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Energy balance of the low-pressure mercury-argon positive column
Physica 29 565-584
Koedam, M. Kruithof, A. A. Riemens, J. 1963
ENERGY BALANCE OF THE LOvV-PRESSURE MERCURYARGON POSITIVE COLUMN by M. KOEDAM, A. A. KRUITHOF*) and
J. RIEMENS*)
Physical Laboratory of the Lighting Division N. V, Philips, Gloeilampenfabriekeu, Eindhoven, Nederland
Synopsis L'energie dissipee dans la colonne positive d'une decharge de mercure-argon a basse pression, comme celle-ci est appliquee aux tubes fluorescentes, est delivree a I'environnemerrt sous trois formes: I'energie de rayonnement, les pertes d'energie dues aux collisions elastiques entre les electrons et Ie gaz, et les pertes d'energie de recombination d 'electrons et d'ions a la paroi. Nous avons examine I'energie rayonnee en fonction de la pression de mercure, de la pression d'argon et du courant electrique, A cet effet I'energie rayonnee dans les raies spectrales les plus importantes a Me comparee a celle d'une lampe a ruban de tungstene etalonnee et a celle de la cratere de l'anode de charbon d'une lampe a are, pour lesquelles les distributions spectrales sont connues, Etant donnees les erreurs possibles d'etalonnage de ces deux sources de rayonnement, les resultats des deux methodes sont en bonne harmonie. L'intensite de la raie A = 185 mfL a ete deterrninee en utilisant le fait que le rendsment quantique du salycilate de sodium soit independant de la longueur d'onde. A cet effet nous avons determine le rapport entre la lumiere fluorescente obtenue par I'energie de la raie A = 185 mp et par I'energie de la raie A = 253.7 ID!L. L'energie de la raie A = 253.7 mu a ete determinee par la methode indiquee ci-dessus. Afin de pouvoir cornparer I'energie electrique dissipee dans la colonne positive a l'energie delivree sous forme de rayonnement dans toutes les directions, il est necessaire de completer les mesures indiquees ci-dessus (qui nous fournissent la luminance energetique de la lampe dans Ia direction normale) avec la mesure de la distribution spatiale du rayonnement, qui en general differe considerablement de celIe d'une surface diffusante, rayonnante suivant la loi de Lambert. Les pertes d'energie dues aux collisions elastiques et les pertes d'energie a. la paroi sont ca.Iculees des donnees trouvees dans la Iitterature. Dans les circonstances examinees la somrne de l'energie de rayonnement de l'energie dues aux collisions elastiques entre les electrons et le gaz et des pertes d'energie ala paroi, correspond suffisamment bien aux valeurs de l'energie dissipee dans la decharge electrique.
1. Introduciion and summary. The positive column of low-pressure mercury-argon discharges has been the subj ect of many publications 1)2) 3) 4), *) Present adress Technical University Eindhoven.
-
565 -
566
M. KOEDAM, A. A. KRUITHOF AND
J.
RIEMENS
mainly because the phenomenon is so important for the operation of the fluorescent lamp. A Jot of data is thus already available. In the present publication the distribution of energy in the positive column of low-pressure Hg-A discharges is analyzed with the aid of these data and of the results of am measurements. Fig. 1 shows the main paths along which energy is transported, as full lines and the paths of less importance as dotted lines. The energie supply is carried off by radiation, volume losses and wall losses. The radiation emitted by the mercury argon positive column is concentrated almost exclusively in the mercury spectral lines. Argon spectral lines are not considered in this investigation. The most important volume losses are energy losses resulting from elastic collisions between electrons and gas atoms; of the wall losses, only the energy released upon recombination at the wall has been taken into account, the other wall losses (e.g. those resulting from de-excitation of metastable atoms) being negligible under the circumstances prevailing in the column. £nergy input
--
-
i~F
~-
I 1
I I
~
I 1
-51
11 I "'I
~l ~
I
.e L :¥; T 6 1
~I
.91 ..
1 1
Radiation
Wall·losses
Volume·losses
Fig. 1. Energy transport in the positive column of low-pressure Hg-A discharges The main paths are represented by full lines, those of minor importance by dotted lines. The rectangles indicate the various forms in which the energy is stored; F stands for the potential gradient in the discharge, i for the discharge current.
The energies in the spectral lines of the radiation produced by the discharge have been determined by reference to a standard source of known spectral energy distribution. The standard sources used were a tungsten strip lamp and the crater in the anode of a carbon arc. Images of the sources of radiation
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
567
were formed at the entrance slit of a monochromator. As radiation detectors a photomultiplier tube was used for the visible and u.v. parts of the spectrum and a lead-sulphide cell for the infra-red part; the radiation at the wavelength of 185.0 m/-L was determined with the aid of a fluorescent layer of sodium salicylate. As shown in fig. 2, the image of the discharge tube is formed in such a way that the measured value Ln(A') represents the energy which is emitted in the direction of the normal to the radiating surface per unit of area, time and solid angle. (A' indicates the wavelength of the spectral line under consideration). In other words: Ln(A') is the radiance in the direction of the normal to the radiating surface. concave mirror
~~ o -. Discharge tube
plane mirror
-
exit slit monocbro "" photo-
materslit entrance
-.''''
-
Fig. 2. Set-up for measuring the radiance, L, of a gas discharge. An image is formed, at the entrance slit of a monochromator, of a small area of the discharge-tube wall, Since the detected beam is in the direction of the normal to the wall area under consideration, the measured value represents L n (= the radiance in the direction of the normal).
To find the radiant emittance, M(A'), one not only needs the radiance in the direction of the normal but that in other directions as well. The investigations to be described here included therefore, radiance measurements in various directions at wavelengths of 253.7, 365, 435.8,546.1 and 577.0/9.0mIJ-. The relation between radiance and radiant emittance for the other mercury spectral lines can be derived from the results of these measurements. The energy output of the column was measured for different values of the mercury-vapour pressure, the argon-gas pressure and the discharge current. Four series of measurements were carried out, all with direct current: series 5(0) - tube wall temperature 40°C (mercury-vapour pressure 6.1 X 10- 3 mm *)), argon pressure 3 mm, discharge current 0.343 A; series 5(1) - tube wall temperature between 10 and 80°C, argon pressure 3 mm, discharge current 0.40 A; series 5(2) - tube wall temperature 42°C (mercury-vapour pressure *l A correction has been applied for the temperature difference across the tube wall resulting from energy being transported through the glass.
568
M. KOEDAM, A. A. KRUITHOF AND
J.
RIEMENS
7.2 X 10- 3 mm *)), argon pressure varied between 1 and 20 mrn, discharge current 0.40 A; series 5(3) - tube wall temperature 42°C (mercury-vapour pressure 7.2 X 10- 3 mm*)), argon pressure 3 mm, discharge current varied between 0.10 and 1.00 A. In series 5(0) the values of the radiant emittance was measured in watLm- 2. Series 5(1), 5(2), 5(3) served to determine relative radiation energy values; with the aid of the results of 5 (0) the radiant emittance in watt .m- 2 is found. Verweij 3) has measured the potential gradient (and hence the energy per unit of column length), the electron concentration and the electron temperature under conditions identical to those for the series 5(1), 5(2) and 5(3). The results of his measurements have been used for determining the wall losses and the volume losses. To verify the results of the measurements and the calculations, the sums of radiated energy, volume losses and wall losses for series 5(1), 5(2) and 5(3) were compared with the applied energy. A satisfactory agreement was found.
2. Radiation measuremeni«. 2.1. The tungsten strip lamp as a standard radiation source. The spectral concentration of radiance, L;., of a thermal radiator is calculated as a function of its temperature T from Planck's radiation law: C1
L;.(T) = - ' J,.s
Here
C1
and
C2
e(A, T)· ct(A) exp[c2/J,.T] - 1
C1
~'S e(J,.,
[
-C2 ]
T) ·ct(J,.) -exp -'-T .
1\
(1)
1\
are constants: C1
C2
= 1.1909 X = 1.438
10-16
10-2
watt .m''. sterad>.
m , "K,
Further:
ct(-1.) is the transmission factor of the window, e(A, T) is the emissivity of the radiating surface. The emissivity of tungsten has been measured by, among other investigators, De VOSS), Larra bee 6) and Ha.rn a ker t) for various values of A and T. Where possible we shall use the emissivity values found by Larrabee, and, if these are not available, the values determined by De Vas. Both La rr abe e and De V 0 s used direct methods for measuring the emissivity, comparing the radiation of the tungsten surface with that of a black body *) See page 3.
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
569
hole in the material. Larrabee introduced an extra correction for radiation which was scattered, e.g. at the lens with which the radiator was imaged on the monochromator slit. Hamaker employed an indirect method, measuring the reflection coefficient of tungsten and deriving the emissivity from this coefficient. The luminance temperature, T L, of the strip lamps used in the work under description has been measured at 650 mu and as a function of the strip current by Dr. W. A. Heusinkveld and Mr. K. Schurer from the Physical Laboratory of the University of Utrecht. A tungsten strip lamp was calibrated by the N.P.L., the N.B.S., the P.T.B., and in the Physical Laboratory of the University of Utrecht. Differences of 3°K, as a maximum, were found in the luminance temperature. The temperature T of the tungsten strip is calculated from the luminance temperature T L with the aid of -
1
= -
T
1
TL
+-,1,0Cz
·In[e(Ao, T) 'ct(}"o)J
(2)
where ,1,0 is the wavelength at which the luminance temperature has been determined, The procedure of our radiation measurements is to have, at the entrance slit of the monochromator, images of, first, the standard radiation source and next of a small area of the wall of the discharge tube, while taking care that in either case the optics of the monochromator are filled to the same degree. The image of the considered area of the discharge tube should be such that the radiation in the direction of the normal to the tube wall is detected (see fig. 2). The photomultiplier signals obtained from the standard source and from the discharge tube are denoted by Ds and D, respectively, The radiance Ln(A') measured in this way follows from the equation
f L ..(T) '-r(A) '5(,1,) . dA ,..- - - - - - Ds(A.') S(A') .,.(/\') D(A')
L (,1,') n
-
(3)
A' being the wavelength corresponding to maximum transmission of the monochromator at given adjustment. -r(A) being the transmittance of the monochromator; in the experiments r(A) is unequal to zero only in a small region around A', s(A) denoting the sensitivity of the photomultiplier tube; L ..(T) representing the spectral concentration of radiance of the standard source at a temperature T. For the band of wavelengths in which, under the prevailing conditions, T(},,) =F 0, we find that S(A) and L .. are practically constant so that S(A} = = S(;tl) and LA = L .."
