Still not right, sorry. And this from some of the smarter folks here, re electronics. Sigh. This is not a personal attack of any kind, just an attempt to educate ;~}
From the geometry, the tube "impedance" at RF is in the few hundreds ohms, the center conductor is tiny indeed in these -- to make it 75 ohms with over an inch ID of the outer conductor, the inner one would have to be well over 1/2" diameter (I'd have to go look it up in a handbook, but after awhile the eyes are close enough for things like this). All the tubes I've looked in use a tiny center conductor to get gas gain where the field gets high near the small radius. Tiny wire in big tube, dielectric constant basically one, high impedance compared to most coax. (the old stuff they used for car AM radios is the exception - air dielectric mostly, and tiny wire, same idea) With dielectric == 1, the impedance of a coaxial affair is a function of D/d - a larger dielectric constant makes it lower for a given size ratio.
However, remember that a mismatched transmission line has it's *lowest* resonant frequency (for ringing) at the point where it is 1/4 wavelength -- so let's work that out and see if that's what matters here.
The tube is a little over a foot long, so the place where that kind of thing happens is far higher in frequency than these couple uS pulses (a full wavelength is ~300/F in meters and mhz, which is why the 2 meter ham band is 145 mhz more or less), and the tube looks like a capacitor for all intents and purposes (with a relatively tiny series L), which is why (partly) someone uses the moniker "charge sensitive" preamp for a circuit designed to capture total pulse energy without looking too hard at the shape of the pulse. There's not much useful info in the shape from a gas tube, that depends on things like where the reaction took place inside the tube, which could be anyplace, (and along it vs across it), and the waveform will vary accordingly in all but saturation (geiger) conditions, which aren't relevant here -- we don't run the tube volts up that high to get into that operating regime where we get constant energy pulse output. We're only interested in knowing how many ions happened in the event.
In this case, the ringing frequency of the mismatched line impedance of the tube itself would be of the order ~100mhz (5 ns per half cycle) so....doesn't matter here, the rest of the circuit will just lowpass all that out and give the correct answer anyway -- Ft on the pnp is lower than that, and the output darlington even lower I think (didn't check, but darlingtons are slow in general). With another piece of differently mismatched coax between the tube and preamp, the number changes, of course, and a long enough cable *could* get you in trouble there.
Basic theory. Known correct. Well tested.
An event creates a certain amount of charge, which we want to collect and amplify. This amounts to a current multiplied by a time, and an integrator is what is most often used for that, though you could usefully put a preamp in front of all of it and integrate later on -- and get better S/N by allowing some voltage drop to occur so that a *power* is developed with that current. The reason most put the integrator first is it's more elegant that way, and cuts the HF noise (from other things) early on in the chain. And the integrator is rarely a perfect one (else the pulse would never return to baseline among other things!) -- so it works out, even though not technically ideal -- an impedance matched preamp would be better for S/N, but luckily we don't need the best we can possibly get here. You'd couple more signal power out of the tube if you didn't load it with so low an impedance, allowing a bit of voltage drop to occur so the old currnent times volts times time = joules thing is happening and the rest has some actual power to work with to swamp its own noises.
Technically speaking, this isn't even a charge sensitive preamp. Even the miller capacity of the FET is suppressed via the low input impedance cascode pnp here! That's where the integration usually is in a CSA, or around the entire amp loop, and there is no explicit C is across the feedback 2.2 meg R here (always some actual C, of course and at 2.2 megs, the parasitic C is about right, actually). Does that actually matter? Only to a pedant, as the circuit will work fine anyway -- it's a current to voltage converter with current gain and both high and low passing, not all explicitly drawn, but there none the less.
The real time constant of the input circuit can't be known without also knowing the R in series with the HV supply for the tube, btw -- the tube is a current source when there's an event, and open circuit when not -- essentially infinite impedance at all times, just one that draws some current when a neutron hits it, for a little while.
The real impedance the input coupling cap sees is that resistor (not shown or specified) in series with the amp effective input impedance (zero by comparison). Talk about a mismatch -- we have about a meg or more at the tube end (with a tiny C across it, intrinsic to the tube and connectors), and basically zero at the amp. But this is an easy signal processing job, and that pedant stuff doesn't matter as much as you may think in this case -- remember the active tech in use when these tubes were really in use was thermionic triodes.... This is, though, why the HV power has to be quiet, as any noise on it will get in here via the series resistor to the supply, and show up as an inpu current (the supply R is a voltage to current converter for noise on the HV).
