Pressure Broadening of Multiply Ionized Carbon Lines
P . BOGEN
European Space Research Institute, Frascati (Italy)
(Z. Naturforsch. 27 a, 210—214 [1972] ; received 24 November 1971)
In a helium plasma with carbon impurity, the pressure broadened profiles of seven C III and
two C IV lines have been measured. The plasma which was produced by magnetic compression had
typically an electron density of 4 - 1 0 1 7 c m - 3 , a temperature of 60 000°K, and a life time of about
0.1 fts. Electron densities have been deduced from the width of the He II 2 = 3203 Ä line. If
AEn'^kT
{AEa> = energy difference between perturbed level i and perturbing level i') the
classical straight line non-adiabatic theory gives values being in good agreement (error < ± 25%)
with measured widths for six lines. For two lines the deviations are larger. For the C IV resonance
line (A = 1550 Ä) with AEu'^>k T, the profile can be explained by hyperbolic path, adiabatic collision theory. The semiempirical Gaunt-factor approximation gives a rough estimate of the width,
but normally the values obtained are too low.
A.
Introduction
p l a s m a l a y e r s s h o u l d b e l o w . T h e t e m p e r a t u r e T is
n o r m a l l y not very critical f o r the interpretation
Numerous
on
investigations
the p r e s s u r e
ionized
been
of
neutral
broadening
a t o m lines emitted
ment between
have
from
carried
and
singly
a plasma.
Agree-
t h e o r y a n d e x p e r i m e n t is w i t h
exceptions within
+ 20%
out
f o r the n e u t r a l 1 ,
line b r o a d e n i n g
T
sufficient accuracy f r o m
has
been
estimated
an a b s o l u t e l i n e
mum
50%
bank.
as f u n c t i o n
of
the v o l t a g e o f
the
of
with
intensity
a n d f r o m the a p p e a r a n c e o f a l i n e i n t e n s i t y
some
±
data.
maxi-
condenser
( o r e v e n m o r e ) f o r the s i n g l y i o n i z e d a t o m s 2 ' 3 . F o r
multiply
ionized
parison
between
ions, nearly no
theory
and
quantitative
experiment
com-
has
been
m a d e although b r o a d e n e d lines o f those ions
have
B. Calculation of the Line W i d t h
F o r the i s o l a t e d i o n l i n e s o b s e r v e d h e r e
b e e n o b s e r v e d in m a n y l a b o r a t o r y a n d a s t r o p h y s i c a l
collisions
p l a s m a s . T h e m a i n r e a s o n f o r this g a p o f
a n d a L o r e n t z i n t e n s i t y p r o f i l e I(AOJ)
t i o n is p r o b a b l y
the e l e c t r o n
informa-
that a n a c c u r a t e m e a s u r e m e n t
density
was not possible
ne
in
of
a r e the m a i n b r o a d e n i n g
It A
\
l(Ao))
=
plasmas because of strong density gradients. There-
chapter:
"Experimental
In this p a p e r w e
describe
1 - 3
with
'
w
1
rr
{Aco —
d)2+w
length
and 0 . 6 c m diameter w a s used h e r e as a light s o u r c e
(see
o r I {AX)
a shifted m a x i m u m can be expected:
these
fore, a long plasma cylinder of about 3 0 c m
electron
mechanism
Arrangement").
measurements
of
1{AX)=
o r
where
the
w =
half-half
2njAk-8)*+(AXhl2)2
width
in
angular
frequency
u n i t s , AXh = f u l l h a l f w i d t h o f the l i n e i n w a v e l e n g t h
p r o f i l e s of C III and C I V lines emitted f r o m a m a g -
units, d a n d d = line shift. M a i n l y t w o m e t h o d s h a v e
netically c o m p r e s s e d plasma w h o s e electron
b e e n u s e d f o r the c a l c u l a t i o n : the c l a s s i c a l
ne
is
deduced
from
the
X = 3 2 0 3 Ä. Since C III
width
(47 eV)
of
the
density
H e II
and C I V
h a v e similar i o n i z a t i o n e n e r g i e s as H e l l
(64
line
line and the s e m i e m p i r i c a l Gaunt f a c t o r
eV)
tion.
(54
eV),
it c a n b e e x p e c t e d that their l i n e s a r e e m i t t e d
from
I n the c a s e AErf
culation can
kT
be replaced
the h y p e r b o l i c o r b i t calby
the s t r a i g h t
the s a m e r e g i o n o f the p l a s m a . T h e r e f o r e the e r r o r s
proximation
o f the l i n e w i d t h a n d ne
b r o a d e n i n g o f a level i h a v e b e e n u s e d
wi + id,=
caused b y
^
in-homogeneous
n0 [l)2
f f f ( v ) {I
2'3
.
