Anodic Oscillations and Noise Generated in Glass Bulb Mercury Arc Rectifiers
line where oscillations or fluctuations appear or disappear． By adjusting slightly the arc current， the ambient temperature or the residual gas pressure， the fluctuations or 盾唐モ奄撃撃≠狽奄盾獅刀hcan be produced or eliminated． In Fig．1−81， the trace of straight line shows the voltage level in the absence of fluctuations or oscillations ． The mean level of
?撃浮モ狽浮≠狽奄盾獅刀h is a little lower than the voltage level of no fluctuation for rectifier C． It is a little lower than the voltage level of no oscillation for rectifier C and a little higher for rectifier F．
The properties of fluctuations and oscillations are summarized in Table 1−1．
The values of the frequency and amplitude show those of ordinary state． The arrows show the dependence of amplitude or frequency upon（a）the arc current，（b）the wall temperature
（c）the residual gas bressure，（d）the magnetic field， and（e）the shunt capacitance． Ihe bending direction of the arrows illustrates increaing， constant or decreasing properties．
DeC．1965． Reports of the Faculty of Engineering， Yamanashi University No．16
（2） Relaxatioll oscillations
Rela文ation oscillations are generated in a circuit composed of a dischage tube，
series resistance and shunt （even stray） capacitance．
（3） Oscillations which origiDate in the space of maximum or minimum pctentia1．33）
There is a maximum or minimum of potential due to the space charge in discharge tubes；aminimum in the regicn between the negative glcw and the Faraday dark space or in front of the hot cathode， or a rraximum in the negative glow or in the ball of fire．
There is a possibility that electrons oscillate in the potential minimum， the same as B． K．
oscillations， and ions oscillate in the potential maximum．
（4） Plasma oscillations34）・35）
（a） electron oscillations （b） ion oscillations
When electrons or positive ions in a initially uni｛orm plasma are displaced in a fixed direction so as to produde a non−uniform concentration depending only on that direction， os6illations take place about the uniform state in the macroscopic electric field produced by the displacements．
（5） Glowing waves36）
An electron beam passing through a plasma produces growing waves by a process that original oscillations gradually grow with the interaction between the beam and the plasma．
（6） Instabilities due to the transition between two states・
（a） Due to the variation of the position or numbers of anode glow， or negative glow （b） Due to the transition between two discharge states37）−44）
Anodic oscillations belong to this type． The transition takes place between
ionization and diffusion，5）・10）−14）・1t））・38）−40）between the anode fall of von Engel type and that of Langmuir type，15）・16）or between the anode glow mode and the ball of fire mcde．39）
（7）Moving striations45），46）
Moving striations are phenomena that luminous striae generally travel from the anode to cathode． They seem to criginate in ancde instabilities．
（8） Instabilities in a lcngitudinal magnetid field47）
Voltage instabilities occur due to enhanced diffusion in a discharge tube located in alongitudinal magnetic field．
On the mechanism of the anodic oscillations in dicharge tubes， the researchers explain as follows；一
（1） PUPP3・ 7）
If positive・ions are arti正iciaHy supPlied to the anode fall， it changes its polarity from positive to negative． The oscillations should be due to the periodic variations of the quantities of positive ions．
（2） Yoshimoto5）
The oscillations in fluorescent lamps are a periodical variation of the anode fall accompanied with a sudden ionization． They occur in the follcwing cases；（a）the quantity of the positive ions generated by ionization in the anode fall is greater than that necessary
Anodic Oscillations and Noise Generated in Glass Bulb Mercury Arc Rectifiers
