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Recent Developments and Future Trends in Electrostatic Generation

by Noel J. Felici

Professor of Electrostatics at Grenoble University

  SYMMETRY has been one of the most fascinating concepts suggested to human thought by the daily observation of Nature. Our own body gave us the first examples of symmetrical, yet not identical, shapes, screws and helices of both kinds are embodied by the insertion of leaves on the stems of many plants. The significance of symmetry for a deeper understanding of the fundamental laws of Nature as been growing since the beginnings of the modern era of science : the Nobel prize was twice awarded for outstanding contributions in that field of theoretical physics.

  In a broader sense, symmetry may be considered as one of the numerous aspects of duality. Duality has become familiar to the mathematically minded man, and can be given a strong foundation by the theory of reciprocal transformations, which may be illustrated by simple examples taken in the very field of elementary geometry. Duality has been felt also by many philosophers as being essential to a satisfactory understanding of the fundamental laws of Nature, at least in the prospects of human thinking. The "contraries" of Aristotle's physics, the "ying" and "yang" of classical Chinese philosophy, the "atoms" and "vacuum" of Democritus and Lucretius are, if not pure dual, at least complementary concepts which can not be thought of separately. A problem, of course, arises, about the true significance of those couples of duals. Are they only "categories", responding to a specific attitude of the human mind towards Nature, or the ultimate components of things? The great Chinese philosopher Lao Tzu, perhaps the deepest thinker mankind has ever bred, took an intermediate, but very interesting position by assuming a single fundamental principle, or ultimate essence of things, which is, in its own, beyond ordinary evidence, but gives rise, by some process of "differentiation" to the "contraries" encountered in the course of common experience. It is not stated, however, that the ultimate principle is not attainable to human knowledge at all, but only that it cannot be felt, or apprehended, together with its dualistic embodiments. That line of thought bears some analogy to the probabilistic interpretation of wave mechanics, but, in this case, it is the duals themselves (waves and corpuscles) which cannot be experienced simultaneously, while a principle, which were underlying to them both, seems to remain anyhow beyond the reach of human mind in spite of the efforts of some lonely thinkers.

  But in no chapter of theoretical physics, perhaps, has duality been an object of revived interest as in electromagnetism. Long before experiment gave any hint of the true nature of the links between electricity and magnetism both kinds of phenomena were paralleled in every treatise on physics. For a while, some investigators tried to find out a possible interaction between the poles of a magnet and those of a voltaic pile. At the opposite, Ampere stated that "when the poles of a voltaic battery are linked together by a conducting wire, their usual electric attractions and repulsions completely disappear and are replaced by a novel kind of forces, which may be evidenced by their effect on a similar circuit". It did not occur to Ampere that some voltage still remained in order to overcome the unavoidable resistances, but his idea of complementarily between stationary electric and magnetic fields was a correct one. In superconductors, for instance, permanent currents can flow without requiring any voltage for their maintenance, and present us with the exact counterpiece of the electric field created by stationary, invariable electric charges. Yet it was only a century thereafter that the idea of a general principle of duality, embracing the whole of electromagnetic phenomena, began to find some acceptance. Einstein's theory of relativity, indeed, was able to provide new evidence while shedding light on the whole body of electromagnetism and removing most of the difficulties encountered in the past. The principle of duality now belongs to the classical notions of science, and the ever-growing importance of high-frequency devices has rendered it useful for the average engineer. In textbooks on electronics, transistors are, for instance, depicted as being, in an approximate way, the duals of vacuum tubes.

  Much more might be said about electromagnetic duality, and it must be admitted that the usual duality principle, useful and significant as it may be, by no means brings the argument to a close. The plain parallelism between electric and magnetic charges cannot be devoid of any meaning, and however queer it may seem to a purely logical mind, there are many reasons to acknowledge the existence of several kinds of electromagnetic duality, of a "duality in dualities" perhaps.

  However complex the theoretical side of the problem may appear, the universal significance of duality is no longer to be denied, even from the viewpoint of practical applications. It is the very fine of thinking that made several physicists aware of the last big gap to be filled in electrical technique, the absence of any significant application of macroscopic electrostatic forces.

  It was a historical misfortune that the so-called "influence-machine" appeared at an early period, when neither its theoretical significance nor its practical interest could be anyhow appreciated. To many people involved in the applications of electrical science it never occurred that influence machines may have any part to play at all, and even in theoretical treatises, quite recently published on the Continent, one can read in the historical abstract that "the first device to be credited with the production of electric currents is Volta's pile, and the first machine which could turn mechanical energy into electrical was Pixii's rotating magnet alternator", thus forgetting that Benjamin Franklin's friction machine could do the same things one century before, not to speak of Franklin's electric wheel which is a very nice example of an electric motor.  

  Much may be said as apologies for that silly attitude. Neither physics nor technology were prepared, until the dawn of our own century, to cope with the problems involved by the very high voltages the influence machine is liable to give. It is natural that for people quite ignorant of insulation techniques a source of high voltage and low current seemed of little use, and that they would prefer, like the cock of Aesop's fable the grain of the voltaic cell to the pearl of immediate generation of high voltage direct current. The same misfortune happened, for the same reason, to the "electrostatic" appliances as well, how efficient and promising they may seem, today. The electrostatic spraying of liquids, for instance, now becoming a first-class tool in broad sectors of industry, yet well known two centuries ago, fell into complete oblivion, and for decades engineers devoted themselves to, the thankless job of improving many inefficient methods of spraying, until a few pioneers, resuming an old experiment known to the Abbe Nollet as early as 1750, showed the astonishing efficiency of electrostatic spraying, which, on an average, saves 70 per cent of the previous expenses in coating products and manpower (Figure 1).

FIGURE 1

ELECTROSTATIC SPRAYING EXPERIMENT

High voltage d.c. is generated by the rotating glass ball (rubbed by hand!) and distributed to the various spraying devices by the insulated chain.

