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Question about paschen's law and fusors

Posted: Sat Apr 12, 2014 10:24 pm
by Doug Coulter
I just ran into something I really don't "get" and perhaps someone here can find my error. I pose the question with some serious detail on my site here: ... 04&start=0

But it boils down to this. I'm running a cylindrical 1" OD grid inside a 6" ID tank sidearm. It lights off right around when my gage is reading 2.2e-2 mbar (.022 mbar)...if I'm making the conversion right, that's 0.01672 torr. I have 50kv on my supply. My calculated distance from grid edge to wall is 6.35 cm, making PxD 0.106172 torr-cm.

If I go by the chart here (from wikipedia) this thing shouldn't run at all no matter what I do, even my secondary ion grid in the larger tank doesn't have a PxD that's even on this chart.
Who's wrong, and why?

Here's the chart from Wikipedia. Could they have meant meters instead of cm? It would make sense if so. Oops, no it wouldn't, not hardly, that would make my PxD even smaller!
Paschen's law curve from wikipedia
.1 is at the very left of the chart - infinite voltage more or less, since the lines are going more or less straight up long before they get there. Something is wrong with this picture.
BTW, the Pfeiffer documentation on my gage says it reads a factor of two high on hydrogen, but at this pressure, I'm not sure if the pirani or the ion gage dominates (they say this for the ion gage part, I believe). If so, it's even more mystifiying, as then the PxD would be half what I calculated above.

Re: Question about paschen's law and fusors

Posted: Sat Apr 12, 2014 11:04 pm
by Andrew Haynes
It look like it matches with 10kv to 1cm at 10 torr, which is 100 of atmo for nitrogen, is that lead, instead of mercury thought?
10-30kv for 1cm at 1 atm, yeah they mean meter, wiki isn't always accurate, they have wrong boiling point and decompose temperature for some acetates aswell

Re: Question about paschen's law and fusors

Posted: Sun Apr 13, 2014 8:25 am
by Peter Schmelcher
Hi Doug,

I think you missed that the graph is for parallel plate field geometry.

The breakdown will start at the strongest electric field (more or less your grid radius) and progress outward where you get into a Townsend avalanche gain region.

Always interested in what you’re doing. Keep up the good work.


Re: Question about paschen's law and fusors

Posted: Sun Apr 13, 2014 3:50 pm
by Doug Coulter
I'm not yet satisfied there is a good answer here. Yes, the field gradient is highest at the grid, but there's no distance there for the PxD thing to work out....and the mean free path at this pressure is quite long. There's probably some field emission, yeah, but not a lot, nothing is pointy - by design.

Edit: This grid is 8 equispaced very straight .020" diameter pure tungsten rods (special order for TIG welding, both cheaper and straighter than the normal scientific sources) retained by rounded off graphite ends. It's just under 1" diameter (the original graphite stock rod I made the ends from is .988" from mcMaster) and the active area is 1.1" long between the ends, which are about .125" thick at the full diameter. The HV feed end has a stub on the back about 3/8" that's threaded for a copper stud to screw into the end of the HV feedthrough, spacing it slightly off the end of the boron nitride insulator that goes to the end of the feedthrough. I don't see any creepy little arcs or flashes back there. The BN in turn is inside a 1.5" OD pyrex tube (for air tightness) that only sticks a little way into the tank.

Re: Question about paschen's law and fusors

Posted: Sun Apr 13, 2014 4:13 pm
by Jim Kovalchick
I have wondered the same thing. A couple years ago my son plotted the voltage at the onset of plasma ignition for varied pressure for both air and deuterium. The shape of the curves showed a left side Paschen behavior for both gases, and the relative plots of the two against each other looked like what is published for parallel plates. However, the distance x pressure in torr-cm bore no resemblance to published data. As I recall the actual plot was far to the left of what you would predict if simply substituted the fusor radius for plate separation.

Re: Question about paschen's law and fusors

Posted: Tue Apr 15, 2014 1:17 am
by Doug Coulter
Yes, Jim, it seems we all see this. My numbers are really similar to what Richard Hull reports as gas "light off" and running pressures, and in fact, the observed curve is so steep that the whole range of "light on" to "light off" is inside one digit of my digital readout. It's more sensitive than the gage! And it's off by factor 10 or so from the published curves... I can kinda-sorta understand why it stays lit up once its going, because the gas is already ionized and so on, but to start where the curves say its (utterly) impossible is a puzzle, and since we all see the same thing, makes me think either the curves are wrong (it's been known before in science to have a bad number that stands for years without challenge - or even a wrong sign, much less the constant) or our understanding is simply wrong - that's not all that uncommon either. I'm just trying to sort out the "whichness of the why" here. As someone said, most of the great moments in science are not "eureka" but "hey, that's funny" and this could be one of those.

