J. Phys. D: Appl. Phys. 20 (1987) 1547-1557. Printed in the UK

F Bastien Laboratoire de Physique des Decharges, CNRS (ER 114), Ecole Superieure d’Electricite, 91 190 Gif-sur-Yvette, France

Received 12 June 1987

Abstract. The main purpose of this review is to expound results related to the production of ordinary sound waves by electrical discharges. Work on different kinds of discharge especially glow, arc and ‘true’ corona, are presented and classified according to the relative importance of different acoustic source terms, namely the ‘heat’ term and the ‘force’ term. Related fields such as lightning and thunder are also dealt with. Different applications are presented but emphasis is given to ‘plasma’ loudspeakers. Fields in which knowledge is not well established are also outlined.

1. Introduction

We present in this article a review of research on both acoustic and electrical discharges.

Although the general principles are well known and certain applications have been treated in numerous empirical works, some aspects of the subject have barely been dealt with. We begin this expos6 with a brief presentation of the general principles, and mention the use of these in different categories of discharge: low- pressure, arc and corona discharge. We will examine a number of applications, principally to loudspeakers, with particular emphasis on loudspeakers using the corona effect.

Finally, aspects which have as yet not been the subject of close study will be overviewed.

2. General principles

In order to present the general principles, we will explain the simple theory developed by Ingard (1966). This theory needs the wave equation for the pressure in the neutral gas and expresses the interaction between the electrons and the ions with the gas in terms of sources in the wave equation. The conservation equation of mass, momentum and energy can be written, after linearisation, as

as - + p. div U = Q a t

p. - + gradp = F dU

at

6 = p - po, p = P - Po, U and S = S - S,, are the per- turbations for density 6, pressure P , velocity and entropy per unit mass S , respectively.

The terms Q, F and H are the rates of transfer of mass, momentum and energy to the neutral gas per unit volume.

This set of equations is not closed; we have to express a relationship between S, p and 6.

The gas being considered as a perfect gas, we obtain:

Using (1)-(4) it is easy to derive the wave equation

1 a2p VZP - “ = - c2 at2

f ( r , t ) + div F(r, t) . ( 5 )

If the fluctuation in the neutral particle density resulting from the imbalance of ionisation and recombination rates is neglected and if adiabatic transformation of an ideal gas is assumed, we get

y - l d H f ( r , t ) = - -

c2 a t

y being the specific heat ratio Cp/C, and c the sound velocity.

Equation (5) is obtained from the linearised equation and the fluid is considered as non-viscous. Nevertheless it can be used to examine the relative importance of source terms and to classify the different

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types of sound sources in gas discharges. Let us now compute the resulting pressure obtained far from a small region in which exist source terms such as (6) and div F .

This calculation can be found in Morse and Ingard (1968). We give here a synthesis useful for the under- standing of the results obtained by different authors.

We take the Fourier transform of equation ( 5 ) , defined as

1 +x P,(r) = g’-x p ( r , t ) eiwt dt (7)

and i2

p ( r , t ) = P,(r) e-iwt dm. (8)

With a similar relationship between f , (r) , f ( r , t ) and F,(r), F ( r , t ) , the equation ( 5 ) becomes

- X

m 2 V 2 P , + -P , = -f, + div F , .

As assumed above, the source terms are zero except within a small region. Furthermore the point of obser- vation is far from the source. The solution of equation (9) for an unbounded region is

C 2 (9)

POW = ’ ’ ’ [f,(ro) - diva F,(ro>l

x g, ( d r o ) d v0 (10) where

is the Green function. Let us consider the case where the source region,

with a characteristic dimension a, is small compared with the wavelength A = (2n/k) (ka 1).

We then get

This result means that this term corresponds to a mono- pole source and the amplitude of the acoustic wave is proportional to [ ( y - l)/c2](a W/at); W = J J J H d V, being the heat energy introduced into the source per unit of time.

The second term of equation (10) can be integrated by parts

g, div, F, = -F, grado g, + divo(g,F,) (12)

and since F, is zero outside the source, the integration over the source region gives

- - - ik(l + -/“I (1 1’ F , dVo) eikr cos 8. (14) 4nr

If in a small volume around r = 0 there is a force F ( t ) we have

Jvolume

and if 8, the angle between B(t) and r is assumed to be constant, the relation (14) gives

(15) This term source corresponds to a dipole term with two parts, one proportional to B and decreasing as (l /r2) and the second proportional to (aB/at) but decreasing as ( l / r ) .

