Ionization Chambers I

1
Ionization Chambers I

• Introduction
• Free-Air Ion Chambers

2
Introduction

• The ionization chamber is the most widely used
  type of dosimeter for precise measurements, such
  as those required in radiotherapy
• Such chambers are commercially available in a
  variety of designs for different applications,
  and may be constructed in a machine shop when
  special designs are required

3
Introduction (cont.)

• If the ion-collecting gas volume can be
  determined by means other than calibration in a
  known field of ionizing radiation, the chamber
  becomes an absolute dosimeter
• This is, however, not usually practicable outside
  of national standards laboratories, and in any
  case it is preferable to work with dosimeters
  having calibrations traceable to such a laboratory

4
Introduction (cont.)

• We will begin by discussing free-air ionization
  chambers
• Chambers of this type, although seldom seen
  except in standards laboratories, experimentally
  demonstrate the concepts of exposure, CPE, and
  ion-chamber absoluteness

5
Free-Air Ion Chambers Conventional Designs

• The definition of exposure requires the
  measurement of all the ionization produced by
  collision interactions in air by the electrons
  resulting from x-ray interactions in a known mass
  of air
• However, the experimental difficulty of doing
  this generally requires one to rely on
  charged-particle equilibrium
• Only in one special design (to be discussed
  later) is dependence upon this requirement to
  replace to replace lost electrons avoided

6
Conventional Designs (cont.)

• A number of different designs of free-air
  chambers have evolved in standardization
  laboratories in different countries, some
  cylindrical and some plane-parallel in geometry
• We will first consider the plane-parallel type,
  such as that used at the NBS in calibrating
  cavity ion chambers for constant x-ray-tube
  potentials from 50 to 300 kV

7
Conventional Designs (cont.)

• The following diagram is a schematic plan view of
  such a chamber, which is enclosed in a Pb
  shielding box to exclude x rays scattering in
  from elsewhere
• At the front of the box is a tungsten-alloy
  diaphragm that is aligned with the x-ray beam
  central axis, and passes a beam of
  cross-sectional area A0 in the plane of axial
  point P
• This is the point where cavity chambers to be
  compared with the free-air chamber are to be
  centered, after the beam has been calibrated and
  the free-air chamber is removed

8
Schematic plan view of a typical standard
free-air ionization chamber
9
Conventional Designs (cont.)

• The plate system inside the box consists of three
  coplanar plates on one side of the beam and a
  parallel high-voltage plate opposite
• The plates are all parallel to the x-ray beam
  axis, and equidistant from it
• The distance of the plates from the beam is
  designed to put them beyond the range of
  substantially all the secondary electrons
  originating in the beam (e.g., electron e1)

10
Conventional Designs (cont.)

• To provide a uniform electric field between the
  plates, a set of wires encircles the space
  between them at both ends and at the top and
  bottom
• The chamber height from wire to wire equals the
  width from plate to plate
• These wires are electrically biased in uniform
  steps to establish parallel equipotential planes
  between the plates
• The guard electrodes also assist in producing
  field uniformity

11
Conventional Designs (cont.)

• Under these conditions the electric lines of
  force (paths followed by and ions) go
  straight across the chamber, perpendicular to the
  plates
• Ions of one sign produced within the larger
  shaded volume (V), and not lost in ion
  recombination, are thus transported to the
  collector plate, electrically connected to the
  electrometer input
• The dimension l is the collector length plus half
  the gap width between collector and guard plate
  at each end

12
Charged-Particle Equilibrium

• The collecting volume V is penetrated by the
  x-ray beam passing through the aperture
• The volume V is common to both V and the volume
  occupied by the beam itself V is shown
  crosshatched in the diagram
• V is the actual volume of origin of the secondary
  electrons whose ionization we wish to measure

13
CPE (cont.)

• The lateral dimensions of the chamber are great
  enough to accommodate electrons like e1, which
  remain within V and thus produce all their
  ionization where it will be collected and
  measured
• The electrons like e2, which originate within the
  defined volume of origin V, may have paths that
  carry some of their kinetic energy out of V,
  where the remaining ionization they produce will
  not reach the collector, but will go to the
  grounded guard plate instead
• This ionization must be replaced by other
  electrons such as e3 that originate in the beam
  outside of volume V

14
CPE (cont.)

• For x-ray tube potentials up to 0.5 MeV the
  electrons have nearly equal tendencies to move
  forward and backward in the chamber, due to their
  initial angular distribution being predominantly
  sideways to the beam direction, and the effect of
  scattering in the air
• Thus the attenuation of the x-rays in the
  distance l, separating the place of origin of
  corresponding electrons e2 and e3, tends to
  cancel, and the charge compensation is nearly
  exact
• Moreover, the effective center of origin of
  electrons is the geometric center P of V and V

