Title Secondary mechanism in townsend discharge domain Sub Title Author 森, 為可(Mori, Tameyoshi) Publisher 慶應義塾大学藤原記念工学部 Publication year 1956 Jtitle Proceedings of the Fujihara Memorial Faculty of Engineering Keio University Vol.9, No.34 (1956. ) ,p.70(8)- 80(18) Abstract In the previous report, the author studied the relation between Townsend's and domain and proved the fact that the both discharge domains are decided by the magnitudes of p(pressure), l(gap length) and Δ(overvoltage ratio). In this report, moreover, the author proceeds to the analysis of Townsend discharge domain itself, makes clear that Townsend's discharge domain is classified into two domains which are quite different in the secondary mechanism generally called γ mechanism by the measurement of the spark discharge formation time: i, e, the domain dominant γi action (the action of the emission caused by the collision of positive against the surface of the as the secondary mechanism of the discharge), and the domain γp action (the action by the radiation of photons which are produced by the or the excitation action of ). Notes Genre Departmental Bulletin Paper URL http://koara.lib.keio.ac.jp/xoonips/modules/xoonips/detail.php?koara_id=KO50001004-00090034 -0008

Powered by TCPDF (www.tcpdf.org) Secondary Mechanism in Townsend Discharge Domain. (Received November 15, 1956) by Tameyoshi MORI*

Abstract In the previous report, the author studied the relation between Townsend's and Streamer discharge domain and proved the fact that the both discharge domains are decided by the magnitudes of p(pressure), l(gap length) and .:1 ( overvoltage ratio). In this report, moreover, the author proceeds to the analysis of Townsend discharge domain itself, makes clear that Townsend's discharge domain is classified into two domains which are quite different in the ~econdary mecha­ nism generally called 'Y mechanism by the measurement of the spark discharge formation time: i, e, the domain dominant 'Yi action (the action of the electron emission caused by the collision of positive ions against the surface of the cath­

ode as the secondary mechanism of the discharge), and the domain r 1) action (the action by the radiation of photons which are produced by the ionization or the excitation action of electrons).

I. Introduction The original Townsend Spark Discharge Thory, that illustrated the ionization by collision (a action) of the electrons in a as the main mechanism and the ionization action by collision (/3 action) of the positive ions in a gas as the sec­ ondary mechanism, is obliged to be revised from the view points of the ionizing energy, the mobility, and the formative time lag of the positive ions. And, as the secondary mechanism an idea is adopted that the action of the electron emmission is caused by the collision of the positive ions against the surface of the cathode (r; action), and by the radiation of photons which are produced by the ionization or the excitation action of the electrons (rp action). In this secondary mechanism** (named r action generally) on the surface of the cathode takes an important role in the spark discharge formation, then a number of electron avalanches are necessary within the spark discharge formative time, for it is necessary for the discharge formation to be maintained by the continuous electron avalanches from the cathode.

* ~ ~ PJ : As:;istant professor at Keio University ** In addition an electron emission action caused by the metastable Crm action) is noticed, however, it is less important in the present study of the author judging from the difference between the a:bove spark discharge formative time and the velocity of the metastable . Therefore, in this report r action iS limitted to

both r p action and t·i action.

( 8) Secondary Mechanism in Townsend Discoarge Domain 71

The theory that thus the spark discharge formation is accomplished by a number of electron avalanches, resembles the original Townsend Thory, though at present it takes 'Y action in place of fJ action. For this reason at present the spark discharge theory including a numder of electron avalanches from cathode is generally called Townsend Theory, and the domain of spark discharge condition applied to such a mechanism is called Townsend mechanism domain or Townsend discharge domain. On the contrary, when a satisfactory space charge is produced by a single electron avalanches and spark discharge occured suddenly, it is hard to consider th;1t the secondary mechanism has any influence on this phenomenon. It is reasonable to consider this domain as streamer Theory domain which adopts a photo-ionization action in gas. In the previous report Cl) the author studied such relations between Townsend discharge domain and Streamer discharge domain with the analysis of discharge wave-form and the calculation of discharge energy, and proved the fact that the discharge mechanism is affected by the magnitude of pressure p (mmHg), gap length l (em), and overvoltage ratio A (%). In this report, moreover, the author will proceed to the analysis of Townsend discharge domain itself, and will make clear the relation between two domains which are mainly represented by 'Yt mechanism and 'Y11 mechanism respectively from the measurment of spark discharge formation time principally, i. e. it is explained that in the air bordering p l (few mmHg em) and A (few %) corresponding the vicinity of p l of the minimum spark discharge voltage, 'Yt domain is at lower p, /,A, and the breakdown of 'Yv mechanism domain is at higher p, l, L1.