The results above will be applied to different cases according to different authors, and the relative import- ance of source term will be discussed in the following sections.

3. Low-pressure discharges

In this section we review some publications related to acoustics in glow discharges or discharges similar to glow, that is, in weakly ionised gases. We are concerned only with a perturbed version of an ordinary sound wave in a neutral gas. Ingard (1966) introduced equation ( 5 ) and applied this result to travelling striations, that is, self-sustained wave-like periodic perturbations in the electron density, electron temperature and electric field. The order of magnitude computed for the sound press- ure obtained in the plasma ( P = 1 mm Hg, ionisation ratio (N,/N,) = T, -- 1 eV and T neutral room temperature) is P = 0.1 Pa.

The results are also used to explain acoustic modu- lation of a plasma afterglow.

The modulation of the neutral gas density caused by the sound wave produced a modulation of the electron density. The relative modulation of the intensity of a microwave signal transmitted through the decaying plasma depends on the relative change in the pressure and hence on the relative change in the pressure pro- duced by the sound wave. This paper also presented a possibility of acoustic wave amplification in the ordinary acoustic mode.

For the case where frequencies are smaller than both the plasma frequency and the neutral-neutral collision frequency, the theory demonstrated that the motion of the neutrals, electrons and ions are in phase with each other and the relative density fluctuations in all three components are the same.

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In others papers, Ingard and Schulz (1967) and Schultz and Ingard (1969) presented extended cal- culations of acoustic wave modes in a weakly ionised gas or acoustic wave propagation in a gas discharge.

A criterion of wave amplification is presented. The amplification mechanism is related to the fact that the perturbation in gas density produced by an acoustic wave perturbs the electron density and thus the rate of energy flow from the electrons to the neutrals.

Let us give some other examples of calculations. The first one is the amplification of an acoustic wave in a plasma subjected to an externally applied static electric field (drifting plasma) (Mantei and Fitaire 1971). It is found that there is a dependence of the wave growth rate on the amplitude and direction of the electric field.

The second is a possibility of acoustic wave ampli- fication at a plasma boundary by means of ion-neutral collisions in the plasma sheath (Fitaire and Mantei 1971). The theoretical result for an argon positive column in a 4 cm diameter tube gives a source term which outweighs the losses for sufficiently high plasma density (B 10l2 cm-3), neutral pressure (B1 Torr) and electron temperature (-5-6 eV).

We now give a summary of some experimental results. Using spherical discharge tubes in an ionic sound wave experiment Alexeff and Neidigh (1963) observed spontaneous oscillations at a pressure of about 1 Torr. These oscillations correspond to ordinary sound waves perhaps related to the acoustic wave instability demon- strated theoretically by Ingard (1966).

In an experiment on helium or neon afterglow plasma, Berlande et a1 (1964) demonstrated the for- mation and propagation of a pressure wave in a weakly ionised gas. During the decay period the light emitted and the absorption of high frequency waves (dependent on the electron density) were periodically modulated. Schulz and Ingard (1967) show an example of acoustic coupling between the discharge and acoustic modes. An acoustic instability of a current modulated argon discharge in a cylindrical tube is investigated experimentally.

In a preliminary paper Fitaire and Mantei (1969a) presented a device used to generate acoustic waves by the temperature modulation of a plasma. A second paper concerned acoustic wave amplification in a plasma (Fitaire and Mantei 1969b).

In a third paper the same authors (Fitaire and Mantei 1972) confirmed experimentally three aspects of the theory of the propagation of sound in a weakly ionised gas. Firstly the source term generation of sound in the neutral gas is proportional to the time derivative of the power input to the electrons from an externally applied electric field. Secondly, at frequencies much smaller than the neutral-neutral collision frequency, the elec- tronic and neutral fluid components move together approximately in phase. Finally, there is possible exper- imental evidence of an amplification (or reduction of attenuation) of an acoustic wave by a plasma.

The experimental arrangement is shown in figure 1. The plasma was about 5-7 cm long in a Pyrex tube ( I =

Generator 2 - 4 GHz

C a v i t y I

Microphone

2-4 GHz (< l00 mW)

Acoustlc

Figure 1. The experimental arrangement used to study the acoustic source term by Fitaire and Mantei. After Fitaire and Mantei (1972).

