Electron drift velocity of an electric arc

[Skaperen]

Seeing the other thread about "How I view AC" and the talk of drift velocity reminded me of a question I had a number of years back, and never found an answer to ... what is the electron drift velocity of an electric arc? I'd be interested in the wide scope of everything from lightning strikes to "neon" lights. Is there a variation based on gas density? ... temperature? ... pressure? What about a vacuum?

 

[dlgoff]

There are a lot of variables to consider for an electrical discharge.

Here's a couple of references from Wikipedia to look at.

http://en.wikipedia.org/wiki/Plasma_%28physics%29"

http://en.wikipedia.org/wiki/Corona_discharge"

And these are only overviews.

 

[Bob S]

If you have a uniform electric field between two electodes, with a voltage V across a gap d, the electric field is E=V/d.

When a gas molecule is ionized, the electron travels toward the positive electrode, and the positive ion toward the negative electrode. The electron is light and moves fast, while the positive ion is heavy and nearly stationary. So only the electron velocity matters.

If the electron travels a distance x in the electric field, it gains an energy Ex. When the electron collides with a gas molecule, it loses all its energy. If the energy gained is sufficient to ionize the gas molecule, a cascade (arc) starts. The energy required to ionize a gas molecule is shown in the table

http://www.science.co.il/ptelements.asp?s=ionization

For nitrogen and oxygen, the number is about 14 electron-volts. So to create an arc, the free electron has to gain about 14 eV before colliding with a gas molecule, in order to ionize it and create another ion-electron pair.

So how far apart are the gas molecules? From basic physics, 22.41 liters of gas at STP (standard temperature and pressure) contains Avagadro's number of molecules. This is sufficient to calculate the gas density in the electric field. If you double the pressure of a gas, the density doubles, and the distance between gas molecules (between collisions) is halved.

You also need to know the average electron velocity.

The maximum electron energy is Ex=½mv², where x is the distance between electron collisions with gas molecules, and m and v are the mass and velocity of the electron, so the maximum electron velocity can be calculated. v_max = (2Ex/m)^½

Once you know the average velocity v_avg and the electrode spacing d. the transit time of the electron in the arc is t=d/v_avg.

I haven't told you everything, but I hope this helps.

Bob S