to sustain the arc， and（b）the arc current is smaller than the saturated electrcn current determined by the cathode temperature． Accordingly the existence of the excess ions is the cause of the oscillation． Ionization and diffusion occur alternately． Therefore the charac−
teristic of the oscillation is determined by the quantity of excess ions． But in this case it
is also influenced by the space charge in front of th6 cathode， that is， by the thermionic emission of the cathode． And generaUy a fraction of the excess ions の
ξ will 6・ ・mpl・y・d…educe the an・d・f・ll
瓦 to be limited by its saturation value or by
negat ive space charge in front of the
Fig． 1−82
time elapsed plasmograph．
by a rapid
o 輪《μ●）
Variation of electron temperature， electron density，
and space potential in one period（Hoyaux and Gans）．
lncrease
approximately when the electron density is a maximum， and undergoes considerable increase at a given moment during the electron density decay， falling off again just befote the next burst of ionization．
It is concluded that the oscillations can be described as a recurrent or quasi−recurrent sdquence・f events， as foll・v・ ・s；
（a） During a period of high ancde fall， a breakdcwn cccurs in the ancde sheath．
（b） During the breakdcwn phase， the electron temperature in the immeadiate vicinity of the anode increases appreCiably；it then returns expcnentially tcwards its normal value．
（c） Immediately afterwards， the electrcn density in the immediate vicinity of the anbde increases， the function being fairly well described by a differene of two exponentials
of 浮獅?曹浮≠戟@periods．
（d） Except during the very short breakdown phase， the anode voltage drop and the electron density in the immediate vicinity cf the anode obey the Langmuir probe theory．
（e） Accordingly， when the electron density falls below a critical value， the anode fa1・1 begins to increase very rapidly， and a new breakdcwn occurs．
（4） Yamaneig）
The density of ions generated by abrupt ionization decays by ambipolar diffusion．
（5）Miyata12）−14）
The period of oscillation can be calculated from the ambipolar diffusion coefficient and the diffusion ｝ength which is equal to the radius of positive column divided by 2，405．
The calculated values agree fairly well with measured results．
from an arbitrary moment in the The main phenomena is a sudden and a slower decrease of icn
cathode．
（3） Hoyaux． and Ganslo）・11）
The electron temperature Te， the electron density （concentration） N and the space potential 1）respect to the anode are given in Fig．1−82 as functions of the oscillation by use of an autosynchronous increase of electron teITperature， followed density． The anode fall is a minimum
225
、：．Tl」 、 t卜 ｛「， ト ｛ 「ぐ ；． ：・A・㍉・i l・r，・t
・・ﾍi｝t・．t づt ． slへ
Dec．1965． Reports of the Faculty of Engineering， Yamanashi University No．16
・ ・ 、毫
ゆ ヲ
・ ［ ：： H ・ ・ 〆 ；¶ 1 ）、、． 1 パ ・ ・「、 「 ・・
（6）、、Mg（〕｝lizg，｝ il5）・16）、 ， 、、 ， ，、 、ソ、、． 、 ，、 ．、
．、、．無日n・d・fl・・tua・i・n、se・m・，、d卵中e・ecurrence・f L・卿i・・yp・ ．、ah・de興、
wi・h・煕・・itiy・ign・and・・n Eng・1・ype an・d・f・11 wi・hゴP・・iti・・i6n・・Whibh i・ ・ea…dby・h・
w・v・・fm・ving．s・・i・ti・n・Thr decay・f i・n d・n・i・y m・y re・亘1・・fr？⊇i｛・垣・hr・trrng元ie，1，d nea隅th撫dC・S w・li・・diff・di・n in・h・weak fi・iq・・fl・㊥g gu・・f i？・・mul〔i二・rilidiひ9・
The above theorles reduce to the commonρonclusion that the oscillations ar｛due
，。a。 t，an，i、i：6。 b。，ween，w。，，。、。、。f、he an。d。 fhll， wピ。ther，h。，e・ak。・bl。d・th6どi・ni−
9♪、」撒 ． ・ ｛ 吋ぞ
zatio亘followed by diffusion or the transition from Langmuir to von Engel type anode fall
さ
a亘d＼whether the ioh density decays only due to diffusion or due、to drift l as Well as dif−
f誌i6n． How infered our case is to be！The experirnents show that the light intensity in・1 ea・e・ilnm・di…ly・f・…he an・d・v・1・・ge ab・u，P・ly d・・P・d・、耳・yaux ・exp輌・n・・sh・w th・・the elect・・n d・n・ity i…ea・e・imm・di・t・ly・ft・・th・ ・npde．v・lt・g・d・・P・d・Th・f・・中・・
m・ymean・h・p・e・en・e．・f・x・i・・d…m・in・・ea・ing P・・h・p・wi止t与9 ihC・ea・e 6f i・n・and th・latt・・m・y acc・mp・ny th・in・・e・・e・f i・n d・n・ity・Thu・th・i・n d・n・ity，will in￠・r・・e immediatly after the anode voltage drops． The density of generated ions may decay by ambipolar diffusion． For simplicity， we assume that the period may depend principally on
