I Controlling the location of a spark between two parallel rods

[Connor11]

TL;DR Summary

two parrel rods, one grounded, the other has ideal supplies on each end, uniform dielectric

Imagine you have two metal rods that are perfectly parrel and separated in by a small distance. One is at ground potential. The other is connected on each end to ideal supplies. The supplies can deliver any voltage waveform you need no matter the current. You desire to change the location that the air ionizes and sparks by using the waveforms of the two supplies. Is this possible? My thought is that each voltage would be less than the breakdown voltage but through the propagation could combine to be greater than the breakdown threshold. I was thinking this problem needs a transmission line model but I don't know how to do that. I was trying to find what I need in Griffiths Introduction to electrodynamics but couldn't. Any recommendations on how to approach this problem or other E and M books to look into would be helpful. Thanks!

 

[Baluncore]

Alternatively;
Imagine a metal rod or line, above and parallel with a ground plane. You then have a transmission line over ground, with air (or a gas) as the dielectric insulation.

Place a signal generator at each end of the rod, to inject a signal into the rod, relative to the ground plane. We define the breakdown voltage to be 100%

If you generate a short 75% voltage-transient pulse into the line, it will propagate along the line until it is absorbed by, or reflected from the pulse-generator at the other end of the line.

If a 75% pulse is generated at the same time, at each end of the line, those pulses will pass somewhere along the line, where their voltages will be summed to 150%, which may break-down the air insulation.

Where those two pulses meet is decided by exactly when those pulses were launched.

To make that system work, it would require that the voltage pulse rises fast, relative to the time needed to propagate along the line.
It also requires the voltage breakdown of the air be well-defined and very fast.

To control the point of breakdown to within one foot, (300 mm), will require pulse-time accuracy, to be controlled to better than one nanosecond.

The line will need to be long. If the line is long, there will be attenuation of the pulse, that will require an initially higher voltage pulse. But the pulse cannot be more than 100% or the pulse generator will fail, so you need a low-loss line, with less than 3 dB attenuation along its length.

 

[DaveE]

It also requires the voltage breakdown of the air be well-defined and very fast.

Which it isn't. The speed of transmission line propagation is much faster than arc creation. At least for voltages close to the breakdown threshold, as described.
Maybe standing waves, so the ions have time to collect?
Or "special" air preparation, like a thyratron or krytron, biased really close to avalanche and waiting for a trigger?

 

[sophiecentaur]

TL;DR Summary: two parrel rods, one grounded, the other has ideal supplies on each end, uniform dielectric

You desire to change the location that the air ionizes and sparks by using the waveforms of the two supplies.

Would this be good enough? Jacob's Ladder will produce an arc that moves along a V shaped pair of conductors.