = ■ ■ ■;
K A
oo
<j) (X) = 2ttx 108 x a^ x N fa (co)-a (go)1 . (3.3.10)
m 0 m^ m e '
0
This means that A (X) is obtained by assuming the low excited state m to m
behave like the ion core in conjunction with the corresponding hydrogen
excited state (using the known oscillator strengths of the m-k
transitions with the sum rule a p proximation), rather than a free
electron as was assumed in formula (3.3.3). Within this approximation,
we therefore have to add d> (X) for each low excited state to 6(X) as m
obtained from formula (3.3.5).
In order to estimate the relative significance of the $m (X) > we
define d>. T (X)= 2 <j> (X) and <i>A TT = 2 <j> (X), where the sum m is over all Ar I m ' A r i l n
m n
3d, 4s, 4p and 5s excited states of Ar I as tabulated in Wiese (1969) and
similarly the sum n over the 3s, 4s and 4p excited states of Ar II. In
the region where Ar I excited states dominate the plasma (see Fig. 3.3.1),
the relative influence of the excited states as far as they were not
accounted for in equation (3.3.5), is therefore given in per cent of 6(X)
as E^r j- (X) = 100 x <J>^ ^ (X) /6 (X) , and similarly
EA r I I (A) = 1 0 0 x 'i>A r I I (A)/6(X ) -
The program used to calculate the results plotted in Fig. 3.3.1 was
also used to find the conditions for a 20 torr shot where E. T (X) and Ar i
0f f
EAr i i^ ) are most significant, defined by N ^ g /Ne (N^g = population of one 4s level of Ar I or Ar II) being a maximum. For Ar I the conditions
for a maximum E. T (X) at p, = 20 torr are: u = 8.4 km/sec, T = 18490 K,
Ar I 1
N = 3.57 x 1018 cm- 3 , Nft = 3.90 x 1018 cm"3 , N eff = 4.14 x 1018 cm"3 ,
e 0 e
= 6.09 x 1018 cm"3 and N. /NeEE = 4.8 x 10"4 . For Ar II we obtain
o 4s e
Nj = 5.41 x 1080 cm”3 , N®ff = 1.14x l O 19 cm”3 , N®ff = 4.77 x l O 18 cm”3 and N. /Neff = 1.6 x 10"4 .
4s e
In Fig. 3.3.4 ^(A) and E^ ^ ( A ) ~ 10.0 are plotted for these conditions. In calculating E(A), no reduction of the ionization
potential was considered. In using formula (2.1.4), the line width AA was taken as 90 Ä for E. T and 300 Ä for E. _T . These values for the
Ar I Ar II
line broadening are of the order of the Stark broadening at these conditions; their significance in Fig. 3.3.4 is that, by using such values for AA, the peaks near the line centres are reduced which shows
the global behaviour of E(A) clearer.
The plot of E^ j-(A) shows that the important Ar I transitions are of the type m-k' for A < 6400 Ä, except for the 4p continuum contribution
(4p-c). The 4s-4p peaks of Ar I have to be considered if two-wavelength interferometry is used with one wavelength > 6400 Ä. As to Ar I plasmas we conclude that formula (3.3.5) gives a very good description even for
these low excited states (15.9% of all Ar I excited states at the condition in Fig. 3.3.4) for A <6400 Ä.
For Ar II, however, the situation is different. The important transitions are now definitely of type m-k" or m-k'" which makes formula
(3.3.3) an inadequate description of these states. But the relative influence of these states is less significant than for Ar I; we have
ef f
seen that was only 1/3 of the value for the Ar I plasma and also the population of these low excited states is only 1.3% of the total excited state population of Ar II at the condition in Fig. 3.3.4. Generalizing the behaviour of Ar II and the higher ions we find:
(1) The known transitions are mostly of type m-k" or m-k"' making formula (3.3.3) inadequate to describe them.