II. Theory When a voltage V higher than static bre~k down voltage Vs is applied to the electrodes impulsively, the time from voltage application to voltage-sudden drop, i. e. (i) statistical time lag Ts which is dependent on the existence of the originally­ present electron useful to the spark discharge formation. (ii) formative time lag Tr. i. e. the time that the present electron takes in ac- complishing the spark discharge by the effect of the electric field.

That is, T!l = Ts + T1 (1) hL7fil,.. __ Within the time lag 11 the electric field of space charge of electron avalanches grows up to a satis­ _j--Tg---, factory value and supperposing with the applied --t electric field promote the ionization action all over Fig. 1. Voltage wave-form of the the gap with acceleration and finally the figure of . the discharge advance is changed abruptly.

1) Tameyoshi Mori:].I.E.E.J. Vol. 2 No.2 P. 54, (1956): J.I.E.E.J. (Home Edition) Vol. 75, P. 1156 (1955)

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Briefly speaking, formative time lag T1 is the advancing time of electron ava­ lanche, and at the end of the formative time lag it is considered that the streamer begins to start at high p, 1, J, condition. On the other hand, at low p, 1, L1, condition is observed. The formative time lag condition in the streamer discharge domain is in principle as follows: Applied electric field = space charge electric field.

This was refered to in the previous report 1). In the Townsend discharge domain it is presumed that " the discharge current grows up to the degree of glow discharge current," and then "the density ncs of the electrons and positive ions just before the surface of the 10 3 positive plate increases to nearly 10 (number /cm ), the level of the density of glow discharge." Tracing back to the negative plate, if the number of the emitted electrons (Nos) from it is considered, it will be Nos= j ncsdvfexp. a!::::10 4--101:i v Now, the basis of the calculation of NuJ can be explained as follows : If the space occupied by positive ions from a single electron avalanchel shows a spheric at its top like the case of the calculations of Meek or Reather, and if multi- electron avalanches occur at the same point, the equation

V= j_7t;3 3

2 L=l ;= v' 6D{:. =~./0.4~~< ) v_ are presented. When calculated with the assumption of the uniformity of the density among v, Nus is showed as in diagram 1 (J=2.5%).

p/(mmHgcm) t_ (sec) I r (em) v ( cm3) [ al erxl I Nos

; 1 1.3x1o-s 0.316 o 132 1 5. n 299 I 4.7x106 I I

1.8x1o-s 1 2.5 0.200 I o. 0335 6. 87 955 I 2.5 X 105 5 [2.1 x 1o-s[ o. 141 ! 2981 I 3.4xl04 i ~~~~~---~~-- 8.00 ------Diagram 1. Calcu]ation of Nos (Ll=2.5%)

From this point of view, the formative time lag T1 under both "'t and 'Yv mecha­ nisms, can be calculated as follows. If an electron Nu=l emitted from the negative plate at the begining (Fig.1. t= Ts)

grows to Nos right after the formative time lag (Fig. 1. Tg= Ts+ T1 ) with the contin- · uance of n times of electron avalanches, the following relation can be obtained.

(10) Secondary Mechanism in Townsend Discharge Domain 73

Cry( ea,t-1 )J" ~ rynenU,t =Nus (2)

n= (o_gNas_ log(ryea.l) (3) If L and t+ are the transit times of the electrons and postive ions respectively between electrodes, the im1ization process time accompanied by a single containing secondary mechanism is for "'t action L+t+~t+ for y v action L (neglecting the transit time of photon) Hence, the formative time lag can be explained as follow. for "'t action Trt=nt+ (4a) for "tv action Trv=nL (4b) The transit time in these eqs. is explained as l L=-­ v_ (5)

