ontheeffectof supplyfrequencyonthepositive
Calculations
Hg-Ar Ac discharge
columnof a low-pressure
P C DROPTandJ POLMAN
Eindhovcn,
Philips Rcscarchlaboratories, NV Philips' Glocilampenfabriekcn,
Netherlands
MS reccivcd28 October 1971.in rcvisedform 29 Novcmber1971
Abstract. Resultsof a thcorctical study of the positivecolumn of a Hg-Ar dischargc
sustainedby an Ac cuffent with a sinusoidalwaveform(per= 3 Torr,psrs= 6 x 10-3Torr,
inefficiencyforwemision withinc.reasing
R= 1.8cm,Ier=0.4{.55 A) showa decrease
supply frequency/ for f<500H2, and an increascin efrciency for />500H2. The
efhciencycao be slightly higher than the Dc efficiencyfor a properly chosenfrequency
(/)l0kHz). A comparisonwith experimentalresults, availablein the literature for
comparabledischarges,is made, indicating a qualitativeagresment.In addition, the
temporal behaviour of a number of plasma quantities is pres€otedfor various supply
frequencies.
1. Inhoduction
*
;
$
It is known from experiments that the efficiency for production of Hg resonance radiation
by the Ac mercury-argondischargeof a ffuorescentlamp increaseswith increasing
supplyfrequency(Campbell1960).
of the electrode
Meyersand Strojny(1959)ascribethis increasemainlyto a decrease
by Koedamand Verwey(1965)have
losseswith increasing
frequencyl Measurements
decrease
as/increases
from
of3 Torr the anodelosses
shownthat for an argonpressure
50 to 400Hz, and that for/> 400Hz theselossesare practicallyindependentofl,
that radial expansionof the arc with increasingfrequency
Campbell(1960)suggests
is responsible
for an increase
in efficiencyof the positivecolumn.Suchan expausionhas
not beenobserved,
of Readand Kerry (1965)and Hasebe
however,in the experiments
and Ka"kizima(1967).
A third opinion has beenput forward by the last authors,who
useda rathersimplesingle-stage
ionizationmodel of the positivecolumnto showthat
with increasingfrequency.
the oc componentof the electrontemperature?" increases
temperature(Ie) causesan increasein the efficiency.
This increaseof the time-averaged
resultsof numericalcalculationson theAc Hg-Ar positive
Thepresentpaperdiscusses
column,basedon a modelof the dischargeplasmawith a five-levelschemeof the Hg
atom.It will be shownthat a minimumin efficiencyof the positivecolumnis found for
f=500 Hz and a maximumfor f=60 kHz. Furthermore,a comparisonof our results
with comparableparametersis made.
with experimentaldata availablefor discharges
for several
Finally,thetemporalbehaviourof a numberof plasmaquantitiesis presented
supplyfrequencies.
t Permanent address: C-entral l,aboratory Ligbt Division, NV Philips' Gloeilampenfabrieken,
Findlqvgn, Netherlands.
562
calculations on the efecr of supplyfrequency on thepo,titiuecolumn
563
In a previous paper (Polman et al 1972) the properties of the positive column in
modulated and pulsedmercury-rare gasdischargeswere theoretically and experimentally
investigated.The theoreticalmodel was basedon the time-dependentcontinuity equations
for the densitiesof Hg(63P0),Hg(63Pr), Hg(6sPg)atoms and the electrons, and on the
energyconservationequation for the electrons.The assumptionwas made that the radial
profiles (describedby Bessel functions) are constant as a function of frequency. The
electronvelocity distribution was assumedto be maxwellian.It wasfound that the average
electron temperature(re) has a minimum value at a frequency for which a maximum
Ie modulation occurs. Reasonableagreementwas obtaiued between the results of the
calculations and the experiments.The reader is referred to the paper mentioned, where
a complete descriptiouof the nonfinear effectsgiving rise to the (re) minimum is given.
Here it is only mentionedthat the sameeffects,which will be explained in 92, also play a
role in the properties of the ec discharge.
