Dosimetry by PulseMode Detectors I

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Dosimetry by Pulse-Mode Detectors I

• Geiger-Müller and Proportional Counters

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Introduction

• This chapter deals with dosimetry by means of gas
  proportional counters, Geiger-Müller counters,
  scintillators, and semiconductor detectors
• The objective of the present chapter is to
  discuss the characteristics of these devices that
  make them useful for dosimetry, and how their
  output signals can be interpreted in relation to
  absorbed dose
• Principles of operation will be introduced only
  to the extent necessary to achieve that goal

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Gas Multiplication

• Any ionization chamber with sufficiently good
  electrical insulation can in principle be
  operated at an applied potential great enough to
  cause gas multiplication, also called gas
  amplification or gas gain
• This is a condition in which free electrons from
  ionizing events can derive enough kinetic energy
  from the applied electric field, within a
  distance equal to the electrons mean free path
  ?e to ionize other gas molecules with which they
  collide

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Gas Multiplication (cont.)

• Thus a single electron can give rise to an
  avalanche, as the number of free electrons
  doubles repeatedly in their flight toward the
  anode
• At atmospheric pressure the minimum field
  strength required for the onset of gas
  multiplication is 103 V/mm

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Gas Multiplication (cont.)

• Cylindrical counter geometry, with a thin axial
  wire serving as the anode and a cylindrical shell
  as the cathode, is often employed
• This provides a sheathlike gas volume immediately
  surrounding the wire, in which the electric field
  strength ? is much larger than the average value
  obtained by dividing the applied potential P by
  the cathode-anode separation

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Gas Multiplication (cont.)

• The electrical field strength ?(r) at radius r
  from the cylindrical axis is given by ?(r) P/r
  ln (a/b), where b is the radius of the wire anode
  and a that of the coaxial cylindrical cathode
• Thus the maximum electric field, ?(r)max, occurs
  at the surface of the wire, where it reaches a
  value of ?(r) P/b ln (a/b)
• ?(b) is approximately proportional to the
  reciprocal of the wire radius for constant a and P

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Gas Multiplication (cont.)

• The gain factor G for cylindrical geometry is
  given approximately by
• where G is the number of electrons that
  arrive at the wire anode per electron released by
  ionizing radiation in the gas volume outside of
  the gas-multiplication sheath surrounding the
  wire

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Gas Multiplication (cont.)

• ?V is the average potential difference (eV)
  through which an electron moves between
  successive ionizing events, which is greater than
  the ionization potential Vi because of energy
  wasted in atomic excitations
• K is the minimum value of the electric field
  strength per atmosphere of gas pressure, below
  which multiplication cannot occur in a given gas
• p is the gas pressure in atmospheres
• P, a, and b are defined as before

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Gas Multiplication (cont.)

• Some typical values of K and ?V in gases that are
  often employed to achieve useful gas
  multiplication in proportional counters are given
  in the following table
• For example, a cylindrical proportional counter
  with a 1 cm, b 10-3 cm, P 1000 V, and
  containing P-10 gas at 1 atm would have a gain
  factor of about 100, while reducing the gas
  pressure to 0.5 atm would increase G to ?2000

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Characteristics of typical proportional-counting
gases
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Gas Multiplication (cont.)

• Although the equation predicts that very large
  gas gain factors are attainable for some
  combinations of parameters, the upper G limit for
  proportional gas multiplication is 104
• Above that value, space-charge effects cause G to
  be less for large groups of initiating electrons
  traveling together than for the few initial
  electrons that might result from the passage of a
  low-LET particle

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Gas Multiplication (cont.)

• It is important in proportional counters that the
  gain factor be the same for all sizes of primary
  ionizing events, so that the gas-amplified pulse
  size will properly represent the relative
  contributions of such events to the absorbed dose
  in the gas

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Gas Multiplication (cont.)

• To obtain useful levels of gas gain, a
  nonelectronegative gas or gas mixture must be
  used, so that the free electrons do not become
  attached to atoms
• A few percent of a polyatomic gas such as methane
  or isobutane is added to the noble gases for
  proportional counting to absorb secondary UV
  photons that are emitted from excited gas atoms
• The energy of such photons is thus dissipated in
  vibrational and rotational motion, instead of
  causing new ionizing events

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Gas Multiplication (cont.)

• In G-M counters the gaseous UV absorber is
  omitted because these photons are essential to
  the process of propagating the discharge
  throughout the tube
• Certain quenching gases (the halogens Cl or Br,
  or organics like ethyl alcohol) are added (5 10
  ) to the filling gas instead, to prevent
  repeated or continuous gas discharge from
  occurring

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Gas Multiplication (cont.)