The
2 \(i\R\ry |2 -[A(z?P)
straight
approxima-
following
equations
1
line
ap-
for
the
:
+iB(z&»)]
it
and
z T =
-
V
min
*
( I f ^ j
\ O )
JTl V
2
itn
|(*'|/?IOI2
Reprint lequests to Dr. P. BOGEN, Institut für Plasmaphysik der Kernforschungsanlage Jülich, D-5170 Jülich, Postfach 365.
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w i t h A,
B,
b functions defined in
a,
=squares
of
matrix
tion
vector
taken
AEw
= energy
and
perturbing
broadening
elements
from
BATES
difference
level
has
means:
w —^ w i
limited
number
of
and
and
into
4,
level
perturbing
i
lower
level
account.
This
(i = lower or upper level). Only
of
levels
i
can
be
The
been
average
over
obtained
GRIEM
in
gives
2
W
^
\(f
velocity
distribution
energy
of
squares
manner
results
a
either
u=(u2)1/l.
discrepancy
of
more
than
10%
how
less a c c u r a t e , s i n c e the c o n t r i b u t i o n s o f
any-
strong
collisions were large.
F o r t h e C I V r e s o n a n c e l i n e w i t h A En' >kT
adia-
batic processes are important and hyperbolic
have
to
be
used.
by
value
The
calculations
SAHAL-BRECHOT
y = 2 w = 0.4-10
ne s
- 6
have
and
been
SEGRE5.
for
_ 1
orbits
7, =
perTheir
4-10
°K
4
has been used.
e q u a t i o n f o r the w i d t h tFse of an i o n line
EN Y*
IkT
AEvi I
matrix
had
b)
o n l y in a f e w c a s e s , w h e n t h e c a l c u l a t i o n s w e r e
k T,
hydrogen,
of
has
taking
semiempirical
h
The
or
v={v~1)~1
formed
approximate
8
\ B \ f)\2
allowed
w.
the f o l l o w i n g
= ionization
and
the
an
a)
a
in-
c l u d e d in the c a l c u l a t i o n . T h i s causes an e r r o r smaller than 1 5 % in the line w i d t h
du = 1 a n d v a constant value,
/ f(v)
posi-
DAMGAARD
perturbed
Upper
taken
|(ij/?|z')|2
the electron
between
i.
been
1,
|(i'|/?|i)|2
elements
of
transitions f r o m the lower and upper
the
level
at
kT
AE„\
f
somewhat
higher
than
T
the
maximum
of
the
C I I I l i n e a n d at s o m e w h a t l o w e r T t h a n that o f
C I V line. F i g u r e 1 s h o w s that this m a x i m u m
the
should
of the emitted line, gse(S k T/\ 2 AEi'i |) = semiempiri- a p p e a r a t a v o l t a g e o f a b o u t 2 0 . 3 k V . T h i s v o l t a g e
cal G a u n t f a c t o r g i v e n g r a p h i c a l l y in
2
].
was
of
electron
density
has been
ne
applied
determined
by
t h e h a l f w i d t h o f the H e II line X = 3 2 0 3 Ä using the
value
one.
C = 2.25 • 1015
between
The
under
in
6,
tiple
ionization
12%
higher
cm
,
/ l
which
cannot
and
The
that
the
follows.
changing
The
the
ionization
plasma
capacitor
the c o n t i n u u m ,
the optically
were
of
measured
(Fig.
to
is
ne
measurement
carbon
C ions,
as f u n c t i o n
mulabout
always ne =
of
was used.
was
deduced
temperature
was varied
voltage,
the
and
of the C I V
1).
A
of
T
the
- 3
CIV
resonance
maximum
is e x p e c t e d ,
state c m
by
that the S a h a
a = 0.83
to b e
of
a,
which
lies
of
value
ionization
equation
can
7* = 5 6 0 0 0 ° K .
known
only
line,
carbon
This
roughly
has
ions
has been
in
the
to
he
The
for
the
the
optically
be
known
C IV
ground
performed
carbon concentration
With
ions to
7ie = 1 . 1 2 / 1 ;
by
two
me-
cm
- 3
ion
cm
- 3
in the initial gas
( d u e to the d o u b l e
,
a
2.5%.