570
M. KOEDAM, A. A. KRUITHOF AND
Hence
L (A') = n
D(A') .L ,(T) A
Ds(A')
J. RIEMENS ----------
JT(J.') T(A) ...dA
(3a)
A
The monochromator setting A' always corresponds with a mercury spectral line. The photomultiplier signal D(x) is measured for various settings x of the wavelength selector drum on the monochromator, with the image of the discharge tube focussed on the entrance slit. With x' corresponding to the maximally transmitted wavelength A' we find for the integral in eq. (3a): 7(.1.) J7(J,,')
A
dA =
Jdx' dA
D(x) D(x') . dx
~
( ell. )
dx
a:=:n'
I
D(x) D(x') dx
= b(A')
x
Eq. (3a) then becomes: Ln(A') =
D(A') .L '(T) .b(A') Ds(X) A •
(3b)
The integral is evaluated graphically and b(A') is found. In order to be able to estimate the random error in Ln(A') which may be expected we must know the random error in the quantities occurring in the right hand factors in eq. (3b). Errors in D(A') and Ds(A') may be neglected in comparison with the error inLA,(T), because the final measuring result is an average of a large number of measurements giving different values of D and Ds . The error in b(A') turns out to be small relative to that in LA'. The error to be expected in LA' is estimated with the aid of equations (1) and (2). The accuracy with which the luminance temperature has been determined may in turn be judged either by comparing the measurements carried out by a number of laboratories, or by considering the measurements to be carried out for the calibration of a tungsten strip lamp step by step. It will be found that in either case, at the luminance temperature of 2600 oK, the error does not exceed ± 3°. The error in the true temperature depends on, among other factors, the accuracy of determining the emissivity at the calibration wavelength (eq.(2)). Larrabee estimates the Lm.S. value of the error at 0.2%. Setting out from eq. (2) we can estimate the error in T to be ± 5° for T being 2900oK. The error of Ln(A') now follows from eq. (3b). Table I lists the values of L n for a number of mercury spectral lines, these values being obtained with the aid of a tungsten strip lamp as standard radiation source in the series of measurements 5(0); the table also gives the estimated random error. L n has been determined from e.g. the luminance temperature of tungsten at the calibration wavelength AD, which temperature is based on the melting
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
571
TABLE I l-« in series of measurements 5(0), as well as the percentage of random error, with the strip lamp used as a standard radiation source ,\
(n'l..I.) 253.7 404.7/7.8 435.8 546.1 577.0/9.0
I (watt.m~~sterad-1) I
percentage random error
71 0.80 2.19 1.21 0.26
4 3 2 25 25
point of gold, T g = 1336°K, so as to comply with the regulations for the international temperature scale of 1948. Recent measurements make it likely that T g = 1337°K (Oishi 9 ) ) or even that T g = 1338°K (Moser, P. T. B.10)). TABLE II The values of L" from table I for To = 1336 and 1338°K and the extreme values of L«, taking into account the random errors nud a change in To to 1338°K L .. in watt. m -·.sterad- 1
i\
{Ill[.I.}
253.7 404.7/7.8 435.8 546.1 577.0/9.0
I
To = 1336°K (I.T.S.) 71 0.80 2.19 1.21 0.26
\
To = 1338°K (Moser) 76 0.83 2.28 1.24 0.27
extreme values \
68 0.78 2.16 1.18 0.25
-
79 0.85 2.26 1.26 0.28
Tabel II shows the effect of a change in T (J on the energy of a number of Hg spectral lines. It also lists the extreme values of L n , taking into consideration the random errors and a possible increase of T g to 1338°K. The instrument indicating the current for the tungsten strip is a possible source of random errors, its reading accuracy corresponding to an accuracy in the temperature of about 2°. The final measuring results are obtained by averaging the results of about 20 measurements using two different strip lamps, one of which is operated at two and the other at three temperatures. Consequently the random reading error of the strip lamp current is negligible when compared with the errors in Ln. The same applies as we have seen previously, to the errors in D and Ds. 2.2. The carbon-arc anode as a standard radiation source. Instead of a tungsten strip lamp one may also use the crater of a carbon-arc anode as the standard radiation source l-). A number of investigators have measured the luminance temperature at a wavelength of 650 mfl- of a carbon-arc anode made of pure graphite. The best value is now thought
572
M. KOEDAM, A. A. KRUITHOF AND J. RIEMENS
to be 3808°K ± IS0 8 ) . E u l e r ll) has determined the emissivity of the crater of a carbon-arc anode at wavelengths ranging from 250 to 1800 mu. The calculated "true" temperature of the crater then is 3995°K ± 20°. Using the above standard radiation source the radiance L n for various mercury spectral lines has been established once more. Under the discharge conditions of series 5(0) we find the values for L n and the random error as listed in table III. TABLE III
L,. in series of measurement S(Ol, as well as the percentage of random error, with the crater of a carbon-arc anode used as standard radiation source
x
I
(watt.m!;:terad- 1 )
(mfL) 253.7 404.7{7.8 435.8 546.1 577.0{9.0
I
percen tage random error 8 5 4 4 3
7\ 0.84 2.29 1.26 0.27
The energy radiated by the carbon-arc anode is calculated on the basis of the melting point of gold, T (f = 1336°K, so as to comply with the regulations of the LT.S. Table IV gives the values of L n based on the measurements carried out by Moser, i.e. with T(f = 1338°K, as well as the extreme values of L n , taking into account the estimated random error and a possible increase of T (J up to 1338°K. TABLE IV The values of L,. from table III for To = 1336 and To = 1338°K and the extreme values of L u, taking into account the random errors and a change in T g to 1338°K ;\
(mfL) 253.7 404.7/7.8 435.8 546.1 577.0
L" in watt.m- 2.sterad-1
I
Tg
=
1336°K (1.1.'.5.) 71 0.84 2.29 1.26 0.27
To
I
= 1338°K (Moser) 76 0.87 2.37 1.30 0.28
I
extreme values 66 0.80 2.20 1.21 0.26
- 82 - 0.91 - 2.42 - 1.35 - 0.29
The crater of the carbon-arc anode when used as standard radiation source has some advantages as well as some drawbacks compared with the tungsten strip lamp. The carbon-arc needs no calibration and the current setting is not critical. However, in the experiments under description the radiation was less stable than that from a strip lamp. Because of its high temperature, the carbon-arc is generally to be preferred over the tungsten strip lamp for measurements in the u.v, region of the spectrum. However, the spread of
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
573
± 20° in the true temperature of the crater leads to the luminance of the crater being less well defined than that of the calibrated strip lamp. The temperature of the latter may be varied, whereas that of the carbon-arc anode has one single well defined value. 2.3. Radiant emittance. In the preceding paragraphs we have discussed a method for the determination of the radiance L n , i.e. the radiance in the direction of the normal to the radiating surface. To find the radiant emittance M, i.e. the amount of radiated energy emitted through the wall of the discharge tube per unit of time and surface area, we will have to determine the radiance in other directions as well. In the case of a diffuse radiating surface we have
M=n·L
(Lambert cosine law)
A discharge needs not necessarily be a diffuse radiator. Under these conditions the radiant emittance may be determined with the aid of a special arrangement for the determination of the angular distribution of the radiation of a small area of the tube surface. This arrangement comprises a diaphragm, fitted as closely as possible to the area of the discharge tube and a photocell provided with a filter which picks out the desired spectral line. z
y
x
photo multiplier
Fig. 3. Set-up for measuring the angular distribu Han of the radiation of Hg-A positive columns. The photomultiplier tube can be rotated in the X-Y plane. The length of arm p is about 1.50 m, hence great with respect to the diameter of the diaphragm (1 em). In the set-up the X-Z plane is opaque with the exception of the diaphragm.
574
M. KOEDAM, A. A. KRUITHOF AND
J.
RIEMENS
The photocell is made to move in a circle, having the diaphragm at its centre, the plane of the circle going through the normal to the radiating surface so that it can rotate around this normal (see fig. 3). Denoting the photocell signal by D(rp, 1}), we find the correction factor f3 for the radiant emittance from: n/2
f3 = ~. n
+n
ISin B· dDJ D(cp, tJ.) . dq:>. D(O, 0)
~=o
rp=-n
The radiant emittance M obeys M = fJ·n·L n
-"'-
_
Radiancs x cos i) (arbitrary units)
Fig. 4. Angular distribution of the radiation at A = 253.7 mu of a small area at the wall of a tube containing a Hg-A positive column. Compare fig. 3. _oiJ _
_
Rodiance x cas {) (arbitrary units)
Fig. 5, Angular distribution of the radiation at A = 435.8 rnu of a small area at the wall of a tube containing a Hg-A positive column. Compare fig. 3.
