Raju, G R Govinda

Rao, C Raja

English

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C. Raja Rao and G. R. Govinda Raju DepaTtmeni of High Voltage Engineeringy Indian Institute of Science Bangalore-12.{Eeceived 26 May 1972, revised 2 January 1973)The Townaeiid energy factor K t which is the ratio of moan energy of agita­tion of the electrons to the mean molecular eneigy is measured in dry air over the range 3 06x10"^’ <  EjN <  76 5x1 0 -”  V om  ^ {E is the electric field strength in V cm-^, and N the gas density in cm-®). In dry air Huxley's solution of the diffusion equation for electron attaching gases yields results which agree well with those obtained by using the diffusion equation for non-attaching gases. Factors influencing the accurate determination of K t have also been briefly discussed.IntrodfctionKor an electron non-attaching gas the steady state diffusion oejuation for electrons drifting in a uniform electric field E (parallel to the Z axis) isIndian J. Phye. 4 7 . 6 6 6 -5 6 4  (1 9 7 3 )T o w n sen d  en erg y  factor for slow  electrons in dry airy^n —_ fiE dnD dz (1)v^hore n  is the electron density, fi the mobility and D the diffusion coefl&ciont. Tlie solution of equation (1) is arrived at by (ionsidoring the proper boundary conditions whieh are, that the emission of electrons is from a point source and that tli(‘, electron density is zero everywhere, i.e , the collector plate, the walls and the cathode, except at the source where it is finite. Two different solutions are given for equation (1) by Townsend (1948) and Huxley & Bennett (1940). Townsend’s solution neglects the boundary conditions at the anode while that by Huxley & Bennett neglects cathode boundary conditions. With reference to figure 1, if i is the current falling on the central disc of radius a and i is the total current arriving at the receiving electrode, then, Huxley & Bennetts’ solution may be written as(2)v^hero h is the distance between the cathode and anode and da® == Equation('2) assumes that the annulus extends upto infinity, but, in practice, the radius of the annulus c has a finite value in which ’ase the solution is modified toi2 =ia-\-ic ( l - A e x p  [ - f J  (< ?» -« ] }... (3)666566 C. R a ja  R ao  and G . R . G ovinda R a juwhere In figure 1 the central disc is surrounded by two annuliiand equation (3) is applicable when the inner and outer annulii are connected together and considered as one, although equation (3) can easily bo extended to a multiple ring collector electrode. Therefore the measurement of R  directly yields the ratio Djfi when the dimensions of the diffusion apparatus are known.In the presence of ionization and electron attachment the steady state diffusion equation for electrons is (neglecting the detachment of electrons from negative ions and recombination of ions)fiJij [■ dn"" D [ ' W -(a - ... (4)where a is tlu^  Townsend’s primary ionization coefficient, and 7} is the attachment coefficient. The solution of equation (4) has been worked out by Huxley (1959) and independently by Lucas (1965).Huxley has shown that the ratio of currents to the annulus a p 6 the portion of electrode a ^  p ^  oo is (a, large enough to eliminate the emrent duo to negative ions)R - : ia h ’ [ ' I a b (5)Towm end energy factor etc,v^lle^ o oleotron current and I  negative ion current557: 1-=  1~  exp + - ^  J exp (XU) B is(6)where B =Q  exi> A^7t—2tdajexp - o x p [ - « 7 * | ^ + ( 2 - . ) » j ‘ j^ " e x p  _ e x p [-« ft| | l+ (2 -s )a | * j^^2_^A_________  -  velocity of electrons W Tfjdiffusion coellicient of electrons ~  D ' Dj/i'=  A2+2A(7/-a).Thus if a set of curves is drawn for an apparatus showing 72 as a function of u, and r/ for given value of A, when u and ?