Quantity of ions produced through arcing

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how would one calculate the number of ions produced per square centimeter when a continuous electrical arc is being produced between two electrodes that are separated by a meter, end in a fine point and have a voltage of 3.4 Mv? assuming standard air temperature and pressure.
 
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The number of ions is related to the current as well as the voltage and gas pressure. Naively it is equal to ½ the current (electrons flowing one way, positive ions the other) however there are some conundrums.

Ions form as electrons get knocked out of shells by ionizing radiation. This process starts with an atom getting hit by a random cosmic ray. This knocks an electron free. The electron accelerates in the electric field until it hits another atom. When the field is strong enough with respect to the gas density (pressure) the electron has enough energy to spew more ionizing photons which in turn ionize more atoms with more electrons accelerating. This effect also happens with the ions, but to a much lesser extent due to their higher masses. This is where the conundrums come in.

It is possible ions will form with larger than +1 charge. This would happen when the electrons build up enough energy to shoot out even higher energy photons. Thus it would happen at higher voltage levels and lower pressures.

Also, there is a technical difference between ions and free radicals. Free radicals are molecules like monoatomic oxygen. While they are electrically neutral, they are very active/corrosive. I assume you want to count both as one set. I don't think radicals carry current, but they do form in discharges. Again, they should be voltage/pressure dependent.

Some small number of ions will collect on the cathode end. This is smaller than the electrons which are lighter and hence faster.

It is also possible some negative ions will form depending on gas mixture, but not many I think, but there will be lots of free electrons and ionizing radiation, so it will happen.

To approach this problem we need to model the gas statistically. We need to find the mean free path length and at least the first moment (the standard deviation). Higher moments might be required. A statistician might help with this. We need to calculate what energies the particles attain (likely just the electrons unless you need exact figures) and what energy the resulting photons will have. An expert in QED might help with this. Then we need to figure out how the gas mixture will behave under the photon flux.

As you can see, this is not a trivial exercise. Running an experiment might be easier. Consider measuring the light (flux and spectrum) discharged?
 
starwarsmat; Welcome to PF.
starwarsmat said:
how would one calculate the number of ions produced per square centimeter
Why do you ask? or what would you do with that number if you knew it's value?
 
Baluncore said:
Why do you ask? or what would you do with that number if you knew it's value?
I am currently an electrical engineering student and I am looking into gas discharge and was curious about it's properties and newer uses it could have in the world.

Now as to the question of current. The reason I didn't choose one in particular is because I wasn't aware of how precise a current I would need for an experiment and was hoping that as part of the answer to my question there would be a formula in which I would be able to input the current for any result I desired.

To Jeff Rosenbury, thank you for your response. I was thinking of performing this experimentally, but I was hoping for a bit of theoretical knowledge first so that i would know what to look for and how much power i would need. As I can see from your post this appears to be quite a complicated question, but I still hope to obtain an answer and to learn how to calculate it again in the future with regards to different variables.

As a side note this is not a homework or coursework problem. This is entirely related to curiosity.
 
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Baluncore said:
By using a magnetic field across the arc path, you can sort the ions present in an arc by mass and charge.

Is there an example of this you can link to? Wouldn't the magnetic field affect the arc? The whole sustained arc process seems rather chaotic (as in non-linear dynamics) to me. Turbulance created by the arc, etc.

Are we talking ions formed to simply sustain the arc? or ions that escape into the surroundings?

I still don't understand how to calculate the number of ions created unless it is simply the number needed to support the current. (like 1A = 1C/S) But that wouldn't cover ions escaping into the surroundings.

I'm terribly ignorant of this sort of thing. So, now I want to understand.
 
For ball park figures, I would not think the heavy ions would count much in the conduction process. If you ignore them and consider that the number of electrons leaving the cathode per second per cm2 is I/e (I is Amps /cm2 and e is the electronic charge). If you knew the drift speed then this could tell you how many free electrons there have to be per cm3. But that's only a minimum figure. It would be possible to get an idea of recombination rate if you timed how long the arc takes to extinguish after the volts are taken away. From that, you could work out the number of them that aren't involved in conduction. From a Google search, it looks as if a Book is needed here as the obvious hits all seem to be qualitative and the papers are way above this level.
 
The arc will be deflected by a magnetic field due to the Lorentz force. https://en.wikipedia.org/wiki/Lorentz_force

Ions and electrons are accelerated by the electric field. They have different mass and charge so travel at different speeds.
A magnetic cross field will cause a variant deflection of particles based on charge and mass.

If you have ever used an electric arc welder near a magnetic clamp you will have seen the arc deflection.
See also arc blow. https://en.wikipedia.org/wiki/Arc_blow
 
http://www.plasma-universe.com/File:Plasma-ranges.gif. We're operating somewhere in the top middle, I think. It does give an idea about electron densities, though, which puts things in perspective.
[Edit: that's what comes of trying to do two things at once - it should be there now.]
 
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Baluncore said:
The arc will be deflected by a magnetic field due to the Lorentz force. https://en.wikipedia.org/wiki/Lorentz_force

Ions and electrons are accelerated by the electric field. They have different mass and charge so travel at different speeds.
A magnetic cross field will cause a variant deflection of particles based on charge and mass.

If you have ever used an electric arc welder near a magnetic clamp you will have seen the arc deflection.
See also arc blow. https://en.wikipedia.org/wiki/Arc_blow
You are correct.

Yet the calculations are complex. The arc adds it's own field which depends on its path (and other things) which depends on its field. For a simple arc I think it can be calculated be calculated. Over longer times/distances and typical conditions I think its chaotic. (I don't know it it's non-linear in hard a vacuum.) I'm not a plasma physics guy.