15
CPE (cont.)

• Consequently the volume Vas a whole is in
  charged-particle equilibrium
• That is, the ionization produced by all of the
  electrons originating in the beam within V is
  equal to all of the ionization produced within
  V, and the correct amount of charge is thus
  measured (neglecting the small effects of
  scattered photons, bremsstrahlung, and ionic
  recombination, yet to be discussed)

16
CPE (cont.)

• Notice that the distance from the boundaries of V
  to each end of the lead box must be greater than
  the maximum electron range also, to avoid
  perturbing the CPE condition
• In summary, one can say that the distance from
  the volume of origin V to an obstruction in any
  direction must exceed the electron range, to
  preserve CPE in the volume V
• Note that elementary volumes within V are not in
  CPE only the volume V as a whole satisfies CPE

17
Accurate Definition of the Mass of Air, m, in the
Definition of Exposure

• Defining the mass of air, m, by which the
  measured charge is to be divided to obtain the
  exposure can be simplified by noticing that each
  photon passing through the defining aperture
  passes through the volume V, except for those
  attenuated or scattered away in the air
• If the fluence is ?0 (photons/m2) at the aperture
  of area A0 (m2), then ?0A0 photons will enter

18
Mass of Air (cont.)

• Ignoring air effects, the fluence ? decreases in
  proportion to the inverse square of the distance
  from the source, as the beam proceeds through the
  chamber
• Simultaneously the area A increases in proportion
  to the square of the distance from the source
• Thus ?A remains constant and equal to ?0A0
  through the chamber

19
Mass of Air (cont.)

• Evidently then the number of electrons produced
  by ?A photons in traversing the volume V, of
  length l (m), will be constant, irrespective of
  the actual cross-sectional area A of the beam in
  V, so long as the path length of each x ray in
  passing through V is not significantly increases
  by the angle ? the x-ray makes with the central
  axis
• In all practical cases the source is sufficiently
  distant that l/cos ? ? l, and this error is
  negligible
• Consequently one can replace the actual volume of
  origin V by a cylindrical volume Vc A0l (m3),
  which is multiplied by the air density ? (kg/m3)
  to obtain the defined mass m (kg) of air

20
Mass of Air (cont.)

• The exposure at the aperture (point P) is thus
  determined by the measurement, which must be
  corrected upward by the air attenuation occurring
  in the distance between P and the midpoint P in
  V
• If Q (C) is the charge produced in V, the
  exposure at point P is given (in C/kg) by
• where x is the distance from P to P, and µ
  is the air attenuation coefficient

21
Proof that the Exposure is Defined at the Plane
of the Aperture

• Although the foregoing argument is reasonable, a
  more rigorous proof of exactly what it is that is
  measured by a free-air chamber would be desirable
• Let A0 be the aperture area, at distance y from
  the source S in the following figure
• ?0 is the energy fluence at point P in the plane
  of the defining aperture
• A disc-shaped mass element of air dm0 ?A0 ds is
  located at P

22
The free-air chamber geometry discussed in the
proof
23
Proof (cont.)

• The electrons resulting from x-ray interactions
  in dm0, if allowed to dissipate all their energy
  in air, would produce a charge of either sign
  equal to

24
Proof (cont.)

• Consider now a second elemental mass of air dm,
  at a distance s from the source, and a part of
  the volume V occupied by the beam and the
  collecting volume V
• dm is irradiated by an energy fluence ?(s)

25
Proof (cont.)

• Thus the ionization produced by the electrons
  that originate in dm will be given by

26
Proof (cont.)

• We assume that this charge is all collected and
  measured (i.e., that CPE exists for volume V,
  and that no ionic recombination occurs)
• The charge due to electrons from elemental mass
  dm is less than that from dm0 by the amount of
  beam attenuation in the intervening air column

27
Proof (cont.)

• The total charge Q generated by electrons
  originating in all of V is
• where s1 is the distance from the x-ray
  source to the front plane of V

28
Proof (cont.)

• Letting x s y and x1 s1 y, the above
  integral can be recast in the form

29
Proof (cont.)

• Since x1 (l/2) is the distance from the
  aperture P to the midpoint P of volume V, we see
  that Q is the charge due to the electrons
  originating in the cylindrical mass ?A0l, exposed
  to the energy fluence ?0 that exists at the
  aperture P, and corrected for attenuation in air
  through the distance from P to P