/ may be simultaneously lound by mea- surmg It at two values t>f A.2. P rogiiA-MMe F or CATiCULATTow OF R Using EciiiATioN (6)For a diffusion length h and collector electrode dimensions a and h the current ratios R are computed for various constant values of u varying ?; over a wide range A survey of the published data on Djfi and attachment coeflficiclit 7} for attaching gases, has enabled us to fix the range of values of u and 7} for calculation of R using equation (6). First u is kept constant at =  1 and rj varied from 0 to 1 at 0.05 intervals and R calculated. This is repeated for values of u varying from 2 to 10. In the second sot of calculations for various constant values of u ranging IVom 0.5 to 10, 7) is varied from 0 to 0.05 at 0 005 intervals and 72 calculated. iSimilarly in a third set of calculations u ranging from 1 to 20, 7j is varied from 0 to 5 at 0.5 intervals and 72 calculated Thus 3 sets of curves showing the values of H as a function of (m, i/) for A — 2, 4 and 8 cm arc prepared. The computer pi'ogramme is written in autocode and has been run on an Elliot 803 model 2 computer The integrand is segmonttni into 20 segments between 0 and 1.In a moderately attaching gas such as dry air wo can neglect tj (sec section 4) and the ratio of currents to inner annulus to the total cmTent to both the aimulii reduces from equation (6) to72 ~  [uida—db)]. (7)658 C. R a ja  R ao  and G . R . G ovinda R a juTypical curveK showing the variation of as a function of m at  ^=  2, 4 and 8 cm are given in figure 2. The above equation enables us to measure =  A) in dry air.CATHODEanode guardK- 2 fa­ze —Figure 2. Curve showing current ratio Ji as a function of v  neglecting aitachmenf-.From 2u = W _  38 92^D “  ” i<iis evaluated. Then the Townsend energy factor(at 25°C), first — average electron energy factormoan energy of notation of the electrons ~  mean energy of tlie gas moleculesis obtained by the relation K  — K JA , where ^ is a constant depending on the energy distribution function of the electrons in the swarm.A ~  1 for Maxwellian Law— 1.141 for Druyvesteyn Law.3. Apparatus and PkoobdttbbThe diffusion apparatus is shown schematically in figure 3. The details of the vacuum system and pressure measurement are given in an earlier paper by Raja Rao & Govinda Raju (1971). Nitrogen (cylinder grade consisting of 99 9 percent N ,^ 0.05 percent Oa and COg 5 p.p.m hy volume), is passed over copper filings maintained at 400“C and then passed over two liquid air traps to remove traces of COg and water vapour respectively. Similarly air is also passed through the two traps to remove moisture.The electric field in the diffusion gap is maintained uniform by means of 5 ‘thick’ guard electrodes to which are applied appropriate potentials from a wellTownsend energy factor etc. 559reticulated power supply through a high stability potential divider chain. These potoiitials are adjusted using a standard cell and a high sensitivity galvanometer. The stability of the field voltage supply is better than 2 parts in 10® and the volt- r,go can be measured to an accuracy better than ±0.5 percent.I^’iguro pSohoraatic diagram of iho oloctiodo syisiom of the dU'fuaion apparatus.The guard electrodes are mounted on three quartz rods fixed on a metal rijig with P.T.T .^E. spacers (1.07 mm thick) between them. The collector electrode IS mounted on a 1/2 in. thick P.T F.E. hnso. It consists of a central disc of nominal diameter 10 mm and four annulii of nominal (outer) diameters of 20, 30, 64 and 85 mm with an air gap of 0.25 ram between them. The anulii are surrounded by a guard ring with an outer diameter of 97 mm. All the rings are made of brass and heavily gold plated to reduco the contact potential differences (from alioiit 200 mV to 40 mV). It is observed that the contact potentials varied with l ime and after a warm up period of about an hour came down to about 1 or 2 mV. The leakage resistance between adjacent rings and between each ring and earth IS greater than 10” 12. The diffusion