2. Results of the calculations
The calculationshave been carried out, as in the above paper by polman et al (1972),
for a Hg-Ar positivecolumn with pressures/a1 : 3 Torr, psr: g x lO-s Torr (determined
by the tube wall temperatureof 42 oC),and tube radiusR: t .8 cm.
Table l. Parametersof the Hg-Ar oc positivccolumn, with p1"= 3 16rr,
pse=6x lQ-sTorr and R:1.8 cm
Parameter
Calculation
Experiment
I (A)
E(V m-t)
P (W rn-t)
t (%)
kT"(eY
0'4
73
2e.2
73.8
1.0
0'4
8l
32.4)
69
1.0
neo (m-3)
r(6sPe) (m-s)
zo(68Pr)(m-3)
(m-3)
no(63Pg)
5 .4 x1 0 1 7
5 .7 x1 0 r ?
g .4 x 1 0 1 ?
1 4 .2 x l0 r z
5x101?
4xl 0rz
4x l 0r7
7x 101?
For the oc dischargeunder theseconditions,the parametersof the positive column
have been calculatedfrom our model. Similar calculationshave previously been made
by Cayless(1963).Our results are given in table l, together with experimentaldata.
The data for the electricfield strengthE, power input P per metrecolumn length,electron
temperaturere and electrondensity reo at the tube axis are taken from verwey (1961);
the excitedarom densitiesns(63P)at the tube axis from Koedam and Kruithot (1962);
and the efficiency from Koedam et al (1963). The efficiency is defined as the ratio
'7
betweenthe radiationoutput and the power input per metrecolumn length.In our model
only the Hg(63P)levelsareconsidered.Further calculations,taking Hg(6tPr) into account,
have shown that in Hg-Ar oc dischargesunder various conditionsapproximatelygo%
of the radiation is emittedin the 253.7nm line (63P1 61Se),and that the efficiencyas
referredto in this paper is representativefor that of -the total radiation output.
For the ec dischargethe current waveform is given by I:Issin(2.J}).
Figure I
showsfor this casethe calculatedefticiencyagainstpolverinout for variousfreouencies
t,,t
'
564
P C D ropandJP ol man
=
the curve for /err: 0'4 A
/and for a number of effectivecurrentvalues/"11 *f ol/2. Front
500 Hz' At this
for/near
smallest
it is seenthat the efficiencyantl the power input are
the average
(j"e)'
consequently
and
particularfrequencythe averageetectrontenlperature
(l0kHz5/54MHz)
the
frequencies
hi-eher
elecrricfield are found to be lorvest.For
discharge
oc
of
the
that
than
higher
be
slightly
to
found
of thepositivecolumnis
efficiency
rvith the same power input. For/> 4MHz the efficiencyapproachesthe DC efficiency
again.
P (W m-r)
production
of uv radiationagainstpower
columnefficiency
Figure1. Positive
'1for
supplyfrequencies
/ (kHz)anda numberof
inputp pernetrecolumnlengthfor various
currentvalueslett:pe,t:3Torr; pfls:Sx l0-3Torr; R: l'8 cm; A, f"n:
effective
0 4 A; B, /err:0'45A; C' /en:0'55A'
!::
-{r
i.
rt
Three time constantsare important for the understandingof the behaviour found,
namely the ambipolar diffusion time rp of the plasma, the energy relaxation time ta
of the electronsand the averagelifetime z* of the excitedHg atoms.It is noted that the
above quantities are badly defined, since the decay of the densitiesand the electron
temperatureis not exponentialin the afterglow of this type of discharge(Polman and
Drop 1972).For the presentargument,however,we shall considerthescquantitiesto be
ps, t*:25 ps 7D-5 ms)' In
consiants.In the presentdischargerB(t*(te('e-2
will
be denoted by a (:)"71
current
lc
of
the
the following, the angular frequency
n*.
