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