Understanding of the
Proportional Counter Pulse
ShapeAndrew Durocher
RARAF
Abstract
Overall purpose is to create an effective way
to extract information from x-ray pulses in
a proportional counter created from an x-
ray microbeam which has pulses arrive in
short bursts of 200 nanoseconds long
about 10 x-rays per pulse.
What is a proportional counter?
• A proportional counter is a type of high
speed ionization chamber used to amplify
signals that contain too few electrons to
observe directly.
• Specifically measuring the voltage, from
the observation a proportional relation to
initial charge inputted into the counter can
be obtained
Geometry of a Proportional Counter
• There is an outer cylinder (cathode) with a negative voltage
• Inside there is a helix with a positive voltage
• Inside that is a central wire (anode) with a much higher positive voltage.
• With this system, electrons inside the counter will drift towards the center while positively charged ions will drift outwards toward the outer cylinder.
Multiplication/Avalanche
• When electrons drift close
enough to the anode.
Approximately the radius
of the anode in distance
the multiplication will start
• This avalanche will create
a large number of
electrons and positive
ions that will be
somewhere around 10^4
times the initial charge.
Operating Regions and
Gain vs. Voltage
• The chamber
geometry, filling gas
and applied voltage
determines the
multiplication.
• There are several
operating regions,
depending on applied
voltage, which are
shown in the figure.
Chamber Potential
for a Single Ion Pair
• P(t) =
• -e is the charge of the electron which is
collected on the anode at time zero. q+(t)
is the charge induced by the positive ion at
its position which is a function of time. C is
the capacity of the chamber.
C
(t)q + e- +
Pulse Shape Equation
for a Single Ion Pair
• P(t) =
• V is the voltage difference between the
helix and the anode, K is the ionic mobility
based off the pressure and gas type inside
the proportional counter.
( )
)/ln(2
1ln(b/a)a
2VKtln e-
2
abC
+
Electron signal and Mirror Charge
• Once multiplication has occurred, the electrons have reached the anode, and created a voltage step
• Though it is not first noticeable due to the mirror charge created by the positive ions
• The positive ions quickly move away due to the charge of the E field and the pulse is created
Equation simplification
• P(t)=Aln( +1)
• A =
• =
• A and are treated as experimental
constants
τ
t
τ
)/ln(2 abC
q −
τVK
aba
2
)/ln(2
Raw data of an alpha particle
Important Raw Data
-4.00E-03
-2.00E-03
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
1.00E-02
-8.0000E-
06
-7.0000E-
06
-6.0000E-
06
-5.0000E-
06
-4.0000E-
06
-3.0000E-
06
-2.0000E-
06
-1.0000E-
06
0.0000E+0
0
1.0000E-06
Raw Data
Raw Data
-6.00E-03
-4.00E-03
-2.00E-03
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
1.00E-02
-1.20E-05 -1.10E-05 -1.00E-05 -9.00E-06 -8.00E-06 -7.00E-06 -6.00E-06 -5.00E-06 -4.00E-06
Series
1
Smoothing the data
• Using excel we took
all the data points,
and fit the data to a
linear least squares
curve also known as
a sliding average
• We use this new
curve as our pulse
Converting the Raw Data
-4.00E-03
-2.00E-03
0.00E+00
2.00E-03
4.00E-03
6.00E-03
8.00E-03
1.00E-02
-8.0000E-
06
-7.0000E-
06
-6.0000E-
06
-5.0000E-
06
-4.0000E-
06
-3.0000E-
06
-2.0000E-
06
-1.0000E-
06
0.0000E+0
0
1.0000E-
06
RAW
LINEST
Our equation compared with data
• This is a graph
showing the how
similar data curve of
an alpha particle is
compared to our
theoretical equation
Alpha Particle and Theory Equation
-0.002
-0.001
0
0.001
0.002
0.003
0.004
0.005
0.006
0.007
0.008
0.009
0.01
-7.0000E-06 -6.8000E-06 -6.6000E-06 -6.4000E-06 -6.2000E-06 -6.0000E-06 -5.8000E-06 -5.6000E-06
lneq
LINEST
Guide Line
• In the initial rise approximately 50-60% of
the total voltage is obtained, if a pulse
looks has multiple humps, by measuring
the height and the number of humps it will
be possible to measure the input x-ray’s
energy, as well as the number of x-ray’s
within the pulse.
Pulse shape combination
• Unfortunately, it is not
guaranteed that pulses
will come at a min of
intervals of 5 nano
seconds, meaning if two
pulses arrive too close
together, they could be
read as one pulse instead
of 2. Our goal is to see
the initial rise of the first
pulse completely before
seeing it jump again.
Good result
0
2
4
6
8
10
12
0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6
2 Pulses
Bad Result
0
0.00001
0.00002
0.00003
0.00004
0.00005
0.00006
0.00007
0.00008
0.00009
0 0.00005 0.0001 0.00015 0.0002 0.00025 0.0003 0.00035 0.0004 0.00045
2 Pulses
Derivative of equation
• Taking our simplified equation, P(t) = A*ln(1+t/ to), then taking the derivative of this, which will give an expression of P(t) rise changes in time, so we can see how to make the initial rise move quickest.
• dP(t)/dt = (A/ to)/(1+t/ to)
• As seen to the right when you plot this new equation and play with A and to you see that changing A changes how quickly the pulse shape rises. So we want a small A, meaning a large b/a ratio.
0
0.0000002
0.0000004
0.0000006
0.0000008
0.000001
0.0000012
0 0.000005 0.00001 0.000015 0.00002 0.000025
derivative of function
derivative with small To
derivative of small A
Conclusion
• Though I was never able to actually test
my work on the actual x-ray microbeam
• I was able to fully understand how the
proportional counter works and advise the
best settings for the proportional counter
to be under.
• Create a system guide line for extracting
results from the data that will be collected
Acknowledgements
• David J. Brenner
• Gerhard Randers-Pehrson
• Stephen A. Marino
• Allen Bigelow
• Guy Y. Garty
• Andrew Harken
• Sasha Lyulko
• Yanping Xu
References
• D.H. Wilkinson, (1950). Ionization
Chambers & Counters. London:
Cambridge University Press. p27-255.
• Frank H. Attix, William C. Roesch, Eugene
Tochilin (1966). Radiation Dosimetry. New
York and London: Academic Press. p1-
122.
• CERN 77-09