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
575
The factor f3 is not necessarily the same for all spectral lines. The measurements under description did show that for the radiation from the mercury argon positive column there are three different values of f3. In the series 5(0) these were found to be: (a) for the resonance radiation at A = 253.7 mu : f3 = 0.615; (b) for the radiation pertaining to spectral lines having one of the 63P levels as their bottom level (e.g. A. = 404.7, 435.8, 546.1 m!L): f3 = 0.551 ; (c) for the radiation pertaining to the lines not mentioned under (a) or (b):
f3
= 0.529.
-"'o
--.-Radiance x cos ". (arbitrary units)
Fig. 6. Angular distribution of the radiation at it = 577.0/9.0 rnu of a small area at the wall of a tube containing a Hg-A positive column. Compare fig. 3.
It can be seen that in all cases the radiant emittance deviates considerably from the values to be found with Lambert's cosine law. For lines pertaining to the groups (b) and (c) the deviation is of the same order of magnitude as the random error. For the series of measurements 5(1), 5(2) and 5(3) no image-forming components were used between the discharge tube and the entrance slit of the monochromator, but the tube was set up to irradiate a magnesiumoxide screen instead. The screen has a scattering effect and a part of the radiated energy will reach the slit. The signal which is detected is directly proportional to the radiant emittance M and not, as with image formation, to the radiance L. As was stated in section 1, the spectral line for It = 185.0 mu requires a special measuring method, since radiation at this wavelength is absorbed by air. Moreover neither the emissivity of tungsten nor that of carbon at It = 185.0 mu is known. In the investigations use was made of sodium salicylate for the determination of M (185.0), this substance possessing, according to Wa.t a.n a b e e P) and Hamman 13) , a quantum efficiency
576
J.
M. KOEDAM, A. A. KRUlTHOF AND
RlEMENS
• Sodium salicytat«
~
-
=
=
--;r-
-a
Discharge UDe
~
/[
c~
Fig. 7. Set-up for measuring the radiant-emittance ratio at A = 185.0 mu and at A = 253.7 mp., Sleeves A, Band C can be shifted. The inside of the window is coated with sodium salicylate. Sleeve A is made of fused silica of the same kind and thickness as the discharge tube; sleeve B is made of a special glass which does not transmit radiation at A = 185.0 mp but does transmit at J. = 253.7 mu: sleeve C is made of soda-lime glass transmitting neither radiations at A = 185.0 mp., nor at J. = 253.7 mu,
25watl m-/
, I
I /
I
I
I
I"
-- .,,
\ \.
\
I ;'~-
x
"
,'&
\
,
\
\
Radiatlan pDslWe \ calumn
,~
,, , , I
15
,
\
\.
"
I
,/ y' :, ,'
\
'
\ \
\
\
\~53.7 \,
\
,, ,
10
\
I
,.Owalt.m-t \
I I I
/
I
\
~
V
g!
, '" ~
.•~
",,'
5
c
O.5~
",+,",-+
/I __ .~ 46.1 1-1--. -t::::::; :-+~T--+--t 'r+-'~ ~ --t--+-·--+--+-t ::-.,--mOi9.O
1---+--+
,+~I::---
b
--t__._+_ _ +_ _•
365.
20
as
2
_
40
5
f
60 BOoC Bath temperature II) do 10-3mm
50
_Reduced mercury vapour pressure
Fig. 8. Power radiated per metre of column length (.70) for a number of spectral lines in the positive column of low-pressure Hg-A discharges. Mercury vapour pressure variable, argon pressure 3 mm (adjusted at 20°C) discharge current 0.40 A. 6, Values measured by Barnes under identical discharge conditions at A = 185.0 and 253.7 mu, The energy values apply to the imide of the discharge-tube wall, The left hand scale is for the radiation at J. = 185.0 IIl[L and 253.7 mu and for the sum curve; the right-hand scale is for the other spectral lines.
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
577
that is independent of the frequency of the incident radiation. Fig. 7 shows the set-up for measuring M(185.0). Around the discharge tube three sleeves are fitted, one made of fused silica and having the same thickness and composition as the wall of the discharge tube, the second made of a special kind of glass transmitting radiation at A = 253.7 mu but no radiation at A = 185.0 mu, the third made of conventional glass which does not transmit radiations at either of these wavelengths. The discharge tube with the sleeves is placed in a second tube, which has a window coated with sodium salicylate on the inside. The space between the two tubes is filled with argon at a pressure of about 70 em Hg. In preliminary experiments the extent to which the sleeves and the tube wall pass radiation at A = 253.7 mfL has been determined. The ratio between the numbers of quanta belonging to radiations at A = 185.0 and A = 253.7 mfL can be found when we measure the intensity of the fluorescent radiation with no sleeve; the first sleeve, the second and the third sleeve successively, at a wavelength where there is no interference by the direct radiation from the discharge. We then find, under the conditions as given for the series of measurements 5(0) : number of quanta at 185.0 mfL = 0.125 number of quanta at 253.7 mu We then calculate for 5(0) conditions: M(185.0) = 25 watt .m- 2 3QOwa{t m- T
Radiation of positive column ...
------ ---
0
,...~~----<
--
..----
_ _ - - - ) ( - _ _ l( _ _ _ l(_ _
1.Owatt.m-T
10.0
435.8
I~+-
546.1 iffl5]--+::-'::"'t ~t-.ti_l=-~~
- -577.aiQa'r--:t:--~=i= ----+-+ o
+404.
3
6 10 20mm _Argon pressure
Fig. 9. Power radiated per metre of column length (:n:) for a number of spectral lines in the positive column of low-pressure Hg-A discharges. Mercury vapour pressure 7.2 X 10- 3 mm (wall temperature 42°C), argon pressure variable, discharge current 0.40 A. 6. Values measured by Barnes under identical discharge conditions at A = 185.0 and 253.7 mu, The values apply to the inside of the discharge-tube wall. The left hand scale is for the radiation at A = 185.0 and 253.7 mu and for the sum curve; the right-hand scale is for the other spectral lines. The scale values are argon pressures at 20°C.
578
M. KOEDAM, A. A. KRUITHOF AND
J.
RIEMENS
Table V lists the values for the power radiated per metre column length for the most important mercury-lines at the wall inside the discharge tube under 5(0) conditions. The values are calculated per metre column length in order to use them when making up the energy balance (see section 3). Figs. 8, 9 and 10 give the corresponding values for 5(1), 5(2) and S(3) conditions. The values have been derived from those for 5(0) conditions. The values of the power radiated at A = 185.0 mfL for 5(1), 5(2) and 5(3) conditions have been found after inserting into a tube coated with fluorescent powder a sleeve made partly of normal fused silica and partly of a special kind of glass not passing radiation at A = 185.0 rnu but passing radiation at A. = 253.7 mu, Assuming that the transmission of radiation at 1\ = 253.7 IDfI- of both sleeve parts is the same, which was checked in a preliminary experiment, we find the ratio between the radiant emittance at 185.0 mp, and that at 253.7 mu by measuring the intensity of the fluorescent radiation at either sleeve part. 50watt m- 1
253.7 ... x
......
x
JOI-----+---+---~"'-----\__7=-___j
0.20
Fig. 10. Power radiated per metre of column length (n) for a number of mercury spectral lines in the positive column of low-pressure Hg-A discharges. Mercury vapour pressure 7.2 X 10- 3 mm (wall temperature 42°q, argon pressure 3 mm (adjusted at 20°C) discharge current variable, t:o. Values measured by Barnes under identical discharge conditions at J" = 185.0 and 253.7 mu, The energy values apply to the inside of the discharge-tube wall. The left-hand scale is for the radiation at J" = 185.0 and 253.7 mu and for the sum curve; the righthand scale is for the other spectral lines.
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
579
The values given in figs. 8,9 and 10 and tables V, VI and VII have been based on a comparison of the radiation from the discharge, with that from a calibrated strip lamp. The figures also contain some of the values measured by Barnes 14) at 185.0 and 253.7 mIL, these are in good agreement with our results. Barnes measured the radiant emittance at the two wavelengths and from the results calculated the radiance with the aid of Lambert's law. It turns out that this is not fully justified at the wavelength of A = 253.7 mIL. Since in the experiments under discussion the radiance at A = 185.0 mIL has not been determined, nothing can be said here about the relation between radiant emittance and radiance at this wavelength. TABLE
v
Power radiated per metre column length; i = 0.343 A, argon pressure 3 mrn, wall temperature 40°C (series of measurements 5(0)) wavelength
I
(m[J.)
I 185.0 253.7 265.2 275.2 280.3 289.4 296.7 302.1 313.0 334.1 365.0 404.7/7.8 435.8 546.1 577.0/9. 0 1014.0 1128.7 1367.3/95.0 1529.5 1692.1/1711.0
power radiated in watt per metre column length strip lamp as standard radiation source 2.9 17.3 0.023 0.0045 0.0079 0,0103 0,034 0.023 0.18 0,094 0.15 0.17 0.46 0,25 0.054 0.036 0.011 0,026 0.035 0.006
I
carbon-arc anode as standard radiation source 2.9 17.3
0.18 0.48 0.26 0.055
3. Energy balance. Figs. 8, 9 and 10 list the power radiated by the positive column of mercury-argon discharges at different values of the mercuryvapour pressure, the argon pressure and the discharge current respectively. The energy transport is further governed by elastic collisions between electrons and gas atoms (volume losses), and by recombination of ions and electrons at the tube wall (wall losses). In the circumstances under description the volume and wall losses can be calculated from the electron temperature and electron concentration, which quantities have been determined by Verweij 3) with probe measurements for the same conditions of mercury vapour pressure, argon pressure and discharge current as for our series of measurements 5(1),5(2) and 5(3).
580 M. - - - - -- - -
KOEDAM , A. A. KRUITHOF AND
J.