Dualistic Picture of a Rotary Energy Converter

  In any machine converting mechanical energy into electrical (or conversely), tangential forces of an electromagnetic origin act on the rotor surface. The specific power of the machine can be expressed in terms of electromagnetic stress (tangential force per unit area) and linear speed.

  Any electromagnetic force can be depicted as being engendered by the mutual interaction of a field of force and an (electric, magnetic) charge, or by interaction of an (electric, magnetic) current with a field of induction. It is commonly admitted that only electric charges and electric currents are "real" whilst their magnetic counterparts remain fictitious notions. It is true that corpuscular physics present us only with electric charges and magnetic dipoles, which are, more or less, correlated with electric motion (even in the case of a neutron, the magnetic moment can be thought of as brought forth by the relative motion of a proton and a  pi- meson, a pair of particles to which the neutron is liable to give rise for extremely short intervals of time). Nevertheless, not only for the sake of symmetry, but also for a deeper understanding of electromagnetic phenomena are charges and currents of both kinds to be taken into account. It means that two species of electromagnetic duality may be considered:

(a) The crosswise duality, which could be labeled duality of the first kind, where correlation occurs for instance between electric charge and electric current, electric field and magnetic induction, etc.

(b) The elementary duality, or duality of the seeond kind, where charges, fields, inductions, electric and magnetic, are paralleled.

  It is true that in many theoretical and practical problems, the duality of the first kind appears to be more suggestive and stimulating, but it is by no means possible to discard the seeond kind as fictitious or meaningless. Neither can each species account for all possible correlations between electromagnetie phenomena, nor be consistent with the other. We must acknowledge, therefore, that all aspects of electromagnetism cannot be apprehended simultaneously, and some of them become veiled in the haze of incomprehensibleness, when the others are clearly felt, and conversely like the corpuscles and waves of quantum mechanics.

  In a purely magnetic machine, like most of the existing equipment, the electromagnetic stress is brought forth by the normal component of magnetic induction BN and the linear electric current density i (f = BN . i) or by the tangential component of magnetic field HT and the magnetic charge density µ, (f = HT . µ). Both formulae are mathematically equivalent, since BN=4 p µ and HT=4 p i; each aspect, however, is related to particular physical facts. BN and µ are both limited by the saturation of iron, but, whereas electric currents of density i must be present to create the stress, the latter is not, in actual machines, applied to the currents themselves. Thanks to the projecting iron teeth, the points of action of the stress are shifted towards the outer surface of those teeth, thus giving a physical meaning to the formula f = HT . µ. We may also say that the stress f  is created by the simultaneous existence of a tangential field component HT  and a normal induction comportent BN; f = (1/4 p )HT . BN.

  The dual of a purely magnetic machine is, of course, a purely electric, or electrostatic one. According to the duality of the first kind, the electric currents of linear density i shall be replaced by electric charges of superficial density s whilst a tangential electric field component ET shall be substituted for the normal magnetic induction BN, and we have f= ET s. That result is, of course, the dual of the second kind of f =HT µ. It is worth while to point out that both kinds of duality reflect some fundamental features of the machine. It is true that a charge density s  must be sprayed on the rotor and subjected to a tangential field ET to achieve energy conversion. It is also true, however, that BN and DN, HT and ET play, in many respects, rather similar roles and make, with their associated component, almost identical geometrical figures. In both electromagnetic and electrostatic machines, BN and DN are much greater than their tangential counterparts HT and ET, i.e., the lines of force, while crossing the gap, always make small angles with the normal to the rotor surface. BN and DN are both physically limited by some fundamental property of matter; magnetic saturation and electrical breakdown. It turns out that both normal components have rather definite Iimits which cannot be lifted to any extent in practice, except by the use of better materials, whereas ET  and HT  are in much more dependent on design and can be considerably improved by careful study of apparently petty details.

The duality of the seeond kind between BN and DN , etc.., thus appears to be significant in many respects, but it is worth while to point out that the electrical quantities associated with them, i.e., e.m.f. for BN and current intensity for DN are duals of the first kind. So the mutual interrelations of both kinds of duality appear to be very intricate, and a theory of electromagnetism that gave a clear and consistent picture of them would be of great value for both scientists and engineers.

Physical Limitations of Electrostatic Machines

Of tremendous importance for the practical significance of any machine are the physical limits of the various components previously referred to. Among them, DN appears to be the most momentous since it determines the current output, which has been so far the weakest aspect of electrostatic gencrators.

Electric induction is determined by electric field intensity and dielectric constant. It might seem quite obvious that we should use an insulating medium of high diclectric constant or permittivity to fill the gap between stator and rotor, thereby embodying the electrostatic counterpart (according to the first kind of duality) of the iron cores of high permeability. Unfortunately, fluid media of high permittivity and with enough resistivity (that is, with relaxation times greater than the working cycle of the machine) are not available today. All liquids with dielectric constants higher than, say, 10 or 12, exhibit s strong ionic conductivities and relaxation times much smaller than 10 -2 s, while the benefit afforded by liquids of low permittivity is too limited and cannot balance the considerable difficulties of design involved by the use of any liquid.

  As we shall see later, the hope of obtaining some liquids of high permittivity in an exceptional state of ionic purity is not so foolish as it might seem ten years ago. Except in the case of water, no insulating liquid has ever been obtained free of electrolytic impurities, and there is little doubt, if any, that the resistivity measurements on "pure" liquids fall short of many orders of magnitude and only reflect various contamination levels devoid of any physical significance. Moreover,the incredible progress of chemistry has given us at least the clue to the practical achievement of unheard of standards of ionic purity. Yet for the moment we must accept the unpleasant fact that only gases with permittivity unity can be employed in practice.

