Interaction of Charged Particles with Matter Flashcards
Classify charged particle interactions with absorber atoms and provide a brief description of each interaction
As energetic charged particles penetrate into an absorbing medium, they interact either with orbital electrons of absorber atoms or with the nucleus of absorbing atoms. These interactions are typically classified as follows:
Coulomb interaction between CP and orbital electrons of absorber atom resulting in:
(i) Elastic scattering (no energy loss but change in direction of motion).
(ii) Inelastic collision referred to as soft or distant collision with impact parameter b much larger than radius of absorbing atom a, i.e., b a, resulting in some energy loss (soft collision loss) through excitation or
ionization of absorber atom.
(iii) Inelastic collision referred to as hard or direct collision with impact parameter b of the order of the radius of absorbing atom a, i.e., b ≈ a, resulting in some energy loss (hard collision loss) through excitation or
ionization of absorber atom.
(iv) In-flight annihilation (applicable to positrons only) of CP with orbital electron of absorber resulting in production of annihilation photons (radiation loss).
Classify charged particle interactions with absorber atoms and provide a brief description of each interaction
Coulomb interaction between CP and nucleus of absorber atom resulting in:
(i) Elastic scattering (essentially no energy loss but change in direction of motion).
(ii) Inelastic scattering referred to as radiation loss with the impact parameter b much smaller than the radius of the absorber atom a, i.e., ba, resulting in energy loss through production of bremsstrahlung (applicable
to light CPs only).
(iii) Penetration of the nucleus of absorbing atom resulting in nuclear reaction (applicable to heavy and intermediate CPs and much less so to light CP).
(iv) Inelastic scattering resulting in Coulomb nuclear excitation and subsequent emission of gamma rays.
Define stopping power and explain the purpose it serves.
In traversing an absorbing medium a charged particle (CP) interacts with the atoms of the absorber and gradually loses its kinetic energy in a large number of
small steps. The mean rate of energy loss per unit path length of the CP of kinetic energy EK traversing an absorbing medium of atomic number Z is defined as the stopping power of the absorbing medium. Stopping power depends on physical properties of the absorbing medium as well on properties of the CP traversing the absorbing medium. Stopping power is considered a property of the absorbing medium in which a CP propagates.Stopping power has an important role in many facets of basic science and technology, and is used heavily in clinical radiation dosimetry based on ionization chambers.
Categorize the interactions that an energetic electron experiences as it penetrates into an x-ray target.
X-ray targets serve as source of x rays and a common feature of all x-ray targets is that they are bombarded with energetic electrons that penetrate the target.
The source of the energetic electrons most commonly is a heated filament ejecting electrons that are subsequently accelerated in an electrostatic field (provided in an x-ray tube) or electromagnetic field (provided in a linac wave guide) to attain kinetic
energy of the order of 50 keV to 50 MeV for medical use and even higher kinetic energy for research purposes.
Energetic electrons strike and penetrate the x-ray target and in traversing it interact through Coulomb interactions with constituents of target atoms, either orbital electrons or nuclei. The Coulomb interactions are either elastic collisions resulting in no energy loss but change in direction of motion or inelastic collisions involving some energy loss as well as change in direction of motion. There are four types of interaction available to incident electron striking an x-ray target and interacting with target atoms:
(1) Elastic collision with orbital electron (no energy loss but change in direction of motion).
(2) Elastic collision with nucleus (no energy loss but change in direction of motion).
(3) Inelastic collision with orbital electron resulting in atomic excitation or ionization associated with energy loss and change in direction of motion (collision or ionization loss).
(4) Inelastic collision with nucleus resulting in radiation energy loss, change in direction of motion, and production of bremsstrahlung x rays.
Discuss categories of x-ray targets with respect to their thickness.
Based on their thickness in comparison to the mean range ¯R of incident monoenergetic electrons in the target material, targets are classified into two main groups: thin targets and thick targets. Thickness of thin targets is much smaller than ¯R while thickness of thick targets is of the order of ¯R .
By definition, a thin target is so thin that incident electrons traverse it without any significant loss of kinetic energy, without significant elastic collisions, and with relatively small radiation loss. In a thin target essentially all radiation interactions are interactions between electrons of incident kinetic energy and the nuclei.
