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Ionization Chambers I

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Title: 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
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