ソ コ ぐ
the mean life time of the decaying iondensity by ambipolar diffusion．
、、、 Whether fluctuations or oscillations take place depends principally on the
＄hape of the anode． The discharge rray take、apath of minimum energy． The oscillations ， appear staヒbLy for the anode having a crater shaped concave and the fluctuations apPe『lr fOr．the anode having a flat front． There is a difference of frequency of a factor of t曾n between l fluctuations and oscillations and the frequency decreases as the arc，current increases for fluctuユtions but contrarily slightly increases for oscilla．tions ．・ This disfinct difference seems to be due to the diffusion lepgth． It may be related to the diameter of p6sitive column for the fluctuations ， but to the diameter of glow ball which decreases with increasing current for oscillations ． The amplitude remains about several volts p−p be￠ause the anode fall is generally of・severaLvolts．．
ロ ，
， 、 』． 3． Properties of Fluctuation8
4 ］
．1．The period of fluctuations
As previously mentioned， fluctuations ， seem to have the following mechanism．
The anode fall increases to a certain．voltage to maintain a state of discharge and then ioni4ation may occur abruptly near the anode， followed by decreasing anode fall due to a plasma newly created；at the same time the excitation increases the light emission． But the new state Of discharge can not sustain and a larger negative space charge grows due to dearth of the llew plasma by ambipolar diffusion of the ions to the wall・ The anode fall re−builds up to maintain the previous discharge state after the ion density decreases to a certain low value． This process will be repeated． The period of recurrence is proportional 北othe mean life time of ions．
Let Dαbe the amlipolar diffusion coeffiecient， A the characteristic diffusion length，
Rthe radius of the positive column andτthe mean life time of ions， then
τ一荒一言；｛百．裏5）2 （・一・）
Anodic Oscillations and Noise Generated in Glass Bulb Mercury Arc Rectifiers
Let vz be the number of ions generated per second per electron， Te the electron t。mp。・at。・e in d・g・ee，ρ th・v・p・・p・essu・e in mmHg， V・ th・i・ni・ati・n p・t・nti・l in v・lt・・
μpthe mobility of positive ion in m2volt−1 sec−1， and a the differential ionization coefficent normalized to a pressure of 1加llimeter． In the positive column where electrons have Maxwellian energy distribution and the generated ions are ballanced with those lost by ambipolar diffusion， we have the following relation48）
〃・一染一D・（2．405R）2・ （・−2）
and we have a constant represented by48）
・一（・V・÷μ・一・グ・）÷・ ・（・−3）
Since the electron temperature 7「θis high compared with the ion temperature T，，
the ambipolar diffusioll coefficient is approximately represented as
D。一μ。脇， （・−4）
θ
where k is Boltzmann s constant andθis charge of an electron．
Elliminating Dαandμ狽from Eqs．（1−2），（1−3）and（1−4）， we have
v・÷α穿・？（2蓑゜5／2・ （・−5）
三
L
e°
｛a）
Fig． 1−−r83
Io4
《bプ
Ionization time， diffusion time and peridd of fluctu−
ations and oscnlations．
Fig． 1−85
LO−2 10会I
pR， pr．坪● （cm．頂mHg）
Te as a function of pR， pr and pro （theoretical）・
Ixloe
ハひ 工 ε
s
ωlxlσ 巴
8
竃
臣 ξ
Σ
8国o
巴＝
1NOO
Fig．
H・de 8． Knigh↑；
Th●Arc Discharg●
P、425
20 40 60 80 100 t20
CONDENSATION TEMPERATURE ｛●C⊃
1：Ls4 Vapor pressure of mercury as a function of condensation temperatqre，
2，27
Dec．1965． Reports of the Facutly of Engineering， Yamanashi University No．16
Expressing T， in gK，ヵin mmHg and R in．cm， and putting a＝0．93， Vz＝10．4 volts and c＝1．1×10−1．for．mercury vapQr， we get ．
…・・9・×・・一・緩（2響5）2・ （・−6）
Let t be period of fluctuations ，彦z ionization time， td diffusion time which includes the mean life timeて ， as illustrated in Fig．1−83， and m a facter given by
。、＿t＝ti ＋彦d． ・ （1−7）
τ τ
Since Eq．（1−1） hapPens to equal the reciprocal of Eq．（1−2） or （1−6）， the fundamental frequency of the fluctuations is described as
