Mitra, D P

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Broken symmetries and excitation modes 161does not vanish, booanse the integral of this term over the quatisation volume remains equal to unity. AVhen v tends to infinitry* v~^  term gives rise to infinitesimal amplitude at every point in space of Boson field such that its integral over all space remains unity. Such terms have been noticed in the theory of quantised field (Goldstone 19G1, 1962, Uraczawa 1965). This idea explains the phenomena of long range correlation in superfluid .system.A c k no w ledg m entThe author would like to thank Prof. N. N. Raina for constant encourage­ment and Mr. R. S. iSharjna for useful discussions.R e f e r e n c e s(^oldstono i). 1961 Nuovo Cimetito 19, 154.GolflHl.one J., SalAm A. & Weinborg S. 1962 Phyft. Rev, 127, 1965.Umeztiwa H. 1966 Nuovo Cimento 40, 450.Indian J. Phys. 49, 161-164 (1975)A  study on discharge oscillationsD. P. Mitra*Dp^parlment of Physios, Presidency College, Calcutta 700012 (Received 26 August 1974, revised 27 November 1974)In a discharge tube operating in the negative resistance region of its V-1 charac­teristics, the negative glow, as pointed out by Sandnloviciii (1968) is a source of solf-excited oscillations.Depending upon the particular experimental set-up in the discharge tube system, the discharge oscillations can be represented by a suitable series or a f)iira]lol resonant circuit. The series and parallel resonant frequencies are not only equal to each other but also equal to the frequency of oscillations. The elements L, R, C of the resonant circuit consist respectively of dischai ge indue- tance and resistance between the anode and the wall at the negative glow region and capacitance of this region including the wall with respect to the surroundiiigs.The essential difference between the elements L, R, G of the circuit re­presenting oscillations in a discharge tube and those dealt with in an ordinaryPreaaijit address ; Department of Physics, University of York, York, England.162 D. P. MitraX, i?, 0  circuit iw that while in the latter case the olomonts are independent of the cunont flowini  ^tlirough the circuit, those in the former case are not so. The natiirti of dependence of these elements on the current is, however, not easy to foresee. The difficulty is all the more immense, since as the results of Sandulo- viciu (1971) show, the resonant frequency has a pronounced dependence on the discharge current. Thus the physical aspect of the exact nature of variation of the circuit el(unents and the resonant frequency cjf with the discharge current is uncertain. This explains why many of the results obtained by Sanduloviciu (1969, 1971) romaiu(?d unexplained. The findings are not only interesting but also a matter of detailed study. In the pieseat communication only a qualitative explanation of some of these findings is offered.From an analysis o f  the data o f Sanduloviciu, one can construct table 1.Table 1Discharge current t{mA)1.7 1.57 1.48 Sanduloviciu (1971)Series impedance 7j {K Q )1.0 1.05 1.26 Sanduloviciu (1971)Discharge inductance L{mH) at(a) Constant gas press (air) 0.123 mmHg, anode- cathodo pot. V in the range 970 <  V <  1260 volts 1.26 1.36 1.46 Sanduloviciu (1969)(b) Constant anode-cathode pot, 970 volts, gas press p  (air) in tho range 0.137 <  p  < 0.177 mniHg 0.86 0.96 1.05 MHeaonant frequency cor(KHz)612 660 688 Sanduloviciu (1971)Tlie above table shows that wr, Z  and L  all increase with decrease in I.Experimentally, I  can be increased by either (a) increasing the anode-cathode potential at a constant gas pressure, or (b) increasing the gas pressure at a constant anode-cathode potential.At the present state of knowledge about the mechanism of oscillations, it is difficult to formulate an adequate theory to explain the above findings. I t  is possible, however, to offer a qualitative explanation as follows.When I  is increased by increasing the anode-cathode potential at a constant gas pressure, the primary electron energy is increased, the secondary electron emission from the tube wall is enhanced, the wall becomes thus more positive because of which the effective potential is reduced. The value of L  arising from the accumulation of charge carriers in front of the anode thus diminishes.A study on discharge oscillations 163Again, when I  is increased by increasing the pressure at a constant anode- cathode potential, the ionizing collision would be more frequent, since the data ot Sanduloviciu correspond to the higher pressure side of Paschen minimum and the field near the cathode will be strengthened duo to increased space charges (Von Engel 1965). The primary electron energy therefore increases and the sequence of changes is the same as in the last paragraph.Thus, the variation of L  with I, M^ hen the latter is varied by the method (a) or (b) is explained.In order to explain the possible variation of Z and a> with /, it may be noted from the usual V-T characteristics of the glow discharge in the negative resistance l egion, that the greater is the discharge current, the loss is the impedance of the disclui-rge, when the circuit representing the oscillations is non-resonant. Again, uiidoj' the l esouant condition, th(^  greater is the discharge current, the less is the resistance of the discharge.The series impedance Z for an L, C, R circuit at a frequency w, is given. . .  ( 1)where the reactanceX  ==: W L-R, X  and hence Z  are, as mentioned above, dependent on I. ing a small variation of Z, on gets from (1)ZJ LZ2Then considor-(2)From this equation, the obvious conclusion is that p.c. change in Z ^  p.c. change in R, the equality holding for resonant condition and inequality for non- resonant condition. Let Z^, R^, X^ and Zg, R^, X^ denote values of the respective parameters corresponding to currents and I 2 ( I i >  12) slightly off-resonantfrequencies and then since, as pointed out above, Z^ > Z^ and R^ > Rvor,X ^ ^ X i  !> 0,1 1 (3)where C\, and Lg, Cg, represent the respective values of the discharge iud ic* tance and wall capacitance corresponding to the currents /j and t^ ,Let us now assume that the wall capacitance is unaffected by the changeo l  d is c h a r c T A  /» i ir r o in + .  c r^ f . f ic i. i:164 D. P. Mitra111 order to te«t the validity of cq. (3), three casen may bo possible, viz.,(i) 0)1= a>jj(ii) oji <  CW2and (iii) wi >  oig-Since from the i>hysical standpoint it has already been established that L  decreases with the increase of /, Hum as / j  >  /g. With the help ofthis relation <  L^) the inequality (3) easily holds for case (i) and case (ii). The inequality may still hold for ease (iii) only when the p.e. increase in w is small, because the case of equality in rates of increase in oj and decrease in L  is evidently ruled out.Thus combining (i), (ii) and (iii), it can be concluded that with decrease in current, tJie value of a> will either remain unaffected (i) or vill increase (ii) or can decrease only slightly (iii). l^ 'lie results of Sanduloviciu within a limited range of observations, ate in agreement with the case (ii) and by extending the region of observations one can possibly obtain results which may be in agree­ment with the cases (i) or (iii).The author wishes to thank Professor S. N. Goswami of Maulana Azad College, Calcutta for several helpful discussions.R e f e r e n c e sSanduloviciu M. 1968 Phyn. Letter 27A, ^13.Sanduloviciu M. 1969 Proc iHh Int. ConJ. on ionised gases {Buchatcsl) 149.Sanduloviciu M. 1971 Le J. De Physique 32, 157.Von Engel A. 1066 Ionised gases, Second Edition (Oxford) 196.

A Study on Discharge Oscillations

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A Study on Discharge Oscillations

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