I am trying to calculate the minimum distance I can have between two electrodes with very high potential difference while still preventing arcing (for something I am trying to build).
The emitter (negative electrode) is made from copper and ends in a sharp point. The open circuit voltage at this emitter is -20KV DC at about 50 uamps.
The grounding "plate" is actually a short piece of copper pipe, arranged so that the axis of the pipe points towards the emitter. This geometry is based on the ion generator shown in the middle of this page.
Right now I have the grounding pipe set so that the edge closest to the emitter is about 4cm away from the emitter. I know this is more than enough to prevent arcing, but I'd like to reduce this distance as much as possible while avoiding arcing under the entire range of conditions (i.e. air pressures, temperatures, humidity levels, etc) that a person may encounter at home, regardless of their location, weather, time of year, etc.
I know that the breakdown voltage of air at STP is 33KV/cm. If I understand this correctly, at -20KV and STP, arcing should not occur if the distance is over 6mm. Is this correct?
How are these distances affected by the geometry of the grounding plates and/or the emitter? Is the distance affected by the fact that I am using a pipe instead of a flat grounding plate?
Would enclosing the assembly in a dielectric material have any impact? (I am thinking of putting the emitter-ground assembly inside an acrylic tube with a diameter just slightly larger than the diameter of the copper pipe). I don't think it should, but just want to make sure.
I am also thinking of having more than one emitter point, each one with its own "grounding pipe" (like they did in the device linked above). Will the number/geometry of emitters affect the distance significantly?
Using a distance of 1.2 cm would be compact enough for what I want, and provide a "safety margin" of 100% over the 6mm "theoretical" distance (I would need 40kv to produce an arc across 1.2cm, which is twice the voltage I am using). Would this margin be sufficient to take into account all these issues and avoid arcing?
If anyone has any links to more info about how to estimate the voltage required for arcing under different conditions, it would be greatly appreciated!
PS: yes, I know the precautions needed to work with high voltages