From
carbon
ion
this v a l u e
density
is
ioniza-
the n u m b e r density ratio of
electrons is
= 4-1017
carbon
and
of
na
1-1016
is d e d u c e d . W i t h a = 0 . 8 3 w e o b t a i n t h e C I V
density
mann's
/iciv = 8.3 • 1015
law
for
the
cm
distribution
- 3
of
.
Using
C IV
Boltz-
ions
over
the different C I V e n e r g y levels w e find
n i 0 = 0 . 6 2 5 nc i v = 5 . 2 • 1 0 1 5
F o r this calculation
the
number
and
of the profile of
resonance
).
exact
calculations.
tion, see a b o v e )
of
line
- 3
1. T h e
2.8%.
intensities
line and
r a t i o o f t h e n u m b e r o f C I V i o n s to the total
of
has
the
the a p p l i e d
thods :
H e II
method
due
carbon
of
mean
for
the
the C I I I 4 1 8 7 Ä
thin wings
a
theoretical6
be used
density was
for
is
and
Using
calculated
except
The degree of
of
T
(n;o = n u m b e r
A~Vl,
helium
than n ; .
- 3
)'
conditions6.
it w a s
of
h
X = 5 8 0 1 Ä l i n e , w h e r e ne = 6 . 9 • 1 0 1 7 c m
as
get
of
thick
experimental
equation
present
described
c m "" 3
the
Saha
the
4-1017
Assuming
we
maximum
sensitive to
For the evaluation
ne=C(ZÜ
value
n e a r its
line b r o a d e n i n g
relation
with
since
is n o t v e r y
formula.
C. Evaluation of the Plasma Parameters
The
used
a
2. Using
Ä,
tion
T has to be k n o w n
the a b s o l u t e intensity
a hydrogenlike
between
C III
cm"3.
oscillator
5
gxG
of C III 1 =
strength,
state
roughly.
and
Saha's
CIV
4187
equa-
ground
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state, a n d
cm
7 = 56 000 °K,
a value of ni0 =
5.4-1015
was d e d u c e d . T h e agreement between the
- 3
derived values of ni0 indicates, that the Saha
two
equa-
tion is s u f f i c i e n t l y a p p r o x i m a t e d f o r C III.
ber
of
n
the v i s i b l e
near
and
UV
lines
tral o r s i n g l y i o n i z e d a t o m s 7 . T h e r e f o r e the
difference AEu'
w i d t h h w)
(being
large c o m p a r e d
ed.
T h e e x p e r i m e n t is s i m i l a r to that d e s c r i b e d
earlier
The
walfwidth
empirical
to
is n o r m a l l y small c o m p a r e d
the c l a s s i c a l straight line m o d e l is well
D. Experimental Arrangement
cause
calculated
Zl/hl
Gaunt-factor
shows
a
energy
the
line
to k T
and
approximat-
with
also
neu-
the
semi-
rough
agree-
b y t h e a u t h o r 6 . It is a s m a l l t h e t a - p i n c h
arrangement
ment, h o w e v e r the values are normally smaller
with
a main
the o b s e r v e d ones.
a
preionization,
a
preheating,
and
dis-
c h a r g e u s i n g a 2 5 k V , 3 /uF c o n d e n s e r b a n k . T h e c o m pression c o i l has a l e n g t h of 3 0 c m and a d i a m e t e r of
4 cm. The
thane
filling
pressure was about 0.4 T o r r H e + me-
Spectroscopic
observations
have b e e n m a d e
axially
at b o t h e n d s . O n o n e e n d , t h e p l a s m a r a d i a t i o n is f o c u s s e d in v a c u u m (i. e.
filling
p r e s s u r e o f the discharge
t u b e ) b y a m i r r o r o n t h e slit o f a 5 0 c m
Ebert-vacuum
m o n o c h r o m a t o r , o n t h e o t h e r e n d it is f o c u s s e d in air
by
a
50
cm
quartz-fluorite
Ebert
achromat
monochromator
electric detector. A
calibration
of
rangement.
The
Relatively
the
carbon
on
the
slit
equipped
of
with
arc was used
for
photo-
absolute
monochromator-photomultiplier
profiles
have
been
scanned
ar-
shot
by
deviations
calculated
and especially the X = 4 3 2 6 Ä
Pertran-
(ioniza-
tion
for
limits C I V
2S
and
2
P)
are i m p o r t a n t
F o r the o p t i c a l l y thin lines, the o b s e r v e d
profiles
fit a d i s p e r s i o n p r o f i l e w i t h i n t h e e r r o r l i m i t s i n all
cases.
3
An
2S1/2
— 3
example
2
is
P 1 2 ? ^3/2
very
well
a n d the e q u a l h a l f w i d t h .
the
T h e interpretation
sonance
line
poses
given
doublet
shows
in
of
expected
Fig.
