You won't be able to ground the negative rail without having an isolation transformer as the negative rail is driven below earth ground when either AC input is negative of the earth ground, which I assume in you country is simply a centertapped 240v with the centertap grounded in your electrical service box (that's how our 240v is here BTW, but most of our house wiring goes between one of the mains wires and ground/neutral, we only wire for 240 for real big appliances like stoves). So trying to "earth" that point will result in shorting the line through your diodes, not good for either one. But you said you could float the scope, and hook its "ground" to the negative rail, so as to get a signal measured source to drain on the fet anyway.
(this is why I ragged on you to get an iso transformer -- every shop should have one, it makes things safer to work on anyway)
In other words, your two mains wires are the outside of a 240v center-tapped transformer (out on the street most likely) with its center tap wired to earth ground either outdoors or in your service box (In USA, both places). Either wire then goes both positive and negative of earth by that much -- roughly 168v peak either way for 120v RMS AC on either half.
If you didn't connect your scope ground to a rail, then the bad waveform above is explained by capacitor ripple (which you can measure on either rail vs earth gnd, and you should see some when the bridge is drawing current -- that's normal and unless it's too big, no problem). In normal operation with your bulk DC circuit, you should see roughly equal and opposite voltage rails with "real ground" as a center-tap -- about the aforementioned 168v no load each at full input voltage. So shorting either rail to ground in your setup won't fly -- you're just shorting out the power company in a potentially expensive way.
In an iron core circuit, the fact that one primary is outside the other isn't a big deal at all -- the "iron" in this case being ferrite, but still hundreds of times more magnetically conductive than air, so a little air here and there just doesn't make a noticeable difference -- it's really how many times a wire goes through the hole that matters most. The gap spacing does -- those shims you mentioned. They are there to control how much net "mu" the core has, and to prevent it from being "too good' and saturating so easily. So in fact by changing this shim thickness you can tune the thing all over the place -- a tiny air gap has more "reluctance" (which in magnet-speak is roughly analogous to resistance) than the length of core material does, because the core material is hundreds of times more magnetically conductive than air is, or thousands, depending on the material. The gap is used to tune that parameter overall as far as what the windings see. It's not normally used in AC circuits, but is often used when there is supposed to be a DC component in say, a switching supply inductor, so the core doesn't saturate. In this case it's cheaper to use more wire to get the inductance back up than tons more core material.
I couldn't easily tell what the square area is on that core, but it looks like about 1 sq inch (sadly, I think distances in "English" while the English have gone metric, but I can understand either).
I'm able to get about 8v/turn without saturation on cores here about that size with no gap, for what it's worth -- if yours is bigger than that in square area, you should be able to get about that much more volts/turn without saturation. In your case, reducing the gap makes it easier to saturate re current (ampere-turns), but willing to take more volts/turn before the same current is drawn (because of the higher inductance you have with more mu). If it turns out that you can't get high enough in drive frequency to make this guy truly happy, reducing the gap would bring the resonance down to where the driver could be happy. In realty, you can't really get "zero" gap as nothing ever fits perfectly, and even .001" is significant with high mu ferrites.
For fanatics about that one, they do make a ferrite loaded epoxy but that's over the top for this -- a small gap is probably what you want anyway to keep the resonance F high.
I have a similar transformer from a Spellman, and while it has more than one resonance, the main one for a lower voltage secondary than I think you have, is much lower than you are reporting (more like 20khz). Something isn't quite right here, yet. You might be wise to extend your measurement with an oscillator down to 10khz or less, and up to a couple hundred. That sloppy made Wallis I have shows about 3 significant resonances, as in that case there enough weird airgaps and two huge (8" diameter) secondary pie windings that all interact with one another in "interesting" ways -- everything has various stray C's to ground and to each other and a lot of leakage inductance and even coupling between the two secondaries. As luck would have it in that case, the main resonance is well inside where the driver is happy, and there's enough leakage inductance for the other resonances to still occur -- right at 3 and 5x the lower one, so it's perfect for a square wave drive(!) -- my Spellman that looks more like yours doesn't have that "feature" and is much tougher a load on the drivers without that series resonant LC in series with it (which I'll have to add externally). It seems to be more or less "built in" to the Wallis transformer, which isn't potted and is very sloppy, made out of a bunch of short square sticks of ferrite, loosely held together with gaps all over the place.
