micro-Marx addendum

One of the issues I've been struggling with is the relationship between switching medium (hydrogen gas), gas pressure, electrode radius, and charge voltage.

The variables get hairy quickly, despite the work by a fellow named Paschen which makes some of it easier.

Well this morning, I found a paper ("Sparking Formulae for Very High-Voltage
Paschen Characteristics of Gases", A.E.D. Haylen, IEEE Electrical Insulation Magazine May/June 2006, vol.22, No.3) which provides the P*D curve for Hydrogen, which at 10,000 volts (stage charge voltage) is 550 Pascal-Meters.

Note that this is by definition between infinite parallel plates. (Generally, since plates with infinite surface area and no edges are inconvenient to fabricate, round plates having a diameter >> gap distance, and with the edges curved into Rogowski or Bruce profiles, are used.)

Setting aside electrode radius temporarily (because it is a variable with much less influence than the P*D product for a given voltage) I should now be able to get into the ballpark for my gap distances (which are, almost of necessity, fixed) so I can finish up the insert (mounting panel) model & drawings.

We care a lot about the stage gap distance for several reasons:

1. the gap distance has to be large enough to hold off the stage charge voltage at the operating pressure, BUT:

2. spark channel inductance is actually important, because at the high currents and high dI/dT we're talking about here, the spark channel is very small, which leads to surprisingly increased inductance per unit length of spark channel, so we want all gaps to be as small as issue #1 will allow, AND:

3. we don't want to waste any more energy (as Joule heating) than necessary in the gaps. Shorter spark channel = lower resistance.

I'll be pretty busy today and tomorrow, and unavailable for the next week or so after that, so I probably won't visit any of this again until late next week.