RIEM ENS
Tables VI, VII and VIII contain, among other values, the volume loss es per unit of column length, found with t he aid of a cur ve measured by K enty, Easley and Bar n e s P}. The latter gives the energy losses resulting from elastic collisions, per electron, in Hg and A , as functions of the elect ron temperature. Wall losses have been calculated from the coefficient for ambipolar diffusion, D a , and the gradient of the electron (ion) concentration at the wall of the discharge tube. Let us designate the number of ions (and electrons) colliding against the wall per second and per unit of column length by N:
( dne) r
N = 2nR·Da· - d
r=R
kT D a = it+· - e where:
it + is the mobility of Hg-ions in argon ;
T e is the electron temperature ; n e is the electron concentration;
k is Boltzmann's constant ;
e is the electron charge ; R is the radius of the discharge tube .
The mobility of mercury ions in helium h as been measured by Bi o n d i 16) . From it, Waymou th and Bi t t er s) derived, among other quantities, the mobility of mercury ions in argon which they found to be: 0.31
it+ = - - m 2.V -l.sec-1
PA
where P A is the argon pressure in mm. Now we take, as is customary for the discharges under consideration here, a Bessel function for nil' so that we obtain : (
dne )
dr
= r=R
2.4 . no
R
no being the electron concentration in the axis of the discharge. The transport energy per electron colliding against a surface is on an average 2kTe• The wall losses per unit of column length amount to:
N '(eVt
+ 2kTe) watt'm-1
where Vi is the ionizat ion potential (Vi(Hg) = 10.38 V). Tables VI, VII and VIII also giv e the wall losses per unit of column length and per second for measuring seri es 5(1), 5(2) and 5(3), respectively.
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
581
TABLE VI Energy input and output of the Hg-A positive column; mercury-vapour pressure variable, PA = 3 mm; i = 0.40 A radiation
volume losses
wall losses
energy output
energy input
(OC)
Hg-vapour pressure (reduced to O°C) (10- 3 mm)
(watt.m v-)
(watt.m- i )
(watt.mv-)
(wa tt.rn t]
(watt.m-v)
10 20 30 42 50 60 70 80
0.50 1.14 2.55 6.23 10.9 21.0 38.8 69.3
8.1 15.9 21.9 22.3 20.0 17.2 14.5 I\.3
19.5 14.5 9.8 5.9 4.7 4.4 4.5 5.5
2.9 2.3 1.9 1.5 1.5 1.5 1.7 2.2
30.5 32.7 34.1 29.7 26.2 23.1 20.7
3104
Wall temp.
r
33.2 34.2 32.5 29.5 25.8 23.8 23.0
19.0
TABLE VII Energy input and output of the Hg-A positive column; wall temperature 42°C (PHg = 6.23 X 10- 3 mm); argon pressure variable; i = 0.40 A Argon press. (mm)
Argon press. reduced to O°C (mm)
Radiation
Volume losses
Wall losses
Energy output
Energy input
(watt.rrrr-)
(watt.m- I )
(wntt.m r-)
(watt.m- I )
(watt.m-1)
0.83 2.79 5.58 9.3 18.6
21.7 22.3 22.4 22.5 23.2
2.1 5.9 14.4 26.8 60.5
3.5 1.5 0.9 0.6 0.4
27.3 29.7 37.7 49.9 84.1
28.4 32.5 39.2 49.6 8l.2
1
3 6 10 20
TABLE VIII Energy input and output of the Hg-A positive column; wall temperature 42°C (PHg = 6.23 X 10-8 mm); PA = 3 mm; discharge current variable Discharge current (A) 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 \.OG
Radiation
I
(watt.m- I ) 6.7 12.6 17.8 22.3 26.7 30.0 33.2 36.6 39.4 42.4
I
Volume losses (watt.m- I ) 2.2 3.9 4.9 5.9 7.0 7.9 9.2 10.3 11.5 12.7
I
Wall losses (watt.m- l ) 0.4 0.8 \.2 \.5 \.9 2.2 2.6 2.9 3.2 3.6
I
Energy output (watt.m- l ) 9.3 17.3 23.9 29.7 35.7 40.1 45.0 49.8 54.1 58.7
j
Energy input (watt.m-t) 9.7 18.2 25.8 32.5 38.9 44.7 50.2 55.2 59.6 63.6
4. Conclusions. Measurement of the values of spectral-line energies in the Hg-A positive column, by comparison with the crater of a carbon-arc anode, or with a calibrated tungsten strip lamp as a radiation standard, is quite feasible. The carbon-arc does not require calibration, in contrast with
582
M. KOEDAM, A. A. KRUITHOF AND
J.
RIEMENS
the tungsten strip lamp, and the current setting of the former is not critical. The values obtained with the two standard sources of radiation are in reasonable agreement. Generally the angular distribution of radiation of such a column is not according to Lambert's law. Experiments carried out with a mercury-vapour pressure of 7.2 X 10-3 mm, an argon pressure of 3.0 mm and a discharge current of 0.343 A yielded for M: M(253.7) = 0.615 nL n .
In the case of the other spectral lines examined during the investigation a correction factor was found for the results as compared to a diffuse radiating surface, viz. 0.551 or 0.529. On the whole, the agreement with the radiantemittance values found by Barnes is good. However, deviations are found in the values of the radiance L at A = 253.7 IDf-L' since Barnes assumed the radiation to be according to Lambert's law. Released-energy values were in general slightly below the values of energy-input obtained by Verweij 3), which is a plausible result since a number of possible sources of energy loss were neglected (compare figs. 11, 12, and 13). The conclusion may thus be drawn that the major items making 40watt m- f
4....· t~
~~
~s-,
~'\.'.
~"x-,
+~ x, ,,,~.,,,. ,
....x
+~"""'-lC
"'c... + .....
20
~t
10
-
o
10
0.5
20
30
2
Ba!h temaerciur»
40
50
60
5
10
20
70
80
50
900C 100.W;
mm -Reduced mercury vapour prassura
Fig. 11. Energy input and output of a Hg-A positive column; mercury-vapour pressure variable; argon pressure 3 mm (adjusted at 20°C); discharge current 0.40 A. - . _. - energy input. - - - - energy output; the radiation has been found by using a tungsten strip lamp as a standard radiation source. - - - - - energy output; the radiation has been found by using a carbon arc-anode crater as a standard radiation source.
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
583
90 watt m- I
),
1/
l' l'l l'
,,'I
II!
l.
I
30
-'~
.... -
·.... i.o.!ll-'-
~_
0,
/'
~~
2
3
6
10
20mm
_ _ Argon pressure
Fig. 12. Energy input and output of a Hg-A positive column; mercury-vapour pressure 7.2 X 10- 3 mm (wall temperature 42°C); argon pressure variable; discharge current 0.40 A. The scale values are argon pressures at 20°C. - . - . - energy input. energy output; the radiation has been found by using a tungsten strip lamp as a standard radiation source. - - - - - energy output; the radiation has been found by using a carbon-arc anode crater as a standard radiation source. eOwatt m:'
4
,oJ,.
.,;It .....;,.-:~
,;./tP
I +
.",;,.k'?
»:A""?+
.'~+
2~V
20
~
/I 0.20
1'"
0.40
O.SO -
0.80 1.00A Discharge current
Fig. 13. Energy input and output in the case of a positive column of low-pressure Hg-A discharges; mercury-vapour pressure 7.2 X 10- 3 mm; argon pressure 3 mm (adjusted at 20°C); discharge current variable. - ' - . - energy input. - - - - energy output; the radiation has been found by using a tungsten strip lamp as a standard radiation source. - - - - ~ energy output; the radiation has been found by using a carbon-are-anode crater as a standard radiation source.
584
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
up the energy balance of this type of columns have now been traced and their magnitudes determined. The authors are very grateful to Dr. W. Verweij for many helpful discussions. They also want to thank Mr. J. A. van Doorenmalen and Mr. A. G. v. d. Kooi for their assistance. Received 23-10-62
REFERENCES lJ Kenty, C., J. appl, Physics 21 (l950J 1309. 2) Waymouth, J. and Bitter, F., J. appL Physics 27 (1956) 122. 3) Verweij, W., Probe Measurements and determination of electron mobility in the positive column of low pressure mercury-argon discharges, thesis University of Utrecht, 1960. Idem Phil. Research Rep. Suppl. 2, 1961. 4) Koedam, M. and Kruithof, A. A., Physica 28 (1962) 80. 5) De Vos, ]. C., Emissivity of tungsten, thesis V.U. Amsterdam, 1953. Idem Physica 20 (1954) 690. 6) Larrabee, R. D.,]. Opt. Soc. Amer. 49 (1959) 619. 7) Hamaker, H. C., Reflectivity and emissivity of tungsten, thesis University of Utrecht. Idem Physica 3 (1936) 561. 8) Heusinkveld, W. A., Electrotechniek 38 (1960) 536. 9) Oishi, J., Awani, M. and Mochizu'ki, T.,]. Phys. Soc. Japan 11 (1956) 311. 10) Moser, H., Otto, J. and Thomas, W., Z. Phys. 147 (1957) 76. Idem Com. Int. Poids et Mesures, Proces Verbaux 21lA (1958) T 67. 11) Euler, J., Ann. Phys. '11 (1953) 203. EUler, J., Ann. Phys. 14 (1954) 145. 12) Watanabee, K. and Inn, C. C. J., J. Opt. Soc. Amer. 43 (1953) 32. 13) Hamman, J. F., Z. angew. Phys. 10 (1958) 187. 14) Barnes, B. T., J. appl. Physics 31 (1960) 852. 15) Kenty, C., Easley, M. A. and Barnes, B. T., J. appl. Phys, 22 (1951) 1006. 16) Biondi, M. A., Phys. Rev. 90 (1953) 730.