And the direction velocities v_ and v+ of electrons and positive- ions in eqs. respectively can be given as follows: In the electric field intensity as found in this study, it is expressed that the direction velocity of electrons is proportional to the square root of the electric field E, and that of positive ions is proportional to E itself. So, for the former, Reather's empirical formula< 3> can be applied as

v_=1.25x107 I !i/41 = 1.25x107 /(1+J)V~ (em/sec) (6a) V p V 41Pl and for the latter, 1 1 v+ =bE=b ( +A)Vs = 1.4x 10 3( +L1) Vs (em/sec) (6b) 0 pl pl where b and bo: mobility of positive ions at p (mm Hg) and 1 mmHg. 3 4 b0 =1.4 x 10 (em/sec) /(V /cm)< ) Then for the investigation of another value n which decides T.r, the ionization factors a and ry contained in eq. (3) is expressed as a function of Efp generally, as

(7) Giving a suffix o to the factors, a and ry which correspdnd to the static break down electric field intensity Es, the next formula can be concluded for the dis­ charge continuance condition:

1) Tameyoshi Mori:J.I.E.E.J. Vol. 2 No.2 P. 54,1956.: J.I.E.E.J. (Home Edition) Vol. 75, P. 1156 ( 1955) 2) L. B. Loeb & J. M. Meek: The Mechanism of the electric Spark, P. 37 (1940) .

(11) 74 Tameyoshi MORI

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As known from experiments, the reliance of ry on the electric field is very little in comparison with that of a, and moreover, in eq. (3) ry has a logarithmic relation to n although a varies linearly for n. So, at least the calculation of n and 11 is concerned, within the domain of overvoltage ratio that the author is working in, 'Y ::::::::: 'Yo (9) can be obtained. Hence (lOa)

(lOb) from eqs. (10) and (3) n = log_!J_!!~ L1a • l (11) As Vs is determined, if the sort of gas and gap condition Pl are given, ac/P, aol, and so 'Yo= ry are determined from the relation Es!P = Vsf.pl. Further more, if the overvoltage ratio J is provided, the applied voltage V = Vs(l+L1) is determined, and then from E I p = VI pl, a I Pi. e. al and Aa·l = al-aol are determind. Hence, setting up an adequate Nos, the number of times n of the electron avalanches necessary for the spark discharge formation is obtained from ~ the above equation. Then, if the sec­ ondary ionization action is caused only ..., 6 .,_\ r----t---t-~~~,,j- "'" by 'Yt action itself, from eq. ( 4a), or by y v action itself from eq. ( 4b ), the for­ mative time lag is obtained. Thus, as n, l-, and t+ are functions of p, l, L1, if the sort of gas is determined, the formative time lag becomes also a function of p, l, A. 1[i = cpl(p, l, J) (12a) Trr' = c!Jr,(P, l, A) (12b) Fig. 2. The calculated formative time lag T 1 ;, In Fig. 2 the calculated values of Trt TrP and the transit time t+• t- of the positive and Tfv are shown where the value of ion and the electron between the gap.

3) H. Reather; Zeits. f. phys. 117, 375 (1941) 4) A. V. Engel und M. Steenbeck; Electrische Gasentladungen I. 182 (1932)

(12) Secondary Mechanism in Townsend Discharge Domain 75

Nos is 10 1 which is estimated as a comparatively reasonable vfllue in accordance with 20 the calculation shown in diagram 1. and an extremely over-estimated value 10 , for p, l, J in air. In addition the transit times Land t+ of electrons and positive ions respectively is presented in the same figure. III. Results and Discussions of the Experiment The circuit used in this experiment (refer Fig. 3.) and the experimental methods are main­ ly the same as that of the previous report. Cl) That is, between Rogowski type parallel­ plate electrodes a steep rectangular impulse voltage below the build- up time 0. 1 fL· sec. was applied and took the terminal voltage wave form Fig. 3. Circuit diagram of pictures by a high-speed brown-tube oscilloscope, the experiment and then measured the time lag Ta from voltage-applied time to spark discharge formation time. For the gas, air was used, and the gap condition was l= 0.5cm p = 2--20 mmHg the voltage application condition was Ll = 2.5--30 % As this experiment was done in Townsend domain, the range of p, l, J is limitted to the value far below the domain of the previous report.