  Among gases the "electronegative" class, i.e., gases including oxidising elements like halogens or oxygen in their molecules, is favoured by an exceptional level of dielectric strength, and it would seem natural to use them in electrostatic generators. Quite unexpectedly, all experiments carried out in the last twenty years with such gases met with poor performance, as far as current intensity is concerned, and the most decisive progress was achieved by dropping them and turning to pure hydrogen, which has the lowest dielectric strength among molecular gases.

  The reason of that apparently strange statement will be found in the commutation problem. Since only d.c. electrostatic machines can, for the present, be of some practical interest, the commutation, that is, the alternate spraying of charges of opposite sign on the rotor, becomes of decisive importance. As long as spraying combs or blades are employed to that purpose, commutation will be made quite difficult by gases giving heavy ions of low mobility, particularly under high pressure, while hydrogen, the ions of which are exceptionally mobile,allows the necessary charge transfer to be performed smoothly and efficiently. That alternative could only be escaped by using conducting seetors instead of insulating rotors or belts, with cornmutating brushes like those extensively employed in d.c. electrornagnetic machines. As far as known, the proper design of such high voltage brushes, fit for industrial continuous operation, is a difficult task. Flashover is not a real problem with electrostatic generators, owing to the very small energy content of the magnetic field of the circuit, but the unavoidable capacitive sparking causes continuous erosion, pollution of surfaces subjected to strong electric fields and erratic operation results long before a reasonable life has been attained.

  So we must realise the disturbing fact that not only all liquids with high dielectric constants, but also most of the apparently best suited gases must have been discarded so far, and quite at variance with the statement that the fluid filling the gap shall allow for the highest values of electric induction, the best results,in practice, have been achieved with hydrogen, a gas of very low electric strength, apart from the exceptional case of the inert gases.

  However unsatisfactory the present technique might seem, it has been, nevertheless, efficient enough to make electrostatic generators competitive for some practical purposes, and this is very comforting. The amount of progress still left to the future, as measured by the ratio between electric inductions in hydrogen and,say, nitrobenzene is truly enormous,and that progress appears the more fascinating, as today technology already gives very promising results.

Ionic Commutation in Electrostatic Generators

We now intend to examine in some detail the mechanism of ionic commutation, the importance of which for good current performance has been already stressed.

  Low-mobility commutation: let us first assume operation in an  electronegative gas, under pressure,and also a substantial clearance between ionising points (or blade)-and the rotor (or belt) surface. All in these conditions are effectively realised, for instance, in belt machines. We may label this type of commutation "low-mobility" commutation, because its striking feature is the very small mobility of both negative and positive ions, due to their high molecular weight and still reduced by pressure. The influence of that low mobility on commutation is further enhanced by the length of the gap the ions must cross when travelling front the ionising points to the sprayed surface. The reduced mobility and the substantial clearance between points and rotor cause the space charge related to a given ionic flow to be very important. Instead of travelling directly in a sharp beam, the ions spread up sidewise and cover a broad strip of the rotor surface.

Figure 2 : Low mobility commutation

The ionic flow I0 is shifted to the left against the movement of the rotor R by the tangential field of the densities ±s and by its own space charge. The neutral line on the rotor surface ( locus of points where s = 0) is thus displaced away from the ionizer I. The field in the gap G, opposite the ionizer, is nearly uniform and equal to En ( or Em). It includes an important contribution from the ionizing field ( dashed lines of force) ( In : inductor at a negative potential with respect to I.

If we refer to figure 2, we see that the effective charge density s is given by 4p s =En-Er where Er  stands for the field in the gap between rotor and inductor* and Er represents the field required to drive the ions in spite of their low mobility. En cannot overstep Em the maximum field intensity or dielectric strength of the gas, whereas Er is of the same order of magnitude. It is true that the field decreases, along a given fine of force, from the points to the rotor, but we must keep in mind that the ionizing field strength is much higher in the vicinity of a sharp point or edge than between flat surfaces. The space charge, according to a general rule, tends to smooth the field distribution, thus enhancing its intensity where it is lowest, i.e., on the rotor surface. For all those reasons Er , is not at all a small fraction of Em , but quite comparable. Er is, in fact, moderately inferior to E'm, the ionizing field strength at the points, which, in its turn, is considerably higher than Em. This also means that the exciting voltage Ue, as being equal to the integral of the field between ionizer and inductor, is accordingly high. Ue comprises two terms, (i) Ur , the integral of the ionising field between point and rotor, (ii) En [ er / e + eg]; er=rotor thickness, eg= gap between rotor and inductor.

  Ue = Ur + En (er / e + eg) .Both terms are of the same order, Ur may reach 40 or 60 kV.

* We use the symbol En , for the effective field intensity in the gap, in order to avoid confusion with the EN of the previous section, which. was assumed to be equal to 4 p s,. Both symbols are equivalent if: (i) the normal component is uniform, that is, at same distance from the spraying device; (ii) the field is active on one side of the rotor only. Were normal components present on both sides, the correct expression for 4 p s, would be 4 p s = EN+E'N

If we introduce a "charging efficiency" h of the spraying device, as being the quotient of the effective charge density s by its theoretical maximum Em/4p we thus see that the efficiency of low-mobility commutation must be very poor, particularly under pressure. Values as low as .1 or .2 are commonly recorded in belt generators.

  High-mobility commutation: this type of commutation is effective when the charge transfer between ionizer and rotor surface is easy enough to minimize space-charge phenomena, thus rendering their influence negligible. The appropriate means to achieve high-mobility operation are: (i) Choice of a gas with high mobility of both kinds of ions; (ii) Reduction of the clearance between ionizer and rotor to a minimum; (iii) Moderate pressure.

Figure 3 : High mobility commutation

The neutral line falls almost in front of the ionizer and only undergoes a small shift at high currents. The field in the gap, opposite the ionizer ( dashed lines of forces) is that related to the threshold voltage of ionization. No line of force originating from the densities +/- s does cross the gap in that region. Only at a distance comparable to rotor thickness becomes the field in the gap uniform to En ( or Em).