by
atoms
Hg(63P)
of
and the concentration
If <.,(rp-r, the dischargecan be regardedas a slowly varying oc dischargeand its
propertiescan be derived from those of a oc discharge.There will be only a small
n"rltion of Ig during the period of the current,apart from a short time interval near the
zerocrossingof the current.lf a)rz-r, t1e,Teand n* remainconstantin time and the
propertiesare similar to thoseof a oC discharge.If rp-t4 u4tE-l, there is no ne moduiation, but a considerable?" modulation is found with a frequency that is twice the
supply frequency.Becauseof nonlinearitiesin the system,a decreaseof the average
temperatu.e(Ie) below its oc value occurs' due to the 7e modulation (Polman et al
there is also an n* modulation, The uv emissionvaries with Te and
lgTr). If
-(r*-t,
will be lower than in the nc case.Forrf:500H2, the effect of the
intensity
the average
calculations on the efect of supplyfrequency on the positiue column
565
]"" modulation is found to be largest,and consequently(re) and will be smallest.It
1
is noted, however,that for large Ts modulation deviations in the tail of the electron
velocity distribution may occur (Polman et al 1972).In that case,the efficiencyfor
f:500H2 may be somewhathigher than has been calculatedfrom our model. In the
remaining frequencyronge r*-l 4
no n* modulation occurs and, due to the
-4rr-r,
nonlinear dependenceof the excitation
rate on Ze, the n* density adjustsitself to that
value correspondingto the highest14 during the period, which is higherthan that of the
oc discharge,as will be shownlater. Moreover,because(f.) is still low, the elasticlosses
will be lower tban in the nc discharge.
Consequently
r7is higherthan its oc valuein this
frequencyrange, as has actually beencalculatedfor l0 kHzsf SaMHz (seefigure l).
Finally,in orderto illustratethe temporalbehaviourof the variousplasmaquantities,
we have plotted in figures2-4 someresultsof the calculationsfor/:50 Hz, 500Hz and
32kHz with,I"u:g'4A. (The valuesof the densitiesgiven are the densitiesat the tube
0
r l4
n l?
3rl 4
n
Figure 2. One half'period of the current | field strength d electron temperature lile,
electron density zeo and excited atom densitieslo (6sp) at the tube axis: Iorr:0.4A;
f=50Hz
axisdenotedas axo).In the 50 Hz case(figure2), where<o-ro-r, it is seenthat the electron temperature
is nearlyconstantandcloseto thatof the0'4 A oc discharge
(l.e: 1.0ev)
apart from a short time intervalnear the zero crossingof the current.This has been
confirmedby a microwavenoise measurement
of ru as a function of time, giving an
agreementwithin l0f with the resultsof the calculations.The electronconcentration
xes aod the Hg(63Pr)atom concentration
,,0(63P1)
have approximatelythe sameu,aveform as the current, but .E',n0(63pg)and to some extent Io and ro(6spo)show a rapid
increaseat the beginningof a half-periodof the current.This is due to the fact that the
electrondensityis very low in this time interval.Becausea certainamount of current
mustffow, the drift velocityr)dand consequently
theelectricfield f must increase
steeply,
causingariseof rg and, in this way,a risein thc productionof Hg(63p)atoms.Sincethe
i'..
':
: il:
...:'
566
P C D roP andJP ol ntan
Hg(63P0)and Hg(63P.r)atoms can only decayby collisionswith electlons,and sinceneo
is stitl low, the concentrationsof the Hg(63P0)and Hg(63P2)atoms increasemore than
that of the Hg(63P1)atoms,which can also decayby a radiativetransition.
Figure 3 givesthe dischargequantitiesfor/:5gg Hz' wherethe maximum r" modulaoccurs'
tion is found-.Figure4 showi that forf:32 kHz only a small changein n0(63P1)
€n
o
\
a. u.
I
F
Q
t-
rlz
3r 14
Figure 3 One half-periodof the current I, field strenglhE, electrootemperature*G,
elitron density n"o and excited atom density no(63Pr)at the tube axis: Ietr=o'4A;
.f:500 Hz.