In my case, this is measured in a 6" long, 6" ID sidearm with a 1" grid (very smooth, no sharp edges anywhere), and a similar effect is measured (but at lower volts for the same everything else) out in the main 14" by 26" tank with another pretty crummy 2 loop tantalum wire grid. So it looks like Paschen's law in how it works, just off by factor 10 or thereabouts. In my case, the grid out in the larger tank is smaller, a crummier grid for fusion, and lights off at around 10 kv when 50kv won't light the one in the sidearm...I am using the grid out in the main tank as a kind of easy-rigged ion source, and it shows significant power gain relative to the "main" grid, much as a control grid in a plasma triode. In fact, that's my usual running mode - I remove gas (I'm using a batch type gas control system) till the main grid will just barely not "light", and then biasing the "ion source grid" to the point where things just start drawing current again. FWIW, the net power gain of this "triode" is on the order of 100 or so, and yes, you can make it oscillate, though what I seem to be seeing with an untuned broadband transformer hooked between the grids is not a true hartley type oscillation (the transformer isn't too good at that low a frequency), but a rather more simple relaxation oscillator - it "goes" at a much lower frequency than the lowest the "transformer" is truly a good tuning for (in experiments testing it outside the fusor it's more like a 20khz-20 mhz kind of bandpass) - it does not include the very audible low or sub khz frequency you can here in my recent video at all - my tests show very little coupling there, and in fact the oscillation seems to happen whether the secondary is in series with the "control" grid or not - FWIW. The secondary phase does make a difference. Hooked up "anti-phase" it suppresses whatever the oscillation effect is to a large extent. But at this frequency, those "in or out" of phase monikers are likely not real meaningfull, since there's around a 90 deg phase shift at the low end of things. The phase that makes it oscillate most easily is the one that should "suppress and stabilize" the main grid current, in fact, EG negative feedback - ion grid goes negative when the main grid does.

Edit: The thread in my forums, linked above has a video with audio where you can definitely hear this oscillation in the audio output of a pair of neutron detectors. That wasn't really my question here, but it IS interesting, especially since the net Q of the fusor is far higher in this mode - about the same net neutron output, but at much less total power input. So far, we see two conditions. If I crank the world up "hard", that's when I get the most neutrons. A recent run showed us right at 10m neuts/second at around 47 ma/45kv input (actually less due to the voltage drop in the ballast R). But my plotting software shows us highest Q (100's of times more) at much lower power inputs - both power and neutrons are reduced, but neutrons don't go down as fast as power does, so the Q is higher down there. That's not the issue I wanted to explore here, but it's data for anyone else wanting to know what I measure here. Part of the measured Q increase could be an artifact of my data collection system - the voltage/current monitors are "slow" but the counters collection never misses a pulse - so one point might show high neutron counts before the power sensing has time to register a pulse of high current, for example. Seems promising anyway, as in the "steady state" of low power oscillatoin, we can trust the average to be right and the neutron count to be right, and we see Q improvements in the 500-2800 range over simple "steady dynamic DC equilibrium" running - the way most run their fusors. For us, if we get 10m neutrons at 2kw input, we see 2 million neuts/second at more like a few watts average input - something pretty interesting, but it's a separate issue. Could be due to nothing more than "kickback" on the series L from the primary of the transformer (which is still in series with a huge 50k ballast R from the power supply in all cases to protect both the supply and the fusor - so the electrical Q) is obviously quite low with 50k ohms in series with around 3.5 mh inductance - at a khz or therabouts. We're currently limited to right at 50kv input (new power supply is not yet online, for 100kv, but coming soon, as quick as I can add some safety features to it), but as we plot the n/s and Q vs voltage, it's rising quite quickly as volts go up within that 50kv limit, and still going up as we run out of voltage, it would not take a lot more to make it put out a lot more fusion/watt or just total fusion - what we see is an exponential rise with power supply voltage within the range we can apply and measure accurately all the way from 20kv up to 50 - with or without series L in the power supply circuit.

Re: Question about paschen's law and fusors

Posted: Wed Apr 16, 2014 11:50 am
by Jeroen Vriesman
Could the discharge be initialized by "microplasma's"?
In other words, looking at the phenomena as a vacuum breakdown in stead of a gas discharge. ... le/ptv.pdf

Maybe it's possible to measure the "noisy current spikes" mentioned in the paper above.

The paper mentions "under 5E7 V/m" as a typical breakdown field strength region, your field strength is 7.9E5 (at 50kV), that is still a factor 64 off, but the paper doesn't mention at which field-strength the micro-plasma's begin.