Condition (i) is best fulfilled by pure hydrogen. Pure nitrogen is not as good, "electronegative" gases giving the worst results. (ii) requires the use of blades instead of rows of needles, since the tangential distance of some points of the sprayed surface to the nearest needle cannot be reduced sufficiently. It also requires a perfectly balanced rotor. (iii) reminds us that pressure is an unfavorable factor. In fact, high mobility commutation can be achieved in a strongly electronegative gas like air or carbon dioxide under two or three atmospheres, provided that the geometrical and mechanical conditions are fully met. At higher pressures, however, only hydrogen can be satisfactory. Above thirty atmospheres even hydrogen cannot insure perfect commutation, since the geometrical requirements (clearance between blade and rotor) become more and more stringent and can no longer be reconciled with reliable operation.

  When perfect commutation is achieved, the ionic flow is restricted to a very narrow volume along the ionizing blade, and the whole process, when viewed from a direction parallel to the edge of the blade, appears as being almost "punctual". The positive and negative zones of the rotor are no longer separated by a broad region sprayed with ions, but come very close to each other, their distance being, at any rate, much smaller than rotor thickness. Thanks to the higher dielectric constant of the rotor material, both zones have a substantial mutual capacitance and are linked by a strong electric flux. The general picture of the electric field, as sketched in figure 3, shows that, in the neighborhood of the commutation zone, the lines of force originating from the charge densities ±s do not cross the gap, but combine together, without escaping out of the rotor. Consequently, all conclusions previously drawn for the low-mobility case are completely upset and the corresponding limitations of s removed.

(a) The ion-driving field Er , no longer intervenes in the formulation of s, since the lines of force, originating from s in the restricted region where Er is active, do not penetrate in the gap.

(b) The exciting voltage Ue does not involve any important term from the field En. Were the commutation fully symmetrical with respect to the ionizing blade, Ue would be independent of s and En.

  In fact, the ionic flow is distorted opposite to the movement of the rotor by the strong tangential field of the densities ±s , and this causes the voltage Ue to depend on s . But the current intensity always increases very rapidly with Ue , and we may say that the machine is, to a large extent, self-excited, since the dielectric flux is maintained by the charge densities themselves rather by the external inductor. We have to deal with something akin to file compound excitation of dynamo machines since the self-exciting field is closely related to s, that is, to the current (Figure 4).

Figure 4 : Charge density v exciting voltage

Full line: experimental curve in an actual machine. Dashed line: theoretical straight line assuming constant Ur and no feedback that is, uniform field in the gap opposite the ionizer and calculating Ue by formula  Ue=Ur+En.(er / e + eg) Abscissas : total exciting voltage 2Ue(an exciting voltage equal to Ue should be supplied at both terminals, in order to insure symmetrical charging of the rotor with + and -densities, thus doubling the current output of the unsymmetrical arrangement. In cylinder machines, a similar Output may still be obtained with only one source of excitation. That source, however, must give a voltage equal to 2Ue).

One also may speak of a "positive feedback" in the pattern of lines of force around the commutation zone. The feedback percentage can be defined as 100 - a , a / 100 being the ratio of the experimental values of dl/dUe to the theoretical ones, assuming uniform field through the whole rotor volume in front of the ioniser,a  is commonly as small as 10 or 20 per cent; it happens sometimes that the feedback percentage oversteps the critical value of 100; in other words the machine becomes fully self-excited and the current, being no longer governed by Ue , suddenly jumps front a low value to a higher one. This phenomenon can be easily prevented by putting resistors across the leads connecting the ionisers to the terminals.

  As a consequence of the positive feedback, the exciting voltage Ue remains unexpectedly low for all values of s. In other words, if one attempted to calculate Ur out of  formula Ue =Ur + En (er / e  + eg ) he would get great values of negative sign. Another interesting consequence is the filet that Ue depends very little on rotor thickness and gap width, but is very sensitive to any increase in the clearance of the ionizing blade. Not only is that clearance essential for Ur, but if also determines the breadth of the commutation zone, that is, the influence between the adjacent positive and negative regions, and consequently, the percentage of feedback excitation.

  Discontinuous transitions from the high-mobility to some kind of low-mobility operation have been sometimes observed. At high intensities, under short-circuit conditions, the ionic flow happens to become instable and spreads suddenly over a substantial area. A very characteristic hissing sound is noticed, while the current output drops considerably. Recovery to satisfactory operation can be obtained by reducing Ue, and I for a while. In practice, that kind of instability disappears as soon as the machine is delivering voltage. For il is easily seen that the tangential field ET opposes to the sidewise spreading of the ions.

  The most important feature of high mobility commutation, however, is its very high efficiency h. Not only can s reach the value Em/4 p , but it is common practice to record saturation values of s greater by 30 or 40 per cent; that is h >1. There is nothing in that fact which would be at variance with the basic laws of electric field. If is advisable to take Em/4 p as the reference standard for s as long as the low-mobility case is contemplated, since Em - Er /4 p  <  Em /4 p

But as Er loses every bearing on s , in high mobility operation, we are no longer bound to consider Em /4p as an ideal Iimit. The rotor having two faces, each of them can be subjected to Em and the true limit is Em / 2 p . For s to reach comparable values, the exciting voltage Ue must remain much smaller than Em (eg  + er / e ) . If so the sprayed rotor surface reaches, at some distance from the ionizer, in the region where the field is nearly uniform, a very high potential, and becomes able to send a new set of fines of force towards any object at ground potential. If, in particular, we provide for a small gap in front of the rotor in that region, some fines of force will be attracted and caught, particularly if the chosen material has a slight conductivity, preventing if from getting too high a potential (Figure 5). One may think that the same results should be obtained by inserting small auxiliary inductors in the immediate vicinity of the ionizer, but, apart from its unmanageable complexity (those inductors should be duplicated at the high voltage terminal, etc.) that device never operates properly, not to speak of its basic lack of dependability, breakdown being very liable to occur between the ionizer and the auxiliary inductors.