A thick target is defined such that all electrons striking it are absorbed in the target and no electrons can traverse the thick target. In practice, the thickness of a thick target is about 110 % of ¯R to ensure that none of the incident electrons can exit the target. On the other hand, the thick target should be no thicker than necessary, so as to minimize the absorption of x rays in the target material. The spectral distribution of thick target bremsstrahlung can be represented as a superposition of contributions from a large number of thin targets, each thin target traversed by a lower energy mono-energetic electron beam having a lower (Eν )max than the previous thin target. In traversing each thin target, the electron loses a small portion of its kinetic energy and enters the next thin target with a lower energy until it attains zero kinetic energy in the last thin target, as shown schematically in Fig. 6.32(B) which depicts a thick target spectrum as a superposition of many thin target spectra of the type shown in Fig. 6.32
Discuss categories of x-ray targets with respect to their atomic number Z.
Atomic number Z and kinetic energy EK of the incident electron beam affect the quality as well as yield of x rays produced by an x-ray target. With regard to atomic number, x-ray targets are classified as low Z targets, intermediate Z targets, and high Z targets.
The statement of (6.161) that x-ray intensity I is proportional to ZE2K reflects the total bremsstrahlung energy emitted per electron absorbed in the thick x-ray target or per electron incident onto the thick target, since the definition of a thick target stipulates that all electrons striking the target will be absorbed in the target.
X-ray yield thus depends on the atomic number Z of the target, as stated in (6.161), but this implies intensity integrated over all photon energies from 0 to maximum as well as over the full 4π solid angle. It is well known that intensity of x rays emanating from an x-ray target is not isotropic and the intensity distribution depends strongly on kinetic energy of the incident electrons. The intensity maximum in diagnostic radiology energy range is at 90° to the direction of the incident electron,
while with increasing kinetic energy the intensity distribution is progressively more forward peaked. This is why with diagnostic x-ray tubes the patient imaging is carried out at 90° to the incident electron beam direction and in radiotherapy treatment the patient is positioned at 0° to the incident electron beam direction
Briefly discuss the important features of x-ray generation in an x-ray target.
(a) Brief characteristics of x-ray production in an x-ray target:
(1) In an x-ray tube or in a linac accelerating wave guide, energetic electrons strike a metallic target and a small fraction of their kinetic energy is emitted from the target in the form of x rays, while most of the kinetic energy carried by incident electrons is converted into heat.
(2) Efficiency for x-ray production, also called x-ray yield, depends on three parameters: target atomic number Z, kinetic energy EK of the incident electrons striking the target, and electron beam current J . X-ray yield increases with increasing Z for constant J and EK; it increases with increasing J for constant Z and EK; and it increases with EK for constant Z and J .
(3) Two types of x rays are produced in an x-ray target: characteristic x rays and bremsstrahlung photons, and both types are produced through energy loss that incident electrons experience in penetrating the target and interacting with atoms of the target.
Characteristic x rays are generated as a consequence of Coulomb collisions between incident electrons and orbital electrons of target atoms, producing excitation
and ionization of target atoms, and creating vacancies in atomic shells of target atoms. As orbital electrons from higher orbits fill these vacancies, transition energy is emitted in the form of discrete photons or Auger electrons with energy that is characteristic of the target material, hence the name characteristic radiation. Energy loss by electrons through this type of interaction is referred to as collision loss or ionization loss and contributes to collision stopping power of the target material. Bremsstrahlung photons are generated in x-ray targets through Coulomb interactions between incident electrons and nuclei of target atoms. Photon spectra produced in this type of interaction are continuous, ranging in energy from zero to a maximum energy hνmax equal to kinetic energy EK of incident electrons (Duane-Hunt law). Energy loss by electrons through this type of interaction is called radiation loss and contributes to radiation stopping power of the target.
(4) Bremsstrahlung spectrum is continuous while characteristic photons contribute discrete spectral lines that are superimposed onto the continuous bremsstrahlung spectrum. The relative proportion of the number of characteristic photons to bremsstrahlung photons in an x-ray beam spectrum varies with atomic number Z of the target and kinetic energy EK of the incident electrons. For example, x-ray beams produced in a tungsten target by 100 keV electrons contain about 20 % of characteristic photons and 80 % of bremsstrahlung photons. In the megavoltage range the contribution of characteristic photons to the total spectrum is negligible in comparison to bremsstrahlung photons.
(5) In the diagnostic energy range (30 kVp to 150 kVp) most photons are produced at close to 90° from the direction of incident electrons striking the target. In the megavoltage radiotherapy energy range (4 MV to 50 MV), on the other hand, most photons are produced in the direction of the incident electron beam striking the target.
(6) Since most of the kinetic energy of the incident electron beam upon striking an x-ray target is transformed into heat, x-ray targets must have the following properties: high melting point, good thermal conductivity, and high x-ray yield, while x-ray producing equipment must have efficient means for cooling the x-ray target.