• When a positive gas ion arrives at the cathode,
  it is neutralized by an electron taken from that
  surface
• If the ionization potential of the gas is more
  than twice the surface work function, there is a
  chance that two electrons instead of one may be
  released
• Since the second electron is then free, it will
  be drawn to the anode and hence will trigger
  another G-M discharge
• A quenching-gas molecule has a small enough
  ionization potential that it can serve as the
  positive charge charge carrier without releasing
  more than the one electron needed to neutralize
  its own charge

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Gas Multiplication (cont.)

• It should be obvious that the central wire must
  serve as the anode, since otherwise the free
  electrons produced by radiation in the counter
  filling gas would travel outward, away from the
  high-field sheath around the wire where the gas
  multiplication occurs
• This sheath is very thin, as can be seen from the
  following considerations

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Gas Multiplication (cont.)

• At a pressure p (atm) the field strength ?(r)
  must equal or exceed pK for gas multiplication to
  occur
• Hence the radius rs of the outer boundary of the
  amplifying sheath region is

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Gas Multiplication (cont.)

• For example in a cylindrical counter containing
  P-10 gas at 1 atm, with b 10-3 cm, a 1 cm,
  and P 1000 V, one has rs 3 ? 10-3 cm
• The sheath thickness is therefore equal to 2 ?
  10-3 cm or 20 ?m, occupying only about 0.001 of
  the chambers gas volume
• The probability that the radiation field will
  produce primary ion pairs within the sheath
  volume, thus giving rise to electron avalanches
  of lesser gain, is nil

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Proportional Counters Operation

• A proportional counter is just an amplifying ion
  chamber with its output measured in terms of
  numbers and amplitudes of individual pulses,
  instead of the charge collected
• The electrometer circuit is usually replaced by a
  preamplifier, a linear amplifier, and a
  pulse-height analyzer, although specific
  requirements of an experiment may also call for
  coincidence circuits, pulse-shape discriminators,
  and other pulse-processing electronics

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Operation (cont.)

• An ionizing event in the present context
  includes all of the ionization that is produced
  in the counter gas by the passage of a single
  charged particle and its ?-rays
• All of the resulting free electrons reach the
  anode wire within 1 ?s
• The measured electrical pulse, however, is
  primarily due to the motion of positive ions away
  from the wire, since they move greater distances
  within the amplifying sheath than the electrons
  do, on average

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Operation (cont.)

• Although the positive ions are much slower than
  the electrons, they virtually all originate
  simultaneously within the amplifying sheath and
  move outward in unison
• Since the electric field near the wire is so
  strong, the positive-ion motion there gives rise
  to a sharply defined fast-rising electrical pulse
  that can be clipped electronically to eliminate
  the later slow component contributed as the ions
  progress outward toward the cathode

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Operation (cont.)

• The cloud of positive ions is small in volume,
  and does not interfere with the ions resulting
  from other ionizing events taking place elsewhere
  in the counter
• The amount of positive charge in a given ion
  cloud is proportional to the number of electrons
  in the associated avalanche, which in turn is
  proportional to the number of ion pairs created
  in the original ionizing event
• Thus the size (i.e., height) of the electrical
  pulse generated by the positive ions is
  proportional to the energy imparted to the gas in
  the initial event, provided that W/e is constant

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Operation (cont.)

• Proportional counters can operate with pulse
  resolving times of about a microsecond where only
  gross pulse counting is required
• If pulse heights are to be measured also, the
  average interval between pulses should be
  greater, approaching the transit times for the
  positive ions (100 ?s) for greatest accuracy
• Reducing the gas gain by lowering the applied
  voltage and replacing that gain by an adjustment
  of the linear amplifier can provide a check on
  whether the pulse-height spectrum is being
  distorted by the proportional counter

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Operation (cont.)

• The following diagram shows how the pulse height
  from a proportional counter (or the charge output
  from an ion chamber) increases as the applied
  potential P is raised
• Two curves are shown, representing initial
  ionizing events releasing 10 and 103 electrons
• Both curves rise steeply at low voltages to reach
  the ion-chamber region, in which the voltage is
  great enough to closely approach complete
  collection of charge without causing gas
  multiplication

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Pulse height from a proportional counter as a
function of applied potential
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Operation (cont.)