Figure 5 :  "Supercharging arrangement "and diagrams of vertical field component and potential of the upper rotor surface vs distance to the ionizing blade

Dashed curves potential of the rotor surface with respect to the ionizer, when traveling to the right (direction of rotor movement). This potential, while being negative in front of the ionizer (voltage drop in the corona discharge) reaches high positive values at some distance, where the field in the gap is nearly uniform.

Full Curve: vertical field component on the upper rotor surface. In front of the ionizer, that component is very strong and negative (equal to -Er). It reverses, however, when the potential of the positive charges + s  has become great enough with respect to the neighboring stationary surface, thus allowing s to overstep Em /4 p .

High mobility commutation thus presents us with the long sought for solution of the problem of "doubly charging" a rotor. Nor, of course, is the rotor sprayed on both faces, since it is only a matter of electric flux, the current being equal to the derivative of that flux I= d y / dt much like the e.m.f. in electromagnetic machines e= d j   / dt.

We are now prepared to understand why hydrogen, thanks to the type of commutation it so largely favors, gives outstanding results in practice in spite of its low dielectric strength.

  The dielectric strength of pure hydrogen, in a gap of a few tenths of a millimeter, may be quoted 24 kV/mm, at 15 atm, or 30 kV/mi-n, at 20. For h =1, s would have the values 64 and 80, in e.s.u. In industrial practice s usually reaches 80 e.s.u. with exciting voltages as low as 25 kV, at 15 atm. Charge densities of 110 e.s.u. have been obtained with the improved structure of figure 5. Quite consistently with the previous discussion, increasing the pressure above 20 atm usually spoils the current output unless an exceptional geometrical perfection, that is, an extremely small clearance between rotor and ionizer, is provided for.

[ e.s.u = unities of electrostatic CGS-SYSTEM. So unfashionably they may appear, nevertheless, they have the important advantage to correspond to the practical orders of magnitude : as sound relations between both systems the following equations may be mentioned:

1 µA corresponds = to 3000 electrostatic unities (e.s.u.) of the current.

30 kv/cm = 100 e.s.u. of the electric field. (Atmospheric air under normal pressure).]

  A very interesting check of the preceding theory was carried out with an experimental machine operating in two different atmospheres. Thanks to the use of a sealed cylindrical rotor with internal stator the gap could be filled up with an electronegative gas of very high dielectric strength, i.e., nitrogen and SF6 mixture. Commutation, however, was still performed in hydrogen. A slight over-pressure of the hydrogen atmosphere prevented any SF6, leakage towards the ionizers.

Figure 6 : CHARGE DENSITY Vs EXCITING VOLTAGE IN THE TWO-GAS MACHINE

(a) Sprayed rotor surface in good condition.

(b) Sprayed rotor surface in poor condition, after ten minutes of operation at maximum current.

(c) Theoretical straight line corresponding to zero feedback and constant U, (in tact, Ur cannot be constant but increases, Of Course, with current, thus causing the slope of the zero feedback segment to be further reduced).

It was found that the excitation curve I(Ue) colisisted of two segments of greatly different slopes. First a very steep one, responding to a feedback percentage of nearly 100 per cent, or more (instabilities), up to charge densities of 70 to 80 e.s.u., followed by a sudden break of file curve, which continued as a new segment having nearly the slope responding to zero feedback (Figure 6). By exciting the machine up to the maximum permitted by overall insulation, a charge density of nearly 140 e.s.u. was obtained without any sign of the curve being flattened by approaching saturation. The hissing sound characteristic of the instability of the discharge and its spreading was noticed when reaching the bend of the curve, it was also found that the nature of the rotor surface (use of various varnishes) and the dielectric constant of the rotor material had a definite influence on the phenomenon.

  That experiment taught us that the stability conditions of the high mobility mechanism are much more important than the dielectric strength of the gap. As soon as the "punctual "commutation fails, any increase in charge density must be paid for by an unacceptable exciting voltage. We previously said that 80 e.s.u. could be easily obtained with 25 kV, but, for 140 e.s.u., 90 kV were necessary, leaving little room for an output voltage! Moreover, the "hissing" discharge soon deteriorates the rotor surface, thus lowering the critical bend in the I(Ue) curve, and simulating some sort of saturation, which is, of course, not anyhow related to the dielectric strength of the gas filling the gap (Figure 6). The influence of rotor permittivity is also of interest. It shows that the instability of ionic flow largely depends on the very strong tangential field prevailing in front of the ionizer, between the positive and negative zones of the rotor. The higher the permittivity of the rotor, the greater the dielectric flux which may link both zones without overstepping a given tangential field strength. A long practical experience with cylinder machines has definitely shown that the "maximum" current considerably depends on the dielectric constant of the rotor material, at Ieast up to six or eight in spite of the detrimental influence of the stray fluxes which are, of course, favored by rotor permittivity.

  We now see that, quite unexpectedly, the limit of a related to the dielectric strength of the gap Em and the Iimit of stability of the high mobility mechanism are nearly the same in hydrogen under 15 or 20 atm, and lead to a maximum s of, say, 100 e.s.u. In electronegative gases, however, both Iimits are widely different as soon as pressure is raised above atmospheric, and in most cases, no room is left for the favorable mechanism of commutation. For instance, adding 2 per cent of SF6 to the pure hydrogen of a cylinder machine cuts the feedback percentage by 50 per cent or more, even for small currents. It is now quite clear why no intense currents can be achieved except in pure hydrogen.