C IV,
2:1
for
difficulties,
values
of
AXh
the
t o g e t h e r w i t h t h e c a l c u l a t e d v a l u e s AXhi
AXh3
are g i v e n in T a b l e
1 . AXh2
and
halfwidths
, AXh2,
AXh3
and
obtained
wavelength
on
AX
is
range
difficult
(Fig.
to
4).
The
determine
ratio
thick C I V
re-
although
the
exact
on
the
far
b y straight line a p p r o x i m a t i o n , s h o w s in m a n y cases
identified
a surprisingly
h o w e v e r , is n o t p e r t u r b e d b y o t h e r lines, a n d
tal
values,
singly
in
ionized
good
a g r e e m e n t w i t h the
contrast
to
many
experimen-
observations
atoms. T h e explanation
is e a s y .
increased nuclear charge Z and main quantum
on
The
num-
wide
dependence
wings,
because there are strong C III lines and other,
fore
(perhaps also C I I I )
the evaluation
wavelength
blet
was
of
AXh
region. The
very
has
lines. T h e line
been
made
total h a l f w i d t h
reproducible
of
AK
Ah l
Ah2
A/lh3
5696
4647
4326
4187
3609
2163
1532
5802
2s3p1P-2s3d1D
2s3s3Si-2s3p3P2
2p3s1P-2p3p1D
2s4fiF-2s5giG
2s 4 p 3 P — 2s 5 d 3 D
2s 3 d : D — 2 s 4 f XF
2 s 3 p * P — 2 s 4 d XD
3 s 2 S i / 2 — 3 p 2 P3/9 |
1.9
0.95
2.1
4.1
6.2
0.46
0.43
0.8
0.55
0.6
3.8
7.6
0.39
0.44
1.0
0.8
0.9
3.6
7.5
0.47
0.49
1.2
0.9
1.1
3.7
7.1
0.45
0.44
1.6
0.84
1.35
1.45
5812
1548.2
3s 2Si/2 — 3 p 2Pi/2 I
2s2Si/2-2p2P3,2 ]
0.024
0.0064
1550.8
2 s 2Si/2 — 2 p 2Pi/2 J 1
non
core,
therein
the
at 5 . 5 Ä + 0 . 1 5 Ä
Transition
the
also
intensity
of the o p t i c a l l y
some
3
which
intensity of the line c a n b e f o l l o w e d up o v e r a
experimental
the
b r o a d e n i n g o f these lines.
c i l l o g r a m is s h o w n in F i g u r e 2 .
The
the
line.
s i t i o n s b e t w e e n the t w o C I I I t e r m s y s t e m s
shot, taking o n e shot a b o u t every 9 0 sec. A t y p i c a l os-
E. Results
between
haps the n o r m a l l y neglected collisions c a u s i n g
another
a
strong
than
a n d o b s e r v e d values are o b t a i n e d in the c a s e o f
A= 5696 Ä
(0.2-6%).
the
levels to b e m o r e hydrogen-like than those of
this
douover
0.02
Table 1. AXh = Experimental halfwidth in Ä for an optically thin layer, Zl/.hi = semiempirical halfwidth, AXh2 — halfwidth
from straight line approximation taking v~1 = (1/v), d / h 3 = halfwidth from straight line approximation taking v = (v2)
AXh4 = halfwidth f r o m hyperbolic orbit approximation. All values of AXh are given for n e = 4 - 1 0 1 7 c m - 3 .
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(arbitrary units)
20
10-\
JO
M
in
c/>
C
JO
M
CO
JO
O
>
5
16
19
20
21
22 U[kV]
Fig. 1.
Fig. 2.
1
1520
1530
1540
1550
1560
1570
1580 A.W
Fig. 4.
Fig. 1. Intensities at 2 = 3627 A (continuum), 2 = 4187
A (C III, two runs), and 2 = 1543 A ( C I V ) as function of voltage of the condensers.
20-
(arbitrary
Ö
M
2
p—I
O
O
C
f
H
units)
Fig. 2. Intensity at 2 = 3 2 1 0 A ( H e l l ) (upper curve)
and 2 = 1544 A ( C I V ) (lower curve) as function of
time. Sweep 0.1 ^s/div.
r
«!
o
z
N
M
Ö
n
>
15-
theoretical
experimental
jo
oCO
10-
z
Fig. 3. The dispersion profile of the C I V 3 2 S 1 / 2 - 3 2 P 1 / 2 , 2 P s / 2
doublet with Zl2h = 2 . 7 A at n o = 6 . 9 ' 1 0 1 7 c m - 3 . Ä constant background intensity of 6 units has been subtracted.