1 cm) created by a several watt 2.4 GHz generator. The electrons of plasma were perturbed with a low-power high-frequency signal (<20 mW - 2-4 GHz) amplitude modulated in the acoustic frequency range (lo2-

Figure 2 shows a recording of the signal detected by 104 HZ).

the microphone as a function of frequency.

2 0

l o g f Figure 2. Recording of the acoustic signal generated by a plasma 6.5 cm long as a function of the frequency W. A slowly varying signal traced with a chain curve corresponds to the term (1 /W) sin(w//2c). After Fitaire and Mantei (1 972).

The rapidly varying oscillations are due to the reflec- tion from the microphone and the ends of the tube, while the slowly varying signal (chain curve) cor- responds to the term

w -1 sin (f) with l = 6.5 cm (length of plasma) and c = 340 m s-l

(sound velocity accounting for the increase in gas tem- perature due to plasma). The term (16) was obtained by integration of a source term [ ( y - l ) / c 2 ] ( a H / a t ) (see equation ( 5 ) ) over a cylinder of length 1.

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4. Arcs

The theory already exposed has been applied to an atmospheric pressure arc, that is, a filamentary dis- charge at thermodynamic equilibrium. A review o l this aspect can be found in Fitaire (1984).

In the case of the arc the term div F of equation (5) is negligible compared with the term [ ( y - l)/c*](aH/ at) (see Dadgar et a1 1979). Let us note that if there is not ionisation-recombination equilibrium a new term has to be introduced in the right side of equation (5) namely - d Q / a t where Q is the gas mass variation per unit of volume and time. It would therefore be necessary to approach the problem with charged particle equations (particle, momentum and energy conservation).

In fact, the acoustic signal amplitude is a linear function of injected electric power derivative (a W/dt), H being almost proportional to W .

An experimental verification has been done by the superposition of current impulse to the average current of the arc (Dadgar et al 1979).

The curves of figure 3 were obtained at the first edge of a positive current impulse or of a negative one. It shows the expected proportionality.

4 Current impulse

W l a r b l t r a r y un l ts I

Figure 3. Acoustic amplitude A as a function of injected electric power derivative (W). (x) , A I = amplitude corresponding to rising edge of positive impulse; (D), A2 = amplitude corresponding to falling edge of positive impulse: (O), A3 = amplitude corresponding to first edge of negative impulse: (A), A4 = amplitude corresponding to second edge of negative impulse. After Dadgar et a/ (1979).

On the other hand, the second edge of the positive current impulse and of the negative current impulse does not give the same result, due to the fact that the heat transfer to the plasma is higher (positive impulse) or lower (negative impulse) relative to the case of the average current.

The sound velocity c increases with the temperature, and as a consequence the amplitude decreases as [ ( y - l)/c*](aW/dt). This relation has been checked on curves obtained experimentally.

Similarly, the acoustic signal produced by an arc oven is due to the variation of the electric power input in this men . More precisely, the excited wave amplitude is related to the temporal derivative of the electric power. This result conforms to the theory and to the laboratory experimental measurements but is not found exactly when measured in industrial installations. This is due to the large temperature gradients existing in the oven cuve and the mobility of the cathode spot producing variations in proportionality between the sound amplitude and the injected electric power deriva- tive (Beji et af 1983).

In the same field, a paper entitled: a corona-type point source for model studies in acoustics (Lim 1981) describes a source using an HF discharge. Physical conditions inside this source probably approach the Conditions of an arc and not those of a corona discharge as long as the corona referred to a pre-breakdown discharge located near the point (high-field region) and far from the thermodynamic equilibrium. The emitted power of this source increases from 47 dB to 90 dB with a frequency increase of 1 to 40 kHz.

A system in which a large amount of energy is brought around a point by a high-frequency (HF) dis- charge at atmospheric pressure is used as an example in Klein’s loudspeaker. This system does not seem to be the object of extended scientific study, but technical study shows that the source term in equation (5) is [(y - l)/c2](aH/dt). A more detailed discussion will be presented in 0 7.

