"Decades" expanation.
GM tubes have no trouble counting at low rates, a few counts per second. As you've seen in the scope plots, the "recovery" time is a few uS up to about 10 uS. The arrival time is also random. When you get close to the count rates that are 1/recovery time- pulses start to "pile up" as the tube is not active during quench. This is called dead time. If you keep increasing the radiation, the tube won't ever get a chance to recover and will actually show a zero count rate eventually- kind of bad and a major problem with counting GM tubes mehtods. A good meter will detect this condition and indicate full scale or over-range etc but many cheap ones don't. Another problem is that you'll wear out the tube pretty fast. A tube has a lifetime measured in total counts, it might be 10^12 total counts but its finite. The quench gas gets used up a little on each recovery.
For a standard counting GM circuit, you can count from a few counts per second (background) up to something like 1/20 of the deadtime rate- about 5 Khz without things getting non linear. This is a 3.5 decade dynamic range. This is fine for many purposes but can give false low readings in high fields and forces you to have 2 meters, a background responding meter and a high range meter. Every one likes background responding meters because you can easily tell they're working. A high range meter will never read anything unless its in a high field- you can never be sure its working. It's "noise floor" is above background so it will just read its minimum level.
If you use techniques like time to count, etc. that setup the bias on the tube and wait for a single count- you can avoid a of the dead time problems and get an equivalent dynamic range of 5 decades, 1 CPS to equivalent of 1e6 CPS- this is a 1 uS of average time to count- 6 "decades". Some counting statistic corrections need to be thought through to give accurate results.
More advanced techniques like Extended range counting that I worked on and patented can improve this further to 9 or so decades by using some fancy statistics and electronics that operate the tube even beyond the time to count range. Watching the tube coming out of quench on a fast rising edge and looking at the statistics of a count happening in this slew time. The time is very small- about a microsecond. Its somewhat complicated- you can read the patents from the early 90's- SAIC/Leidos was the assignee and Ken Valentine(RIP) and John M. Wettroth (me) are listed as inventors on most. Dust off your fancy math texts, it does gets deep- all I can remember today is that it relied on Parseval's theorem. Have fun.
The Extended Range Counting Technique (ERG) was invented under a contract for the US Navy for the Multifunction Radiac set- the current "end all be all" survey instrument in the fleet today. The idea was to give a sailor one instrument that would just read what was there from background up to rates that would kill you in an hour. All are possible on a Nuclear Warship or Sub. I haven't thought of a better way to do this since the early 90's so maybe this is it.
What everyone would like to have is meter that reads properly in any field. Generally there are low rate meters like GM tube friskers that are used at low rates and high rate techniques like Ion chamber meters that measure average ion current in a non avalanching gas for high rates. Victoreen has made very low range Ion Chamber meters (455) that do a pretty good job of measuring background and are probably the closest to a perfect meter- probably 6 "decades". In general, most techniques cover a a few decade range and used together they give the full range required. It takes a fair amount of sophistication to keep all this high range/low range in mind in a Nuclear emergency. You would like to give a basic user something that "just worked".
"All" sensors have some working dynamic range - its especially pernicious with radiation detectors because the rates are random and the consequence can be dire.
I revised this later to correct some inconsistencies and perhaps make it clearer. A rich topic.
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