gap length is variable over a range of 0 to b cm by moving the collector plate (anode) axially through a Wilson seal and is measured with a micrometer to an accuracy of ±0.001 cm. The insulator le ^  Ihroughs for the electrical connections to the oollootor rings are made of P.T.V.E.The source of electrons is a glow discharge between a sphere (Jf) and a per- luratod plate (W), both made of brass. The glow discharge ourrent can he varied smoothly and it is less than 200/tri for all the pressures used. To prevent cloo- hons from entering the diffusion gup fi-om the sides, the glow is contamed m a pyrex glass oyUnder. To avoid photons liberated from the glow discharge reach­ing the diffusion region the plate N is made of two metal plates with non-aligneo560 C. R a ja  R ao  and G . R . G ovinda R ajuperforations so that the photons are almost prevented from reaching the anode or walls of the diffusion chamber through the source hole. The use of glow discharge for a source of electrons seldom has the disadvantage that the gas may become Jieated during the course of measurements. In order to keep errors due to temperature changes to a minimum tliroughout the experiments, the glow discharge is switched on just before the ratio of currents is taken.The stream of electrons produced bj’^ the glow discharge pass into the space between N  and G where tlrcy acquire a steady state of motion in the same electric field E as that prevailing between 0 and A (in the diffusion gap) Some of jjui electrons enter the diffusion gap through a small hole O (1 mm diameter) in the cathode and move through the gap under uniform electric field E to the anodeThe experimental parameters arc so chosen that all negative ions entering the source hole are collected by the central disc. In order to render negligible the effects of Coulomb repulsion, the total electron current entering the diffusion gap is restricted to about 2 x  A. These currents are measured with an E i.L. 33B Vibron electrometer indicator unit used in conjunction with a A 33B converter unit. The absolute accuracy of the current measurements is about ± ld )  percent.The measurements are made in the pressuie range 2-10 terr and for electric fields greater than 8V/cm.4 . F a OTOIIB iN riiU B N IN G  T ffE  ACCU RATE D ETERM IN ATIO NEactors inlluoncing the accurate determination of K t or Djfi in an attaching gas are briefly discussed in this section Detailed discussion for non-attaching gases has boon given by Crompton & Jory (1962) and Crompton et al (1965).In equation (5) the denominator shows that the total current is the current collected by an annulus extending to infinitj^ but, in practice, the outer radms c of the outer annulus is finite, and hence the ratio of ratios corresponding to equation (3) in non-attaching case should be used. In this investigation the ratio cjh is found to lie between 0.5 to 2.18 for the diffusion gap lengths used and tlic error that may creep in duo to this approximation is observed to be negligibly small. This is consistent with Crompton et al (1965) who observed in almost a similar diffusion apparatus, for the same electrode geometry, with the most widely divergent electron stream, loss than 0.004 per cent of the electron swarm lies out­side a radial distance of 4 cm.All analysis of the field produced by guard electrode system is made using the equation (Crompton et al 1965)., _  E L + S  ?Z  UNnrIl) e.in{N7rgj2l)~  I  ^ ^ Nn U N ticH) NngjZl '(8)Townsend energy factor etc. 561Mdicrc substituting 2 =  10/6 cm, c =  5 cm, A =  8.17 cm and  ^ =  0.167 cm, 0, iJic potential at any point within an axial cylindrical volume of 10 cm in diameter la found within ±0.18 per cent of the value corresponding to a uniform field.The influence of non-unilorm surface potentials over the receiving electrode appears to bo the factor most likely to limit the accuracy at small