  It is also clear that the capabilities of ionic commutation are practically exhausted and that any step towards higher charge densities would first require fundamental progress in the commutation problem rather than discovery of new gases of unheard of dielectric strength. We are still unable to turn to good use the abilities of the N2+SF6 mixture, which should allow at least 200 e.s.u. This statement must not be understood as a message of despair. So little effort has been spent in the whole world on those problems, compared to the gigantic expenses devoted to many other developments, so great is still the part of empirical observation contributed by isolated individuals in the progress achieved so far, that we must consider the development of electrostatic machines as still following the paths of preatomic age. The fact that machines of very poor design, as seen from a purely scientific viewpoint, can be serious competitors for equipment embodying elaborate technology, is very comforting in the prospect of the immense wealth of possible progress still ahead of us.

High Current Electrostatic Generators

  As previously explained, the use of hydrogen is still the only practicable way of obtaining substantial currents in spite of its very limited dielectric strength. Some efforts have been made in the laboratory of the French National Centre for Scientific Research (C.N.R.S.) with the assistance of S.A.M.E.S. to embody the known technique in actual machines of relatively important power. Attention has also been paid to the feasibility of multipole machines giving very strong currents, at least for electrostatic standards.

  For the present , only cylindrical machines have been constructed. That kind of structure involves stringent limitations in size, since the clearance between rotor and ionizer is so essential. The elastic expansion due to centrifugal forces and favored by the very low modules of organic materials is the limiting factor. For the standard running speed of 3,000 r.p.m., the maximum rotor diameter is 15 to 18 in. The length of the cylinder, however, may be much greater, if we choose a "drum" structure (cylinder closed at both ends) rather than a "bell" shape( Figure 7) .

Figure 7 : " Bell"  and Drum" structures

The shaded area outlines the internal stator.

Two insulated semi-shafts provide the necessary connections to excitation and output terminals

The dynamical stability  of the drum rotor is, of course, much higher, and it is much less liable to sidewise buckling under centrifugal forces, even. at considerable lengths. On the other hand, however, the drum rotor cannot be convenient for very high voltages, since the shafts must be utilized as electrical leads for the internal stator, rather than being insulated at a "floating" intermediate potential as in the "bell" machine. As a rule, two-pole machines, i.e., machines giving the highest voltage for a given diameter, must have the "bell" structure, but all machines with four poles (or more) may be designed with drum rotor, with considerable improvement of the geometrical precision.

  The average tangential stress is ETd; d 8 ~80 e.s.u. (electrostatic unit), with the very conservative value ET=15 kV/cm=50 e.s.u. we obtain 4,000 dynes/cm2, and, since the linear speed can reach 150 to 180 ft/sec, or roughly, 2,000 cm/sec, the specific power per unit area is 2 W/cm2. The maximum rotor surface which may be safely anticipated being 10,000 cm2~ the maximum power per unit, for cylindrical structure and hydrogen insulation, turns out to be 20 kW.

  Machines of bigger size may, of course, be contemplated, but a drastic reduction of speed could not possibly be avoided, that is, the power output, instead of being proportional to the cube of linear dimensions as it is at constant angular speed, will be related to a lesser exponent, the square, for instance, if we assume constant linear velocity. The specific weight (and price) of the machine will then increase with size, and we thus sec that the preceding figure of 20 kW per unit nearly reflects an optimum in specific price and power. As far as cylindrical machines are concerned, higher powers would be better achieved by parallel coupling of several generators rather than by an elephantine unit of poor efficiency in many respects.

  The parallel coupling of electrostatic generators is a very easy business indeed. One electronic regulator can control as many units as required without any alteration of its structure. That means that an electronically controlled battery of generators has the lowest specific price per kW, since the electronic gear is nearly as expensive as each electrostatic unit. This conclusion holds even more in the case of highly stabilized machines, where the electronics must be very elaborate.

  Concerning the current output, it is, of course, proportional to the number of poles, the power remaining substantially constant as long as the stator pitch is large enough to accommodate and insulate the inductors without lowering the mean tangential component between ionisers ET.

The minimum pitch, in that respect, is 2 to 2.5 in.; with ET=15 kV/cm, the minimum voltage turns out to be 75 to 95 kV. A 20 kW unit, then, should be able to give at least 200 mA.

At present, no actual machine giving such an output has yet been tested, but the development is in rapid move and construction of several units in progress. A 9.5 in. rotor proved to be able to give 100 kV, 30 mA; or 270 kV, 8 mA.

Another 12 in. generator was very satisfactory at 300 kV, 10 mA, and tested for a short time at 400 kV, a similar unit is expected to yield at least 60 to 70 mA in the near future. The difficulty of obtaining centrifugated glass cylinders from the French glass manufacturers has impeded progress towards higher powers in so far as if prevented us from benefiting by the full length allowed to "drum" rotors by mechanical stability. Till now rnost of the statoric glass cylinders have been manufactured by the age-old process of blowing, which limits the initial mass of glass to such an extent that no long cylinder of, say, 1 ft diameter can be made. The above quoted figures were obtained with short rotors of no more than 12 to 15 in. in useful length. We would stress, however, that the present limitation is not in the least a technical one (since glass cylinders of much bigger size are quite conventional products), but originates in the well-known difficulty of convincing a mass-production minded industry to include in its elaborate programmes the manufacture of prototypes.

Disc Generators

The cylindrical rotor was selected for its obvious mechanical advantages, but the fact that centrifugal expansion occurs in the very direction of the ionising field is very awkward, since it prevents the critical clearance of the ionising blades from being well defined as soon as a diameter of, say, 15 in. is attained.

Dise structure is by no means interesting for small diameters. Due to the unavoidable clearances bctween ionisers, shaft, dise edges, etc., only a narrow zone of the dise surface is left for useful operation, and, since the distance between neighbouring disks must be substantial to accormnodate ionisers, inductors, etc., that zone lias an area considerably smaller than a cylinder of similar diameter and having a length equal to flic spacing of the disks.