• At still higher voltages the gas-multiplication
  threshold is passed and the proportional-counting
  region begins
• The factor-of-100 difference between the two
  curves in the ion-chamber region extends
  throughout the proportional-counting region as
  well, while G rises from 1 to 104

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Operation (cont.)

• Further increase in the applied potential results
  in gain factors that are so large that
  space-charge effects limit the growth of the
  larger pulses, and strict proportionality of
  pulse height with the number of original
  electrons no longer holds
• This is the region of limited proportionality

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Operation (cont.)

• Finally, at still higher voltages the two curves
  merge, indicating that initiating events of
  different sizes produce equal output pulses
• This is the G-M region
• Increasing the voltage beyond the G-M region
  results in spontaneously repeated or continuous
  electrical discharge in the gas

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Proportional Counters Use with Pulse-Height
Analysis

• If the amplified output from a proportional
  counter is connected to a multichannel analyzer,
  the number of pulses of each height (i.e., in
  each channel) can be counted to obtain a
  differential distribution of counts per channel
  vs. channel number, as shown in the following
  diagram

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Pulse-Height Analysis (cont.)

• To facilitate the calibration of the pulse height
  h in terms of absorbed dose to the counter gas,
  some proportional counters are equipped with a
  small ?-particle source with a gravity-controlled
  shutter
• This source can send a narrow beam of ?-particles
  through the counter along a known chord length ?x

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Pulse-Height Analysis (cont.)

• The expectation value of the dose contributed to
  the gas by each ?-particle can be written as
• where dT/?dx mass collision stopping power
  of the gas for
  ?-particles,
• ? gas density in the
  counter,
• ?x chord length, and
• m mass of the gas

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Pulse-Height Analysis (cont.)

• This value of dose is to be associated with the
  pulse height h? at which the ?-particle peak
  appears
• Since the h-scale is linear vs. event size, the
  dose contributions by a pulse of any size is
  thereby known, assuming W/e to the the same for
  all event sizes

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Pulse-Height Analysis (cont.)

• The total dose Dg in the gas, represented by the
  distribution in the figure, can then be obtained
  by summing over all the counts, each weighted by
  its pulse height h expressed as dose
• where N(h) is the distribution of counts per
  channel vs. channel number h

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Pulse-Height Analysis (cont.)

• Evidently such a proportional counter can be used
  as an absolute dosimeter, by virtue of the
  built-in ?-source
• Dg can of course be related to the dose in the
  counter wall by cavity theory
• The most important example of proportional
  counters that are used with pulse-height
  analyzers in dosimetry applications is the Rossi
  counter, a commercial model of which is
  illustrated in the following diagram

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13-mm-I.D. tissue-equivalent proportional counter
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Pulse-Height Analysis (cont.)

• These counters are usually made with spherical
  walls of A-150 tissue-equivalent plastic, and are
  operated while flowing a tissue-equivalent
  counting gas through at reduced pressure,
  typically 10-2 atm
• Proper adjustment of the gas pressure allows
  simulation of biological target objects such as
  individual cells, in terms of the energy lost by
  a charged particle in crossing it
• This is the primary experimental instrument used
  in microdosimetry

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Proportional Counters Applications without Pulse
Height Analysis

• Proportional counters of various designs are also
  used for many applications in which pulse-height
  analysis is not used
• The main advantages of proportional counters over
  G-M counters in this connection are
• their short pulse length (1 ?s) with practically
  no additional dead time, accommodating high count
  rates, and
• the capability of discriminating by simple means
  against counting small pulses that might result,
  for example, from background noise, or ?-ray
  interactions in a mixed ? neutron field

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Geiger-Müller Counters Operation

• The gas-amplified pulses in a G-M counter come
  out approximately the same, regardless of the
  size of the initiating event
• If the resulting pulse size is larger than the
  counter-circuit threshold ht, then the pulses
  will be counted if they are too small, they will
  not
• As a result, since the pulse size gradually
  increases as a function of applied potential, one
  would expect to see a step function in the
  count-rate-vs.-voltage curve where the pulse
  height begins to exceed ht

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Operation (cont.)

• The step is actually S-shaped, due to the
  Gaussian distribution of pulse sizes produced in
  the counter even under ideal G-M conditions
• At the applied potential P1 no counts are
  obtained
• At P2 the pulses in the ideal G-M counter are all
  larger than ht, as shown by the solid curve inset
  in the following figure
• In that case a flat plateau would be observed, as
  indicated by the solid curve in the graph of
  count rate vs. P

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The counting plateau in a G-M tube. The solid
curve is an ideal G-M plateau that would be
seen for a narrow distribution of pulse heights.
The dashed curve has a residual slope within the
G-M region because of the presence of a
low-amplitude tail on the pulse-height
distribution (see inset).
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Operation (cont.)

