What is the reason that you would like to calculate this? The Paschen curve was derived with a parallel plane setup and thus a homogeneous field. Several different types of gases and pressures were used. My questions to you are: 1. What kind of electrode arrangement are you considering? 2. What gas type and pressure?

If we would consider a parallel plane setup, small gap distance and/or low gas pressure (p.d. < 5 atm.mm, the range in which paschen's curve is valid) the fact will be that the lowest possible breakdown voltage would be roughly 350 Vpeak at atmospheric pressure and with a gap distance of 7 micron. This is a physical phenomenon, reducing the gap distance further results in an increase in BD voltage. The travel distance of an electron (injected at the cathode for example) to the anode is decreased thus the probability of the electron colliding with and ionizing a gas atom (before being recombined at the anode) is decreased -> higher breakdown voltage. Next to that the acquired kinetic energy of the electron might be insufficient because of the short gap distance -> increased BD voltage (this is something different than the mean free path between collisions, which has to do with gas pressure)

Therefore I would say that below roughly 350 Vpeak in a parallel plane setup with 1 atm air it is not possible to have any breakdown(without actually momentarily making a galvanic contact).

(Processes such as streamer and leader are not in the scope of your question because of your super low voltage)

Have you measured a breakdown at 10V?

If yes than please share details.

Regards,

Dennis van der Born, TU Delft, The Netherlands

Dear Denis, thank you for your answer. It is really useful. The reason of my question is that I investigated the dynamics of a rolling disk on flat surface. There was a question if the disk loses contact with the surface during the rolling and before its halt. You can find the schema of experiment in attachment. We have detected the disk loses contact, and we can measure the time of losses of contact, but the question is what accuracy does this system have, what is the minimum distance between the disk and the surface can detect this method.

Dear Yury,

If I understand correctly, you have I voltage source of 10 V which is connected to a disk which is rolling on a plane. The plane is connected to the - pole of the DC source with a current measuring device (shunt resistor, with voltage measurement) connected in series. So if there is contact a current will flow proportional to the resistance of the entire circuit (shunt + resistance of wires and plane + resistance of disk contact area on the plane).

About the accuracy of the system:

Breakdown will not occur as already explained. Therefore, current will only flow if there is even a minimal contact between disk and plane. This implies that the minimum detectable distance is limited by the roughness of the surfaces of the disk and plane (Protrusions can already make contact and consequently carry current before the rest of the disk has touched the plane). If the surfaces would be perfectly smooth, the system would be infinitely accurate(The smallest possible distance gives no current).

However, the measurement device also limits the accuracy. For example, if a very small contact area exists between disk and plane, a very small current will flow(high resistance because of this small contact area). It is possible that this small current is not detected by the measurement device and thus it seems that the disk is still separated from the plane, while it actually is not.

So in total,

-Know the surface roughness of plane and disk

-Know the sensitivity, minimum detection(what is the noise level!?) and accuracy of the current measuring device.

-Maybe it is interesting to simulate the positions of the disk during rolling and the consequent surface contact area. Or make an estimation of the minimum contact area for example, check the corresponding electrical resistance, calculate current and check if this is detectable by the current measuring device.

(In total I think that this detection method is quite good!)

Best Regards,

Dennis

Hi Yury, it is an interesting discussion between you and Dennis.

Now from me a little comment. The current measurement via the shunt is fine, but the size differences of the current at strong contact and breakthrough in small columns are the problem. Since you actually interested in the changes, I would measure with a Rogowski coil.

Bes regards

Hans-Peter

Dear Hans-Peter, thanks for your comments. It is a very good addition to improve the quality of measurements.

Dear Yury, after I looked at your experimental arrangement again and talk of breakdowns, perhaps a counter-question. Which spark model are you using? The various problems of contact have already been pointed out by Dennis.

I'm interested in this question because we have examined such spark problems a few years ago. Due to the initially sharp edge and wear the spark conditions vary marginally.

Best regards

Hans-Peter