Disc generator

For diameters of, say, 2 ft and if we contemplate moderate voltages (100 to 200 kV), the conclusions are different. The clearances and the spacing being constant, the disc geometry becomes much more attractive. Not only is the useful area of a given array of discs greater than  that of a cylinder of similar bulk, but the centrifugal forces now act perpendicularly to the ionizing field, and cannot, in a perfectly balanced machine, interfere with the vital clearance between rotor and blades. Both linear speed and rotor surface may be much greater than in a big cylinder machine of comparable size, and the output power will again rise as the cube of dimensions. The feasibility of units giving, for instance, 200 kW (and several amperes) and accommodated in a pressure tank of less than 100 cu ft seems reasonably established.

Electrostatic Generators vs Rectifiers

  This, of course, is the vital question for the industrial and commercial prospects of electrostatic equipment. The electrostatic machine is, in fact, intruding in a realm where most of the needs are fulfilled by rectifying circuits. It is, moreover, handicapped by the relatively poor level of its scientific basis, as compared with the tremendous amount of work, contributed by the most brilliant physicists and engineering teams, devoted to electronic tubes, gas-filled rectifiers, or semiconductors. It would be silly to try to foresee the future of competition in a field where all techniques are so rapidly moving, but some general principles may be established.

  In any electrical generator, means must be provided to create an integral of electric field at least equal to the required voltage. In voltaic cells and rotating machines, that integral, apart from the small influence of internal resistance, is just identical to the voltage. In rectifying circuits, the integral must be "virtually " twice the voltage in the simplest case, i.e., we have to provide rectifiers the total peak inverse voltage of which is twice the tension between terminals. In many rectifying circuits, the ratio is greater than 2, being 4 or 6, for instance.

  Not only must rectifiers be provided, but also overall insulation must be guaranteed. In more general terms, we can say that, for creating a given voltage, we have to pay at least for the technical embodiment of the integral of electric field previously referred to. This is the minimum price for a given voltage.

  In the case of low-voltage d.c., this price is virtually zero. The smallest air-gap can withstand up to 400 V without breakdown, the expenses are, then, only determined by the specific current capacity of the equipment. No wonder that low voltage rotary converters hardly compete with rectifiers. In the generating machine, means are provided to create a uscless magnetic flux which could be dispensed with, and the bulk of the machine is in no way related to its voltage. Any rectifier of enough conductivity is a dangerous competitor, as soon as it has the very small p.i.v. required.

  The situation is much more favourable with electrostatic generators. As long as their numher of poles remains in reasonable Iimits, their bulk and price are determned by the integral of the tangential field ET, which is equal to voltage, rathier than by the power output. The technical means, necessary to insulate the voltage, are in no way more expensive than those required for rectifying circuits, since we have to deal with the most favourable case of constant d.c. We thus see that conipetition is very likely to be favourable to electrostatic machines when the power required is substantially that generated by a unit the dimensions of which are those corresponding Io the voltage rating.

  Conversely, that statement makes clear how tremendous is the impact of specific power on competition. In the past, a machine able to give 100 or 200 kV would have a current output as feeble as . 1 mA. A battery of several dozens of Wimshurst machines was necessary to achieve a few milliamps. Since the bulk and manufacture of that battery was in no way related to its voltage, the picture was very much like that of a big dynamo-machine versus a silicon rectifier. No industrial need at 100 or 200 kV being fulfilled with as little current as . 1 mA, the Wimshurst generator could not possibly get any significance in practice.

  With the advent of modern electrostatic generators, this figure was multiplied by ten (in belt machines) and nearly 100 for hydrogen insulated cylindrical generators. That is, the belt machine is very competitive in the 1 mA range, the cylinder machine up to 10 or 20 mA. Going further, we must put in parallel more and more belts, or cylinders, and the competition becomes less and less favourable.

  Electrostatic generators may be competitive in another respect. We must pay to create a given integral of electric field, but we must also pay for smoothing or stabilising currents. If ripple has to be eliminated, we must pay for big smoothing capacitors, and (or) polyphase rectifiers, and (or) elaborate electronic control. It so happens that electrostatic generators can meet the requirement of medium or high stability very easily, since it responds to their own nature. Without any storage capacitor, their current remains a continuous flow with very small ripple. Moreover, the electronic control is much simpler and much more efficient than with electromagnetic circuits, because electrostatics are akin to electronics, and a powerful machine can be governed by a very cheap triode like 6BK4. For those reasons, we may say that electrostatic generators can be very attractive for relatively big currents, like 50 or 100 mA, if constant voltage, or better, high stability are necessary. Their prospects would be poorer, conversely, when only gross current output is needed, for instance in a problem of charging capacitors.

Conclusion

  This paper was intended to give a reasonable outlook of the present stage of development, and to emphasise the necessary trends of further progress. We saw that specific power still remains the principal factor, and electrostatic equipment could not have entered the realm of practice, had not its value been improved by orders of magnitude.

  We must also keep in mind that the present stage does not in the least reflect the ultimate capabilities of those machines. The fact that hydrogen, a gas of low dielectrie strength, is favoured in contempt of all theoretical expectations, reveals how the present technique still follows the paths of empirical invention, and is still unable to take advantage of fully establislied scientific principles.

  We claim to have obtained in hydrogen, more than 100 e. s. u. But electronegative gases could improve that figure by a factor of three, were the commutation problem properly solved. And a multidisc machine, with conductive interconnected sectors, should give in such conventional environnient more than 10 kW per cu ft, as it was recognised by John G. Trump as early as 1930.[1]

  And we shall not be Iimited, perhaps, to gaseous insulation. Modern chemistry, the progress of which is properly amazing, at least gave the clue to a problem which, a few years ago, still appeared as impossible as atomic bombs or cosmic voyages may have seemed in 1859.

  Never could the electrical engineer utilise the nurnerous "insulating" liquids of organic chemistry because of their ionic conductivity. Only mineral oil, i.e., hydrocarbon mixtures, and some chlorinated compounds found acceptance in electrical technology. Their dielectric constants are 2 and 4.5, respectively. All attempts to use liquids with higher permittivity completely failed.