• In actual G-M tubes there is a residual slope in
  the plateau region, as shown by the dashed curve
  in the diagram
• This is caused by a small-pulse tail on the
  Gaussian distribution of pulse heights, as
  indicated by the dashed curve in the inset of the
  diagram
• These small pulses are mostly produced by the
  ionizing events that occur during the period
  before the G-M tube has fully recovered from the
  preceding discharge

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Geiger-Müller CountersDead Time

• Immediately after a discharge the positive space
  charge so weakens the electric field near the
  wire that gas multiplication cannot occur
• Thus the tube does not respond to radiation at
  all until the positive-ion cloud starts arriving
  at the cathode and the electric field strength
  gradually builds up again
• As that takes place, the tube becomes capable of
  responding to an ionizing event with a discharge
  of less than full size

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Dead Time (cont.)

• The true dead time is the time from the start of
  the preceding pulse until the tube recovers to
  the point where a minimum-sized pulse can be
  generated
• The recovery time is the time until a full-sized
  pulse is again possible, as shown in the
  following diagram
• The threshold peak size ht necessary for counting
  by a G-M counter circuit is considerably less
  than the average pulse size that would be
  generated by a fully recovered G-M tube when it
  is being normally operated at a potential in the
  middle of the G-M plateau

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Dead time and recovery time of a G-M tube
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Dead Time (cont.)

• The minimum time between detectable pulses will
  be less than the recovery time
• This is the pulse resolving time, but is more
  commonly referred to as the dead time in place
  of the narrower definition above

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Dead Time (cont.)

• If an ionizing event occurs during the true dead
  time, it causes no electron avalanche and hence
  has no effect on the tube
• This is called nonparalyzable dead-time behavior
• If an ionizing event occurs after the end of the
  true dead time, but before the resulting pulse is
  large enough to be counted (i.e., gt ht), not only
  will that event go uncounted but a new dead-time
  period will begin
• This is called paralyzable dead-time behavior

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Dead Time (cont.)

• Obviously, a G-M counter exhibits dead-time
  behavior that is intermediate, being a mixture of
  the paralyzable and nonparalyzable cases
• Reducing the detectable pulse-height threshold ht
  tends to decrease the paralyzable component

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Dead Time (cont.)

• If m is the observed count rate, n is the true
  count rate, and ? is the pulse resolving time,
  then for the nonparalyzable case the correction
  for dead-time counting losses is
• and for the paralyzable case
• which must be solved for n iteratively
• In the limiting case of small dead-time counting
  losses, (n ltlt 1/?), both types reduce to

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Dead Time (cont.)

• At high values of the true count rate n, the
  value of m approaches 1/? asymptotically in a
  nonparalyzable counter
• However, in the paralyzable case m reaches a flat
  maximum at n 1/?, then gradually decreases with
  further increases in n because of overlapping
  chains of dead-time periods
• Thus a low reading of a G-M counter may result
  from a strong radiation field if the dead-time
  behavior is predominantly paralyzable

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Geiger-Müller Counters Applications

• Since G-M counters are only triggered by ionizing
  events, producing discharge pulses of more or
  less the same size regardless of the initiating
  event, the observed output conveys little
  information about the dose to the counter gas
• Nevertheless G-M counters are used in some
  dosimetry applications because they offer several
  advantages

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Applications (cont.)

• They require little if any further amplification,
  since pulses of 1 10 V can be obtained directly
• They are also inexpensive and versatile in their
  construction and geometry
• Thus they are often used in radiation survey
  meters to measure x- and ?-ray fields in
  radiation protection applications
• When equipped with a thin ( 1 mg/cm2) window
  they can also be used to detect ?-rays

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Applications (cont.)

• Scale calibrations of G-M counters, if given in
  terms other than the count rate, should always be
  suspect because of the lack of dose response
• Because most G-M tubes are constructed of
  materials that are higher in atomic number than
  tissue or air, they exhibit strong
  photoelectric-effect response below 100 keV
• Enclosing the G-M tube in a suitable high-Z
  filter tends to flatten the overresponse at low
  energies

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Typical energy-dependence curves of the response
relative to tissue dose for survey meters
containing G-M tubes of the following types (a)
uncompensated, and (b) compensated with metallic
filters to produce flatter response.