| MadSci Network: Physics |
Hi Anthony,
Okay, I got to admit: this is a hard one. I think if you want a really proper answer, you should ask a specialist to run simulations for you, and the general three-dimensional time-dependent simulation in a complex gas mixture like air you need for this looks pretty formidable. That said, I'll take a stab at the problem for you. (Coincidentally, a large portion of my PhD dealt with the simulation of laser-created plasmas in molecular media, which is a strongly related problem)
As you have noticed, if you create a plasma in air, it is in general not stable. There are in fact multiple reasons for this, each of them producing its own type of instability
The most serious problem you are dealing with is the fact that the plasma doesn't start out straight. This has to do with the way the plasma is generated. If you just put a large voltage across a gap, initially, nothing happens. Then, when a stray electron enters the gap, perhaps by a cosmic ray, perhaps by thermionic emission, a so-called Townsend avalanche [1] is started. This in essence means that the electron is accelerated in the field, producing more electrons as it collides with gas molecules and ionizes them. If the voltage is sufficient, this ionization is faster than the recombination, and a plasma forms.
The problem is that this process is stochastic and quite random. Worse, recent research indicates [2]that this beginning plasma is quite unstable and will branch out on its own. This means that just using two electrodes and hoping for the best isn't going to work
Now, it's a pity you rule out the use of lasers in your question, because that was what I was going to suggest. By using a laser, it's possible to produce free "seed" electrons throughout the entire gap. These "seed" electrons will lead to a much more regular and fast plasma formation, which will produce a much straighter spark. You can achieve a similar effect by using an electron beam between the gaps, or, theoretically, by using ionizing radiation (a radioactive material in a lead casing with a hole in one side), but that all seems even worse than the laser. What you can do is start the plasma by bringing the electrodes very close together and then gently pull them apart; the very short plasma you start out with will be almost straight because there is no room to branch, and pulling it apart gently will just cause the plasma to "grow" from the many free electrons that are in it, eliminating the statistic instabilities and branching.[2]
Suppose you actually managed to get an initially straight plasma, it will not stay straight. The first reason for this are so-called magneto-hydrodynamic [3] (MHD) instabilities. In essence, the current going through the plasma produces a magnetic field, which acts on the current in the plasma via the Lorentz force [4]. This gives the plasma a tendency to contract. It also makes it possible that the plasma becomes unstable as kinks form. Imagine the plasma becoming slightly arced. The left leg of the arc now starts attracting the right leg, forming an ever higher arc. These types of MHD-instabilities are particularly strong if the current is very high. If the current is not very high, the Ohmic resistance of the plasma is high, and this makes a bending of the plasma more difficult, as it increases the path the current has to take. This can act as a stabilizing force. The best way of doing this is using a power supply that behaves strongly like an ideal current source (rather than a voltage source).
One final problem you have to deal with is a very banal one. As you dissipate energy in the plasma, the temperature rises. Now, by Archimedes' law, hot gases rise. This means your plasma will take on an arc-like shape (hence the name "arc plasma"). There is not a whole lot you can do about this really.
I also have a remark about transporting electricity in air. The limit in conductivity in air is given by the Spitzer limit [5], which, for this type of plasma [6](Electron temperature around 1 eV, Coulomb logarithm around 5 for a dense plasma) 3 mSm/m, which is about 5x1012 times worse than copper. Furthermore, this plasma will produce nitrogen oxides and ozone, both of which are toxic. Both of these issues limit the practicality of this approach in transferring power.
Summarizing, it's going to be difficult to create a straight plasma. Your best practical bet might be putting the electrodes close together and then pulling them apart. However, even if a straight plasma is created, it won't stay straight due to its tendency to rise, and the possibility of magneto-hydrodynamic instabilities.
I hope this helps in your experiments
Regards,
Bart Broks
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