Koedam, M. Kruithof, A. A. Riemens, J. 1963
ENERGY BALANCE OF THE LOvV-PRESSURE MERCURYARGON POSITIVE COLUMN by M. KOEDAM, A. A. KRUITHOF*) and
J. RIEMENS*)
Physical Laboratory of the Lighting Division N. V, Philips, Gloeilampenfabriekeu, Eindhoven, Nederland
Synopsis L'energie dissipee dans la colonne positive d'une decharge de mercure-argon a basse pression, comme celle-ci est appliquee aux tubes fluorescentes, est delivree a I'environnemerrt sous trois formes: I'energie de rayonnement, les pertes d'energie dues aux collisions elastiques entre les electrons et Ie gaz, et les pertes d'energie de recombination d 'electrons et d'ions a la paroi. Nous avons examine I'energie rayonnee en fonction de la pression de mercure, de la pression d'argon et du courant electrique, A cet effet I'energie rayonnee dans les raies spectrales les plus importantes a Me comparee a celle d'une lampe a ruban de tungstene etalonnee et a celle de la cratere de l'anode de charbon d'une lampe a are, pour lesquelles les distributions spectrales sont connues, Etant donnees les erreurs possibles d'etalonnage de ces deux sources de rayonnement, les resultats des deux methodes sont en bonne harmonie. L'intensite de la raie A = 185 mfL a ete deterrninee en utilisant le fait que le rendsment quantique du salycilate de sodium soit independant de la longueur d'onde. A cet effet nous avons determine le rapport entre la lumiere fluorescente obtenue par I'energie de la raie A = 185 mp et par I'energie de la raie A = 253.7 ID!L. L'energie de la raie A = 253.7 mu a ete determinee par la methode indiquee ci-dessus. Afin de pouvoir cornparer I'energie electrique dissipee dans la colonne positive a l'energie delivree sous forme de rayonnement dans toutes les directions, il est necessaire de completer les mesures indiquees ci-dessus (qui nous fournissent la luminance energetique de la lampe dans Ia direction normale) avec la mesure de la distribution spatiale du rayonnement, qui en general differe considerablement de celIe d'une surface diffusante, rayonnante suivant la loi de Lambert. Les pertes d'energie dues aux collisions elastiques et les pertes d'energie a. la paroi sont ca.Iculees des donnees trouvees dans la Iitterature. Dans les circonstances examinees la somrne de l'energie de rayonnement de l'energie dues aux collisions elastiques entre les electrons et le gaz et des pertes d'energie ala paroi, correspond suffisamment bien aux valeurs de l'energie dissipee dans la decharge electrique.
1. Introduciion and summary. The positive column of low-pressure mercury-argon discharges has been the subj ect of many publications 1)2) 3) 4), *) Present adress Technical University Eindhoven.
-
565 -
566
M. KOEDAM, A. A. KRUITHOF AND
J.
RIEMENS
mainly because the phenomenon is so important for the operation of the fluorescent lamp. A Jot of data is thus already available. In the present publication the distribution of energy in the positive column of low-pressure Hg-A discharges is analyzed with the aid of these data and of the results of am measurements. Fig. 1 shows the main paths along which energy is transported, as full lines and the paths of less importance as dotted lines. The energie supply is carried off by radiation, volume losses and wall losses. The radiation emitted by the mercury argon positive column is concentrated almost exclusively in the mercury spectral lines. Argon spectral lines are not considered in this investigation. The most important volume losses are energy losses resulting from elastic collisions between electrons and gas atoms; of the wall losses, only the energy released upon recombination at the wall has been taken into account, the other wall losses (e.g. those resulting from de-excitation of metastable atoms) being negligible under the circumstances prevailing in the column. £nergy input
--
-
i~F
~-
I 1
I I
~
I 1
-51
11 I "'I
~l ~
I
.e L :¥; T 6 1
~I
.91 ..
1 1
Radiation
Wall·losses
Volume·losses
Fig. 1. Energy transport in the positive column of low-pressure Hg-A discharges The main paths are represented by full lines, those of minor importance by dotted lines. The rectangles indicate the various forms in which the energy is stored; F stands for the potential gradient in the discharge, i for the discharge current.
The energies in the spectral lines of the radiation produced by the discharge have been determined by reference to a standard source of known spectral energy distribution. The standard sources used were a tungsten strip lamp and the crater in the anode of a carbon arc. Images of the sources of radiation
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
567
were formed at the entrance slit of a monochromator. As radiation detectors a photomultiplier tube was used for the visible and u.v. parts of the spectrum and a lead-sulphide cell for the infra-red part; the radiation at the wavelength of 185.0 m/-L was determined with the aid of a fluorescent layer of sodium salicylate. As shown in fig. 2, the image of the discharge tube is formed in such a way that the measured value Ln(A') represents the energy which is emitted in the direction of the normal to the radiating surface per unit of area, time and solid angle. (A' indicates the wavelength of the spectral line under consideration). In other words: Ln(A') is the radiance in the direction of the normal to the radiating surface. concave mirror
~~ o -. Discharge tube
plane mirror
-
exit slit monocbro "" photo-
materslit entrance
-.''''
-
Fig. 2. Set-up for measuring the radiance, L, of a gas discharge. An image is formed, at the entrance slit of a monochromator, of a small area of the discharge-tube wall, Since the detected beam is in the direction of the normal to the wall area under consideration, the measured value represents L n (= the radiance in the direction of the normal).
To find the radiant emittance, M(A'), one not only needs the radiance in the direction of the normal but that in other directions as well. The investigations to be described here included therefore, radiance measurements in various directions at wavelengths of 253.7, 365, 435.8,546.1 and 577.0/9.0mIJ-. The relation between radiance and radiant emittance for the other mercury spectral lines can be derived from the results of these measurements. The energy output of the column was measured for different values of the mercury-vapour pressure, the argon-gas pressure and the discharge current. Four series of measurements were carried out, all with direct current: series 5(0) - tube wall temperature 40°C (mercury-vapour pressure 6.1 X 10- 3 mm *)), argon pressure 3 mm, discharge current 0.343 A; series 5(1) - tube wall temperature between 10 and 80°C, argon pressure 3 mm, discharge current 0.40 A; series 5(2) - tube wall temperature 42°C (mercury-vapour pressure *l A correction has been applied for the temperature difference across the tube wall resulting from energy being transported through the glass.
568
M. KOEDAM, A. A. KRUITHOF AND
J.
RIEMENS
7.2 X 10- 3 mm *)), argon pressure varied between 1 and 20 mrn, discharge current 0.40 A; series 5(3) - tube wall temperature 42°C (mercury-vapour pressure 7.2 X 10- 3 mm*)), argon pressure 3 mm, discharge current varied between 0.10 and 1.00 A. In series 5(0) the values of the radiant emittance was measured in watLm- 2. Series 5(1), 5(2), 5(3) served to determine relative radiation energy values; with the aid of the results of 5 (0) the radiant emittance in watt .m- 2 is found. Verweij 3) has measured the potential gradient (and hence the energy per unit of column length), the electron concentration and the electron temperature under conditions identical to those for the series 5(1), 5(2) and 5(3). The results of his measurements have been used for determining the wall losses and the volume losses. To verify the results of the measurements and the calculations, the sums of radiated energy, volume losses and wall losses for series 5(1), 5(2) and 5(3) were compared with the applied energy. A satisfactory agreement was found.
2. Radiation measuremeni«. 2.1. The tungsten strip lamp as a standard radiation source. The spectral concentration of radiance, L;., of a thermal radiator is calculated as a function of its temperature T from Planck's radiation law: C1
L;.(T) = - ' J,.s
Here
C1
and
C2
e(A, T)· ct(A) exp[c2/J,.T] - 1
C1
~'S e(J,.,
[
-C2 ]
T) ·ct(J,.) -exp -'-T .
1\
(1)
1\
are constants: C1
C2
= 1.1909 X = 1.438
10-16
10-2
watt .m''. sterad>.
m , "K,
Further:
ct(-1.) is the transmission factor of the window, e(A, T) is the emissivity of the radiating surface. The emissivity of tungsten has been measured by, among other investigators, De VOSS), Larra bee 6) and Ha.rn a ker t) for various values of A and T. Where possible we shall use the emissivity values found by Larrabee, and, if these are not available, the values determined by De Vas. Both La rr abe e and De V 0 s used direct methods for measuring the emissivity, comparing the radiation of the tungsten surface with that of a black body *) See page 3.
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
569
hole in the material. Larrabee introduced an extra correction for radiation which was scattered, e.g. at the lens with which the radiator was imaged on the monochromator slit. Hamaker employed an indirect method, measuring the reflection coefficient of tungsten and deriving the emissivity from this coefficient. The luminance temperature, T L, of the strip lamps used in the work under description has been measured at 650 mu and as a function of the strip current by Dr. W. A. Heusinkveld and Mr. K. Schurer from the Physical Laboratory of the University of Utrecht. A tungsten strip lamp was calibrated by the N.P.L., the N.B.S., the P.T.B., and in the Physical Laboratory of the University of Utrecht. Differences of 3°K, as a maximum, were found in the luminance temperature. The temperature T of the tungsten strip is calculated from the luminance temperature T L with the aid of -
1
= -
T
1
TL
+-,1,0Cz
·In[e(Ao, T) 'ct(}"o)J
(2)
where ,1,0 is the wavelength at which the luminance temperature has been determined, The procedure of our radiation measurements is to have, at the entrance slit of the monochromator, images of, first, the standard radiation source and next of a small area of the wall of the discharge tube, while taking care that in either case the optics of the monochromator are filled to the same degree. The image of the considered area of the discharge tube should be such that the radiation in the direction of the normal to the tube wall is detected (see fig. 2). The photomultiplier signals obtained from the standard source and from the discharge tube are denoted by Ds and D, respectively, The radiance Ln(A') measured in this way follows from the equation
f L ..(T) '-r(A) '5(,1,) . dA ,..- - - - - - Ds(A.') S(A') .,.(/\') D(A')
L (,1,') n
-
(3)
A' being the wavelength corresponding to maximum transmission of the monochromator at given adjustment. -r(A) being the transmittance of the monochromator; in the experiments r(A) is unequal to zero only in a small region around A', s(A) denoting the sensitivity of the photomultiplier tube; L ..(T) representing the spectral concentration of radiance of the standard source at a temperature T. For the band of wavelengths in which, under the prevailing conditions, T(},,) =F 0, we find that S(A) and L .. are practically constant so that S(A} = = S(;tl) and LA = L .."