TI
o
E
ff;
,..-t',*',,*?j.j
',,1::*:i.l
:.;
'
..i.:l
,, '.1
*
^n
cJ
\
rl4
ql 2
3 r l4
Figure 4. One half-periodof the current I, field strength4 electrontemperatureftIe'
elitroo density z.o and excited atom deosity zo(63Pr)at the tube axis: /err=0'4A;
f:32kHz
Calculations on the efect of supplyfrequency on the positiae column
567
and that the maximum value of 7e is higher than its oc value (seealso table l). Further
the time interval betweenthe maximum values of
calculationsshow that at/:l0kHz
E and I is zero, while zs(63P1)has adelay of rl4 comparedto L Ie and.I are approximately in phase. With increasingf it has been found that, compared to the maximum
value of 1, for/> 100kHz the maximum value of E showsa delay which is largest (a/10)
at/:500 kHz and which decreasesagain to zero atf:4 MHz. We thus concludethat the
dischargeis approximately 'inductive' for 50 Hz<.f<l kHz, 'resistive'from I kHz to
At this
l00kHz, then slightly'capacitive'andfinally'resistive'againnearf:4MHz,
Iast frequency the modulation depth of Ie is decreasedso much that the discharge has
the sameproperties as a Dc discharge(with the samepower input).
3. Discussion
In our model of the lc positive column the efficiencyr1is found to have a minimum at
,f-5mHz; it increaseswith increasing/to slightly above its oc value for/il0kHz,
and finally approachesthe Dc value for/:4 MHz.
It is intcresting to compare our results with experimentaldata. Unfortunately, most
experimentsas describedin the literature have beeucarried out under conditions different
from those used in our calculations.However, a qualitativecomparisoncan be made.
It should be noted that in the computations an ideal sinusoidal waveform has been
postulated,while in practice slight deviations from this waveform will occur, especially
tielow about I kHz.
Readand Kerry (1965)measuredthe intensity of 253'7nm emissionas a function of
the frequencyin the positive column of a Hg-Ar dischargewith constantpositive column
power P:50 W m-1. Their resultsshow a slight minimum near/=200-500 Hz, and an
increasewith increasingf to a value slightly above the oc value forfT2A kHz. However,
this last effect is not very clearly beyond the experimental error. With regard to the
in conditions,the agreementwith the resultsof our calculationslooks qualidifferences
tatively rather good.
Damelincourt and Scoarnec(1970) have qualitativelymeasuredn(63P2)againstfrequency and have found an increaseof this density with increasingf from 5@Hz to
20kHz,just as found in our calculations.
On the dischargeas a whole-that is, including the electroderegions-more data are
available(eg Campbell 1960).However, comparisonwith our resultsis difficult, since
the anode lossesare known to depend on the supply frequency(see$1 of this paper).
Above 500Hz the electrodelossesremain nearly constant(Koedam and Verwey 1965),
and any changcin efficiencymust be due to changesin positive column efficiency.In
with increasing
fact, it hasbeenfound that the efficiencyof the fluorescentlamp increases
(Campbell
calculations.
However,
with
our
1960),
in
accordance
frequencyup to 20 kHz
(Hasebe
Kakizima
1967)is
and
cannot
be
exceeded
the
oc
efficiency
that
the statement
not supportedby our results,which show that the efficiencycan slightly exceedthe pc
value, especiallyif the frequencyis taken higher than the valuesused so far.
The increasein q with increasingfrequencywill be the more pronouncedthe lower
the electrontemperatureof the discharge,for example,when using a higher current.
Indeed, our theoreticalresults indicate that the efficiencyof the positive column, as
compared with the 50 Hz value, is more favoured by frequencyincreasewhen using
higher input powers(seealso figure l).
t',a
568
P C Drop and J Polman
References
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CaylcssM A L96JBr. J. appl. Phys'14 863-9
(London: IEE) pp 207-1I
DamelincourtJ J and ScoamecL 1970Proc.Int, Con!. on GasDischarge,r
31-44
HasebeK and Kakizima T 1967Electl EngngJapanE7
Koedam M and Kruithol A A 1962.Pirur'ca2E E0-100
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MeyersG A and Strojny F M W 1959lllunr.Engng3465-70
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;-,i)
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1',: