Strong electric field and dielectric breakdown

[Northprairieman]

Say you had two needles sticking out of an insulator in an air-filled chamber covered by an aluminum foil cup. The needles are charged to a high enough electric field to cause dielectric breakdown of air. Will a spark go from needle to needle? Or will the needles cause an induced negative charge on the aluminum foil and hence will a spark go from the needles to the foil?

 

[Hesch]

Will a spark go from needle to needle? Or will the needles cause an induced negative charge on the aluminum foil and hence will a spark go from the needles to the foil?

I assume that both are charged to a positive electric potential and that the foil is somehow grounded (otherwise the foil cannot be negative charged ):

There are some characteristics (don't rember their names) describing at which conditions (airpressure/field strength/distance) a spark will go. At atmospheric pressure a spark has no problems crossing a short distance. At lower airpressure sparks are more likely to cross longer distances. That's because sparks are created by a domino effect: An electron is accelerated in the electric field and craches into some air molecule, breaking away another electron that also will be accelerated. The speed of an electron must be within some limits to be able to break away another electron. At low pressure where an electron will have to travel a "long" distance before it meets an air molecule, the accelerating electron will probably have reached a speed above some limit. But if we increase the distance between anode/cathode the field strength and thus the acceleration will be lower, so: here we go again.

So if we have an anode and a cathode in low air pressure at short distance, maybe a spark will not go straight, but will choose a long way round between anode/cathode as the field strength is lower following this route.

( Oops: I found something here: http://en.wikipedia.org/wiki/Paschen's_law )

So field strength, airpressure, type of gas are needed.