In order to classify Ts and T1 which are included in 7~, ultraviolet ray of constant intensity was applied at the surface of the negative plate, and Ta was measured about 40 times under the same p, l, J condition. Fig. 4. (a), (b), (c) and (d) show an example of the Laue-plotted meas­ ured values of Tg, i. e. taking the measured values of Ta on the hori­ zontal axis, and on the vertical axis logarithmically graduated percent- Fig. 4. (a) The measured time lag Tg of the electric spark. age of measurement N which do not break down within an optional Ta among the total measured values. 10 o~__J'-----!,.--ll~___y,~___J__---i-8--'---,-!no ----'-----;,'?2--'--f,4-;--~---:,,6,.---L.---;,a Tg(~I0- 6 5) Fig. 4. (b)

(13) 76 Tameyoshi MORI

As thess results show, the measured values of the time lag approach the similar normal distributions and well coincide with the

10 0 80 60 '-=' !\." ~fo...t I l.?n in'\. t:i r::::: [J_ .1-z.s% f~ .._. - +--- ·-1-- - +-- t---\ , r----~ ,__ [ '!~ I-- 20 l I I~ !---- H f-."' ! ! I ' ~~ 0=/0mmHg !"------I L =05 em r------.. I : I I ~\ ~ ..... r--J 2 4 6 ""' IZ 14 16 I"" Tq (x 10-5 5)

Fig. 4. (c) Fig. 4. (d) empirical formula

N=exp(-- ~s)xlOO (%) (13)

From the slope of the linear part of this characteristic, the mean time lag a­ (mean Ts), and from Ta where this linear line cuts N=lOO%, the formative time lag T1 is determined respectively. Thus in Fig.5 the mean time lag, and in Fig. 6 (a), (b), (c) and Fig. 7, the form­ ative time lag are given by 0- marked curves. From these characteristics the follow­ ing can be said: i) 0' and T1 decrease rapidly as J in­ creases at the same pl. This characteristic is very similar to the results obtained by Tilles, C5> WhiteC6>,

i 0 : P-2mmH9 I I X : J J ,,r ~ l =OSCm A: 10 • 8 t== o: 20 , ...... '\ r--- ]"~ r--. I ~ ~ i t-t- ~~ r-r--, I ~ ifP I I I ~ ~ ~ --~ 8 !--+-·· 1-- 6 t-- f- -+- r= ij$ I -+ I 10 IS 20 Ll (%) .1 (%)

Fig. 5. The mean time lag (f (sec) Fig. 6. (a) The measured formative time lag T 1

5) A. Tilles; Phys. Rev. 46, 1015 (1934) 6) H. J. White; Phys. Rev. 49, 507 (1936)

(14) Secondary Mechanism in Townsend Discharge Domain 77

Wilson<7>, Schade<8>, Fisher and his co­ workers, <9> and Fletcher. <10>

Therefore, the characteristics of T1 de­ pending firmly on J are the common characteristics without relation to the magnitudes of pl and discharge domains. ii) Suppose p, lis constant at a certain critical value of J ··· .do= h(P, l) ··· , and suppose l, J, is constant at a certain value of P ···Po= fz(l,J) ···, the measure­

ed values of T1 and a- show a large change.

~r-r-r-+--r-+-+-+-+-+-+-+-+-+-+-+-+-~ r-r-r~~~~~-+-~-+-+-+-b-b-~-+-+~

1~-0~~~~~~~-+.~~~~~~~~~~ 10 IS ZO .t:l (%) Fig. 6. (b)

4 f---+--1--+--1--l----+-+--+-+-+------t-t--

Fig. 6. (c)

At l=0.5cm ane L1=2.5% this bordering value shows Po=5--10mmHg. iii) At the vicinity of such a border value T 0 -N charactenstic does not present a normal distribution curve as eq. (13) shows.