My wild guess (would be interesting to measure): the plasma ignites when the current starts to show spikes, could also be a bit hard to measure, since the current would be around 1E-10 A, but only the AC component is enough to show the spikes.
Assuming that the micro plasma's are not self quenching when the pressure is around 1Pa, I cannot find that much data about discharges in the 1Pa pressure region, most data is about higher pressures (the paschen curve) or very low pressures (vacuum breakdown), my guess is that this is the region where the two of them meet and the micro-plasma's which initiate the vacuum breakdown can also ionize the gas, while at higher pressures the Townsend current is responsible for initial ionization (or some radiation is geiger mode)

I a few days a will have a huge pile of data from a former vacuum switch factory, maybe there are some useful measurements in there.

Re: Question about paschen's law and fusors

Posted: Wed Apr 16, 2014 3:03 pm
by Doug Coulter
Well, at least this is plausible. Just about everything in there has some adsorbed gas...which is something I heard can be responsible for "vacuum breakdown". The P in the PxD can be really high right near such a surface if something lets that gas free. I'll be able to see small little current pulses at high speeds (again) soon, my good DSO ate a lightning bolt from a faraday probe, and the new one hasn't yet arrived. Any HF is pretty easy to see if you just put a probe a couple inches (and on the other side of the PVC pipe) from the main HV at the feedthrough - you get decent capacitive coupling doing that. That isn't what fried the old scope - that move is a pretty safe one. I accidentally put a stock probe onto a 2" wire faraday probe while the fusor was running and it had several kV on it at the time, toasting one of the 4 channels and the trigger stuff...our plasmas are extremely net negative at a distance from the "action" - the probe was 17" away from the sidearm I do fusion in. I found out the hard way, and now ground every feedthrough in the big tank just in case - some (rated at 5kv standoff, but for thermocouple use) arc over if I don't - even with nothing hooked to the vacuum side). I will check for that when the new scope (GDS 2204a) arrives.

That factor of just about exactly 10 is still suspicious in the sense that it's the type of math error that tends to get made (since we work base10, and use many different units some of which come out around factors 10 (pascals come to mind - even though it's been ages since I've seen anyone use it in practical gages)) and overlooked due to too much respect for "authority". FWIW, I use mbar, but that's mainly because I have a bunch of Pfeiffer stuff and they "think" in those units. Looks to me like someone might have had a conversion issue. This is one we all see...there's no question something is a little odd here. And apples fell from trees for millennia before Newton comes along and takes credit for some equations about gravity...

Think how complex plain old electronics would be if we used all these different units for the same thing - abvolts, statvolts, volts....farads, cm... coulombs, faradays, amp hours...but EE's wisely just use one set because our stuff has to work, not just produce equations that don't need pi or c in them by mixing up units (and assuming you know some authority did used mixed units in the same equation, since in most cases, they don't say they did) - we go for function, not "pretty" (in the typesetting sense) math. /rant

Re: Question about paschen's law and fusors

Posted: Thu Apr 17, 2014 12:48 pm
by Jeroen Vriesman
Doug, before posting my "microplasma hypothesis" I looked at different sources of PxD data, both theoretical and measurement results.
The graph on wikipedia is more or less correct, some measurements show a dependency of the graph on the total distance, so PxD isn't the best value to look at anyway.

But I don't see the factor 10 anywhere, the wikipedia graph seems correct to me, that's why I looked at it from the "vacuum breakdown" perspective.
In my previous post I mention "under 5E7 V/m",

This paper mentions:

"Typical measured values of the breakdown field are around 150...250 MV/m, and field enhancement factors between 40...70 for copper." or 3.6E7 +/- 1.3E7 V/m
Well, that is for copper, I don't know the field enhancement factor for tungsten, some sources state a breakdown field strength of 1.6...1.9E7 V/m, so the "enhancement factor" can be higher.

To state the hypothesis:
a) microplasma formation is the beginning of vacuum breakdown
b) in UHV self-quenching of the microplasma's prevents vacuum breakdown, until the field strength is high enough to prevent self-quenching
c) at pressures where the paschen curve goes to "infinity" (still far away from UHV), the gas can prevent the self-quenching of the microplasma's
d) (c) causes the plasma "light up" and that should happen at voltages where the current spikes begin (difficult to define "begin"...)

a and b seem to follow directly from the spikes mentioned in ... le/ptv.pdf

Measuring the spikes is not that difficult, but to measure where they "begin" might be a bit hard, maybe there is a field strength with a clear beginning, maybe it just drops below measurable currents.
This can be measured in UHV, no breakdown needed to see the spikes.

A bit of theoretical backup (you know, stuff from the guys who think the speed of light equals 1 :) ) might be handy to see if (d) is true, or to point at "what to measure", answering questions like "is there a minimum microplasma energy needed to light up the gas" etc.

very interesting, will do some more reading on it.

Re: Question about paschen's law and fusors

Posted: Thu Apr 17, 2014 12:54 pm
by Jim Kovalchick
Doug et al,
In poking around at this issue I found this paper that discusses some of the factors influencing Paschen discharges in a non-planer geometry involving a hollow cathode. I think it may help the discussion.

Jim K

file attached