table of contents:
Chapter 1. Basic Radiation Physics_1.3 Electron Interactions
Chapter 5. Treatment machines for External beam Radiotherapy_5.5 Linacs
Chapter 1. Basic Radiation Physics
1.3 Electron InteractionsAs an energetic electron
高能電子 traverses matter, it interacts with matter through Coulomb interactions with atomic orbitic electrons and atomic nuclei.
Through these collisions the electrons may lose their kinetic energy (collision and radiative losses) or change their direction of travel (scattering).
Energy losses are described by
stopping power; scattering is described by
scattering power.
The
collision between the incident electron and an orbital electron or nucleus of an atom may be
elastic or
inelastic.
In an elastic collision the electron is deflected from its original path but no energy loss occurs, while
in an inelastic collision the electron is deflected from its original path and some of its energy is transfered to an orbital electron or emitted in the form of bremsstrahlung.
Energetic electrons experience thousands of collisions as they traverse an absorber, hence their behaviour is described by a statistical theory of multiple scattering embracing the individual elastic and inelastic collisions with orbital electrons and nuclei.
The type of interaction that the electron undergoes with a particular atom of radius a depends on the impact parameter b of the interaction, defined as the perpendicular distance between the electron direction before the interaction and the atomic nucleus.
- For b>>a the electron will undergo a soft collision with the whole atom and only a small amount of energy will be transferred from the incident electron to orbital electrons.
- For b=a the electron will undergo a hard collison with an orbital electron and an appreciable fraction of the electron's kinetic energy will be transferred to the orbital electron.
- For b> a the incident electron undergoes a radiative interaction (collision) with the atomic nucleus. The electron will emit a photon (bremsstrahlung) with energy between zero and the incident electron kinetic energy. The energy of the emitted bremsstrahlung photon depends on the magnitude of the impact parameter b; the smaller the impact parameter, the higher the energy of the bremsstrahlung photon.
1.3.1 Electron-orbital electron interactions
- Coulomb interactions between the incident electron and orbital electrons of an absorber result in ionizations and excitations of absorber atoms:
----Ionization: ejection of an orbital electron from the absorber atom;
----Excitation: transfer of an orbit electron of the absorber atom from an allowed orbit to higher allowed orbit (shell).
- Atomic excitations and ionizations result in collisional energy losses and are characterized by collison (ionization) stopping powers.
1.3.2 Electron-nucleus interactions
- Coulomb interactions between the incident electron and nuclei of the absorber atom result in electron scattering and energy loss of the electron through production of X ray photons (bremsstrahlung). These types of energy loss are characterized by radiative stopping powers.
- Bremsstrahlung production is governed by the Larmor relationship, which states that the power P emitted in the form of photons from an accelerated charged particle is proportional to the square of the particle acceleration a and the square of the particle charge q, or:
- The angular distribution of the emitted photons (Bremsstrahlung) is proportional to
where θ is the angle between the acceleration of the charged particle and a unit vector connecting the charge with the point of observation and β is the standard relativistic v/c.
- At small velocities v of the charged particle (β-->0) the angular distribution gose as
and exhibits a maximum at 
. However, as the velocity of the charged particle increases from 0 towards c, the angular distribution of the emitted photons becomes increasingly more forward peaked.
- The angle at which the photon emission intensity is maximum can be calculated from the following relationship:
That for β-->0 gives
and for β-->1 gives
, including that in the diagnostic radiology energy range (orthovoltage beams) most X ray photons are emitted at 90° to the electron path, while in the megavoltage range (linac beams) most photons are emitted in the direction of the electron beam striking the target.
- The energy loss by radiation and the radiative yield g increase directly with absorber atomic number Z and the kinetic energy of electrons. The radiation yield for X ray targets in the diagnostic radiology energy range (ab.100keV) is of the order of 1%, while in the megavoltage energy range in amounts to 10%-20%.
