1
Cavity Ionization Chambers:
•
Ion chambers in general vary a great deal:
Volumes vary from ~0.005 cc to ~800 cc. Currents vary from ~1 pA to ~1 µA.
•
Thimble-Type Chambers: a fundamental tool for medical dosimetry physics.
•
Cylindrical or spherical cavities in which an electric field is applied between a
conductor coated on the surface of the wall and a collector electrode along the
center of the cavity:
High voltage (~300v)
power supply
Collection
volume
V
A
Wall
Electrometer
Guard electrode
Insulator
•
The voltage on the inner electrodes is high! It usually uses a triax cable to include
a guard. Often the wall is C-552 or graphite.
•
The current collected is very small (calculation later).
•
The guard electrode grounds the current that leaks between the wall and collector
electrodes. The leak mainly occurs along the surface of the insulator separating
the electrodes but the cable joining the ion chamber to the electrometer can leak
as well – especially if the triax cable is kinked and bent a lot which always seems to
happen in a busy hospital.
•
The guard defines the collection volume of the ion chamber.
•
The chamber wall, source of charged particles, is often (not always) made thick
enough to establish CPE or TCPE that is fully characteristic of the photon
interactions taking place in the wall material or thin enough to not perturb the
fluence of charged particles if charged particle dosimetry is of interest.
Lecture 25 MP 501 Kissick 2016
2
•
Condenser-Type Chambers:
•
A condenser chamber is not connected to an electrometer. Instead, a high voltage
is placed between two electrodes as shown below, from Attix, page 310:
•
The condenser chamber can be thought of as a cavity in parallel with a capacitor.
Switch
Collection
volume
V
•
Ccapacitor
Cchamber
The combined capacitance of the chamber and the capacitor is C = Ccap + Cchamb .
And the initial charging voltage is P1.
•
After irradiation, one gets the remaining voltage, P2.
•
The charge collected from the chamber, ∆Q , is given by
∆Q = Q1 − Q2 = C ( P1 − P2 )
Lecture 25 MP 501 Kissick 2016
3
•
Since, the voltage across the chamber varies during the irradiation, there must be
recombination of some ions before they can reach the electrodes. This means that
some ions produced will not be collected – a correction for this is discussed later.
-- The recombination depends on voltage, so other chambers make efforts to keep
the voltage constant.
•
Parallel Plate Chambers:
•
The voltage across the plates is kept constant.
•
One or both of the plates is thin enough, and conducting, to allow minimal
attenuation or scattering of incident electrons or low energy photons.
•
The plate separation can be very small and also can be variable (That is what an
extrapolation chamber is). In this way, one can get close to a surface dose.
Collection
volume
A
V
Collector electrode
•
Guard electrode
If the collector electrode is too thick, then extra electrons can be knocked out by
photons, primary charged particles, or δ-rays. All of which will lead to an increase
in positive charge. If charged positive originally, then it will appear as though
fewer ions were created. If originally charged negative, then, it will appear as
though more ions are created.
primary e-
Collector
electrode
primary γ
e-
e-
Lecture 25 MP 501 Kissick 2016
4
•
This ‘polarity’ effect can be corrected for by taking measurements with both
polarities, and averaging the results.
•
All chambers should have triaxial cables to guard against current leakage so that it
is not accidentally included in the measurement.
•
Charge and Current Measurements:
•
Important – the charge collected and current measured are very small !
•
Example: Dose to air in the cavity is 1 Gy and the volume of that air at 22oC, and 1
atm is 1 cc, then the amount of charge of one sign is found by the following:
Dair =
Therefore,
Q=
Q
M
W

 e


 air
Dair M
D ρ V
= air air
(W / e) air (W / e) air
or,
Q=
•
(1J / kg)(1.29 ×10 −3 g / cc)(1cc)(10 −3 kg / g)
= 3.80 ×10 −8 C
(33.97J / C)
This is small. In radiotherapy, a dose like this can take only 30s of continuous beam
on time, and so the current would be:
i=
∆Q 3.80 x10 −8 C
=
= 1.27nA
∆t
30 s
•
A typical ammeter cannot measure this small a current, and is also the reason why
you should treat your triax cable with care! A typical DMM can sense ~2 mA. A
high end one can sense ~20 µA with 107 Ω input impedance.
•
An electrometer is used. It is a very high impendence voltmeter that can be used
to measure current or voltage on a calibrated capacitor on which this collected
charge is accumulated. An electrometer typically has 1014 Ω input impedance. They
can cost between 2 to 10 thousand dollars.
Lecture 25 MP 501 Kissick 2016
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•
Charge Measurement Specifics:
•
Modern electrometers use operational-amplifiers (op-amps) to amplify the voltage.
The simplest possible configuration for an electrometer would be the following:
op-amp
+
Pi
V
P0=GPi
Where G is the gain of the op-amp. The above does not show the feedback on the
op-amp or the ion chamber’s and its cable’s inherent capacitance, Ci.
•
Consider this circuit (not the most typical!): (ion chamber extra ground not shown)
For charge measurements*
Ri
Ion chamber
C
-
+
Q or dQ/dt
-
* Replace with “
•
S
Ci
Pi
R (megaohm)
+
G
V P0
“ for current measurements
The negative charge Q flows from the ion chamber and responds to a negative
potential, Pi. The op-amp produces an output voltage, P0 given by:
P0 = GPi
Lecture 25 MP 501 Kissick 2016
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•
The total potential across the capacitor, C, is P0 − (− Pi ) , and it holds a charge,
C ( P0 + Pi ) .
This capacitor is in parallel with the inherent capacitance, Ci (the
chamber and the cable). Therefore the ion chamber charge is as follows:
Q = C (P0 + Pi ) + Ci Pi = CP0 + (C + Ci )Pi = C (GPi ) + CPi + Ci Pi
We can assume a large gain approximation: CG >> Ci and G +1 ≈ G :
Q = CGPi = CP0
(see Attix, page 322 for typical values of G and Ci)
•
Smaller capacitors, C, allow for smaller charges to be measured: the output voltage,
P0, is inversely proportional to C:
P0 ≅
Q
C
•
Current Measurement Specifics:
•
One needs to replace the capacitor, C, above with a very large, megaohm resistor, R.
•
The current, I, that passes through both R and the inherent Ri is as follows, by
using P0 = GPi :
i ( R + Ri ) = P0 + Pi = (G + 1) Pi
We can assume small inherent resistance and large gain approximations: R >> Ri
and G +1 ≈ G :
i≅
•
GPi P0
=
R
R
Therefore, large resistors, R, allow for smaller currents to be measured.
Lecture 25 MP 501 Kissick 2016
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•
A typical Triax mode circuit that you should memorize! Note that the circuit
inside the dotted box floats at high voltage – careful when you open the device!
•
There are other ways to connect things together, such this coax mode circuit with
an external high voltage supply:
Coax Mode
(external HV supply):
+
C
R (megaohm)
Ion chamber
-dQ/dt
+12v
+
+
-
-12v
Vout
+
ground
common
ground
•
Note that with the resistor for feedback to the inverting input makes the op amp
circuit look like a high pass filter (see appendix for more info). Op amps act to
force the inverting input (-) have equal voltage to the non-inverting input (+).
•
Next lecture starts to explore the dynamics of the gas and ionization inside the
chamber.
Lecture 25 MP 501 Kissick 2016