I note you have the other leg of the magnetic circuit exposed and available. I've gotten fantastic results by putting a few of the primary turns on that other leg so as to have some leakage inductance between primary and secondary, and Glassman does that on purpose in their designs. Makes it a lot easier to drive that fast edge into what is otherwise a fairly high Q tuned circuit -- the leakage L there means it doesn't present such a low impedance load to the driver for that part of the spectrum. I've had it cut quiescent current from hundreds of ma to a few, and everything gets a lot happier at that point.
Until you get into heating issues, you can just use one primary for testing and it may work better that way anyway. No need to parallel them till you're getting to high enough input currents to heat the wire ohmically. At any rate, you shouldn't notice much difference in anything with just one compared to both in parallel unless something else is wrong.
(I'm going to find a nice looking hysteresis curve for ferrites and put it up here to illustrate something -- you really shouldn't be seeing that rise in resonance with voltage with that big core and big gap unless you're well outside the ratings of the transformer, or pushing them real hard). Your rise in resonance indicates (if too large) that you're getting to where the BH curve bends over and so the material looks like lower mu (a straight line from the origin has less slope plotted as B vs H).
Yes, plasma is a hard load to drive indeed, and the dependency of current draw on gas pressure is intense to say the very least. This is why we use a series ballast resistor in the 50-100k range and spend so much time with gas control. The way it works out, we're working on the very steep part of the left-hand side of the Paschen law here.
- Paschen's law from wikipedia
If there's too much gas, current will rise more or less without limit until evaporated metal atoms get involved, at which point it gets to a pretty good short circuit (arc welder -- 20v, 100's of amps). As you go down in gas pressure, there's not as many ions and electrons to carry current, and less of the gas is ionized as a proportion of the total gas present too, so in a narrow range, you can drive it with reasonable kit.
A plasma has negative resistance -- the more current you try to put across it, the lower the voltage goes, due to more current carriers coming into play -- this is
on top of Paschen's law, so the plot above isn't the whole story at all. We are trying for the opposite extreme from an arc welder here, and even a moment of high peak current (from the stack capacitors) can take you to "arc welder" conditions. You need an absolute current limit (series resistor) of under an amp or so at these sizes to prevent that happening every single time it lights off. Which is why you can make a neon lamp blink with a series R and a parallel C. The arc mode from peak capacitor current drives the voltage on the cap well below the original "strike" voltage of the lamp, which goes out as soon as the cap can't bring all the big currents into it.
The lamp then goes out, and the cap recharges to the strike voltage again, and the cycle repeats. Same thing can happen in a fusor, and often does. In the case of the lowly Ne-2 bulb, the strike volts are about 110, and the stable sustain volts at very low current is about 70, but during a capacitor discharge can go much lower while the current is high.
Here's a link to two books about just this phenomenon.
In my fusor, without an ion source to help, the entire range of gas pressure I can run does not change the least significant digit in a two digit (plus exponent) gas gage display. It's
that critical. If you can't get to "can't light it off" vacuum, then that's your next issue -- you really want to get at least order of magnitude better vacuum than that when you're not putting in gas, to be running in reasonably pure conditions when you are. Two orders is better yet.
With an ion source, I can hugely increase the working range towards lower pressure, and therefore higher voltage at reasonable currents. In that case I can go down to 1.6e-2 mbar up to 2.2 e-2 millibar. Without the ion source, it just goes out below 2.2 e-2 mbar. This is so repeatable and so stable, you can use it to calibrate a gas gage against (in your case, directly as we have the same basic fusor dimensions). But that's another thread.
Posting as just me, not as the forum owner. Everything I say is "in my opinion" and YMMV -- which should go for everyone without saying.