Fig. 4. Experimental profile of the C I V 2 2 S 1 / 2 - 2 2 PI/ 2 , 2 P s / 2 resonance doublet at n e = 4 - 1 0 1 7 c m - 3 , nio-l — 1.6-10 1 7 c m - 2 .
• — x — • Experimental profile with values of two different runs.
Dispersion profile for /I2h = 2 . 4 - 1 0 - 2 A and an estimated intensity background of about 2 units.
05790
5795
5600
5605
5810
5815
5820 Ä IÄ1
to
i—i
w
Fig. 3.
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four
runs.
following
From
way:
this
value
First w e
we
find
obtain
from
radiative transfer for a h o m o g e n e o u s
I = B(
=
bB
minus
broadened
line
instead
lowing induced
2
3
4
and
neglecting
hAXh
-1
+
AX2
(
r =
x
induced
emission
30
[see
of
8,
Eq.
2 f
0.69
l =
angular
abI
=
cm).
frequency
collision
units
wave-
and
al-
emission
l-Ah
X2
2 m c2 n-io'f
"i0 ' AX2+(AXh/2)2
the
optical
taking
optical
thickness
and
2
, f2 = 0 . 0 9 5
= 5.2-1015
coefficient,
(68,16) ]
AXh
UAXh
(AX+AXa)2
he
optically
effective absorption coefficient =
Xt = 1 5 5 0 . 8 Ä
1
= 2.573 Ä
AXa
e 2 X2
S e c o n d l y we use the equation f o r x of a
Adding
distance
2 m c2 " i O
function,
length of the optical layer =
length
a
in the d e n o m i n a t o r w e o b t a i n
layer
_ J ) / l o g e = log 2/log e =
Kirchhoff-Planck
sorption
with
In this e q u a t i o n w e put the n u m e r i c a l v a l u e s
t h i c k n e s s , v, =
T~
of
line
r = log (
(B
the
l-e~x)
the o p t i c a l t h i c k n e s s at the h a l f w i d t h o f an
thick
in
AX.h
the equation
cm
(see
- 3
4
), X = 1550 Ä,
the
Then
5.5 Ä
the
width
2-10~
agreement
2
Ä.
The
not given in
error
of
of
experimental
f o l l o w s f r o m x*/0.69
factory
5
=
ni0
.
W i t h a r b i t r a r y A/ih = x, w e d r a w t h e c u r v e
At
{jx
1= 30 cm,
the p r o f i l e
value
with
for
AXi h = 2 . 4 - 1 0
the
of
calculated
r*.
- 2
width5
the theoretical
the c a s e / l £ V j > l ,
the e x p e r i m e n t a l
r(zU).
measure
Ä
. T h i s v a l u e is in satis-
=x/AXh
accuracy
of
we
value
is in
the
of
value
is
estimated
the
order
of
40%.
1
of
exp
\
IkT j
the two
lines
X2 = 1 5 4 8 . 2
Ä
H. R . GRIEM, Plasma S p e c t r o s c o p y , M c G r a w - H i l l B o o k Co.,
N e w Y o r k 1964.
H . R . GRIEM, Phys. R e v . 165, 258 [ 1 9 6 8 ] .
H. R . GRIEM, B r o a d e n i n g of Spectral Lines b y Charged Particles, University of M a r y l a n d , P h y s i c s 2 4 8 [ 1 9 7 0 ] .
D . R . BATES a n d A . DAMGAARD, P h i l . T r a n s . R o y S o c . L o n -
I thank the K F A
tal e q u i p m e n t
and
Jülich f o r the l o a n of
in c o n s t r u c t i o n a n d o p e r a t i o n o f t h e
5
6
7
8
experimen-
M r . I. POLLARD f o r technical
help
experiment.
S . S A H A L - B R E C H O T a n d E . R . A . SEGRE, A s t r o n . a n d
Astro-
phys. 1 3 , 1 6 1 [ 1 9 7 1 ] .
P. BOGEN, Z . Naturforsch. 25 a, 1 1 5 1 [ 1 9 7 0 ] ,
J. P. CONNERADE, Astrophys. J. 1 6 3 , 4 1 7 [ 1 9 7 1 ] .
A . UNSOLD, P h y s i k der Sternatmosphären, Springer-Verlag.
Berlin 1955.
d o n , Ser. A 242, 101 [ 1 9 4 9 ] .
Unauthenticated
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