Depending on the open loop voltage gain of the amp, which I've not looked at hard, but it's high, essentially the transconductance of the fet driving 82 k ohms via the cascode pnp with elimination of the DC bias current of the fet via the clever inductor. Fets are all over the place on IDss, which is why the source R is also a good idea. We have a high pass filter or differentiator due to the inductor.
The effective value of the 2.2 meg resistor for frequencies the amp can pass (see that inductor - it's not a DC amp) is....zero, yup, or pretty close! (check this in the simulator) -- it would be 2.2 meg divided by the amp open loop voltage gain which is a fairly large number (100?) so call it 20k. And even though I spit out that figure above as 7 hz -- no one caught it (heh;-), so I now know that no one knows basic opamp closed loop theory (at least who has yet posted, other than myself). Or didn't realize that it applies here. So these words need to be read and understood.
Just because you didn't draw the opamp symbol doesn't mean you didn't make one -- and this is pretty close to some current opamp (and transimpedance amp) designs in most of the ways that matter. It just lacks a non inverting input (as did many of the older designs from Philbrick). And it has several things in it doing high pass too -- all those bypass caps but mainly the inductor which probably sets the main corner high pass frequency and the rest don't really matter for skinny pulses in the few uS range.
Since we've made a virtual ground (for AC) with the 2.2 meg feedback from the output, the effective AC *input* impedance there is basically zero, or low anyway -- and hooking even a big leaker across that makes no difference (unless the leaker is noisy, like a diode being hit by X rays! Or one with shot noise or 1/F noise in the leakage), any more than it does in an inverting opamp circuit when you hook a resistor from the - input to ground at the virtual ground point at the minus input. when you do this, you lose the advantages of low noise at high impedance a FET has, but it really doesn't matter that much here. The signal is, gratefully, loud anyway.
Guys, I'm not making this up! Sorry if I sound negative here -- not intended -- but I just can't let factual error pass completely unmolested, as we're not the only people listening here -- some people are just learning electronics, and big misconceptions will lead them astray in later efforts. This is dead center of my expertise. Other things, sure, there are people who know more or have more experience. This stuff, nope.
If you like, I can get a "real" analog chip designer on my team (Joe Sousa who works for LTC in that capacity) to comment further...this is a fine design, but perhaps not as well understood here as it could be. You probably own some of his (working!) designs now and use them every day. He maintains an antique opamp forum too, at http://www.philbrickarchive.org/
BTW. Way not dumb on this stuff. Designs A/D's for a living for LTC, mainly.
I was simply pointing out that going for certain things (like insulation) in extremis was indicative of a misunderstanding and superstition -- neither are good for being able to repeat results like we demand in science.
Sure, no harm keeping things clean, but this is like thinking you need an atomically sharp screwdriver tip to turn a 10-32 screw. You don't! And as I pointed out, shielding may make far more difference, since it has to have 10k to one goodness to even get to 0 dB signal to noise(!), and it's not trivial to get a couple hundred times that to really ignore noises around a fusor. That's one of two reasons to put the preamp right on the tube. The other is that not only is coax not a perfect shield, but it's also a capacitor in parallel to ground, which will "eat" some of the charge signal from the tube.
Remember, these are not working in a range where the resonance of a mismatched cable of reasonable length makes *any* real difference. Off by orders magnitude unless you've got a whole spool of wire in there.
Changing the leakage currents from a ten thousandth of what matters to a millionth really doesn't make much difference. Anything you think that did, there's something else going on -- where the rosin spattered or peanut butter smeared while you were breadboarding or similar could do things like that for example. Of course, you keep things clean no matter how you do it, that's just basic prudence and hygiene, and some things like rosin can be hygroscopic and become quite conductive with time due to that and other effects, like electro-migration (electroplating by another name, only not desired here).
But I've had air wiring fail too -- amazing how a cat hair can enter into the equation....They seem to seek out things like that to bridge, collect dust and dampness, and so on downhill we go.
For a reality check on what I'm saying, take an ohmmeter and measure track to track leakage R on a clean PCB. I want to see the ohmmeter that will do that -- they exist (and I have one), but not the Radio Shack, bench-grade that only go up to 20 megs. The number is going to be giga-ohms in nearly all cases. The number is higher yet if the board has solder mask or a good coating. And a cat hair laying on a coating may not affect that -- it can actually be better than air in that regard, given the dust issues.