1.3.3 Stopping powerThe inelastic energy losses by an electron moving through a medium with density ρ are described by the total mass-energy stopping power
, which represents the kinetic energy Ek loss by the electron per unit path length x, or:
consists of two components: the mass collision stopping power
, resulting from electron-orbital electron interactions (atomic excitations and ionizations), and the mass radiative stopping power
, resulting from electron-nucleus interactions (bremsstrahlung production):
- has an important role in radiation dosimetry, since the dose D in the medium may be expressed as:
where
is the fluence of electrons.
- is used in the calculation of electron range R as follows:
where Eki is the initial kinetic energy of the electron.
- Both and are used in the determination of radiation yield (also referred to as bremsstrahlung efficiency) Y as:
- The stopping power focuses on the energy loss by an electron moving through a medium. When attention is focused on the absorbing medium, one is interested in the linear rate of energy absorption by the absorbing medium as the electron traverses the medium. The rate of energy absorption, called the linear energy transfer (LET), is defined as the average energy locally imparted to be absrobing medium by an electron of specified energy in traversing a given distance in the medium.
- In radiation dosimetry the concept of restricted stopping power
is introduced, which accounts for that fraction of the collisional stopping power
that includes all the soft collisions plus those hard collisions that result in delta rays with energies less than a cut-off value
. In radiation dosimetry this cut-off energy is usually taken as 10 keV, an energy that allows an electron just to traverse an ionization chamber gap of 1 mm in air. Delta rays are defined as electrons that acquire sufficiently high kinetic energies through hard collision so as to enable them to carry this energy a significant distance away from the the track of the primary particle and produce their own ionizations of absorber atoms.
1.3.4 Mass scattering powerWhen a beam of electrons passes through an
absorbing medium, the electrons undergo multiple scattering through Coulomb interactions between the
incident electrons and
nuclei of the absorber.
The angular and spatial spread of a pencil electron beam can be approximated by a
Gaussian distribution.
The multiple scattering of electrons traversing a path length
l through an absorbing medium is commonly described by the mean square angle of scattering
that is proportional to the mass thickness
ρl of the absorber.
Analogously to the definition of stopping power, the International Commission on Radiation Units and Measurements (ICRU) defines the mass scattering power
T/ρ as:
The scattering power varies approximately as the square of the absorber atomic number and inversely as the square of the electron kinetic energy.
Chapter 5. Treatment machines for External beam Radiotherapy_5.5 Linacs5.5.1 Linac generations
5.5.2 Safety of linac installations
5.5.3 Components of modern linac
5.5.4 Configuration of modern linacs
5.5.5 Injection system
5.5.6 Radiofrequency power generation system
5.5.7 Accelerating waveguide
5.5.8 Microwave power transmission
5.5.9 Auxiliary system
5.5.10 Electron Beam transport
5.5.11 Linac treatment head
5.5.12 Production of clinical photon beams in a linac
5.5.13 Beam collimation
5.5.14 Production of clinical electron beams in a linac
5.5.15 Dose monitoring system
Medical linacs are cyclic accelerators循環加速器 that accelerate electrons to kinetic energies from 4 to 25 MeV using non-conservative microwave RF fields非保守微波射頻場 in the frequency range from 1000MHz (L band) to 10000 MHz (X band), with the vast majority running at 2856 MHz (S band).
- In a linac the electrons are accelerated following straight trajectories in special evacuated structures called accelerating waveguides加快波導.
- Electrons follow a linear path through the same, relatively low, potential difference several times; hence linacs also fall into the class of cyclic accelerators, just like the other cyclic machines that provide curved paths for the accelerated particles (e.g. betatrons).
- The high power RF fields used for electron acceleration in the accelerating waveguides are produced through the process of decelerating electrons in retarding延緩 potentials in special evacuated devices called magnetrons and klystrons 磁控管和速調管.
Various types of linac are available for clinical use. Some provide X rays only in the low megavoltage range (4 or 6 MV), while others provide both X rays and electrons at various megavoltage energies.
A typical modern high energy linac will provide two photon energies (6 and 18 MeV) and several electron energies (e.g. 6.9.12.16 and 22 MeV)
5.5.1 Linac generations During the past 40 years medical linacs have gone through five distinct generations, making the contemporary machine當代機 extremely sophisticated in comparison with the machines of the 1960s. The five generations introduced the following new features:
- Low energy photons (4-8MeV): Straight-through beam; fixed flattening filter; external wedges; symmetric jaws; single transmission ionization chamber; isocentric mounting.