A related field is pulsed discharges. Pulse discharges can produce sound impulse. The impulses in air are the most usual examples. The rapid transition to arc produces an increase in pressure producing a shock wave or a sound according to injected energy in the system. (This energy is dependent on the external circuit.) One example of the design of an impulse gen- erator can be found in Wyber (1975) and an example of a pulse discharge sound source in Shibayama et a1 (1984). It is interesting to note that the phenomena producing this impulse sound are also useful to explain the transition from pre-breakdown to arc in some cases. For example, let us consider a short point-plane gap in air with a positive potential applied to the point. The pre-breakdown produces an increase of temperature in the narrow channel discharge. This temperature increase produces an increase in pressure (sound pro- duction) but as the wave expands the neutral density N inside the channel decreases. This decrease induces an increase in E/N (where E is the electric field), which

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can produce the transition to arc (Marode et al 1979, Bastien and Marode 1979, 1985). Another kind of special case corresponds to used electrical current in a wire or solid, this solid being volatilised (see, for example, Sanchez Pina et a1 1983). This particular device does not correspond to the problem studied here even though after the explosion a plasma is created in the gap.

Lightning is another aspect of discharge and the sound produced (thunder) is well known.

Several mechanisms explain the generation of sounds in thunderstorms. The first corresponds to the shockwave produced by arcs, as an impulsed arc, (Few et a1 1967, Few 1969) but we have now a long and tortuous channel. Then, it seemed possible to consider the observed sound as a result of the convolution of pulse with a channel shape function. Each pulse is an N-shaped wave that is to say a wave where the pressure is a function of space with two vertical transitions (see Ribner and Roy 1982). Another mechanism proposed for acoustic generation is the electrostatic stress of the cylindrical charge distribution of the stepped leader (Colgate and McKee 1969). According to the authors the electrostatic sound pulse is roughly 1/300 of the subsequent main stroke.

Furthermore it has been observed that thun- derstorms can produce infrasonic signals with periods in the range 0.4-1.0 S and peak-to-peak amplitudes up to 1 Pa (Balachandran 1979). Other observations give periods of 0.5 S and amplitudes of about 0.1 Pa (Bohannon et a1 1977) or frequencies of about 1 Hz and amplitudes of a few 10” Pa (Balachandran 1983). The mechanism involved is generally the sudden reduction of the electrostatic field in a thundercloud following lightning discharges (original theory, Wilson 1920 and Dessler 1973) but Few (1985) introduced another process; namely, the electrical heating of air by positive streamer systems.

5. Corona

A sound can be produced by using a corona discharge. As seen previously, we used the term corona to desig- nate a pre-breakdown discharge near a sharp electrode. Inside this ‘true corona’ the electron temperature is relatively high (some eV) but the temperature of ions and neutrals remains almost equal to the ambient tem- perature. Consequently the plasma can be qualified as ‘cold’. True corona discharges present different features depending on the polarity of the point, the gas, the point radius and gap length but different regimes can usually be distinguished (see Goldman and Goldman 1978).

For a point (radius in the range of 100pm) with a positive polarity in air, there are three regimes as the voltage (and current) increases:

(i) The domain of autostability (burst pulses, pre- onset streamers).

(ii) The domain of the pulseless glow corona. (iii) The domain of the stable impulse discharge

(pre-breakdown and breakdown streamers) with pulses regularly spaced in time.

For the same conditions with negative polarity on point we have:

(i) The domain of autostabilisation. (ii) The domain of discharge with regular pulses

(iii) The domain of continuous current discharges.

The Trichel pulse frequency is greater than 100 kHz for currents greater than about 20pA. Otherwise the frequency of breakdown streamers is in the 10 kHz range.

Consequently both polarities can be used to produce sound but usually the negative point allowed higher current (of the order of 100 pA) in a range in which positive point produces pre-breakdown streamers with a disturbing noise. Furthermore in the regime generally used the discharge itself can be divided into two parts: a small one ( ro = 200 pm for a point radius of 50 pm) around the point at which ionisation takes place, and a larger drift region in which only one kind of ion (positive or negative) takes place (see figure 4). These ions are positive with a positive bias point, or negative in elec- tronegative gases with a negative bias point. In this unipolar region ions produce a net force on air molecules. As seen previously, the corresponding term in equation ( 5 ) is divF.

(Trichel pulses).

2

\ I

t

1

Figure 4. A sketch of a ‘true corona’ discharge between a point and a grid. 1, ionisation zone (characteristic dimension ro); 2, drift or unipolar zone.

This aspect corresponds to the difference with the system studied in a previous section.

Discharges such as corona are used in numerous devices, some of which will be presented in the next section, but little fundamental work has been performed. Some results can be found in an old paper on pressure effect of ion current by Lob (1954). We will sum up here the experimental and theoretical work of Matsuzawa (1971, 1973).

