VII.
GASEOUS ELECTRONICS
Academic and Research Staff
Prof. S. C.
Prof. E. V. George
Prof. G. Bekefi
J. J. McCarthy
W. J. Mulligan
Brown
Graduate Students
J. Golden
D. Prosnitz
G. J. Raff
A.
TONKS-DATTNER RESONANCES IN ION LASER
Tonks-Dattner resonances have been observed in an argon ion laser discharge.
These resonances enable one to calculate the electron temperature of the plasma.
The discharge was contained in a 40-cm quartz tube (2 mm i. d.) surrounded by
a 12 mm o. d. cooling jacket.
The resonances were observed by shining a 35. 1 GHz
source on the discharge and observing the power reflected as a function of discharge
The electron density was determined at each resonance by measuring the
current.
frequency shift of the TE011 mode of a microwave
described elsewhere.
Tonks-Dattner
cavity.
(This method is
fully
)
resonances are the result of standing waves which may form between
the plasma sheath and the point where the driving frequency
2
2
= n(r) e 2/ME o
plasma frequency (wp(r)).[
o (r)
and M the electron mass.]
Schmitt et al.
,
(w) is
equal to the local
where n(r) is the electron density
have used a WKB approximation to obtain
the following condition for the existence of a standing wave.
(4-_\
m+
+
=
K ra
ar
K dr =
a
O
where m
2-
2
1/ 2
Mpjr
--
dr,
O
is the resonance index (m= 0, 1, 2...), T the electron temperature,
tube radius,
and ro the point where
tion density profile w 2 (r)= o2 J(
OPo
(3kT
3 k)
.40
a
5
r)to
2aw
( )
TrZ
m+
2
o = c p(r
/
2.405 J 1 (2. 405)
).
a the
They then assume a Bessel func-
obtain
2
Po
1-
J 2 (2.405)
2
5J (2 .405)
I "
W_
o
This work was supported by the Joint Services Electronics Programs (U. S. Army,
U. S. Navy, and U. S. Air Force) under Contract DAAB07-71-C-0300.
QPR No.
103
2
3
4
5
URRENT
W
(P),
6
9
7
CURFOO(A)
Fig. VII-1.
Tonks-Dattner. resonances in the reflection
of an argon ion laser discharge.
(a) 3. 0 Torr,
(c) 4. 1 Torr.
(b) 3. 5 Torr.
(d) 4. 7 Torr.
ARGON
25
O
D
+
A
4.7
4.1
3.0
3.5
Torr
Torr
Torr
Torr
2.2
2.6
3.5
2.7
eV
eV,
eV
eV
m RESONANCE INDEX
Fig. VII-2.
2 plotted against the Tonks-Dattner resonance index.
p
The
resonance spacing enables calculation of electron temperature.
QPR No. 103
100
(VII.
GASEOUS ELECTRONICS)
The expression above may then be used to determine the electron temperature.
Figure VII-1 shows the resonances as a function of discharge current.
plotted against the resonance index m,
ure VII-Z shows (o/( p ))
p
the average plasma frequency,
p
ME
Here
slope of these lines determined the designated electron temperature.
The
is
) e
(
Z
where (Lo p
p
Fig -
we have assumed that
W2
2 <<1."
5J (2.405)
J 2 (2. 405)
p
1
An instability
in the discharge prevents us from obtaining a full range of resoFigure VII-3 shows the electron temperatures calculated
nances at lower pressures.
8-
6
Fig. VII-3.
S4
z
U
*
Electron temperature of argon ion
laser as calculated from m = 1
Tonks-Dattner resonance.
2
I
0
0
0.1
0.2
0.3
I
0.4
0.5
pr (Torr-cm)
uing the single resonance for which the most data were available (m= 1).
that this gives good qualitative
It is seen
agreement with Schottky theory.
We realize that this method can only yield approximate figures for the electron
temperature as all computations depend on the assumed density profile.
A radiom-
eter is being constructed so that more accurate temperature measurements
may be
made.
D. Prosnitz, E.
V.
References
1. L. D. Pleasance and E. V.
2. H. J.
Schmitt, G. Meltz,
QPR No. 103
George, Appl. Phys. Letters 18,
and P.
G. Freyheit, Phys.
101
101
557-561 (1971).
Rev. 139A 1432 (1965).
George