Archive for July 21st, 2015
Given this hairball circuit:
Feeding the output voltage into the ‘scope, with AC coupling to strip off the DC bias, produces this:
Those cute little spikes seem to be gamma ray ionization events: they are always positive-going, there are no similar negative-going pulses, they occur irregularly at a few per second with occasional clusters, and generally seem about like random radioactive events. The picture shows a particularly busy interval; mostly, nothing happens and the baseline voltage wobbles around in a low frequency rumble.
For what it’s worth, the shielding around the circuit completely eliminates not only 60 Hz interference, but everything else, too: astonishingly good results from a fairly simple layout.
Taking a closer look at one pulse:
(Vigorous handwaving begins)
The tallest spikes are typically 20 mV above the baseline, corresponding to peak output current of 20 mV / 12 kΩ = 1.5 µA and a chamber current of 1.5 µA / 100×106 = 15 fA.
They’re generally 5 ms wide, which is orders of magnitude longer than the actual ion generation time, but the area under that spike should be more-or-less proportional to the area under the actual impulse.
If you grant that and agree those pulses look mostly triangular, their integral is:
1/2 x 15 fA x 5 ms = 40 fA·ms = 40 aC
That’s “a” for “atto” =10-18 = a billionth of a billionth = hardly anything at all.
Indeed, seeing as how one coulomb contains 6.2×1018 electron charges, that pulse represents 250 ion pairs, at least assuming a zero-current baseline.
Gamma rays arrive with various energies, produce ionization trails of various lengths, and don’t necessarily traverse the entire chamber, so the pulses have various heights & widths; you can see smaller pulses sticking up out of the grass in the first scope shot. Assuming all those average out to five “big” pulses every second, the chamber collector electrode passes 200 aC/s into the transistor base → 200 aA → 0.20 fA. At 1 fA per 100 µR/h, that’s 20 µR/h of gamma background.
Frankly, I don’t believe any of that to within an order of magnitude, but given that a free-air monitor counting alpha + beta + gamma background in NYC seems to be averaging 10-ish µR/h, it’s not entirely out of line.
π x 4.52 x 3.5 = 220 cm3
So assuming a somewhat unreasonably large pure-gamma dose of 10 µR/h in that volume will produce:
10x10-6 x 2.08x109 x 220 = 4600x103 ion pairs/h = 1300 ion pairs/s
That’s about five “big pulses” per second, under the stack of assumptions thus far, and seems absurdly close.
An old NIST report on Calibration of X-Ray and Gamma-Ray Measuring Instruments says that 1 R/s (that’s per second, not per hour) produces a current of 300 pA/cm3 in an “ideal ionization chamber”. Scaling that down to 10 µR/h and up to the chamber volume gives an average current of 180 aA. That’s absurdly close, too.
Note bene: Because 1 C = 6.241×1018 ion pairs, 2.08×109 ion pairs is 333×10-12 C and, if you do that in one second, you get 333 pA of current from your ideal 1 cm3 ionization chamber. Those two approaches should be equally close.
(Vigorous handwaving ends)
Again, I don’t trust any of the values to within an order of magnitude and surely made a major blunder in running some of the numbers, but the results seem encouraging.
The coaxial cable’s capacitance could explain why the pulses look like triangles: the capacitance integrates a rectangular current pulse into a voltage ramp. The cable measures 200 pF and the scope input adds 13 pF, but let’s call it 200 pF across the 12 kΩ emitter resistor. Raising the voltage across that capacitance by 20 mV in 2 ms requires a current of:
200x10-12 x (20 mV / 2 ms) = 2 nA
Dividing that by 100×106 gives a chamber current pulse of 20×10-18 = 20 aA: three orders of magnitude less than the original guesstimate. That suggests the (handwaved) 15 fA chamber current, amplified by the absurd gain of two stacked Darlingtons, easily drives the cable capacitance. Something else causes the ramp.
The chamber itself has 10 pF capacitance, but it’s not clear to me how (or if) that enters into the proceedings. The entire collection of ions appears in mid-air, as if by magic, whereupon the +24 V chamber bias voltage draws them (well, the positive ones, anyway) to the transistor base without appreciable voltage change.
Perhaps the triangle represents the actual arrival of the ions: a few at first from the near side of the trail, a big bunch from the main trail, stragglers from the far side, then tapering off back to the baseline.
That’s definitely more than anyone should infer from a glitch produced by a pair of transistors…