30
Proof (cont.)

• The exposure at point P (aperture) is

31
Proof (cont.)

• The measured charge (assuming no recombination
  occurs) per unit mass in cylindrical volume A0l
  is

32
Proof (cont.)

• Hence the exposure at point P is related to the
  value of Q/m by
• where m is the mass of air in the cylindrical
  volume A0l

33
Scattered X-rays in the Chamber

• In the preceding treatment µ was taken to be the
  narrow-beam attenuation coefficient for the
  x-rays passing through air
• This supposes that scattered photons do not
  result in measurable ionization in the chamber
• That is not strictly the case, as can be seen
  from the following diagram
• Initially ignoring the plastic tube, we see that
  photons h?1 and h?2 are x-rays scattered out of
  the beam, which interact with other air atoms to
  launch electrons e1 and e2, respectively, thus
  producing excess ionization in the volume V

34
Measurement of the ionization due to scattered
x-rays in a free-air chamber by the plastic-tube
method
35
Scattered X-rays (cont.)

• Likewise photon h?3, a bremsstrahlung x-ray
  emitted by electron e3, may give rise to another
  electron e4, which produces unwanted ionization,
  since the exposure is supposed to exclude
  ionization due to bremsstrahlung produced by the
  electrons that originate in the defined mass of
  air

36
Scattered X-rays (cont.)

• The ionization contribution due to scattered and
  bremsstrahlung x-ray can be determined as follows
• A tube of nearly air-equivalent material such as
  Lucite, extending the full length of the
  ion-chamber enclosure, is positioned inside the
  chamber so that the x-ray beam passes through it
  from end to end without striking it
• The tube must have walls thick enough to stop the
  electrons originating inside it, but thin w.r.t.
  attenuation of the scattered x rays, so that they
  may escape unimpeded

37
Scattered X-rays (cont.)

• The plastic is completely coated with conducting
  graphite, and biased at half of the potential of
  the HV plate to minimize field distortion
• The ratio of the ionization measured with the
  tube in place to that with the tube removed will
  approximate the fraction fs of the total
  ionization that is contributed by scattered and
  bremsstrahlung x rays

38
Other Causes of Electric-Field Distortion in
Parallel-Plate Chambers

• Parallel-plate free-air chambers such as the NBS
  design must have a uniform electric field between
  the high-voltage plate and the collector-guard
  plates, to assure that the dimensions of the
  ion-collection volume V and the length of the
  volume V are accurately known
• The electrical lines of force must go straight
  across, perpendicular to the plates

39
Electric-Field Distortion (cont.)

• To accomplish this, in addition to the
  graded-potential guard wires already mentioned,
  it is also important that
• all the plates be parallel to each other and to
  the beam axis, which must be perpendicular to the
  front and back boundaries of the volume V,
• the collector and guard plates be coplanar, and
• the collector be kept at the same electrical
  potential as the guards (usually at ground)

40
Electric-Field Distortion (cont.)

• Even the contact potentials of the surfaces of
  these plates must be the same (e.g.,
  electroplated with nonoxidizing metal) if local
  electric-field distortion near the gaps between
  them is to be avoided
• Null-type electrometer circuits, which maintain
  the input potential at its initial value
  throughout the period of charge collection, are
  essential for this application

41
Electric-Field Distortion (cont.)

• The first diagram illustrates the distorting
  effects of non-coplanarity of the guard and
  collector plates, and the second diagram of
  having the collector surface at a different
  potential than that of the guard
• Note that ?HV averaging removes the error in the
  second diagram, but not in the first

42
Effect of collector (C) misalignment with guards
(G)
43
Effect of collector plate surface potential being
higher ( 1 V) than guard plates
44
Variable-Length Free-Air Chamber

• This chamber consists of two telescoping
  cylinders with the x-ray beam passing along their
  axis through holes at the centers of the two flat
  ends
• The holes are covered by windows W of conducting
  plastic to keep out stray electrons and provide
  electrostatic shielding for the collecting
  electrode inside
• The x-ray beam is defined by passing it through
  an aperture of known area in a fixed diaphragm,
  aligned with the chamber axis

45
The variable-length type of free-air chamber
46
Variable-Length Chamber (cont.)

• The ions formed throughout the chamber are
  collected on an off-center telescoping metal rod,
  correcting for ion recombination as necessary
• The chamber shell is operated at high potential
  (e.g., ?5000 V) and is enclosed in a Pb-lined box
  to keep out scattered x rays
• The diameter of the collecting rod is made small
  enough, and its position far enough from the
  x-ray beam, that only a very small (lt0.01) loss
  of ionization results from electrons striking it