- Medium energy photons (10-15MeV) and electrons: bent beam; movable target and flattening filter; scattering foils; dual transmission ionization chamber; electron cones.
- High energy photons (18-25MeV) and electrons: dual photon energy and multiple electron energies; achromatic bending magnet; dual scattering foils or scanned electron pencil beam; motorized wedge; asymmetric or independent collimator jaws.
- High energy photons and electrons: computer controlled operation; dynamic wedge; electronic portal imaging device (EPID); multileaf collimator (MLC).
- High energy photons and electrons: photon beam intensity modulation with MLC; full dynamic conformal dose delivery with intensity modulated beams produced with an MLC.
5.5.2 Safety of linac installations
The complexity of modern linacs raises concerns as to safety of operation from the point of view of patients and operators. The International Electro-technical Commission (IEC) publishes international standards that express, as nearly as possible, an international consensus of opinion an relevant technical subjects;electron linacs are addressed in detail by the IEC. The IEC statement on the safety of linac (IEC 60601-2-1, p.13) is as follows:
- "The use of electron accelerators for radiotherapy purpose may expose patients to danger if the equipment fails to deliver the required dose to the patient, or if the equipment design dose not satisfy standards of electrical and mechanical safety. The equipment may also cause danger to persons in the vicinity附近 if the equipment fails to contain the radiation adequately and/or if there are inadequacies in the design of the treatment room"
The IEC document addresses three categories of safety issues - electrical, mechanical and radiation - and establishes specific requirements mainly for the manufactures of linacs in the design and construction of linacs for use in radiotherapy. It also covers some radiation safety aspects of linac installation in customer's treatment rooms.
5.5.3 Components of modern linacs
Linacs are usually mounted isocentrically and the operational systems are distributed over five
major and distinct sections of the machine, the
- Gantry;
- Gantry stand or support;
- Modulator cabinet;
- Patient support assembly (i.e. treatment table)
- Control console.
A schematic diagram of a typical modern S band medical linac is shown in Fig. 5.4.
Also shown are the connections and relationships among the various linacs linac componets; however, there are significant variations from one commercial machine to another, depending on the final electron beam kinetic energy as well as on the particular design used by the manufacturer.
- The length of the accelerating waveguide depends on the final electron kinetic enrgy, and ranges from ~30cm at 4 MeV to ~150cm at 25MeV.
- The main beam forming components of a modern medical linac are usually grouped into six classes:
- Injection system
- RF power generation system
- Accelerating waveguide
- Auxiliary system
- Beam transport system
- Beam collimation and beam monitoring system.
5.5.4 Configuration of modern linacs
At megavoltage electron energies the bremsstrahlung photons produced in the X ray target are mainly forward peaked and the clinical photon beam is produced in the direction of the electron beam striking the target.
- In the simplest and most practical configuration在最簡單，最實用的配置, the electron gun and the X ray target form part of the accelerating waveguide and are aligned對齊 directly with the linac isocentre, obviating無須, 省卻the need for a beam transport system. A straight-through photon beam is produced and the RF power source is mounted in the gantry.
- The simplest linacs are isocentrically mounted 4 or 6 MeV machines, with the electron gun and target permanently永久 built into the accelerating waveguide, thereby requiring no beam transport nor offering an electron therapy option.
- Accelerating waveguides for intermediate (8-15MeV) and high (15-30MeV) electron energies are too long for direct isocentric mounting and thus are located either in the gantry, parallel to the gantry axis of rotation, or in the gantry stand.
A beam transport system is then used to transport the electron beam from the accelerating waveguide to the X ray target.
The RF power source in the two configurations is commonly mounted in the gantry stand. Various design configurations for modern isocentric linac are shown in Fig. 5.5.
5.5.5 Injection system
The injection system is the the sources of electrons; it is essentially a simple electrostatic accelerator called an electron gun.
