Marx Generator design Considerations

[FonziDaytona]

Hi all,

I’ve decided it’s time to build a Marx generator and am having some trouble finding information/formulas relating to firing rate.

I’m planning for a very controlled fire instead of fast as possible. I’d like to push a firing button and have it fire. I plan to use some high voltage vacuum relays (large Jennings type) that I have to both isolate the charging power supply (protection) and to trigger the Marx.

I’ve got 12 40kV (Possibly good for higher?) 2nF doorknob capacitors (so going for 12 stages) and some 2W 1Mohm old carbon composition resistors. I plan to use two in series for 2Mohm per stage.  Charging comes from a Glassman -50kV at 6mA power supply.

Could anyone help me determine the firing rate? How is this determined under ideal conditions (I know there are corona losses and whatnot)?

Also, for triggering the Marx, am I correct in assuming that I can use the second relay to basically short the first stage?

Thanks!
Matt

[klugesmith]

How much voltage will be across your charging resistors?
In my experience, 2-watt carbon composition resistors in the single-digit-megohm range were pretty nonlinear at even 2 or 3 kV.
Might have been a 20% curvature in I-V chart, which is ideally a straight line, and some significant non-reversible resistance changes.

Fortunately the R value is not critical in a Marx generator application.
You might want to do some experiments with a shorter stack, before damaging many of your precious old resistors.

[davekni]

Analog simulation is a great way to see performance.  LTSpice is my favorite tool (and free).  Corona estimation and simulation will be tricky.  Goal is to minimize corona by mechanical design, rounded structures for exposed nodes at edges of tower.

[FonziDaytona]

There will be up to 25kV across each resistor. Seems a stretch but these seem to be the go-to resistor for others…

10-4 on rounded corners/edges. All of the hardware I plan to use avoids edges and sharp corners. Spark gaps made from some old stock proper spark gap terminals I found on eBay. Nickel plated brass, 1/2in diameter, look like bullets and threaded.

From examining a basic layout, it looks like charging time is based on the final capacitor, right? So if I have 12 stages with 2M ohm per stage, that’s 48Mohm total, which should take 0.1 seconds to charge the final capacitor (2nF).

-Matt

[klugesmith]

>> So if I have 12 stages with 2M ohm per stage, that’s 48Mohm total, which should take 0.1 seconds to charge the final capacitor (2nF).

Like Dave said, do a simulation or learn the math. The 48M string (including its taps) is charging all the capacitors.

[Anders Mikkelsen]

It's worth looking into bulk ceramic resistors for marx generators, these are the modern replacement for carbon composition, with similar pulse handling while being less temperamental.

[FonziDaytona]

>> So if I have 12 stages with 2M ohm per stage, that’s 48Mohm total, which should take 0.1 seconds to charge the final capacitor (2nF).

Like Dave said, do a simulation or learn the math. The 48M string (including its taps) is charging all the capacitors.

Okay, so then 24nF, (12*2nF) and 48Mohm total resistance, a little over 1 second charge time?

“Learn the math” - This is what I’m asking help with. Why even reply with something like that? Yeah, I could go ask one of my consultants, but this is the internet and we are all here for help or to contribute where we can…

[klugesmith]

Do you want to make a spectacular Marx generator and skip the learning EE part?
There's no trivial answer, because even the first capacitor's charge formula is complicated by sharing of resistor(s) with the rest of the string.
Partly charged first capacitor is the source voltage for second stage charging, etc.

What you just said (total of R's x total of C's) is a simple but very conservative upper bound, if you also multiply by 5 for charging to 99% instead of 63%.
If the answer is tolerable then you are done.

If you want to confidently figure your charge time within a factor of 2, or even a factor of 10,
learning and applying a simulator like LTSpice might be faster than making an analytic solution.  Can get prompt review at this forum!
R-C Marx charging is simple enough that you could set up transient analysis in a spreadsheet, from scratch, but learning a simulator app would be more useful in general.

Good luck!   I had to edit this post after it appeared mostly in strikeout type.  'cause I wrote resistor(s) with square brackets instead of parentheses.

[edit] One of the pictures in today's Wikipedia article about Marx generators
shows a demonstration I witnessed at Maker Faire 2009, San Mateo, California.
 https://upload.wikimedia.org/wikipedia/commons/6/6b/Zap%21.jpg

[klugesmith]

Please review this. Probes are on C1 and both ends of C6 and C12. Looks like C12 got to about 84% in first second, but at 100 ms it's barely started to charge.


[edit] This isn't much different from a continuously distributed RC line, whose transient behavior has been important in integrated circuit design for more than 50 years.   I bet one could find, via Internet, an analytic formula giving the voltage waveform at various places on the line.   Probably extra simple for the far end of line. But waveform won't be shaped like canonical RC charging waveform.
[edit edit] For example, see figure 3 here: https://dl.acm.org/doi/pdf/10.1145/217474.217557
It shows far end waveform, with timescale normalized to total R x total C.   Looks very close to our 12-stage lumped model. That was fun!

[FonziDaytona]

Thank you for all of that, it’s very helpful in understanding the process happening. I should have mentioned that precise timing isn’t important here since this is just for fun/personal mad scientist work 

I had forgotten about the capacitor charge time constants starting at about 60% and then taking many more to get close to 100%. This looks to extend things out a bit using 2Mohm resistors per stage, so I’ll probably scrounge some more resistors for this. They can be had pretty cheaply on eBay when buying in quantities.

Here’s a shot of the setup so far. I have a large vacuum relay (Jennings rp900) to use for isolating the power supply between shots. I’ll be installing another, similar, vacuum relay to use for triggering the first stage. Also visible is one of 13 TDK doorknob capacitors that I’ll be using and one of the electrodes for the spark gaps.

[malte0811]

This isn't much different from a continuously distributed RC line, whose transient behavior has been important in integrated circuit design for more than 50 years.   I bet one could find, via Internet, an analytic formula giving the voltage waveform at various places on the line.   Probably extra simple for the far end of line. But waveform won't be shaped like canonical RC charging waveform

Finally something in this forum where my main job becomes vaguely useful: We usually look at RC trees, not just lines, and I am not sure if there are results on that special case. But at least for trees we do not have a closed formula, only some closed approximations. The easiest would be Elmore delay, which gives you a (pretty good) estimate of the time to 50% of the input voltage, as well as an estimate of the slew/rise time. Elmore is also nice in that it is easy enough to use as the objective function for algorithms. If you need more accurate values, "asymptotic waveform evaluation" is a good search term, but at that point you might as well run a SPICE simulation unless you want to evaluate it for a very large number of trees.

[FonziDaytona]

Time for an update:

Finished up my relay setup. One will be used to charge the Marx while the other will be used to trigger it. Pressing the trigger button disengages the charging relay so as to isolate the power supply from the Marx stack.

Got a nice little Glassman -50kV multiplier and transformer. It’s rated for 6mA but the guys on the Fusor forum have pushed them much higher (though 6mA should be plenty). You need your own driver for this, which I used my easternvoltageresearch drsstc board for, after some non permanent modifications to it.

Getting closer!