Target cooling is less of a problem in megavoltage x-ray production than in the diagnostic energy range because the efficiency of x-ray production is at least an order of magnitude higher in the megavoltage range (∼10 %) in comparison to the diagnostic range (<1 %).
Requirements for cooling of x-ray tubes used in imaging are more stringent than requirements for cooling of x-ray tubes used in radiotherapy for two reasons: to achieve short exposure times the instantaneous tube currents used in imaging are one to two orders of magnitude higher that in radiotherapy tubes. Moreover, focal spots in imaging tubes are much smaller than those in therapy tubes resulting in more sophisticated methods for cooling of imaging tubes (e.g., rotating anode) compared to therapy tubes which employ stationary targets.
The term “beam quality” is used to indicate the ability of an x-ray beam to penetrate a water phantom. List at least six x-ray beam quality “specifiers” or indices
Beam quality specification or beam quality indices.Many beam quality indices have been developed and are in use, but none of them is simple, universal, and easy to use. Best-known indices are as follows:
(1) Measurement of complete x-ray spectrum produced in an x-ray target and emitted by x-ray producing equipment for diagnostic or therapeutic use gives the most rigorous description of beam quality. However, a complete x-ray spectrum is difficult to measure directly under clinical conditions because of the high photon fluence rate that causes significant photon pile up in the detector. Indirect techniques have been developed for this purpose, but are cumbersome. Examples are measurement with diffraction spectrometer using Bragg reflection on a single crystal and registering the intensity of x rays as a function of wavelength or measurement with high resolution detector using 90° Compton scattering from a known sample and reconstructing the actual spectrum from the scatter spectrum using the Klein-Nishina function.
(2) Measurement of half-value layer (HVL) is practical for beam quality description in the diagnostic x-ray energy region (superficial and orthovoltage x rays) because of strong dependence of the attenuation coefficient on photon energy. In the superficial energy region HVL is usually quoted in millimeters of aluminum, in the orthovoltage region in millimeters of copper. In the megavoltage region, however, HVL is not used for beam quality specification because in this region the attenuation coefficient is only a slowly varying function of photon energy. To minimize effects of radiation scattered in the attenuator the HVL should be measured under “good geometry” conditions that imply a narrow radiation beam and a reasonable distance between the attenuator and the detector to minimize the number of scattered photons reaching the detector. Moreover, the ionization chamber used in HVL measurement should possess an air equivalent wall and a flat photon energy response throughout the beam energy spectrum.
(3) Nominal accelerating potential (NAP) was used in early radiation dosimetry protocols as a matter of convenience and is related to the kinetic energy of incident electrons striking the target. It is defined in terms of the ionization ratio measured with a 10×10 cm2 field in water phantom on central beam axis with an ionization chamber at 100 cm from the target and at depths in water of 20 cm and 10 cm. The measured dose ratio at the two depths in water was linked with a nominal accelerating potential which was then used for selection of dosimetric parameters.
(4) Ratio of “tissue-phantom ratios” (TPR20,10) at depths of z = 20 cm and z = 10 cm in water phantom for a 10×10 cm2 field at 100 cm from the target. TPR at depth z itself is defined as the ratio of doses DQ and DQref where DQ is the dose at depth z and DQref is the dose at a reference depth, typically chosen as 5 cm or 10 cm. TPR20,10 is used for megavoltage beam quality specification in many national and international dosimetry protocols. It is similar to the NAP concept, however, through the TPR ratio it accounts for the actual penetration of a given clinical beam in water.
(5) Megavoltage beam quality specification can also be quoted with percentage depth dose (PDD) for a 10×10 cm2 field at a depth of z = 10 cm in water phantom that is positioned at a distance of 100 cm from the target. Percentage depth dose at depth of 10 cm is defined as the ratio of doses DQ and DP multiplied by 100, where DQ is dose at depth of 10 cm in water and DP is the dose at depth of dose maximum in water for the given megavoltage beam. Effects of electron contamination of the thick target x-ray beam can be minimized with a lead scattering foil placed into the
photon beam.
Betatrons used clinically in 1950s and 1960s typically operated in the 25 MV x-ray mode. When 25 MV linacs were introduced into clinical service in the early 1970s, percentage depth doses they produced in water were significantly shallower (less penetrating) than those produced by 25 MV betatrons. How was this surprising finding explained and rectified?
In summary, both the x-ray target and flattening filter of high energy linacs should be made of materials with as low as possible atomic number Z to maximize the beam effective energy and as high as possible mass density to minimize the space occupied by the two components
Refer to last problem in compendium chapter 6