47
Variable-Length Chamber (cont.)

• The chamber dimensions are such that, in its
  collapsed condition, electrons originating in the
  x-ray beam where it crosses the fixed central
  plane cannot reach the walls in any direction
• Likewise no electrons from the window W are
  capable of reaching the central plane

48
Variable-Length Chamber (cont.)

• After an ionization measurement Q1 is made in the
  collapsed condition, the chamber volume is
  expanded by a length ?L (as much as twofold),
  while keeping the chamber midplane and the
  defining aperture fixed relative to the x-ray
  source
• A second ionization measurement Q2 is then made

49
Variable-Length Chamber (cont.)

• The ionization component measured from the volume
  A is the same as that from A except for a slight
  (lt1) increase due to decreased beam attenuation
• The same can be said for volumes B and B, except
  that the attenuation effect is in the reverse
  direction, canceling that for A to A (assuming
  linear attenuation, which is accurate to within
  0.01 for attenuations lt 1)

50
Variable-Length Chamber (cont.)

• Therefore the observed increase in ionization (Q2
  Q1) must be due only to the electrons that
  originate in crosshatched volume V1 in the center
  of the chamber
• Those electrons will all run their full range in
  air and produce their full complement of
  ionization that will be measured directly in
  accordance with the definition of exposure
• They need not remain in volume V to do this,
  since ions are collected from A and B as well

51
Variable-Length Chamber (cont.)

• If A0 is the aperture area (m2), ?L is the length
  of chamber expansion (m), and ? is the air
  density (kg/m3), then the exposure at the
  aperture is given by
• where x is the distance from the aperture to
  the fixed central plane, µ is the narrow-beam
  attenuation coefficient for the x-rays in air, fs
  is the fraction of Q2 Q1 that is produced by
  scattered and bremsstrahlung x rays, and fe is
  the fraction lost due to any electrons being
  stopped by the collecting rod and inadequate
  chamber radius

52
Variable-Length Chamber (cont.)

• The advantages of this design of free-air chamber
  over conventional designs are several
• There is no dependence of the measurement upon
  CPE. Since the electrons originating in V1
  cannot escape from the ion-collecting volume,
  there is no need for replacement of lost
  electrons
• There is no need for electric-field uniformity,
  plate alignment, or maintenance of the collector
  at ground potential
• The air mass can be defined more accurately, as
  the uncertainty in the length of the collecting
  volume in a conventional chamber is eliminated.
  ?L can be determined by a precision screw, or
  even gauge blocks if desired

53
Variable-Length Chamber (cont.)

• It is necessary to cover the collecting-rod
  insulators at both ends of the chamber with
  conducting cups to avoid instability caused by
  charge collection on the insulator surfaces
• In general it is a good idea to minimize the bare
  surface area of insulators facing into the
  collecting volume of any ion chamber, to avoid
  this kind of instability
• This holds true for cavity chambers as well as
  free-air chambers

54
High-Energy Free-Air Ion Chambers

• Free-air chambers are practical mainly with
  x-rays generated at energies between 10 and 300
  keV
• At higher energies the range of the secondary
  electrons in air becomes so great that the size
  of the chamber becomes prohibitively large

55
High-Energy Chambers (cont.)

• Joyet suggested employing a longitudinal magnetic
  field in a conventional free-air chamber to bend
  electron paths into spirals and thus prevent
  their striking the walls even for x-ray energies
  up to 50 MeV
• Joyet pointed out that, as photons are increased
  in energy, the secondary electrons produced in
  Compton and pair-production events become more
  energetic but more forward directed

56
Schematic plan view of a parallel-plate free-air
chamber with magnetic field and solid
air-equivalent filters
57
High-Energy Chambers (cont.)

• The maximum side-directed (90) component of the
  secondary-electron energy resulting from 50-MeV
  photons is only about 3 MeV, as shown by the
  dashed curve on the right ordinate of the
  following diagram
• The solid curve shows the magnetic field strength
  necessary to bend such electrons into spiral
  paths of radius 6 cm, which would prevent
  electrons from striking the wall in the chamber
  shown in the previous diagram

58
Maximum transverse energy Ee sin ? of the recoil
electrons for incident quanta up to 50 MeV, and
intensity of the magnetic field for the
containment of the recoil electrons between the
parallel plates
59
High-Energy Chambers (cont.)

• The fatal flaw in this design is that it is not
  really a free-air chamber
• To produce CPE in the collecting volume a
  sufficiently thick layer of solid
  air-equivalent material must be provided
  upstream to build up an equilibrium population of
  electrons passing through the ion-collecting
  region
• One may as well make a thick-walled cavity
  chamber out of the air-equivalent material instead