Three sound sources were built with a flat brass wire grid as the positive electrode, and with the negative electrode made of a great many steel needles placed

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equidistant to each other in such a way that they are distributed within a circle. The needles have points which are about 0.05 mm in radius of curvature, and are perpendicular to the wire grid.

The sound sources are electrically supplied with a DC current on which is superimposed an AC current of RMS value I . In the electric circuit, the sound source is assumed to be a resistance R shunted by a capacitance c.

The RMS value I’ of an alternative current through R is expressed as

I’ = 41 + ( U C R ) ~ ] ” ’ ~ (17)

where o is the angular frequency. The force acting on the air has an RMS F given by

F = (d/b)I’

d is the distance between electrodes; b is a coefficient defined on the basis of experimental results, and approximates the ion mobility. Let us consider a con- stant field E with a unipolar ion density p . With b being the ion mobility and S the electrode surface, we get F = dSpE and I’ = SpbE. Therefore we obtain F = (dI’/ b). This result is obviously only an order of magnitude but it can be used as a relation in which b is a parameter with the dimension of a mobility.

The sound pressure obtained theoretically for a point source for an observer far from that source is given by (15). Therefore the direction perpendicular to the wire grid the pressure p is given by

p =&[l 4nrc + (&)2]1’2

and from (17) and (18) we obtain

This formula has been verified experimentally by Mat- suzawa. Figure 5 gives frequency responses of different sound sources for Io = 0.35 mA (DC current) and I = 0.38 mA (RMS value of superposed AC current) and r = 50 cm (distance from source).

Comparison between experiments and calculated results from equation (19) and b = 2.2 cm2 V S-’ agrees satisfactorily for the 0.2-1 kHz range. Furthermore, the b value lies in the order of the ionic mobility value in air at atmospheric pressure.

A formula for the directivity is also obtained assuming that the force is uniformly distributed over the cylindrical region of radius a between electrodes. The result shows good agreement when compared with the experiments.

In Matsuzawa’s paper the term [ ( y - 1)/c2](aH/at) is not taken into account.

Let us examine the importance of relative term d ivF and [ ( y - l/c2)](aH/at) in the case of true corona discharges.

Let ro be a characteristic dimension of the ionisation zone and L a characteristic length of the unipolar zone. We must first evaluate the order of magnitude of ( W ) ,

I i a )

I- -... .,

80 i c 1

70 -

1 2 10

Frequency i kHz 1 Figure 5. Frequency responses of sound sources built by Matsuzawa for direct current I = 0.75 mA, AC current I = 0.38 mA at a distance 50 cm. (a) Source 1 : (b) sound source 2; (c) sound source 3. (. . e ) , experimental: (-), computed from equation (19) with b = 2.2 cm2 V” S”. After Matsuzawa (1973). The sound pressure is measured in dB reference: 2 x Pa.

the average energy injected from electrons in the ion- isation zone and (%) the average force applied on the unipolar zone.

The electric field near the limit of the two zones is evaluated as Eo (lower limit for ionisation). The field is assumed to be linearly decreasing from ro to L in the unipolar zone and the ion density, equal to p. at the boundary, decreases as the square of the distance. We get (9) = poEor?j L as an order of magnitude. Inside the ionisation zone (W) = joEor i = poV,Eori (io is the current density and V, is the electron drift velocity).

In order to appreciate the relative term influence we have to compare

1 y - l a w 4nr c2 a t “-

and

- ( -+;S) 4nrc 1 a% a t C

z is a characteristic time.

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We compare three terms

or

Y - 1 VePoEora PoEorZ POEO4L C2 t CT r

that is

Y - 1 VerO " L 1 - L "

c2 z C t r

Using Hartman (1984) results one can find for a point radius of 50 pm a characteristic dimension ro = 200 pm. Assuming Eo = 2.4 X lo6 V m-l we have V , = 1.4 X lo5 m s-l, furthermore y = 1.4, c = 300 m s-l.

y - 1 VerO 0.4 1.4 x lo5 200 x 1.2 x low4

Consequently

"" - c2 z 3002

- z

- z

At a distance r = 1 m with L = 2 X cm we get

L 1 L 2 x 1 2 x 10-2 "

C t S I " 300 i" 1

6.6 x = 2 x 10-2 +

z

Consequently (20) = (21) if ( l / t ) = 370 Hz. l/zissome- thing like the frequency.