Two type of electron gun are in use as sources of electrons in medical linacs:
----Diode type
----Triode type
Both electron gun types contain heated filament加熱絲 cathode and a perforated grounded穿孔接地 anode; in addition, the triode electron gun also incorporates a grid三極管電子槍還集成了一個網格.
Electrons are thermionically熱 emitted from the heated cathode, focused into a pencil beam by a curved focusing electrode彎曲聚焦電極 and accelerated towards the perforated anode through which they drift to enter the accelerating waveguide.
The electrostatic fields used to accelerate the electrons in the diode gun are supplied directly from the pulsed modulator脈衝調製器 in the form of a negative pulse delivered to the cathode of the gun.
In the triode gun, however, the cathode is held at a static negative potential (typically -20kV). The grid of the triode gun is normally held sufficiently negative with respect to the cathode to cut off the current to the anode.
The injection of electrons into the accelerating waveguide is then controlled by voltage pulses, which are applied to the grid and must be synchronized 同步with the pulses applied to the microwave generator. A removable triode gun of a high energy linac is shown in Fig. 5.6(a).
5.5.6 Radiofrequency power generation system
The microwave radiation微波輻射used in the accelerating waveguide to accelerate electrons to the desired kinetic energy is produced by the RF power generation system, which consists of two major components:
- An RF power source
- A pulsed modulator
The
RF power source is either a magnetron or a klystron
磁控或速調管. Both are devices that use electron acceleration and deceleration in a vaccum for the production of high power RF fields. Both types use a thermionic emission of electrons from a heated cathode and accelerate the electrons towards an anode in a
pulsed electrostatic field; however, their design
principles are completely different.
- The high voltage (~100keV), high current (~100A), short duration (~1s) pulse required by the RF power source (magnetron or klystron) and the injection system (electron gun) are produced by a pulsed modulator.
The circuitry電路 of the pulsed modulator is housed in the modulator cabinet, which, depending on the particular linac installation design, is located in the treatment room, in a special mechanical room next to the treatment room or in the linac control room. - A magnetron is a source of high power RF required for electron acceleration, while a klystron is an RF power amplifier that amplifies the low Power RF generated by an RF oscillator commonly called the RF driver.
5.5.7 Accelerating Waveguide
Waveguides are evacuated or gas filled metallic structures of rectangular or circular cross-section used in the transmission of microwaves.
波導是疏散或充 氣的金屬結構，矩形或圓形斷面中使用的微波傳輸。Two types of waveguide are used in linacs:
- RF power transmission waveguides and
- accelerating waveguides.
The power transmission waveguides transmit the RF power from the power source to the accelerating waveguide in which the electrons are accelerated.
- the Electron are accelerated in the accelerating waveguide by means of an energy transfer from the high power RF fields, which are set up in the accelerating waveguide and are produced by the RF power generators.
- The simplest kind of accelerating waveguide is obtained from a cylindrical uniform waveguide by adding a series of dises (irises) with circular holes at the centre, placed at equal distances along the tube. These discs divided the waveguide into a series of cylindrical cavities that form the basic structure of the accelerating waveguide in a linac.
The accelerating waveguide is evacuated to allow free propagation of electrons. The cavities of the accelerating waveguide serve two purposes:
- To couple and distribute microwave power between adjacent cavities;
- To provide a suitable electric field pattern for the acceleration of electrons.
Tow types of accelerating waveguide have been developed for the acceleration of electrons:
- Travelling wave structure.行波結構
- Standing wave structure.駐波結構
In the travelling wave structure the microwaves enter the accelerating waveguide on the gun side and propagate towards the high energy end of the waveguide, where they either are absorbed without any reflection or exit the waveguide to be absorbed in a resistive load or to be fed back to the input end of the accelerating waveguide. In this configuration only one in four cavities is at any given moment suitable for electron acceleration, providing an electric field in the direction of propagation.
In the
(5.3)
. The parameter Brad has a value of 16/3 for light charged particles in the non-relativistic energy range
(5.3)
. The parameter Brad has a value of 16/3 for light charged particles in the non-relativistic energy range
