Memo on photomultiplier     Hartmut Gemmeke 8.11.98

1. Gain adjustment

For online trigger and data reduction we want an adjustment of the gain
of all channels to a precision of better than 5%. We have two
possibilities to achieve the gain adjustment of a photomultiplier
channel, on the one hand by HV variation at the PMT on the other hand by

a variable gain preamplifier. A cheap possibility to generate variable
HV is to build a Greiner or Cock Craft Walton generator. But this method

is sorrily not possible to be used due to the high noise level connected

to these generators. The high dynamic range of signals (16 bit) seeks
for a very low noise level to guarantee especially for small signals
still a reasonable (e.g. 2% for an 8 bit signal) signal to noise level.
Other commercial computer controlled HV systems are relative expensive
(Super Kamiokande ~ 75$/channel, without cables). These systems would
have a sufficient signal to noise ratio. We can also use a collective
HV-supply per mirror (400 PMTs) with 20 PMT on one cable tree and one
fuse. Such a system will be very cheap (~ 17$/channel) including
cabling. But we have to have in mind the extra costs to build a variable

gain preamplifier (~ 5$/channel extra costs). The gain of the PMTs have
to be low enough (< 5*10**4) to protect passively the photomultiplier
before burn out by moon or other light shocks. In the case of HV gain
control we may do without a preamplifier if we implement a fast control
of the gain (spare ~ 8$ per channel). Also this solution with a higher
gain of the photomultiplier is not allowed because of the than shorter
lifetime of the PMTs, see next chapter. But a collective supply and
variable preamplifier will be in either case by 45$ per channel cheaper
than a variable HV solution.


2. Photomultiplier Lifetime

The lifetime of photomultiplier is limited by the collected charge at
the anode. The handbook of Philips on PMTs give lifetimes of collected
charges of 300 to 1000 C. Paul Previtera gave a value of 540 C for the
XP 3062 (obtained from Philips). To calculate from this value a useable
gain for the PMT we need some parameters from the experiment:

* Lifetime of AUGER ~ 15 years

* DC input current due to noise should be in the order of Iinp ~ 2.7
pe/100ns = 4.3 pA (value of Bruce Dawson from HighRes experience). A
second order star will increase light input by a factor 2.65, the
scattering light of the moon by a similar order of magnitude, and the
full moon by a factor 30 yielding a maximum input current of 129 pA.
Including these cases the average DC input current might be more in the
range of 10 pA.

* Minimum gain (5*10**4) necessary to build a simple preamplifier
with good  signal to noise ratio and 5 to 10 ns risetime.I assume the
pulses will be integrated (100ns) on a switched capacitor in a pipeline
with the Flash ADC. The short risetime of the preamplifier is necessary
to yield sufficient digital Cerenkov suppression. An array for switched
capacitors are necessary. Two for low and high gain. Furthermore we have

to double this pair for measurement and readout.

* The collected charge due to muons, showers and Cerenkov radiation I
assume as negligible against the DC background. Roughly 200 Hz * 70 pe +

10 Hz * 1000 pe < 0.01pA

Under these assumptions we get per PMT a charge Q of 120 C safely a
factor 4.5 off from the above given ageing limit:

Q =<Iinp> * gainPM * fraction of day operational * seconds per year *
lifetime of AUGER

=10pe / 100ns * 1.6*10**-19 C/pe * 5*10**4 * 1/3 * 3*10**7 s/year * 15
years = 120 C.


3. Signal to Noise Ratio (S/N)

The signal to noise ratio of the PMT cathode-signal or the inverse of it

for a given number of photoelectrons npe(t) in a time interval t is
determined by the bandwidth df: N/S     =   sqrt (2 * df/(npe(t)/t)).
This formula simplifies further if we assume a switched integrator to
N/S     =    sqrt(1/npe(t)). In the case of an approximately gaussian
fluctuation of the background we get for the energy resolution RE an
about 2.36 higher value: RE      =    dE/E    =    2.36 / sqrt(npe(t).
For the signal to noise ratio at the anode of the PMT we have to include

the statistics of the photomultiplier. This statistical error can easily

be measured by the relative SER resolution of the PMT and yields an
additional factor for the inverse S/N or RE: N/S     =
sqrt((1+SER**2)/npe(t)). For the XP 3062 the obtainable SER will be
better than 1.4 (my best guess is 1.2) and therefore the inverse S/N
will be in the range of 1.7/sqrt(npe(t)). For the background of 2.7 pe
we get an N/S = 1.04 and for a box car sum over 10 samples we get N/S =
0.33, a sufficient good resolution if we want to trigger at more than 66

pe in the sum trigger. This threshold is a rough estimate depending on
the actual parameters in the experiment. Its momentary value is given by

the condition to reduce the triggers from 10 MHz to 200 Hz, assuming a
gaussian distribution of the noise around 27 and a N/S = 0.33.


4. PMT-type

To guarantee a good single photoelectron resolution (SER) the gain of
the first two dynodes of a PMT should be high. That can be achieved by
covering also the first two dynodes with bialkali, as done in the XP
3062 of Philips. An 8 dynodes tube is very much sufficient to obtain the

necessary gain of 5*10**4 and will have a gain reserve of 20 for ageing.

That meeans also a tube with 6 dynodes may be sufficient. A typical gain

distribution of a 8 stage tube at 1100 V in our application would be 14,

7, 3, ..., 3 from dynode1 to dynode8, summing up to a total gain of
7*10**4.


5. Linearity of PMT Output

As was pointed out by Daniel Camin within our collaboration a passive
divider chain has a strong dependency on the DC-load of the input. He
made a nice Spice model of the divider and includes the PMT as a
distributed current gain chain. He got a strong non-linear 2% behaviour
of this model if the output current exceeds roughly 1 % of the divider
current. Therefore he concludes the necessity of an active divider. That

is so far correct within this model.

But if we limit our gain to values around 5*10**4 we have as maximum DC
anode current at moonshine 5*10**4 < = 6.5uA. The medium current value
due to cosmics will be clearly below this value.

If we allow maximum 3% deviation from linearity, we may work also with a

passive divider and 100uA divider current. But we have to use as a trick

(to get not a 4% deviation) a relative small voltage between last dynode

and anode. I simulate the gain behaviour of dynodes by an 0.7 exponent
at dynode difference-voltages.

Also an active divider is fine. I have only some old arguments about the

necessary (temperature) stable current gain Beta (30-40) in my back
head, which was necessary to guarantee stable operation and which was
not available for low cost application. Perhaps Daniel you may supply me

with some realistic HV-transistor data for my simulations. Are these
transistors also as SMD-versions available?


6.Statistics of PMT-noise signals

If we have a Poisson statistical background in the switched integrator
with a mean value of m=2.7 pe we get the following probabilities and
integrated probabilities to observe 0 to 7 photoelectrons (also given
for m=5.4 pe):

#of pe                0      1      2       3      4     5      6     7
Pi(m=2,7) [%] 6.7 18.1 24.5  22.0 14.9 8.0  3.6   1.4
sum(p) [%]      6.7 24.9 49.4  71.4 86.3 94.3 98.0 99.4
Pi(m=5.4) [%] 0.5  2.4  6.6   11.8 16.0 17.3 15.6 12.
sum(p) [%]      0.5   2.9  9.5   21.3 37.3 54.6 70.2 82.2

With some special coding or normal data compression we can spare a lot
of
space and time in data transmission. Also in case of a cosmic trigger
most of the pixel of a triggered mirror and neighbour minor will contain

only a low number of counts.