弓一一η｝τ一1 91；1°−2・緩（2 讐5）2（・／・）・ （・−8）
The frequency or period may be determined by Eq．（1−8）．
As apparent in Fig．1−61 to Fig．1−68， the．excltation takes place in the surroundings of the anode． It has not become clear directly with experiments whether the fluctuatiOns ， may be due to a trans iton form an ordinary path in front of the anode to the surroudings of the anode or a recurrence in only the surroudings of the anode． But we assume that the i、onization occurs immediatly near the front surface of the anode and make use of the data gf the positive column in front of the anode to calculate the frequency．
（1） The vapor pressure P is determined by the temperature of condensed m．ercury near the cathode or at the base edge of the condensation dome49）． Figure 1−84 shows mercury vapor pressure as a function of condensation temperature．
（2） The elecrron temperature 7「』is obtained by pR−Te curve48）・50）in Fig．1−85，0r experimental one given by Hoyaux and Gans51）−53）in Fig．1−86． Besides the above， there are experimental data given by many reserchers including Killian54）． All the relUlts lie nearly in the same values． Above all， Hoyaux and Gans have given plentiful data． The value P is denoted as reduced pressure in Hoyaux and Gans paper． The theoretical values in pR−Te lie higher than experimental results．
（3） The factor m depends upon the time interval that is required for the ion density tb decrease to a certain value and for the anode fall to re−build up thereafler， and may possibly depend on the amount of residual air， impurity gases， ioniztion by metastable
詳ハ
｝ ご
∫
Fig． 1−−86
pR−一 Te ｛P
hoyaux ond Gan3 Peduced Pressure｝
IO− 10−1 10
pR，pr， pr・ ⊂Cm．mmH。｝
Te as a functions of pR， pr and pro（experime嘩al）．
■
「〆
Anodic Oscillations and Noise Generated．in Glass Bulb Mercury Arc Rectifiers
atoms， a blast of mercury vapor from the cathode spot49）， drift in electric field near the anode， the local heating by the anode， or other ambiguity of discharge． Also， the value of m for evacuation type valve may differ from that of sealed−in type， because， in the fgrmer case， the pressureクof mercnry vapor may differ from the saturation vapor pressure．
Ipapurity gases may consist of CO， CO2 and H， from graphite anode， water vapor from the glass and mercury， and organic gases from sealing grease． They may be produced during the performance after the mo皿ting of the valve， degassing， or from the contamination of mercury． The devices were not always operated in physically ideal conditions． For instance，
the residual gases may vary the effective vapor pressure♪and electron temperature Te in Eq．（1−8）and the evacuation may make the vapor pressureク unsaturated． In fact， it occasionally hapPened that the frequency of fluctuations varied apPreciably for the same c町rent for rectifier D． The value m varies according to whether the theoretical pR−T￠
curve or Hoyaux s experimental curve is used for the calculations． In this paper the former is mainly used． The causes affecting m are so complicated that it is difficult to predict reasonably the value of m． The value m should be taken as about two or four but may be extended to about ten， according to the characteristics of discharge．
2． The effect of current
It is difficult to calculate directly the effect of current on the frequency as a func−
tional relation． The temperature measured near the cathode at a value of current determines the vapor pressure， which．gives the electron temperature T』by the help of 1りR−T』curve．
Thus Eq，（1−8）will be available． The values of the frequency calculated by assuming〃z
＝7are shown by the cross points in Fig．1−15． Those by assuming m＝10 are shown by the cross points in Fig．1−16． They agree reasonably well with experimental results．
3．The effect of ltemperature
The increase in ambient temperature raises the vapor pressure and the gas tempera−
ture． It is also difficult to give a functional relation between the frequency and the tempera−