570
M. KOEDAM, A. A. KRUITHOF AND
Hence
L (A') = n
D(A') .L ,(T) A
Ds(A')
J. RIEMENS ----------
JT(J.') T(A) ...dA
(3a)
A
The monochromator setting A' always corresponds with a mercury spectral line. The photomultiplier signal D(x) is measured for various settings x of the wavelength selector drum on the monochromator, with the image of the discharge tube focussed on the entrance slit. With x' corresponding to the maximally transmitted wavelength A' we find for the integral in eq. (3a): 7(.1.) J7(J,,')
A
dA =
Jdx' dA
D(x) D(x') . dx
~
( ell. )
dx
a:=:n'
I
D(x) D(x') dx
= b(A')
x
Eq. (3a) then becomes: Ln(A') =
D(A') .L '(T) .b(A') Ds(X) A •
(3b)
The integral is evaluated graphically and b(A') is found. In order to be able to estimate the random error in Ln(A') which may be expected we must know the random error in the quantities occurring in the right hand factors in eq. (3b). Errors in D(A') and Ds(A') may be neglected in comparison with the error inLA,(T), because the final measuring result is an average of a large number of measurements giving different values of D and Ds . The error in b(A') turns out to be small relative to that in LA'. The error to be expected in LA' is estimated with the aid of equations (1) and (2). The accuracy with which the luminance temperature has been determined may in turn be judged either by comparing the measurements carried out by a number of laboratories, or by considering the measurements to be carried out for the calibration of a tungsten strip lamp step by step. It will be found that in either case, at the luminance temperature of 2600 oK, the error does not exceed ± 3°. The error in the true temperature depends on, among other factors, the accuracy of determining the emissivity at the calibration wavelength (eq.(2)). Larrabee estimates the Lm.S. value of the error at 0.2%. Setting out from eq. (2) we can estimate the error in T to be ± 5° for T being 2900oK. The error of Ln(A') now follows from eq. (3b). Table I lists the values of L n for a number of mercury spectral lines, these values being obtained with the aid of a tungsten strip lamp as standard radiation source in the series of measurements 5(0); the table also gives the estimated random error. L n has been determined from e.g. the luminance temperature of tungsten at the calibration wavelength AD, which temperature is based on the melting
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
571
TABLE I l-« in series of measurements 5(0), as well as the percentage of random error, with the strip lamp used as a standard radiation source ,\
(n'l..I.) 253.7 404.7/7.8 435.8 546.1 577.0/9.0
I (watt.m~~sterad-1) I
percentage random error
71 0.80 2.19 1.21 0.26
4 3 2 25 25
point of gold, T g = 1336°K, so as to comply with the regulations for the international temperature scale of 1948. Recent measurements make it likely that T g = 1337°K (Oishi 9 ) ) or even that T g = 1338°K (Moser, P. T. B.10)). TABLE II The values of L" from table I for To = 1336 and 1338°K and the extreme values of L«, taking into account the random errors nud a change in To to 1338°K L .. in watt. m -·.sterad- 1
i\
{Ill[.I.}
253.7 404.7/7.8 435.8 546.1 577.0/9.0
I
To = 1336°K (I.T.S.) 71 0.80 2.19 1.21 0.26
\
To = 1338°K (Moser) 76 0.83 2.28 1.24 0.27
extreme values \
68 0.78 2.16 1.18 0.25
-
79 0.85 2.26 1.26 0.28
Tabel II shows the effect of a change in T (J on the energy of a number of Hg spectral lines. It also lists the extreme values of L n , taking into consideration the random errors and a possible increase of T g to 1338°K. The instrument indicating the current for the tungsten strip is a possible source of random errors, its reading accuracy corresponding to an accuracy in the temperature of about 2°. The final measuring results are obtained by averaging the results of about 20 measurements using two different strip lamps, one of which is operated at two and the other at three temperatures. Consequently the random reading error of the strip lamp current is negligible when compared with the errors in Ln. The same applies as we have seen previously, to the errors in D and Ds. 2.2. The carbon-arc anode as a standard radiation source. Instead of a tungsten strip lamp one may also use the crater of a carbon-arc anode as the standard radiation source l-). A number of investigators have measured the luminance temperature at a wavelength of 650 mfl- of a carbon-arc anode made of pure graphite. The best value is now thought
572
M. KOEDAM, A. A. KRUITHOF AND J. RIEMENS
to be 3808°K ± IS0 8 ) . E u l e r ll) has determined the emissivity of the crater of a carbon-arc anode at wavelengths ranging from 250 to 1800 mu. The calculated "true" temperature of the crater then is 3995°K ± 20°. Using the above standard radiation source the radiance L n for various mercury spectral lines has been established once more. Under the discharge conditions of series 5(0) we find the values for L n and the random error as listed in table III. TABLE III
L,. in series of measurement S(Ol, as well as the percentage of random error, with the crater of a carbon-arc anode used as standard radiation source
x
I
(watt.m!;:terad- 1 )
(mfL) 253.7 404.7{7.8 435.8 546.1 577.0{9.0
I
percen tage random error 8 5 4 4 3
7\ 0.84 2.29 1.26 0.27
The energy radiated by the carbon-arc anode is calculated on the basis of the melting point of gold, T (f = 1336°K, so as to comply with the regulations of the LT.S. Table IV gives the values of L n based on the measurements carried out by Moser, i.e. with T(f = 1338°K, as well as the extreme values of L n , taking into account the estimated random error and a possible increase of T (J up to 1338°K. TABLE IV The values of L,. from table III for To = 1336 and To = 1338°K and the extreme values of L u, taking into account the random errors and a change in T g to 1338°K ;\
(mfL) 253.7 404.7/7.8 435.8 546.1 577.0
L" in watt.m- 2.sterad-1
I
Tg
=
1336°K (1.1.'.5.) 71 0.84 2.29 1.26 0.27
To
I
= 1338°K (Moser) 76 0.87 2.37 1.30 0.28
I
extreme values 66 0.80 2.20 1.21 0.26
- 82 - 0.91 - 2.42 - 1.35 - 0.29
The crater of the carbon-arc anode when used as standard radiation source has some advantages as well as some drawbacks compared with the tungsten strip lamp. The carbon-arc needs no calibration and the current setting is not critical. However, in the experiments under description the radiation was less stable than that from a strip lamp. Because of its high temperature, the carbon-arc is generally to be preferred over the tungsten strip lamp for measurements in the u.v, region of the spectrum. However, the spread of
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
573
± 20° in the true temperature of the crater leads to the luminance of the crater being less well defined than that of the calibrated strip lamp. The temperature of the latter may be varied, whereas that of the carbon-arc anode has one single well defined value. 2.3. Radiant emittance. In the preceding paragraphs we have discussed a method for the determination of the radiance L n , i.e. the radiance in the direction of the normal to the radiating surface. To find the radiant emittance M, i.e. the amount of radiated energy emitted through the wall of the discharge tube per unit of time and surface area, we will have to determine the radiance in other directions as well. In the case of a diffuse radiating surface we have
M=n·L
(Lambert cosine law)
A discharge needs not necessarily be a diffuse radiator. Under these conditions the radiant emittance may be determined with the aid of a special arrangement for the determination of the angular distribution of the radiation of a small area of the tube surface. This arrangement comprises a diaphragm, fitted as closely as possible to the area of the discharge tube and a photocell provided with a filter which picks out the desired spectral line. z
y
x
photo multiplier
Fig. 3. Set-up for measuring the angular distribu Han of the radiation of Hg-A positive columns. The photomultiplier tube can be rotated in the X-Y plane. The length of arm p is about 1.50 m, hence great with respect to the diameter of the diaphragm (1 em). In the set-up the X-Z plane is opaque with the exception of the diaphragm.
574
M. KOEDAM, A. A. KRUITHOF AND
J.
RIEMENS
The photocell is made to move in a circle, having the diaphragm at its centre, the plane of the circle going through the normal to the radiating surface so that it can rotate around this normal (see fig. 3). Denoting the photocell signal by D(rp, 1}), we find the correction factor f3 for the radiant emittance from: n/2
f3 = ~. n
+n
ISin B· dDJ D(cp, tJ.) . dq:>. D(O, 0)
~=o
rp=-n
The radiant emittance M obeys M = fJ·n·L n
-"'-
_
Radiancs x cos i) (arbitrary units)
Fig. 4. Angular distribution of the radiation at A = 253.7 mu of a small area at the wall of a tube containing a Hg-A positive column. Compare fig. 3. _oiJ _
_
Rodiance x cas {) (arbitrary units)
Fig. 5, Angular distribution of the radiation at A = 435.8 rnu of a small area at the wall of a tube containing a Hg-A positive column. Compare fig. 3.
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
575
The factor f3 is not necessarily the same for all spectral lines. The measurements under description did show that for the radiation from the mercury argon positive column there are three different values of f3. In the series 5(0) these were found to be: (a) for the resonance radiation at A = 253.7 mu : f3 = 0.615; (b) for the radiation pertaining to spectral lines having one of the 63P levels as their bottom level (e.g. A. = 404.7, 435.8, 546.1 m!L): f3 = 0.551 ; (c) for the radiation pertaining to the lines not mentioned under (a) or (b):
f3
= 0.529.
