First, you need to acquire some Geiger-Müller Tubes (at least 2 if you'd like to build a cosmic ray detector). I chose the SBM 20 tubes for $25 each because I could order them off of Amazon, but if you're willing to take a chance on Ebay, you can get similar tubes in the $10-$20 price range. Fun fact: I read that a lot of these tubes were created by the Soviet Union during the Cold War.

At a high level, Geiger-Müller Tubes work as follows: the tube is filled with an inert gas like Helium and Argon (These are examples of noble gases that are unlikely to undergo reactions). When an incoming high energy particle entires the tube, some of the gas may be ionized. At least a few hundred volts are applied across the tube, and the resulting electric field (remember that electric field is a function of applied voltage) causes positive ions to move towards the cathode of the tube and free electrons to drift towards the anode. As these ions and electrons move, if the electric field is strong enough, they will cause further collisions and therefore further ionization events in the tube. The ionization of the gas lasts on the order of a few microseconds, and when the electrons reach the tube's anode wire a current pulse (which in our case we measure as a roughly 1.5 volt pulse) we can process the resulting signal as a hit. At this point the there is a high positive charge near the anode (due to the positive ions that have accumulated there). This weakens the electric field and the avalanche of ionizations will terminate. The tube will settle back into its initial state until another incoming ionization particle sets off an avalanche again.

(note: avalanche image from http://en.wikipedia.org/wiki/Townsend_discharge)

We need to provide the GM tube with a high voltage across its anode and cathode for this process to kick off. To do so, I'll use boost converter circuitry that I found here. (You can see my relevant circuitry in an included image on this page). The '555 timer is wired in astable mode such that it outputs pulses at it's Q output pin. C1, D1, R1, and R2 all control the amplitude of the pulses, but for our application I don't believe that the values you select will matter too much. Whenever the '555 timer outputs a positive pulse at Q, the transistor Q2 attached to Q will turk on, allowing current to flow through the inductor. At a certain point, the voltage at Q1's gate will rise enough to turn Q1 on. When Q1 turns on, the reset pin of the '555 will be triggered (note that it is active low). This causes the output at Q to go low, which causes Q2 to shut off. When Q2 shuts off, the inductor will do what inductors do: attempt to maintain the current that was previously flowing through it. The voltage across the inductor will spike, and a burst of current will flow through the inductor, through diode 2 (the diode prevents any current from flowing backwards and damaging the inductor) and into C2, where a high voltage will accumulate. R5 is a potentiometer. The one that I chose ranges from 0 to 100 ohms. The value of R5 determines the point at which Q1 is turned on, which in turn determines how much current the inductor will seek to preserve and therefore how big a voltage spike it will experience. In summary, the potentiometer's value determines what voltage level you will achieve. If you follow my circuit exactly, you should be able to range from about 30 volts to 500 volts stored in C2.

Note: Instead of using a '555 timer (which my professor called outdated), you could instead use an output pin of a micro-controller to provide pulses (PWM).

It is important that any parts that will be exposed to high voltage are rated appropriately. Here are the key components I used for the HV supply and their Digikey listings.

'555: LMC555CMX ($1.07 each)

Diode D2: 641-1018-1-ND (1 KV, 1 Amp) ($0.27 each)

HV Capacitors (C2, C3): 709-1039-1-ND (1 KV) ($0.48 each)

Inductor: 445-3823-ND (10 MH, 410 mA, 3.41 Ohm) ($3.02 each)

Potentiometer: CT2154-ND ($5.34 each)

The other resistors, capacitors, and diodes hooked to the '555 will not be exposed to high voltage and therefore you can use more off of the shelf components.

Some important notes on debugging:

The current flowing to the GM tubes is extremely small. If you attempt to measure the voltage after the diode with a standard multimeter or oscilloscope, your multimeter/oscilloscope will load the circuit and you will not be able to detect the high voltage! I got around this by measuring *before* D2. There is a lower impedance at this point of the circuit and therefore you will be able to see the high voltage on a standard oscilloscope. Another approach would be to get a very large resistor (on the order of 1 Giga-ohm and place it in series with your oscilloscope).

When debugging, start with the potentiometer turned to its lowest value, and then slowly turn it and watch the resulting voltage. If there is a point at which the voltage suddenly drops down again, it could be that one of your parts is failing (double check that everything is soldered well and that your components are rated for high enough voltage and current). It could also be that your measuring device is still loading the circuit too much.

Next, we'll wire up the tubes to the HV supply!