ture． The frequency mainly depends upon the vapor pressure， which is determined by the cathode temperature． The dependence of frequency on the cathode temperature will be obtained by the same way as above． The values calculated by using m＝5 are shown by the cross．points in Fig．1−26． They agree fairl夕well with the measured results．
4． The effect of residual gas pressure
The residual gases consist mainly of air and additionally impuriy gases evaporated from the grease at ground seals and exhausted from the graphite anode． Though it is known that the residual gases have effects on the cathode fall and the potential gradient in the poSotive column， the following may occur in our case．
（1） Electron attachment
If the impurity gases form negative ions by electron attachment， this negative ions collide with positive ions and the process of recombination is completed， a loss of electrons may be caused and lead to enhanced value of Dα． The electron attachment in the mixture of mercury vapor and helium gas has been studied by Biondi．55） It is well known that N2 does not form negative ions by electron attachment and O2 is attached by an electron．
There are no data on the electron attachment in the mixture of、mercury vapor and air．
229
Dec．1965． Reports of』the Faculty of Engineering・Yamanashi University No．16
（2） The variation of mobility
In the mixture of gases，、 the mobility may vary according to Blanc s law．56）Assum−
ing。mixtu・e・f m・・cu・y v・p・・and・iτ・・bin・・y mixtu・e and・lect「°n．tempe「atu「e as
、。n、，an、， w。，an，、1。ul。…h・m・bili・y f・・m Bl・n・ ・．1・w・、 Th・m・bility cal・ul・ted dec，ea、e， a， th。，。，idu。l g・， pressu・e in・・ea・e・，・・nt・a・y．t・・xp・・im・nta1・esult・・＊
Therefore we must take another standpoint， to． explain the effect of residual gas P，ess。，e． Th。 i・ni・a・i・n m・y dec・ea・e in t・・d・n・e・e・idu・l g…In・pi…fth・dec「ease
。f m。bili、y，、h。 i。n d。n，ity neccessa・y t・・u・t・in・1・w・・an・d・瑚m・y dec・ea・e f・・t・r・nd
。lec、，。n，m。y b。1。，t by the att・・hm・nt t・・xig・n m・lecul・・C・n・equently・・h・p・・i・d・f recurrence、may decrease・
5．The effect of、magnetic field
The ambip。1。， diff。、i。n…ffi・i・nt D。（B）in・1・ngitudin・l m・gn・ti・fi・ld is descibed aS 57）一一一59） ． ．．． ．
D・（B）−irgll，ll；i；−Bift B2， （1−9）
wh。，e B i，、h。 m。g。。・i、 flux d・n・i・y， oa， ・nd P・i・・h・m・bili・y・f p・・i・i・・i・n・nd・lect・・n・
re、pec・iv。ly． Th・v・1u・・fμ。 i・（2．2…2・・9）×1・−2 m2 v・1・−1 sec−1 a・1mmHg・nd°
・C・・）−62・。ndμi，（1．33 t・1．78）×10 m・v・lt−・sec−1 by th・p・・b・mea・u・em・nt・・（1・06 t°
1．22）×10m2 volt−1 sec i by the equation
μ・−2．4・×…3tt（m・v・lt−1 see−1）・ （1−1°）
withλe in m， at l mmHg andO°C．63）
We take the mean of the values obtained by the probe measurement，1．51×10 m2 volt−1 sec−1． In rectifier C， fluctuations appear at smaller current and at very high
、。mp。，a・u・e nea・・he an・d・． Assuming th・m・・cu・y・・p・・p・essu・e 1・27×10−2 mmHg at 50
・C。nd th。 t。mp。，atu・e 200・C n・a・the an・d・， w・・bt・inμ・−3 m2 v・lt− ・ec ・nd pe＝2・06
×103m2 volt−1 sec−1． Equation（1−1）and（1r−9）give the frequency f（B）in the pressence of magnetic field as follows：一
∫（B）＝D（B）＝．． 1− ． （1−11）
1＋μ・μρB2 ∫ D・
Th。 f，equ。n。y cal。・ul・t・d f・・m Eq．（1−・・）is sh・wn by・h・・u・v・（・）in Fig・1−39・whi・h gives the similar tendency to the experimental results．
6．The effect of external circuit elements （1） The effect of power supPly
Exp。，im・nt・w・・e・・din・・ily d・n・und・・th・feed f・・m・d・g・n・・at…Th・p°we「
，。u，ce and th。，upPly lin・・m・y h・ve a・ea・t・nce q・mp・nent・， whi・h might have an・ffect on the fluctuations or oscillations ． Though the generatgr is replaced with batteries to
、。mp。，e・he effec・・f・h・p・wer s・urce，・h・・e i・n・diff・・en・e・Th・・ef・・e・h・g・eat・・p・・t・f
、he exp。，im・n・， hav・been d・n・u・i・g・h・g・n・・a…until・SCR p・wer supPly・eplaced it・
Th。 SCR p。wer supPly，・h・ugh・littl・n・i・y， h・v・n・effect・n・h・wav・f・・m・a・d th・
P・・P6・・i…f・h…cill・・i・n・・Thu・・th…cill・ti・n・a・e n・t i・fluenced by．P°we「s°u「ces・
ee It has b6en given dy Welveij that the mobility of electron in the・mixture of mercury vapor and argon gas has the same tendency as our calculation for ions．63）
280 z