On Doug's advice, I bought a Russian type BETA-2 pancake Geiger tubes on eBay from seller annakozub. Unfortunately, these tubes are no longer available.
This tube is the kind that is shaped like a shallow disk measuring 56mm in diameter and 8mm thick. There is a thin mica window specified to be 10-14u thick. The case is the cathode, and the anode is a spiral grille. The 15cm2 window is specified to capture 65% of incident beta radiation. I confirmed the specified 1pps background pulse rate. See the attached english language data sheet that came with the tube.
This tube runs at 400VDC with a 2Meg load. This load resistor was suggested by Doug. When the tube fires the voltage at the anode drops to 100V and pulls 150uA through the 2 Meg load. Doug thinks the 2Meg load might still be too stiff, considering the low 100V on-state of the tube.
I built a power supply around a CCFL inverter from http://www.goldmine-elec.com g16565. The TDK transformer has the part number TDK 23 TN 16EPC-T06
It takes about 2.5VDC to produce a rectified and filtered 400VDC, and the current draw is 65mA under a 5Meg load. Under this load, the efficiency is only ~50%.
If you want to build one of these, Doug recommends a more efficient CCFL supply from Digi-Key.
The CCFL's work great for me,
and I like the JKL types, which use the proper square loop core material
and draw far less current in that Royer oscillator design than the dumb
ones from TDK -- good battery life. Factor about 4, it's a pretty serious
mistake that TDK made there. 289-1025 is the good one at digikey. I buy
those in bulk and they work down to a volt or so (with 300v out of a doubler).
I can send you more super good fast diodes if you need them, they are rare,
I have no idea if the camera ones are any good -- these are "perfect".
You got me curious to find out how good these disposable camera diodes are. I just
measured the input current of one of these converters running from 5V
without load, and got 82mA. Then I added a halfwave rectifier to the
output, and the current did not budge from 82mA. Then I measured the
DC voltage that was developed as 840VDC with a 10Meg DVM and the input
current to the converter went to 97.2mA. These diodes may not be
perfect, but they certainly are transparent when rectifying 840VDC
peaks at 10s of kHz, which peaks are likely to be symmetric, thus
standing off 1.6kV.
I added a three transistor LDO (Low Drop Out) linear regulator circuit that takes unregulated 3V from 2 Alkaline C cells and drives the CCFL module around 2.5V to obtain a regulated 400V at the output. The three transistors are wired in a triple PNP Darlington sequence.
The triple PNP Darlington chain does double duty: it senses the voltage dips in the 400V supply that are caused by the 150uA firing of the Geiger tube to drive the TOC-TOC speaker, and also senses the average voltage of the 400V rail for regulation.
The first of two 2N3906 transistors gives enough current gain to get the input current down to a couple hundred nA. The second of these 2N3906 continues the current gain and drives the TOC-TOC speaker with it's free leg - I mean collector. The last PNP is a TIP32 with collector saturation under 200mV at a 100mA load and at 80% drop in beta.
The little flat 1"x0.2" speaker has an 8_Ohm impedance and takes 125ma pulses from the middle PNP to make a tic-tic sound. A special resonant tic-2-TOC converter greatly amplifies the sound. Much of the energy in the 100us pulses is inaudible, until the tic-2-TOC converter makes it audible.
A 51V Zener serves as the reference against which to regulate the 400V output. A quiet 50-60V neon bulb would have worked as a reference too, perhaps with an adjsustment of the resistors connected to the trimpot. The remaining network of resistors forms the feedback bridge. The 10MEG resistor driving the zener may have a loose 20% tolerance. The other leg in the resistor bridge with 7.5Meg+200k trim pot+1Meg sets the 400V output.
The pulse output at the collector of the middle PNP with the 8Ohm speaker load has a 2V peak a few us wide, that drops to 1V for 100us then turns off. This output seems to work fine driving my frequency counter. You will need a counter that counts down to 1Hz (1pps) to monitor background radiation at rest.
One last thing to consider is that this regulator topology is not necessarily self starting, but it is easy to make it start reliably. I chose to add a 470uF/6.3V in parallel with the output TIP32 PNP to serve as the quick-start for the power rail of CCFL inverter. A resistor in parallel with the collector-emitter pins of the TIP32 may also be used to supply a minimum operating power for the CCFL inverter. 500_Ohms was enough for my CCFL. A more efficient CCFL can live with a larger resistor. Just be sure that the resistor does not supply more than about half the normal running current of the CCFL, so the regulator can do it's job.
The 470uF cap at the output PNP also serves to choke out the pulses that are amplified by the Darlington chain.
If you want to use rechargeable batteries, I single 3.6V Li-ION cell or three NiMH cells in series for 3.75V should be used. A wall wart from 3V to 6V will work as an alternate to the batteries, but the dissipation on the TIP32 goes up to 250mW from a 6V supply.
Keep in mind that the Geiger tube cathode/case operates at -50V below the positive battery terminal, and the anode operates 350V above the positive battery terminal. So, don't ground the tube case.