Understanding Plasma Charge Distribution

[Steven Sesselmann]

Hi guys,

For lack of a better forum, I post here...

I have been puzzling over this problem for a while, and I can't find a simple solution.

If you have a closed dielectric vacuum tube with a rarefied gas and at one end you have a cathode and at the other end you have an anode, then inside the tube you have several conducting rings, which are electrically floating....

What potential will the rings reach when a plasma is generated in the tube from the anode cathode potential?

a) equal negative charges, from electrons hitting the rings
b) equal positive charges, from ions hitting the rings
c) graduated charges as in a voltage divider between anode and cathode

Any thoughts or references to a paper that might explain this woukld be helpful.

Steven

[Frank Sanns]

The fact that there are equal number of positive and negaive charges does not change the fact that there is a net E field by the potential difference between the cathode and anode. E varies with 1/r^2 and the voltage then will vary with 1/r. If the rings are isolated then it the potential will be the same as a function of r if they are there or not.

Frank Sanns

[DaveC]

Steven -

Refer to a text with a section on glow/plasma discharge for the details. VonEngle is one, and most undergrad physics books have an understandable section.

The voltage gradient down the tube will be non-uniform, in the vicinity of each end electrode. The floating electrodes will assume the potential of the plasma at the intermediate locations, which will change only slightly, since the mid portion of a long tube under plasma discharge has only a small potential gradient.

The plasma also has a radial field, which depends on what is happening at the tube walls.


Dave Cooper

[Steven Sesselmann]

Thanks guys,

Plasma behaviour is quite complicated, but I am starting to get my head around how it works.

My reason for bringing up the subject is an idea I have to solve the problem of sputter coating inside dielectric tubes. My experience is that glass or ceramic tubes tend to get a brown coating on the insides after only a couple of hours run, which renders the inside of the tubes conductive, resulting in dielectric breakdown.

By inserting a number of metal funnels, the ions can be kept away from the walls, thereby extending the tube life. These metal funnels are common in VanDeGraaf acellerators, but vastly more complicated, as they are laminated and extend to the outside of the tube, where I think they incorporate a resistor voltage divider. I assume they do this, because they want a steeper voltage gradient than 1/r.

As my objective is simply to extend the tube life, I guess that could work...., see diagram.

Steven

[Doug Coulter]

Steven,

Yup, sputtering is one of the villains we have to deal with, and clever mechanical design is our main weapon. Or at least in my experience, the one that works best. I've done a goodly amount of skull sweat on this one.

As noted above, the potential doesn't necessarily divide up uniformly -- that 's the reason for the various dark spaces, stripes and so on, often named after the guy who looked at them first or hardest. Many whole careers have gone into that one, and of course it all very much depends on things like ratios of size of the thing to mean free path, gradient per gas amount, and stuff like that. It's a fun topic for sure.

What you show in this picture will work, I think -- I've done similar things that did. As long as the path to the insulator is "long" and the mean free path isn't "too short", sputtered stuff will tend to follow fairly straight lines and shadowing it will collect it before it harms insulators. If the path is long enough, what ever was sputtered will cool too and be dust instead of something that sticks well.

The Van DeGraff use of corona rings uses air itself for the resistive divider. In their case there's hopefully no plasma at all either in the belt tube or the accelerator tube. It seems at above certain voltages (often quoted here as the 50kv range) a potential won't necessarily divide up even -- you will have a non uniform gradient in most media, glow or not. This is well born out by things we've tried here. So you try and get things so that no more than that will be across any one gap, and the entire thing becomes a lot more manageable. There is just a huge difference between what an electrode does sitting in air at 50kv and 100 kv. In one case you are starting to see some static effects, and a spark gap length that is still fairly proportional to volts. Above about 100kv, it's a whole new world. You can get arcs in air far longer than the proportional amounts, due to streamer formation and so on -- I once had a 10 foot spark from 120kv that went about 5 feet off a 4" standoff, turned 180 and came right back to a ground less than a foot away from the exposed point. It's to avoid that stuff that you use the rings in air to make sure that the field can't concentrate someplace. Bleed a little off as corona before something worse happens is basically the idea, and prevent any particle from seeing the full supply volts.

[Richard Hull]

I had the same initial reaction as Dave did, having read VonEngle extensively. But remembering Von Engle's admonitions given throughout the book, I feel the experiment must be done.

Von Engle noted that in any given situation what you see or measure is aplicable to that exact situation only, especially if you wish to develop mathematical formulae from experiment. He warned against extrapilation to predict even slightly more complex plasma or gaseous conduction scenarios. This is proof that with plasmas, the devil is in the details and devilish they are.

Probing plasmas is fine, but probably it is as close to a macroscopic example of the Heisenberg effect as you can find. As long as one keeps this in mind and allows for it you can try and extract some sort of useful data from the effort.

The classic voltage distribution in a simple, plain, anode-cathode Crookes tube with its well known uneven distributions would never hold to the multi-floating electrode arrangement posited here. I think this would indeed be more akin to a divider of sorts with plasmic resistance and conductance charging the rings as isotropic capacitances. This assumes no significant electrical loading via connections to any or all of the individual disks, but leaving them floating.

It is possible that perhaps a twenty foot long tube with 36-inches between floating electrodes might perform much like 6 Crookes tubes between each electrode with uneven distributions between each floating pair, but if closely spaced, as in the latest diagram, any such regions between would be microscopic between plates while the overall plasma gradiant along the tube would appear quite uniform or at least smoothly stepped.

As Franklin spoke, "Let the experiment be done".

Richard Hull

[Starfire]

Steven,

Relative to what? voltage is a differential and always seeks an equal balance - if you measure relative to ground, the ring [ or any ring ] will be at full positive voltage because no currant flows - if you measure to positive it will also have maximum negative voltage - this assumes your measurement instrument has infinite impedance and draws no current - the plasma does not have a voltage gradient unless you impose one.

You can test easily using a pentode tube which has its electrodes concentric but if your measurement instrument presents an impedance the results will be distorted. - but maybe I'm wrong as Richard says - it is an experiment that needs to be done.

[Dustinit]

I see that if each ring had an equal devision of the supply that, depending on the emission charecteristics of the material, that it has the same configuration as an electron multiplier and therefore the rings closer to the positive will have more current drawn and have a lower propotional voltage untill the 'gain' of each element from secondary electron emission is equal. This would suggest that a logarithmic charge distribution on the elements would occur with the largest differences between electrodes towards the negative end of the tube.
As richard says, The experiment needs to be done.
Dustin

[Steven Sesselmann]

I agree...

If the experiment has not already been done, it needs to be. I think the simplest way to do it, is to use the copper fittings that George Schmermund suggested in this post;

viewtopic.php?f=12&t=5023&hilit=copper+ ... tor#p32331

Drop the whole thing inside a boro glass tube with a KF 25 flange at either end, then attach a simple ion source to one end, and a vacuum cathode to the other end.

Let me see if I can pull a few strings...

Steven

[Chris Bradley]

Steven Sesselmann wrote:
> Let me see if I can pull a few strings...

D'you mean, like a ship-in-a-bottle? Will you slip some clever fold-flat construction into the tube, and as you pull so it all pops up into place!? I'll be waiting for the youtube video of that!