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Plasma Acoustics
A-History
1-Singing arc:
One of the first realizations of plasma acoustic was the experiment of the singing arc. The modulation of the intensity of an electric arc produces sounds. The phenomenon is a reduction of what happens in the atmosphere when the weather is stormy. The lightening produces thunder in a very similar process.
It was rapidly clear that the pressure variation was correlated to a rapid variation of heat. Because of natural convection and arc instabilities, it was not possible to obtain a stable effect with a reasonable power consumption using an arc in free air.
2-Thermophone:
A first improvement of such a device was the Thermophone, in this case, the heat is produce in a nearly closed chamber with a tungsten filament and an acoustic diverging profile (horn) is used to increase the efficiency.
they were however several severe limitations to the system. The low frequencies were not reproduced because the small size of the heated region was unable to produce enough expansion of the air. On the other hand, the high frequencies were not reproduced because of the thermal inertia of the filament.
3-Ionophone:
The German technician Siegfrid Klein has found a nice solution for the high frequency limit by the use of a semi-confined high frequency arc.
Several products were commercialized using this system: Ionophone by Magnat in Germany, Ionovacs in the states. These "hot plasma" tweeters were always combined with usual loudspeakers to reproduce the lowest frequencies.
4-Cold plasmas:
I was unaware of these developments when I realized for the first time a corona speaker in my student room in 1978. My idea was to use the electrical force produced by several coronas to move directly the air without mechanical parts but in the same way than a usual speaker. In practical, my prototypes were able to produce from a continuous pressure (wind) to very high frequencies with a very flat response. When I presented my prototypes, there was a great confusion in the public mind (and even in the scientific community) with the previous plasma realizations.
In order to clarify the situation I started to make in my conferences a distinction between "hot plasma sources" based on thermal effects and "cold plasma sources" based on forces effects (see Plasma-Etymology page).
Up to now only a few Plasmasonic Headphones (Audio Reference 1985) and Tolteque Speakers (A.H.L 1992) where commercialized at dissuasive prices and with youth imperfections (lifetime of electrodes, low efficiencies). Although all these defects seems to be solved and that the production cost could be reduced by mass production under the one of usual speakers, the market seems not ready anymore for an acoustic new technology. In fact, the public interest has move (or has been moved) to other mass products (the only other possibility is that the human species in becoming dumb). However, one day perhaps...
B-Theory
1-General remarks:
Although in many cases (when the size of the source is small compared with the wavelength) the source can be considered as quasi-stationary (but an usual propagation problem as to be considered outside from the source), we should consider the general propagation equation in presence of sources (which is more general and quite easy to interpret).
2-Propagation equation with sources:
The derivation of the propagation equation is based on the use of the local equations of conservation of matter and momentum. The equations needs first to be transformed into a linear one (and then are valid only for small perturbations), the linearization is valid for acoustic pressures small compared with the normal pressure which is in general verified (1 Pa = 94 dB = 10-5 Bar). The equations are then combined to eliminate the neutral speed and then to obtain a relation between pressure and density variation. The next step is the use of the state equation of the fluid in order to obtain a linear equation between pressure, density, and heat variations. If moreover we ignore viscosity forces (which lead to very complex effects in acoustic) we obtain the following equation:
The first member of this equation represent the "free" propagation and the second one the sources. It then appears clearly that the sources are of two types: temporal variation of heat or local variation of force.
1- The temporal variation of heat is used in "hot plasma" speakers, note that the effect is proportional to the frequency (the more rapid the variation the bigger the effect) and then for low frequencies the effect is negligible. This kind of speakers is then used as tweeters and has to be filtered to be linear.
2- The force term do not on his side depends on time and is then linear in terms of frequency response. The fact that the force has to be localized in space is easy to understand: a constant force in the whole space will produce a rise of pressure but no propagation.
C- Conclusion:
Although the corona in the glow regime produces some heat, it can be easily shown that, for the audio frequencies, the thermal effect is negligible compared with the force source. At the opposite in the high frequency arc regime (several MHz), the mono polar area (the shield), is smaller than the mean free path and there is no oriented movement transferred to the neutrals and only the thermal effects are significant.