This calculation gives a limit of 370 Hz for the rela- tive importance of the 'force' term and the 'heat' term.

Obviously this result is very rough but it at least proves that the relative importance of terms must be discussed for high frequency.

Nevertheless 'corona' sources have no limit in low frequency, which is not the case for the 'arc' sources.

Let us note that the relative importance of terms varies (the 'force' term is the most important) for short distances.

6. Related topics

In this section we present topics not strictly related to acoustics in gas discharges but giving interesting results in this field.

The first topic is the interaction between sound and the ionosphere. For example, the interaction of an acoustic wave of artificial origin with the ionosphere as observed by vertical HF sounding at total reflection levels (Blanc 1984).

A second topic is the fluid flux created by a corona discharge. This phenomenon, known as electric wind, has been studied for many years. The mechanism is well known (see, for example, Robinson 1961, 1962).

Nevertheless, some aspects of the electric wind have been studied recently. Bondar and Bastien (1986) exam-

ined the conversion efficiency from electrical energy to fluid kinetic energy. It is shown that an increase in fluid velocity leads to a higher conversion efficiency.

A third topic is the problem of instabilities of gas dielectrics with ion injection. This question has been extensively studied for liquid dielectrics but nearly not at all in the case of gases. The reason is the difficulty in obtaining the injection of ions into gases. Corona discharges are the best means of obtaining relatively large injection of ions. But there are no clear limits between the ionised zone and the ion drift zone. Conse- quently, the theoretical model becomes extremely com- plex to solve numerically.

Nevertheless an instability problem, with practical applications, has been the object of several studies, namely the improvement of heat transfer from a surface with electric wind.

It is interesting to see that the controversy between scientists is not closed.

Some authors (Kohya et al 1983) found that the primary cause of the heat transfer rate increase under corona discharge is simply forced convection by corona wind. Conversely, Bradley and Hoburg (1985) pre- sented a mobility-gradient-driven electrohydrodynamic instability has a viable mechanism in augmenting forced convection heat transfer. This fact shows an example of a possible instability in hydrodynamics with internal forces (force inside the volume). The presence of this 'volume force' is also a characteristic of the plasma acoustic.

7. Applications

We shall examine here plasma loudspeakers and other applications of gas discharges in acoustics. Plasma loud- speakers will be divided, according to Bondar (1982b, c) into two classes,'hot-plasma' loudspeakers and 'cold- plasma' loudspeakers according to the mode of sound production.

7.1. Hot-plasma loudspeakers

In these devices the sound is produced by the modu- lation of heat produced by the discharge. The cor- responding term in equation ( 5 ) is [ ( y - l)/c2](dH/dt). This type of loudspeaker has been mainly developed by Klein. The first models used by Klein are in fact thermoionic, the sources of ions being a heated source. The ions produced are subjected to a constant field with a modulated superimposed field (Klein 1946a, b). But later, Klein introduced a field obtained by a HF high tension (Klein 1951a, b). The device is essentially formed with a point electrode (HF high tension at about 20000 V), a counter electrode for starting and a grounded electrode (see figure 6), (Klein 1979a, b).

Consequently the temperature near the point increases up to 1000 "C.

The sound source is like a monopole and is essen- tially efficient for high frequency (above 10 kHz).

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I

I \ \ \ \

Grounded spherical electrode

S ta r r i ng e lec t rode

H F hgh-vo l tage b iased e lect rode

Figure 6. A sketch of Klein’s loudspeaker. After Klein (1 979a).

The previous result shows that the efficiency decreases with m .

A version of this system has been recently com- mercialised as a tweeter by Magnat?. The system seems to give a reasonable production of by-products, nitro- gen, oxygen and ozone. The low production of ozone is due to the high temperature in the source. Concerning the nitrogen oxide precise measurements do not seem to be available. In the next section we discuss ozone production in the case of low-temperature sources.

It can be noted that this kind of sound source is very close to the flame source. See the general presentation in Babcock et a1 (1967), the experiment in Burchard (1969), Fitaire and Sinitean (1972) and attempt of theory, neglecting the time dependent variations in flame dimensions in Sodha et a1 (1978).

This kind of system produced a very high level of sound in a range above 10 kHz.

For example, in order to study the response of laboratory rodents to the frequencies at which their hearing is most sensitive, Ackerman et aZ(1961) used a loudspeaker working on the principle of Klein’s loud- speaker. They obtained very-high-pressure levels in the range 1040 kHz, up to 132 dB (reference: 2 X Pa).

