Determining the Optimum High Voltage for PMT s

Transcription

1 Determining the Optimum High Voltage for PMT s Bertrand H. J. Biritz April 4, 006 In any experiment which uses photo-multiplier tubes, one needs to determine the optimum high voltage for each tube. Optimum in this case means amplifying as much signal as possible while still keeping the noise as low as possible. The three tests to be discussed here are: counting, dual discriminator and coincidence. As is to be expected not one test is the ultimate test. Instead all three need to be used in order to determine the optimum high voltage for the PMT. There is the question of how to begin, especially as the discriminator setting affects the outcome of the test. Have the discriminator threshold too low and you will not be able to distinguish signal from noise. While having it too high would result in a much smaller signal rate than can actually be achieved. In either case the optimum high voltage would not be very reliable. A good starting point then is to take the output of the PMT and look at it with an oscilloscope. Increase the high voltage until you start to see a nice signal typically on the order of 50 to 100 mv at around 1,00 V. Then set the discriminator such that the signal is above the threshold while the noise isn t. To a certain extent you are biasing the results, but only by about 100 V which is around 10% of you high voltage. There are two more remarks which need to be made here. First, most calibration runs take a long time. If at the end of the run one noticed the test had not been set up properly, then one could potential have wasted an entire hour or maybe even two! There are a lot of test to be performed in a short amount of time, so the order of the day is: haste not waste. Make sure everything is set up before starting a run, taking an extra two minutes to check everything could save you an hour later on. You should always write down the thresholds of the discriminators, along with their output pulse widths and whether or not you are in Burst Guard mode. Also, for the coincidence test you have to write down the high voltages of the other counters. Lastly, in each test you will be incrementing the high voltage of one or more PMT s and then measuring the number of events in a certain time interval. For the counting and dual discriminator test this time interval varies during the run, while for the coincidence test it will remain fixed. In most cases you will not be actually using the time interval data. However, in order to compare PMT s you would need to divide the count by the time interval as it varied for each PMT. In any case, it is always better to have too much data than too little.

2 180F Lab notes by Bertrand H.J. Biritz 1 Counting This test is the simplest of all three, both in setting up and also evaluating the data. Just connect the output of the discriminator to a scaler and record how many counts you have during a certain time interval at a particular high voltage. Then increment the high voltage by 5 V and count again. Then graph the logarithm of the count versus high voltage. This should be done until the count just skyrockets after going past some voltage value. At that point the dynodes of the tube are at such a high potential that electrons are popping out at random. The optimum voltage is found where there is a plateau in the graph. ow the question is, for how long should one count? Well, that depends upon how accurately you want your count to be. For this test the percentage uncertainty goes like one over root, i.e. D 1 p or D p Plugging in some numbers: / As can be seen from the table you need to get at least 100 counts in order to have a 10% uncertainty in that value. 1,000 counts gets you down to 3% while 10,000 finally puts you at the 1% level. How is this affected by taking the logarithm of the count? The uncertainty L would given by L D dlog d D D 1 p

3 180F Lab notes by Bertrand H.J. Biritz 3 Which would make the table L ow back to the question of how long one should count. At relatively low high voltages (1,00 V to 1,400 V) the count rate will also be low, so it will take some time to reach even the 10% uncertainty limit 0 minutes maybe. However, this rapidly decreases to a count time of one minute. Towards the end, 10 seconds are even enough to get to the 1% level. log(counts) High Voltage, kv

4 180F Lab notes by Bertrand H.J. Biritz 4 The purpose of this test is to mainly see whether there are light leaks in the counters. This does not mean the test has to be performed both with the lights on and off. As can be seen from the graphs below a light leak is easily seen. log(counts) Lights On Lights Off High Voltage, kv Dual Discriminator This test is similar to the previous one, with the only difference being two different discriminator threshold s are used called low and high for reason s which will become clear shortly. Also, one needs to use a fan out unit in order to apply the PMT signal to the discriminators. One yet again measures the count for a certain period of time and then increments the high voltage by 5 V. As for the graph, this time one plots the ratio of the low discriminator count divided by the high discriminator count versus high voltage. The optimum high voltage is found where the ratio is at it s minimum note that I did not say unity. The obvious question is what the two discriminator thresholds should be. The low threshold should be the setting you eye-balled from the initial set-up with the oscilloscope. 50 mv higher is what the high threshold should be set to. This difference in the threshold s was empirically determined by myself via trial and error. As in the previous test, one needs to know the uncertainty DD. This time around we are dealing with a ratio of counts, so H! ; where L and H are the low and high counts and L and H are the uncertainty in the low and high count respectively.