values of the j)araiucter EfN. Despite the use of gold plained metal surfaces tlii'oughout the (‘ollcctoi* electrode to minimise eifects of this kind, there is evidence to suggest lJuit under certain experimental conditions, the contact potential over the surface of the anode may have been neither uniform nor constant. This results in the I'liLio changing slightly after a few minutes when the ratio is read at next higher and previous EfN  repeated. Because of this effect some possibility exists that the results recorded at tho lowest field strengths may be in error. This possibility is reduced by commencing every series of results for a given pressure ail the lowest field strength.PresMure.s loss than 2 teiT are not used and the maximum error m the measure- iiuuit of pressure at 2 torr is less than 2 per cent with further reduces for higher piessuros used As mentioned earlier the accuracy to which tho field strength iH measured is ±0 ,5  i)ei cent.Crompton et al (1965) suggest that the lowest value of the field strength should be 3V/cni in order to keep the errors from contact potential differences Within acceptable limits but m this study field strengths less than 8V/cm are not used.it is observed that, in the curve showing It as a function of u neglecting iiUiiclimont {fj =  0) an error of ± 1  per cent in the measurement of E causes an ci jTH' of ± 2  7 xicr cent in u for h ^  2 cm if E <  0.8; an error of ±1.7 jicr cent III a for A =  4 cm if E <  0.5; and an erj'or of ± 1  iier cent in u for A =  8 cm if U 0.'35. But preliminary experiments show that for E <  0.8 for h ~  2 cm, !' <  0 6 for for =  4 cm and E <  0.5 for A =  8 cm yield more consistent values of TJjfi or K t and closer in agreement with the results obtained by previous worker.Tho ratio of currents given by equation (6) is computed by us for h =  2, 4, luid 8 cm and for various values of u and v/ and tho ratios show that in dry air the tittachment coefficient 'ijIN cannot be evaluated accurately. For example, at any value of EfN  say EfN =  61.3 X 10"^''V cni“ {Efp =  20), where T/fN is maximum lu dry air and equal to 11.95 >; 10-2“ cm  ^ {yfp =  0.tK)39), Dfp =  1.6. The com- putod ratio of currents for /i =  4 is 0 .4lj2. Tho ratio of cun*ents usually is measured h' ail accuracy of about 0.5 jicr cent. Aii uncertainty of ±0.5  per cent in this 'vill give a value of yfN  =  24.5 X lO-^ ® cm  ^ and less than 3.06x XO"®® cm  ^ (y//p - 0 008 and less than 0.001) which mean an error of over cent per cent; this error will inoreaso further at lower values of EfN. But tho error caused in ova- hiation of Dfp, or K t with tho same uncertainly in ratio R in less than ±2 ,5  perS62 C. Raja Rao and G. R. Govrnda RajuL-oiit. Heuco using equation (7), only values of u and hence K t for both Maxweh lian and Druyvesteyn laws of the distribution of the velocities are determined, Here also lOr is observed to depend on EjN  but not on N.6. ResultsTo check the leliability of the diffusion apparatus, experiments are carried out, in nitogen. The results obtained for shown in figure 4 generally agicod with those of Crompton k  Sutton (1952) within 5 per cent provided approprito experimental parameters are chosen. In agreement with Ciompton & Sutton the values of K t are observed to be independent of N  at any value of EjN in nitrogen.t/^, (vew"* twr-*)4. Vuluos ol Townaond Entugy Factor K a 'm  iiignigeii as a function of rioaoni, wort : o Maxwrli -1- C'roinplto>j & Sntto (195f)o DruyvoBtoyn X Townsend & Bailey (1921)□  Naidu & Prasad (1968)The results obtained for K t in a moderately attaching gas such as dry air sJiovm in figure 5 along Mdth those of jirevious workers. The lesults in dry air also agreed with those of Cromjiton et al wdthin 6.per cent and no pressure depen- (leuc-e was observed. These values together with the results of previous workers, are shown in figure 