-"'o
--.-Radiance x cos ". (arbitrary units)
Fig. 6. Angular distribution of the radiation at it = 577.0/9.0 rnu of a small area at the wall of a tube containing a Hg-A positive column. Compare fig. 3.
It can be seen that in all cases the radiant emittance deviates considerably from the values to be found with Lambert's cosine law. For lines pertaining to the groups (b) and (c) the deviation is of the same order of magnitude as the random error. For the series of measurements 5(1), 5(2) and 5(3) no image-forming components were used between the discharge tube and the entrance slit of the monochromator, but the tube was set up to irradiate a magnesiumoxide screen instead. The screen has a scattering effect and a part of the radiated energy will reach the slit. The signal which is detected is directly proportional to the radiant emittance M and not, as with image formation, to the radiance L. As was stated in section 1, the spectral line for It = 185.0 mu requires a special measuring method, since radiation at this wavelength is absorbed by air. Moreover neither the emissivity of tungsten nor that of carbon at It = 185.0 mu is known. In the investigations use was made of sodium salicylate for the determination of M (185.0), this substance possessing, according to Wa.t a.n a b e e P) and Hamman 13) , a quantum efficiency
576
J.
M. KOEDAM, A. A. KRUlTHOF AND
RlEMENS
• Sodium salicytat«
~
-
=
=
--;r-
-a
Discharge UDe
~
/[
c~
Fig. 7. Set-up for measuring the radiant-emittance ratio at A = 185.0 mu and at A = 253.7 mp., Sleeves A, Band C can be shifted. The inside of the window is coated with sodium salicylate. Sleeve A is made of fused silica of the same kind and thickness as the discharge tube; sleeve B is made of a special glass which does not transmit radiation at A = 185.0 mp but does transmit at J. = 253.7 mu: sleeve C is made of soda-lime glass transmitting neither radiations at A = 185.0 mp., nor at J. = 253.7 mu,
25watl m-/
, I
I /
I
I
I
I"
-- .,,
\ \.
\
I ;'~-
x
"
,'&
\
,
\
\
Radiatlan pDslWe \ calumn
,~
,, , , I
15
,
\
\.
"
I
,/ y' :, ,'
\
'
\ \
\
\
\~53.7 \,
\
,, ,
10
\
I
,.Owalt.m-t \
I I I
/
I
\
~
V
g!
, '" ~
.•~
",,'
5
c
O.5~
",+,",-+
/I __ .~ 46.1 1-1--. -t::::::; :-+~T--+--t 'r+-'~ ~ --t--+-·--+--+-t ::-.,--mOi9.O
1---+--+
,+~I::---
b
--t__._+_ _ +_ _•
365.
20
as
2
_
40
5
f
60 BOoC Bath temperature II) do 10-3mm
50
_Reduced mercury vapour pressure
Fig. 8. Power radiated per metre of column length (.70) for a number of spectral lines in the positive column of low-pressure Hg-A discharges. Mercury vapour pressure variable, argon pressure 3 mm (adjusted at 20°C) discharge current 0.40 A. 6, Values measured by Barnes under identical discharge conditions at A = 185.0 and 253.7 mu, The energy values apply to the imide of the discharge-tube wall, The left hand scale is for the radiation at J. = 185.0 IIl[L and 253.7 mu and for the sum curve; the right-hand scale is for the other spectral lines.
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
577
that is independent of the frequency of the incident radiation. Fig. 7 shows the set-up for measuring M(185.0). Around the discharge tube three sleeves are fitted, one made of fused silica and having the same thickness and composition as the wall of the discharge tube, the second made of a special kind of glass transmitting radiation at A = 253.7 mu but no radiation at A = 185.0 mu, the third made of conventional glass which does not transmit radiations at either of these wavelengths. The discharge tube with the sleeves is placed in a second tube, which has a window coated with sodium salicylate on the inside. The space between the two tubes is filled with argon at a pressure of about 70 em Hg. In preliminary experiments the extent to which the sleeves and the tube wall pass radiation at A = 253.7 mfL has been determined. The ratio between the numbers of quanta belonging to radiations at A = 185.0 and A = 253.7 mfL can be found when we measure the intensity of the fluorescent radiation with no sleeve; the first sleeve, the second and the third sleeve successively, at a wavelength where there is no interference by the direct radiation from the discharge. We then find, under the conditions as given for the series of measurements 5(0) : number of quanta at 185.0 mfL = 0.125 number of quanta at 253.7 mu We then calculate for 5(0) conditions: M(185.0) = 25 watt .m- 2 3QOwa{t m- T
Radiation of positive column ...
------ ---
0
,...~~----<
--
..----
_ _ - - - ) ( - _ _ l( _ _ _ l(_ _
1.Owatt.m-T
10.0
435.8
I~+-
546.1 iffl5]--+::-'::"'t ~t-.ti_l=-~~
- -577.aiQa'r--:t:--~=i= ----+-+ o
+404.
3
6 10 20mm _Argon pressure
Fig. 9. Power radiated per metre of column length (:n:) for a number of spectral lines in the positive column of low-pressure Hg-A discharges. Mercury vapour pressure 7.2 X 10- 3 mm (wall temperature 42°C), argon pressure variable, discharge current 0.40 A. 6. Values measured by Barnes under identical discharge conditions at A = 185.0 and 253.7 mu, The values apply to the inside of the discharge-tube wall. The left hand scale is for the radiation at A = 185.0 and 253.7 mu and for the sum curve; the right-hand scale is for the other spectral lines. The scale values are argon pressures at 20°C.
578
M. KOEDAM, A. A. KRUITHOF AND
J.
RIEMENS
Table V lists the values for the power radiated per metre column length for the most important mercury-lines at the wall inside the discharge tube under 5(0) conditions. The values are calculated per metre column length in order to use them when making up the energy balance (see section 3). Figs. 8, 9 and 10 give the corresponding values for 5(1), 5(2) and S(3) conditions. The values have been derived from those for 5(0) conditions. The values of the power radiated at A = 185.0 mfL for 5(1), 5(2) and 5(3) conditions have been found after inserting into a tube coated with fluorescent powder a sleeve made partly of normal fused silica and partly of a special kind of glass not passing radiation at A = 185.0 rnu but passing radiation at A. = 253.7 mu, Assuming that the transmission of radiation at 1\ = 253.7 IDfI- of both sleeve parts is the same, which was checked in a preliminary experiment, we find the ratio between the radiant emittance at 185.0 mp, and that at 253.7 mu by measuring the intensity of the fluorescent radiation at either sleeve part. 50watt m- 1
253.7 ... x
......
x
JOI-----+---+---~"'-----\__7=-___j
0.20
Fig. 10. Power radiated per metre of column length (n) for a number of mercury spectral lines in the positive column of low-pressure Hg-A discharges. Mercury vapour pressure 7.2 X 10- 3 mm (wall temperature 42°q, argon pressure 3 mm (adjusted at 20°C) discharge current variable, t:o. Values measured by Barnes under identical discharge conditions at J" = 185.0 and 253.7 mu, The energy values apply to the inside of the discharge-tube wall. The left-hand scale is for the radiation at J" = 185.0 and 253.7 mu and for the sum curve; the righthand scale is for the other spectral lines.
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
579
The values given in figs. 8,9 and 10 and tables V, VI and VII have been based on a comparison of the radiation from the discharge, with that from a calibrated strip lamp. The figures also contain some of the values measured by Barnes 14) at 185.0 and 253.7 mIL, these are in good agreement with our results. Barnes measured the radiant emittance at the two wavelengths and from the results calculated the radiance with the aid of Lambert's law. It turns out that this is not fully justified at the wavelength of A = 253.7 mIL. Since in the experiments under discussion the radiance at A = 185.0 mIL has not been determined, nothing can be said here about the relation between radiant emittance and radiance at this wavelength. TABLE
v
Power radiated per metre column length; i = 0.343 A, argon pressure 3 mrn, wall temperature 40°C (series of measurements 5(0)) wavelength
I
(m[J.)
I 185.0 253.7 265.2 275.2 280.3 289.4 296.7 302.1 313.0 334.1 365.0 404.7/7.8 435.8 546.1 577.0/9. 0 1014.0 1128.7 1367.3/95.0 1529.5 1692.1/1711.0
power radiated in watt per metre column length strip lamp as standard radiation source 2.9 17.3 0.023 0.0045 0.0079 0,0103 0,034 0.023 0.18 0,094 0.15 0.17 0.46 0,25 0.054 0.036 0.011 0,026 0.035 0.006
I
carbon-arc anode as standard radiation source 2.9 17.3
0.18 0.48 0.26 0.055
3. Energy balance. Figs. 8, 9 and 10 list the power radiated by the positive column of mercury-argon discharges at different values of the mercuryvapour pressure, the argon pressure and the discharge current respectively. The energy transport is further governed by elastic collisions between electrons and gas atoms (volume losses), and by recombination of ions and electrons at the tube wall (wall losses). In the circumstances under description the volume and wall losses can be calculated from the electron temperature and electron concentration, which quantities have been determined by Verweij 3) with probe measurements for the same conditions of mercury vapour pressure, argon pressure and discharge current as for our series of measurements 5(1),5(2) and 5(3).
580 M. - - - - -- - -
KOEDAM , A. A. KRUITHOF AND
J.