7.2. Cold-plasma loudspeakers

These kind of loudspeakers use a ‘true’ corona as a sound source. The discussion on the relative magnitude

t Plasma loudspeakers, Magnat MP02.

”

of terms and also some experimental evidence show that ‘cold-plasma loudspeakers’ are able to reproduce all frequencies not just high frequencies as in hot-plasma loudspeakers. Nevertheless this type of loudspeaker does present some difficulties, which we shall discuss later.

For the moment let us describe some experimental devices used to build cold-plasma loudspeakers. As early as 1926, in patents No 264.811 and No 265.958, Allgemeine Elektricitats Gesellschaft presented a device with a point bias with a high tension but the presence of an insulator seems to show that this loud- speaker works more like an electrostatic loudspeaker than a plasma one. In 1930 Irwing Wolff presented a corona sound reproducer, see figure 7. Halus and Holcomb (1957) conceived a design for several electrode loudspeakers. One of the possibilities is shown schematically in figure 8. The point is at the negative

Conica l cont rg l e l e c t r o d e

A n n u l a r e l e c t r o d e

/ W # Pointed e lec t rode

Figure 8. A sketch of one of the features of the ‘ionic triode speaker’ proposed by Halus and Holcomb. After Halus and Holcomb (1957).

polarity, and the mid-gap conic electrode is used in order to control the current. A two-electrode version was also presented. Devices with wire were presented by Brown (1962). It is strange to note that the author presents the effect as an ‘unknown electro-kinetic phenomena’ (!?). An example of a possible con- figuration is given in figure 9.

Other devices with a point (negative) can be found in Seligson and Lanier (1969) and with wire in Doucet (1973). Bondar (1981,1982a) presented a device where rows of points with different polarities were separated

/ ELectrode /

””-”””_ .-4 Gr I d

P o i n t (spikes 1 Insulating m a t e r i a l

E l e c t r o d e

Figure 7. A sketch of a sound reproducer proposed by Wolff. 1 = High potential direct current generator. After Wolff (1 930).

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Acoustics and gas discharges

Insulating suppor t s

F l a t e l e c t r o d e

Figure 9. A schematic perspective view illustrating one of the possible features of loudspeaker proposed by Brown. After Brown (1 962).

by insulating plates (see figure 10). This is only one of the different configurations realised and experimented on by Bondar.

More recently, after the work of Bondar, an ear- phone was developed and marketed by Audioreference (Fourriitre 1984, 'anonymous' 1985) (see figure 11).

It is also possible to find a general description of a loudspeaker in Tombs (1955), an electrical charac- teristic of a corona loudspeaker (without acoustical study) in Yamaguchi (1971), an experimental result and interpretation in Lob (1954) and Bolle (1958), and a presentation of a possible original system in Ostroumov (1982). This last author does not seem to be aware of previous work in this field.

Insu lated p la te

/ Polnted electrode

+U Figure 10. A sketch of a loudspeaker experimented on by Bondar. After Bondar (1981).

Furthermore, Fransson (1965) used a corona sound producer to perform acoustical measurements on musi- cal wind instruments.

In spite of many efforts and of the advantages of this kind of loudspeaker, several difficulties prevent its industrial development for the moment.

The first difficulty is the very low efficiency of energy conversion. Even for continuous neutral movement (corona wind) the efficiency of energy conversion from the electric field to mechanic movement is very low; it is of the order of (vh/vi) (where v), is the fluid velocity

and Vi the ior, velocity) (see Bondar and Bastien 1986) but for sound production this efficiency is even lower. The dynamic pressure is IpVi for a hydrodynamic flow and the acoustic pressure is about pcV, for a plane wave (V, is the acoustic fluid velocity). As a result the efficiency for sound is the efficiency for hydrodynamics multiplied by (Vh/c). With an average value V,, = 6 m sK1 we get (vh /c) = 2 X This evaluation gives an efficiency of the order of In practice, the efficiency obtained is even lower. For example, in the case of the Matsuzawa loudspeaker, for a modulated current of 0.38 mA corresponding to 3 kV of modulation, the injected power is about 1 W (the con- stant current is not taken into account). The author

G r i d s

P o i n t

Figure 11. A sketch of an earphone developed by Bondar. After Fourriere (1984).

quotes a 70 dB sound at 0.5 m. In the direction per- pendicular to the loudspeaker plan the acoustic power is then about W. The yield of this loudspeaker is about Let us note that 70 dB is not a maximum, as an example Bondar reaches 82/84 dB at 1 m with his corona loudspeaker.