5 180F Lab notes by Bertrand H.J. Biritz 5 Which becomes DD D 1 H L!! C L H H : ow if we divide both sides by.dd/.l=h / in order to get the percentage uncertainties (squared)! DD! L D C H ; DD L H but L =L D 1= p L and H =H D 1= p H so we have DD DD D 1 L C 1 H ; which then gives us the percentage uncertainty of the ratio given the counts L and H r DD 1 DD D L C 1 H : The uncertainty in H will always be higher than that of L simply because of the experiment. The lower threshold counter will see more events than the higher counter. If we plug in some percentage uncertainties L =L H =H DD =DD As in the case with the previous test: initially you need to count for a longer time in order to get the uncertainty reasonable. After the first few high voltage increments though the time can be shortened, until at the end the time interval is back down to ten seconds.

6 180F Lab notes by Bertrand H.J. Biritz 6 50/ High Voltage, kv 3 Coincidence Both of the previous tests could not measure the relative efficiency of one counter with respect to another. Instead they just measured how many particles went through the detector. For actual data taking we need to know the efficiency of the entire system though. This is the purpose of the coincidence test, which is a little more complicated. What one does is choose counters close to one another and then form two coincidences. The first is of all counters while the second is of the counter(s) which is(are) already optimized. This means all but one counter is at or near the optimum high voltage while the counter to be optimized has its voltage changed. For the graph one plots the ratio of all counters to optimized counters versus the optimizing high voltage. This allows you to see how many particles a particular counter detects relative to the others and hence its efficiency. At the optimum high voltage the ratio will plateau and remain constant even when the high voltage further increased. This plateau is not necessarily at 1, it might be as low as 0.5. There are actually two types of coincidence test: two counter coincidence and sandwich technique. As the name suggests the former uses only two counters, while the later uses a minimum of three to a maximum of four (which is a limited due to hardware constraints). Hence there are numerous combinations and permutations that can be done. The above is all fine and good, but a picture always helps. All three experiments have the fundamental set-up shown below (with possible an extra counter somewhere). Say you want to find the optimum high voltage for counter C. With the two counter coincidence you can have the combinations C1C or CC3, where you would form the ratios C1C/C1

7 180F Lab notes by Bertrand H.J. Biritz 7 or CC3/C3. For the sandwich technique you would form the ratio C1CC3/C1C3. As there are three coincidence units per slot one is actually able to do the sandwich and one of the two counter tests at the same time one just needs four scalars. If instead you want to optimize C3 you could form the ratios: CC3/C or C1CC3/C1C. There are two things to note. First, CC3/C is not the same as CC3/C3. Second, C1C3/C1 would not be a good test as the counters are far apart instead one uses C1CC3/C1C. As in the previous two test one needs to have error bars associated with each ratio measurement. This time we use the binomial error, which means the uncertainty in the efficiency is given by r.1 / D where is the number of events the optimized counter(s) see. Plugging in some numbers (note: the numerator is symmetric about D 0:5) so in order to get an uncertainty of 1% with an efficiency of 90% one needs to collect at least 900 events. As a final note, even though the ratio reaches a plateau which is independent of high voltage, one still needs to take noise into account. When comparing with the plot of the counting test one can see after some high voltage the counter is amplifying noise as well, which is not where you want to operate the PMT. Hence one needs to operate at the beginning of the plateau.

8 180F Lab notes by Bertrand H.J. Biritz 8 c1cc3/c1c High Voltage, kv