| T O P I C R E V I E W |
| Alchemy2 |
Posted - 01/11/2015 : 21:44:28
More freaking math!!! 
Not too bad here... just thought I'd share some good technical info for the group...
Dead time is basically, the MINIMUM time that a GM tube can actually record real counts. In what is known as a non-paralyzable model, it is assumed that the counts can be registered such that the ion cascade in the tube has sufficiently settled to permit the next counting event. However, an event CAN happen during the return to normal operation, and this does affect the true counting of a GM tube detector.
n = m/(1-mT); where n is the TRUE counts, and m is the CPM/CPS seen on the unit, with T being the dead time in microseconds.
So, if I have a 50uS dead time, with m = 1000CPM, then n = 1000/(1-1000*0.000050) = 1052.6 CPM. I have a ~5% error in true counts in this example. The smaller the T, the more accurate the counts are.
So what you do to determine this value for your particular GM detector system is to use what is called a 2-source technique. The sources do NOT need be calibrated. What IS important is that you have them positioned such that when either one is being used alone, the "blank" source is acting like the sources minus their active media. Two calibrated radioisotope sources and an acrylic disk work well, but you could put say, glazed uranium pottery chips in a tin, and have a thorium mantle in a second tin as sources. You just use an empty tin of the same size/shape as the blank when doing only one source! Use your imagination...
Okay, so here's what is done: I use 3 minutes to count the background. Divide the counts seen on the accumulated total counts 9minus what was at start of timing) and divide by 3. This CPM value is mB.
then, use source one, and count for three minutes, allowing for the counter to get to the CPM value first - say 30s before starting the timing. Take the total counts difference between timing, similar to the background. This value is m1.
Repeat with source 2, and this is m2.
Combine sources together and repeat as above. this value is m12.
T = X(1-(1-Z)^0.5)/Y
where; X = m1*m2-mB*m12; Y = m1*m2(mB+m12)-mB*m12(m1+m2); Z = Y(m1+m2-m12-mB)/X^2
If you have a calculator with multiple memories, the math is easy to do. Still, not overly hard to get the numbers.
This method takes into account the counts for varying amounts, and takes the background into account as well.
That's it!
Using the 50uS above example, this means that the MAX unimpeded or max response I can get with a GM tube in this case is ~20000CPS. Most tubes are linear and start to slope off response after around 10-15000CPS. Since 20000 cps (1/.00005) is 300 kCPM, I have no issues with my SBT-11A tubes being able to count such that the CPM values on the counter module are maxed out before the limit is reached. Results will vary with tube, voltage setting, and so on.
Alchemy2
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| 2 L A T E S T R E P L I E S (Newest First) |
| Alchemy2 |
Posted - 01/12/2015 : 21:23:28
Hi Craig!
The dead time comments are valid - that is exactly why there are errors in counts due to the gap between counts.
50uS translates to 20000CPS, or as you say, 1200000CPM. If you look at most curve data on GM tubes, they tend to slope off flat around 10-12 kCPS and by 20 kCPS, the rate is way off linear. Most GM tubes are linear in CPS/CPM to gamma response until ~10000CPS.
While this has nothing to do with tube efficiency, it is useful for recorded counting. Most tubes like the LND 7317 are at best 20% efficient or less. Hotdog SBT-20 tubes re more in the 5-10% regime, and even lower near the threshold keV values like Xrays and soft beta energies.
The formulae take into account some of the statistical and physical issues with determining the dead time, so timed counting is valid for these measurements, because these data include the dead time.
I mainly wanted to validate that the SBT-11A tube system is nominally operating as the extension cable (~450mm) has parasitic capacitance which under non ideal or poor conditions might limit the count rate by swamping the tube's capacitance. In this case, no, as 50uS is rather nominal for GM tubes operating properly, and my evaluation by maxing out the tube and counter electronics means that neither are limiting the tube response up to at least what the counter display can handle.
A2 |
| Craig |
Posted - 01/12/2015 : 20:30:34
* I have to study and think about A2's contribution --before I can respond directly/usefully, but in the meantime:
* Dead time, and the specified top end response of a Geiger counter is an important topic to be aware of when reading a hot sample. Nominally/normally, one would assume that the 50uS of dead time in A2's first example could be divided into 60 seconds to get a response cut-off point of 1,200,000cpm --but that is not the case. _At_ that actual (not the indicated/displayed) rate, the statistical distribution of *clicks* (if they could have all been counted) --would sort out as having half of the clicks coming in at a rate that's too fast (too soon) for the dead time. Since only the slower half would actually get counted, the displayed CPM would be considerably less than (what would have been) the real count.
* As you're probably well aware, Geiger counters miss about 98% of the gamma passing through the G-M tube, as is attested by far higher counts (at least up to a few MeV or so) out of scintillator crystals of similar exposed cross-section. So when I talk "actual count" via a Geiger-Mueller tube here, I only mean the two percent (or so) which can be counted at low levels.
** While over a million CPM, or the specified 350,000cpm top end of a (Medcom/SEI) "Inspector's" response is way much more than those of us doing background radiation monitoring or even hot wipes need to concern ourselves with, look at what happens via an audio/pulse connection (perhaps using the supplied mini-plug to USB cable). The square wave pulse output of my old Inspector is a millisecond wide (0.001 second, or 1000 uS) --such that half the (would be) count to a PC based data logging program is "piled up" and lost at 60,000cpm (but that's still plenty high for most of us).
* Another caution is that the initial CPS or CPM displays of nearly all Geiger counters that I'm aware of are based on a very short sampling period, which gets shorter still at higher CPM rates. While this is a good feature for making a fast radiation disaster survey, I strongly suggest that you only do timed counts for background monitoring --or as you might extract same from a data logging spreadsheet.
Craig
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