RIEM ENS
Tables VI, VII and VIII contain, among other values, the volume loss es per unit of column length, found with t he aid of a cur ve measured by K enty, Easley and Bar n e s P}. The latter gives the energy losses resulting from elastic collisions, per electron, in Hg and A , as functions of the elect ron temperature. Wall losses have been calculated from the coefficient for ambipolar diffusion, D a , and the gradient of the electron (ion) concentration at the wall of the discharge tube. Let us designate the number of ions (and electrons) colliding against the wall per second and per unit of column length by N:
( dne) r
N = 2nR·Da· - d
r=R
kT D a = it+· - e where:
it + is the mobility of Hg-ions in argon ;
T e is the electron temperature ; n e is the electron concentration;
k is Boltzmann's constant ;
e is the electron charge ; R is the radius of the discharge tube .
The mobility of mercury ions in helium h as been measured by Bi o n d i 16) . From it, Waymou th and Bi t t er s) derived, among other quantities, the mobility of mercury ions in argon which they found to be: 0.31
it+ = - - m 2.V -l.sec-1
PA
where P A is the argon pressure in mm. Now we take, as is customary for the discharges under consideration here, a Bessel function for nil' so that we obtain : (
dne )
dr
= r=R
2.4 . no
R
no being the electron concentration in the axis of the discharge. The transport energy per electron colliding against a surface is on an average 2kTe• The wall losses per unit of column length amount to:
N '(eVt
+ 2kTe) watt'm-1
where Vi is the ionizat ion potential (Vi(Hg) = 10.38 V). Tables VI, VII and VIII also giv e the wall losses per unit of column length and per second for measuring seri es 5(1), 5(2) and 5(3), respectively.
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
581
TABLE VI Energy input and output of the Hg-A positive column; mercury-vapour pressure variable, PA = 3 mm; i = 0.40 A radiation
volume losses
wall losses
energy output
energy input
(OC)
Hg-vapour pressure (reduced to O°C) (10- 3 mm)
(watt.m v-)
(watt.m- i )
(watt.mv-)
(wa tt.rn t]
(watt.m-v)
10 20 30 42 50 60 70 80
0.50 1.14 2.55 6.23 10.9 21.0 38.8 69.3
8.1 15.9 21.9 22.3 20.0 17.2 14.5 I\.3
19.5 14.5 9.8 5.9 4.7 4.4 4.5 5.5
2.9 2.3 1.9 1.5 1.5 1.5 1.7 2.2
30.5 32.7 34.1 29.7 26.2 23.1 20.7
3104
Wall temp.
r
33.2 34.2 32.5 29.5 25.8 23.8 23.0
19.0
TABLE VII Energy input and output of the Hg-A positive column; wall temperature 42°C (PHg = 6.23 X 10- 3 mm); argon pressure variable; i = 0.40 A Argon press. (mm)
Argon press. reduced to O°C (mm)
Radiation
Volume losses
Wall losses
Energy output
Energy input
(watt.rrrr-)
(watt.m- I )
(wntt.m r-)
(watt.m- I )
(watt.m-1)
0.83 2.79 5.58 9.3 18.6
21.7 22.3 22.4 22.5 23.2
2.1 5.9 14.4 26.8 60.5
3.5 1.5 0.9 0.6 0.4
27.3 29.7 37.7 49.9 84.1
28.4 32.5 39.2 49.6 8l.2
1
3 6 10 20
TABLE VIII Energy input and output of the Hg-A positive column; wall temperature 42°C (PHg = 6.23 X 10-8 mm); PA = 3 mm; discharge current variable Discharge current (A) 0.10 0.20 0.30 0.40 0.50 0.60 0.70 0.80 0.90 \.OG
Radiation
I
(watt.m- I ) 6.7 12.6 17.8 22.3 26.7 30.0 33.2 36.6 39.4 42.4
I
Volume losses (watt.m- I ) 2.2 3.9 4.9 5.9 7.0 7.9 9.2 10.3 11.5 12.7
I
Wall losses (watt.m- l ) 0.4 0.8 \.2 \.5 \.9 2.2 2.6 2.9 3.2 3.6
I
Energy output (watt.m- l ) 9.3 17.3 23.9 29.7 35.7 40.1 45.0 49.8 54.1 58.7
j
Energy input (watt.m-t) 9.7 18.2 25.8 32.5 38.9 44.7 50.2 55.2 59.6 63.6
4. Conclusions. Measurement of the values of spectral-line energies in the Hg-A positive column, by comparison with the crater of a carbon-arc anode, or with a calibrated tungsten strip lamp as a radiation standard, is quite feasible. The carbon-arc does not require calibration, in contrast with
582
M. KOEDAM, A. A. KRUITHOF AND
J.
RIEMENS
the tungsten strip lamp, and the current setting of the former is not critical. The values obtained with the two standard sources of radiation are in reasonable agreement. Generally the angular distribution of radiation of such a column is not according to Lambert's law. Experiments carried out with a mercury-vapour pressure of 7.2 X 10-3 mm, an argon pressure of 3.0 mm and a discharge current of 0.343 A yielded for M: M(253.7) = 0.615 nL n .
In the case of the other spectral lines examined during the investigation a correction factor was found for the results as compared to a diffuse radiating surface, viz. 0.551 or 0.529. On the whole, the agreement with the radiantemittance values found by Barnes is good. However, deviations are found in the values of the radiance L at A = 253.7 IDf-L' since Barnes assumed the radiation to be according to Lambert's law. Released-energy values were in general slightly below the values of energy-input obtained by Verweij 3), which is a plausible result since a number of possible sources of energy loss were neglected (compare figs. 11, 12, and 13). The conclusion may thus be drawn that the major items making 40watt m- f
4....· t~
~~
~s-,
~'\.'.
~"x-,
+~ x, ,,,~.,,,. ,
....x
+~"""'-lC
"'c... + .....
20
~t
10
-
o
10
0.5
20
30
2
Ba!h temaerciur»
40
50
60
5
10
20
70
80
50
900C 100.W;
mm -Reduced mercury vapour prassura
Fig. 11. Energy input and output of a Hg-A positive column; mercury-vapour pressure variable; argon pressure 3 mm (adjusted at 20°C); discharge current 0.40 A. - . _. - energy input. - - - - energy output; the radiation has been found by using a tungsten strip lamp as a standard radiation source. - - - - - energy output; the radiation has been found by using a carbon arc-anode crater as a standard radiation source.
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
583
90 watt m- I
),
1/
l' l'l l'
,,'I
II!
l.
I
30
-'~
.... -
·.... i.o.!ll-'-
~_
0,
/'
~~
2
3
6
10
20mm
_ _ Argon pressure
Fig. 12. Energy input and output of a Hg-A positive column; mercury-vapour pressure 7.2 X 10- 3 mm (wall temperature 42°C); argon pressure variable; discharge current 0.40 A. The scale values are argon pressures at 20°C. - . - . - energy input. energy output; the radiation has been found by using a tungsten strip lamp as a standard radiation source. - - - - - energy output; the radiation has been found by using a carbon-arc anode crater as a standard radiation source. eOwatt m:'
4
,oJ,.
.,;It .....;,.-:~
,;./tP
I +
.",;,.k'?
»:A""?+
.'~+
2~V
20
~
/I 0.20
1'"
0.40
O.SO -
0.80 1.00A Discharge current
Fig. 13. Energy input and output in the case of a positive column of low-pressure Hg-A discharges; mercury-vapour pressure 7.2 X 10- 3 mm; argon pressure 3 mm (adjusted at 20°C); discharge current variable. - ' - . - energy input. - - - - energy output; the radiation has been found by using a tungsten strip lamp as a standard radiation source. - - - - ~ energy output; the radiation has been found by using a carbon-are-anode crater as a standard radiation source.
584
ENERGY BALANCE OF THE LOW PRESSURE
Hg-A
POSITIVE COLUMN
up the energy balance of this type of columns have now been traced and their magnitudes determined. The authors are very grateful to Dr. W. Verweij for many helpful discussions. They also want to thank Mr. J. A. van Doorenmalen and Mr. A. G. v. d. Kooi for their assistance. Received 23-10-62
REFERENCES lJ Kenty, C., J. appl, Physics 21 (l950J 1309. 2) Waymouth, J. and Bitter, F., J. appL Physics 27 (1956) 122. 3) Verweij, W., Probe Measurements and determination of electron mobility in the positive column of low pressure mercury-argon discharges, thesis University of Utrecht, 1960. Idem Phil. Research Rep. Suppl. 2, 1961. 4) Koedam, M. and Kruithof, A. A., Physica 28 (1962) 80. 5) De Vos, ]. C., Emissivity of tungsten, thesis V.U. Amsterdam, 1953. Idem Physica 20 (1954) 690. 6) Larrabee, R. D.,]. Opt. Soc. Amer. 49 (1959) 619. 7) Hamaker, H. C., Reflectivity and emissivity of tungsten, thesis University of Utrecht. Idem Physica 3 (1936) 561. 8) Heusinkveld, W. A., Electrotechniek 38 (1960) 536. 9) Oishi, J., Awani, M. and Mochizu'ki, T.,]. Phys. Soc. Japan 11 (1956) 311. 10) Moser, H., Otto, J. and Thomas, W., Z. Phys. 147 (1957) 76. Idem Com. Int. Poids et Mesures, Proces Verbaux 21lA (1958) T 67. 11) Euler, J., Ann. Phys. '11 (1953) 203. EUler, J., Ann. Phys. 14 (1954) 145. 12) Watanabee, K. and Inn, C. C. J., J. Opt. Soc. Amer. 43 (1953) 32. 13) Hamman, J. F., Z. angew. Phys. 10 (1958) 187. 14) Barnes, B. T., J. appl. Physics 31 (1960) 852. 15) Kenty, C., Easley, M. A. and Barnes, B. T., J. appl. Phys, 22 (1951) 1006. 16) Biondi, M. A., Phys. Rev. 90 (1953) 730.