Possibilities of improvement in efficiency exist but have up to now not been developed.

The second problem is more technical and concerns the oxidation and evolution of the surface of the electrodes.

A third problem is the electrostatic noise (small discharges at the surface of insulator) for some con-

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F Bastien

figurations, and last, but not least, is the production of ozone.

The production of ozone can easily reach an efficiency of 10 g kW" h" (see Lecuiller 1980, Peyrous and Lapeyre 1982) with a 100 W loudspeaker (electric power), the production is 1 g h-'; inside a 50 m2 room the concentration of 0.1 ppm is reached after 15 S . This concentration (0.1 ppm) represents a reasonable value for the maximum allowable concentration of ozone for an 8 hour working day. Note that a concentration greater than 1.2 ppm by volume and longer than 7 h per day, significantly affect the growth of young rats (Mittler et a1 1979).

Obviously using gases like nitrogen suppresses ozone production, but this is not very convenient. Other ways are possible but results on this problem seem not to have been published up to now.

Note that all these problems are less acute for ear- phones. Only one point produces much less ozone, and furthermore the efficiency of the system is increased. The explanation is perhaps the increase of the term 9 / r 2 as r decreases.

7.3. Other applications

We will only give a brief outline of applications other than loudspeakers.

7.3.1. Microphones. The use of discharges as micro- phones is theoretically possible. Tests in our laboratory show that this possibility is not only theoretical but it seems that it has not yet been applied industrially. Note that a thermoionic diode has been used as a sensitive and inexpensive detector in low-pressure gas (Dayton er a1 1963, Cooper and Tripp 1971).

7.3.2. Arcs. Some applications related to arc noise have been developed.

The acoustic control of the electrode position in arc ovens is founded on lhe relation A = K(d(l V)/dt) where A is the amplitude of the sound, Z the arc current, V the voltage drop and K is a coefficient. From this relation Nadeau er a1 (1982) obtained V = (l/kZ) J A d t and then the arc length L by means of a linear relation between V and L. This method can be used to determine the time evolution of the voltage in the column of an electric arc (Drouet and Nadeau 1982).

An acoustic control of the length of a welding arc is also presented by Drouet er a1 (1982).

Some noise reduction tests have been performed on arc furnaces by stabilising the arc with KOH (Beji et al 1983). A reduction of 2 to 8 dB was observed with the liquid-phase apparition but no noticeable reduction was observed during the fusion of scrap-iron.

Another specialised application is the study of press- ure waves due to arcing faults in a sub-station (Drouet and Nadeau 1979).

This fault can produce the collapse of a building housing a large sub-station! The paper presents the study of the amplitude of the pressure wave generated

by an AC arc with current from 10 A to 80 kA and with arc length from 8 mm to 15 m burning in air for up to one second. The pressure variation A is proportional to the variation of the electric power for a small variation of A relative to the atmospheric pressure. This result is in agreement with the theory. Furthermore an empirical formula is given relating the pressure variation ampli- tude to the short-circuit current and the response time of the protection system.

7.3.3. Noise from high-voltage lines. A final field of 'application' is the audible noise due to corona effects in the conductors of very-high-voltage lines. The irregu- larity of corona produces a sound with a spectrum from fundamental frequency of applied tension up to 15 kHz. The sound intensity is dependent on the weather, with its maximum under rain, a little less under smog and with its minimum in dry weather (the exception is very hot weather, see Gary and Moreau (1973)).

Many papers have been published in this subject, for example see Juette and Zaffanella (1970) and Taylor er a1 (1969). Gary er a1 (1983) give an experimental correlation between radio interference and audible noise around overhead transmission lines.

8. Conclusion

The practical applications of acoustics in discharges are up until now not very numerous, but there is a great deal of potential in this field. Acoustics in plasmas also present a theoretical interest, because it is one of the rare examples of sources in volume. An example in a different field can be found in Bruneau er a1 (1986).

Moreover, acoustics of discharges is only one part of the vast field of electrohydrodynamics in plasma. This field harbours many practical possibilities (modi- fication of boundary layers, flow measurement) as well as theoretical ones (hydrodynamics with forces in vnlume, dectm-bydrodymmk instabilities).

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