7) R. R. Wilson; Phys. Rev. 49, 1082 (1936) 8) R. Schade; Zeits,f. Phys. 104, 487 (1937) 9) G. A. Kachikas and L. H. Fisher; Phys. Rev. 88, 878 (1952) 10) R. C. Fletcher; Phys. Rev. 76, 1501 (1949)

(15) 78 Tameyoshi MORI

Refer Fig. 4 (b) P=5mmHg .:1=1096 ) ( Fig. 4 (c) P=10mmHg .::1=596 iv) From the above (ii) and (iii), bordering on such a critical value of p, I, 4, it is considered that the secondary mechanism of spark discharge formation is differ­ ent from each other. v) From the diffeience between the formative time lag and the transit time of electrons and positive ions, it is presumed that a leading factor of the secondary mechanism is below the critical p, l, J, · ·.... 'Yt action and above the critical p, l, J, ...... 'Yv action. The conclusion of article ( v) is founded on the following ground:

Refering Fig. 4, Fig. 6, and Fig. 7 and comparing the measured values of T1 and the transit times L and t+, for the critical condition (p, l, J)0***. At (p, I, L1)<(p, l, Ll)o (Low Townsend domain ...... arbitrary name]

t+< T1 (14 a) and At (p, l, J)>(P, l, J)o. (High Townsend domain ... ··· arbitrary nameJ

L< T1

"At the High Townsend domain, 'Yi action is not effective but ry 1, action is dominant" On the contrary, at the Low Townsend domain of which the formative time lag is more than t+, suppose the spark discharge mechanism is depending on 'Yv action,

T1 p (calculated value)< T1 (measured value) 20 is concluded when Nos is not only 10", but also 10 • By this reason from the above supposition of 'Yv action such a long formative time lag can not be explained. Hence,

"At Low Townsend domain, ry1, action is not effective, but 'Y1 action is dominant." As the border area of these two domains is the shifting domain between 'Yi action and ry 1, action, the formative time lag changes rapidly as Fig. 6 and Fig. 7 show. Moreover, at this shifting border, even if p, l, J is in a constant condition, as the effective forces of 'Yi and ry1, actions are possible to change slightly from one to another, it is observed that the repeated distribution curves come off the normal distribution as in Fig. 4(b) p = 5mmHg, J = 1096 or p = 10mmHg, J=5% (mentioned at the above article (iii)J.

*** (p, l, 4)0 shows (p, l, 4 0) where p, l are constant.

and (p0 , l, 4) where l, 4 are constant.

(16) Secondary Mechanism in Townsend Discharge Domain 79

IV. Conclusion In this study the discharge under the given gap condition and voltage application condition belongs to Townsend discharge domain which goes through the glow discharge metastably within the time from the begining of spark discharge to the formation of the arc discharge that is the final step of the breakdown. However, from the results of this study, it became obvious that this discharge domain should be classified into two domains by the measurement of the formative time lag as Low Townsend domain where 'Yi action is dominant and

High Townsend domain where 'Y 11 action ts dominant.

So far, Prof. Miyoshi Cll) has explained that all of Townsend domain is occupied by 'Yi action as the secondary mechanism, and that the space charge effect in a discharge advancing process is classified into 'Y- domain (Townsend discharge domain······ differential space charge effect) and 'Y+ domain (glow discharge domain······ non- differential space charge effect) He concluded by comparing the reserved energies before and after spark discharge breakdown. But the author concludes as above after the analysis of all processes of the breakdown. Hence, comparing prof. Miyoshi's conditions with the author's, the following revisions can be made. r- domain--~ 'Yt domain

r + domain --~ y p domain Moreover, in addition to the previous report of the author, the discharge domains, in concluston, can be classified into three as 'Yt domain ~ Townsend discharge domain { . : ry 11 domam I ~ Streamer discharge domain. 8 So, the domain, which SchadeC > studied in a non-active gas and H 2 corresponds to the Low Townsend domain; and the domain which Fisher and others<9; used as an object of their studies in air and N 2 corresponds to the High Townsend domain. Besides the formative time lag of this report, there are current build-up form and voltage-shift form which may be employed in the study of the same problem. About these the author should like to have another occasion to report. This research was carried out at Keio University sponsored by the Ministry

10) Yasunori Miyoshi; Research on the Electric Discharge Form (21 showa)

(17) 80 Tameyoshi MORI of Education under the leadership of Dr. K. Honda, professor of Tokyo University. The author is very much obliged to Dr. T. Somiya of Keio Unversity, Dr, Y. Miyoshi of Nagoya Institute of Technology and the gentlemen of Honda Laboratory as well as to Dr. Honda for their encouragement and advices, and expresses deep gratitude to Assistant T. Ueki of Keio University and Mr. S. Ota, student in the post-graduate course of Keio University for their co-opera,tion in this work.

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