  Conductivity, however, does not appear as an inherent feature of such liquids. Only water has ever been obtained in such a state of purity that the measured conductivity really reflects spontaneous ionisation. Indirect measurements of dissociation constants reveal that methyl alcohol and ethyl alcohol are also ionised, to a much lesser extent than water, the calculated resistivity of the latter being 1010 or 1011 ohm.cm. It is natural, however, to expect such liquids to be noticeably dissociated, since they react spontancously on alkali metals, giving hydrogen by electron exchange between free protons and metal atoms.

  But not all liquids with high permittivity do react on sodium. That kind of reaction seems much more related to a particular structure of the molecule (mobile H atoms linked to O atoms or influenced by multiple bonds) than to the electric dipole moment, which determines the bulk permittivity. No free protons can be suspected in nitrobenzene, in spite of a dielectric constant of 36, greater than those of both methyl and ethyl alcohols. Nevertheless, nitrobenzene is no technical insulant, since its resistivity of 107 to 108 ohm.cm gives a relaxation time of say, 10 -4 sec.

  It seems quite certain that the measured conductivity of organic fiquids is not in the least related to their own dissociation, but only results from pollution. Remarkable efforts were made, in 1913, by an ingenious physicist, to clear up that problem.[2] With stubborn obstination he applied to most refined purification techniques of his time to highly polar liquids like acetone, sulphur dioxide, etc., spending weeks -and months - to eliminate tiny causes of pollution. He, however, clearly realised that he could not reach any ultimate state of purity, and correctly concluded that every improvement of the purifying techniques will bring a further increase in resistivity, and that all figures previously given for the resistivity of so-called "pure" polar liquids were devoid of any meaning and fell short of many orders of magnitude.

  The chief difficulty of such experiments is the incredible sensitivity of polar liquids to very small amounts of impurities. A concentration of 10-11 of a dissociated electrolyte is enoughto explain the conductivities measured by Carvallo. This also seems to banish every hope of using such liquids in practice, because any technical structure would cause enough pollution to spoil in a very short time the result of very long and toilsome work. As it was said to me with some humour by Mr. C. G. Gartont in 1952 [*], "You will spend months to purify such a liquid and your efforts will be wasted in a few minutes -- or seeonds -- as soon as it comes into contact with some piece of oxidised metal or even with humid air " . Such a message clearly meant that any endeavour to use liquids should in fact be abandoned. I, nevertheless, continued to cherish a faint hope that chemistry might work a new wonder [3] and I am happy to have lived enough to see it.

* Now Head of the Physics of Materials Department, E.R.A., Leatherhead.

  To obtain pure water, Kohlrausch had to perform nearly 100 vacuum rectifications with incredible care. But, since the advent of synthetic ion-exchangers, we can tap water as pure as Kohlrausch's at a rate of flow of gallons per minute! Swimming pool nuclear reactors, for instance, require such water by the ton.

  As soon as ion-exchangers were applied to those "impossible" polar liquids, it was felt that the so long hoped for wonder might occur. With a very crude apparatus, we obtain a continuous flow of acelone more resistant than Carvallo's unique sample. For Mr. Garton's despairing statement is no longer valid, because we have not to deal with a static method of purification, like rectification, bu with a dynamical one, the measured resistivity reflecting a kinetic equilibrium between pollution and depollution, as in many living processes. One may wonder how Nature can maintain such precise concentrations of various ion species in our blood, in spite of many perturbing factors. We, of course, know, that many mechanisms involving essential organs like kidneys must be uninterruptedly at work for such a marvellous result being achieved. Ion-exchangers can do the same with highly polar liquids since they continuously eliminate the ions as our kidneys do for Na+ and CI-.

  As a matter of fact, acetone and nitrobenzene have been obtained at levels of purity which exceed by orders of magnitude the best results ever claimed. Since acetone reacts on alkali metals, it must be really dissociated and cannot becorne a sound proposal for electrical purposes. Nevertheless, resistivities as high as 1011 ohm.cm have been recorded. Nitrobenzene, on the other hand, seems to be amenable to a higher standard of purity in a very regular and dependable manner. Resistivities of 5. 1011 ohm.cm have been obtained continuously at a flow rate of nearly one gallon per hour. Nitrobenzene aiso seems much less sensitive to pollution. It should be realised that the preceding figure is quite similar to those claimed for commercialised liquid insulants of low permittivity. The corresponding relaxation time (1.5 sec) is quite enough for operation in electrostatic generators, since the tirne of transfer never exceeds 10-2 sec.

  It would be foolish, of course, to take the solution for granted, and to anticipate, for the near future, d.c. power transmission by nitrobenzene insulated electrostatic generators. But the fact that a clue has been discovered reminds us that the prospects of electrostatic generation are by no means Iimited Io small machines for paint spraying, electrical testing, or nuclear research. The tremendous forces displayed by the Coulomb field of electrons are very difficult to harness for the benefit of industry, reluctant as they are, because of their incredible power, to submit to the yoke of regular and reliable operation. They have, nevertheless, been turned to good use during the last decade for applications of considerable economical impact, electrostatic paints-praying and portable high voltage machines being valuable exaniples. Let us remember that these are the portents of a new era of electrical engineering, where the symmetry of electromagnetic duality shall, at last, emerge from the cold limbo of theory to be embodied in many useful appliances and reveal its hidden power for the benefit of mankind.

References

[1] John G. Trump : " Vacuum Electrostatic Engineering", Massachusetts institute of Technology, 1933.

[2] Jean Carvallo : "Conductibilité electrique des liquides purs", Annales de Physique, 1914.

[3] Noel J. Felici : Direct Current , June , 1953


Reprint from article published in DIRECT CURRENT, December, 1959, Vol. 4, No. 7


"DIRECT CURRENT" - Published by Garraway Ltd., 11 Kensington Church Street, London, W.8 and printed in England ky Diemer & Reynolds Ltd., Eastcotts Road, Bedford


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