5 However, it was observed that consistent values wore ohlaiiied only if the ratio hjp was kept between 0.4 and 1. The exact significance oi' this criterion is not clear. Wo bohevo that the various factors Avhioh restrict i-he use of equations (b) and (7) (e (/., tlie current due to negative ions entering througli the source hole must fall on the central disc and the spread of the electronsdiffers greatly from that of ions) hecomc iiioresingly significant when tJio value of h jp  falls outside this range.E/>, (vem^ torr')Toymae'nd emrgy factor etc, 503Ji'i'Tim’ 5 ValuoH of Townsonrt Engergy Faotor K  in dry aii as a function ofProseni work : • Mawcll• DiuyvcfitoynX Townsend &, Tizard (1013) A Huxley & Zaazou (1040)+ Ciompton et a l (1953)□  Res & Hory (1964)Table 1. Values of Dj/i ai N =  32 65xl0^®cm"E I N x W ^ i Y  cm2) Eq (2) Eq. (9) Eq (7)(a)‘ (b)++ (a) (b) (a) (b)3.065 0 23 0.20 0.35 0 26 0.24 0.236 13 0.51 0.60 0.39 0.33 0.52 0 529.2 0 80 0 78 0.41 0 34 0.80 0.75(a)+ D Ifi values at A — 4 cm, (b)+^  D jf i valuos at =  8 cmThe ratio D//t was observed to bo somewhat dependent on h and the magni­tude of this effect is shown in table 1 The values obtained at lower sfiticings were generally larger. From a consideration of spatial dependence of the energy distribution, Parker (1963) has deduced that differences of up to 20 percent could ho observed between Dj/i values at ‘.arious diffusion lengths. In a recent paper, tVaneey (1969) has roderived the spatial dependence of the energy distribution iiHsumiiig a constant collision cross-section and deduced that the ratio of currents isf , Dmab  ^ 1 f - 2a /y^ 6^g\ 2(kTiiE-D)Bh^} ^ I I ’Ji =  1 - i l - (9)564 C. Raja Rao and G. R. Govinda RajuwhorG m in the mass of electron, a — (elm)E (e =  charge on an electron), k is Boltzman’s constant, T is the gas temperature andrm^ML^6(fc!T)2M being the mass of a gas molecule and L its mean free path. By siibstituting m ^  9.1091 X 10-31 kg, a ^  1.7588 X mH-\ i f  =- 46 5 X 10-2’ kg, L ^  4^2 xEaiom =  35 5 x l0 “ ®m and kT —  ^98xlO-2iJ, avc* get ~  1.313xlO“3Ji; (E in Fm” i).Using the measured ratio of currents, Dj/i values have been calculated using the equations (2), (9) and (7) and compared in table 1. Though Francey’s solu­tion prcidicts that Dj/i values decrease with increasing diffusion l(*ngth at the Hjmie value of EjN, the observed difference is siiialler possibly because the assiimptioiiH made by Francey ai‘e inapjiicable at higher values (if EjN.AcknowlbdqtjmentsOne (if us (C.R.R.) is thankful to the University Grants Commission (.f India for the award of Senior Research Fellowship. W(’ thank Professor Gojialakrisliiui fo his kind encouragement.RefbubnoesBailoy V. A. 1925 Phil. Mag. 50, 825.Crompton R. W, Elfurd M T & Gaac’oipne J (1965) Jml. J. Phyft IB, 409 Crompton R. W , Jusloy L G. H. ' Sutton B. J. 1963 Proc Boy. Soc. A218, 507. Crompton R. W. & .lory R. L. 1962 Aust. .7. Phys 15, 461.Crompton R. W.& Sutton D. ,T. 1952 Proc Boy. Soc A215, 467.Francey J. L A. 1969 J. Phij&. B. Atom Mole. Physics 2. 680.Huxley L G. H. 1959 Aust J. Phys. 12, 171.Huxley L G H. & Bennett F. W. 1940 Phil. Mag. 30, 396.Huxloy L, G. II. & Zaazou A. A, 1949Prof. Boy, Soc. A196, 402.Lucaq J. 1966 Int J  Electron 18, 419.Naiclu M. S & Praaad A N. 1968 Bnt. J. Appl, Phys {J Phys. D) 1. 703.Parker .1. H. 1903 Phys. Rev., X32, 2090Rao C. Raja & Raju G. R Govinda 1971 J  Phys. D: Appl Phys 4. 494 Roos J. A. & dory R. L 1904 Ausl. J. Phys. 17, 307.Townsend J, S, E. 1948 Motion of Slow Electrons in Oases (London ; Hutchinaoid Townsend J S E. & Bailoy V. A 1921 Ph i Mag. 42, 873 Townsend. .1 S E. &, Tizard, H T 1913 Pioc Boy Src. A88, 330.

Townsend Energy Factor for Slow Electrons in Dry Air

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Townsend Energy Factor for Slow Electrons in Dry Air

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