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Home , Betatron, Cavity magnetron, Microwave cavity

11/10/2020

Outline

Chapter 4 • Brief history of radiation generators High Energy Machines • Betatrons • Radiation Dosimetry I • Linear accelerator: resonant cavities, magnetrons, , and

Text: H.E Johns and J.R. Cunningham, The • Linear accelerator: components of the physics of radiology, 4th ed. accelerator head http://www.utoledo.edu/med/depts/radther – Thomotherapy

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General considerations for high-energy machine • Depth-dose properties: – High penetration – Delivery of maximum dose at a depth – Minimal low-energy contamination – Skin sparing • Field flatness (not a requirement anymore) • Constant output and monitoring • Sharp field edges (penumbra)

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Evolution of radiation generators Betatrons 1895 - Roentgen discovers X-rays 1913 W.E. Coolidge develops X-ray tube • Device for accelerating 1931 E.O. Lawrence develops a • Electrons from a filament are injected 1932 1MV Van de Graff accelerator installed, Boston, MA (USA) • AC performs two functions: 1939 First medical cyclotron for neutron therapy, Crocker, CA (USA) – Electrons are bent into a circular path 1946 20MeV electron beam therapy with a Betatron, Urbana, IL (USA) – Changing magnetic flux creates E-field 1952 First Co-60 teletherapy units, Saskatoon (Canada) accelerating electrons 1956 First 6MeV linear accelerator, Stanford, CA (USA)  • Electrons spiral 1958 First proton beam therapy (Sweden) d = V dt inward until reach 1959 First scanning electron beam therapy, Chicago, IL (USA) equilibrium orbit 1976 First pion beam therapy, LAMPF, NM (USA) • They are accelerated 1990 First hospital based proton therapy, Loma Linda, CA (USA) as they travel around 1994 First C-ion facility HIMAC (Heavy-Ion Med. Accelerator in Chiba, Japan) at equilibrium orbit Yoichi Watanabe, MPHY5170/TRAD7170, http://www.tc.umn.edu/~watan016/Teaching.htm

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Betatrons • As the electrons get faster they Example 1 idle time need a larger to • A long solenoid has a diameter of 2R=12 cm. When a keep moving at a constant radius current I exists in its windings, a uniform magnetic field orbit, which is provided by the of magnitude B=30 mT is produced in its interior. By increasing magnetic flux decreasing I, the field is caused to decrease at the rate of • After electron attains its maximum 6.5 mT/s. Calculate the magnitude of the induced energy (pt. C) the field at the orbit electric field E at r=8.2 cm from the axis of the solenoid. is decreased, and electron spirals R outward to strike the target d A. 10.0 mV/m = V = E  2r; B =  /(R2 ) • Betatron can be a source of B. 31 mV/m dt r electrons or x-rays (with a target) C. 75 mV/m d d(BR2 ) dB = = R2 • Radiation is produced in pulses D. 143 mV/m dt dt dt • Efficiency is very high, but the E. 200 mV/m R2 dB (610−2 )2 E = = 6.510−3 =143mV/m dose rate could be low due to 2r dt 28.210−2 inefficient injection of electrons

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Cyclotron Cyclotron • For sources of protons and other heavy particles • Massive particle moves through relatively small potential difference many times • Magnetic field is used to bring the particle to an accelerating region • High- oscillator mv2 F = Bqv, = Bqv creates potential difference r between D’s and is used for • Due to increase in mass particle 2r 2m acceleration t = f −1 = = may get out of step with the E field t osc v Bq

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Example 2 Linear Accelerators • A deutron (m=3.34x10-27 kg) circulates in a cyclotron of radius 53 cm and operating frequency 12 MHz, • A charged particle can be accelerated while beginning approximately at rest at the center. The moving through a potential difference between electric potential between D’s is 80 kV. How many passes will it complete before reaching the edge of the two electrodes cyclotron? • Arranging electrodes in a certain configuration v = 2rf final and using electromagnetic wave rather than a A. 80 mv2 m(2rf )2 K final = = = static potential difference allows for higher beam B. 105 2 2 3.3410−27(2 0.5312106 ) energies and intensities C. 130 = D. 150 2 −12 18 • Two main components: power source and resonant E. 200 2.710 J 6.2410 J / eV 16.8MeV 3 5 cavity K pass = 28010 =1.610 eV = 0.16MeV

n = K final / K pass =16.8/ 0.16 105

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Linear Accelerators Linear Accelerators

• II. RESONANT CAVITY FOR GENERATION OF HIGH POWER • I. POWER SOURCE PULSES: 1. Why not DC: Problems of electrical breakdown, physical size of 1. At high , ordinary resonant circuits become impractical. Also electrical equipment problems of radiation loss 2. Apply technique of repeated pulses, V = nv 2. Hollow cavities as resonant circuits () - Need oscillating form of power supply 3. The quality factor, or Q value, of a resonant circuit or cavity is defined as 3. Leads to principle of cyclic and linear accelerators Q = energy stored in cycle/energy lost in cycle 4. has to be short enough to accelerate electrons in a For a circuit, Q ~ 102, whereas for a cavity, Q ~ 104 reasonable distance 4. Achieved through devices called magnetrons and klystrons 5. S-band microwave technology, developed for in WWII, has a 5. Cavity feature in both power sources and accelerating structures frequency of ~ 3 GHz or = 10 cm ROLE OF RESONANT CAVITIES IN LINEAR ACCELERATORS 6. High power is also needed to ensure sufficient energy gain per cycle 1. Cavity acts as an acceleration module 2. Multiple cavity arrangement can act as an RF - 3. Multiple cavity arrangement can act as a high power oscillator - magnetron P.J. Biggs, AAPM Review course 2010 P.J. Biggs, AAPM Review course 2010

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RC circuit Example 3

U V0

V0 +U − IR = 0; I = dq / dt = d(CU ) / dt dU V +U − RC = 0 0 dt RC =100106 10−6 =100 dU U V −t / RC − = 0 U = V0 (1− e )= dt RC RC 100 1− e−100/100 =1000.632 = 63.2 −t / RC ( ) U = V0 (1− e )

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Cavity Principle Cavity Principle • In general, =(LC)-1/2 for a resonant • design is derived circuit, so one needs very small L and from a simple resonant circuit. The C to obtain high frequencies: use of components of such a circuit need to cavities as a form of resonant circuit become smaller as the resonant since they have low L and C frequency increases • Only the electric field plays a role in • The , resistance and electron acceleration (along the axis inductance become the faces and of a cylindrical cavity) sides of a pill box such that the entire • Electric field configuration in surface is made of conducting cylindrical microwave cavity with material hole on axis for electrons to pass • When this cavity is excited, strong Hole for electrons through is only slightly modified electric fields are generated • Efficient transfer of energy to electron perpendicular to the faces that beam, i.e., low energy losses, since alternate in sign with the frequency for a resonant circuit Q ~ 102 (where of the oscillation Q=f0/2f and 2f is FWHM), Electric, magnetic field configurations for whereas for a cavity, Q ~104 P.J. Biggs, AAPM Review course 2010 lowest resonant mode P.J. Biggs, AAPM Review course 2010 17 18

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Example 4 Magnetron

• Generator of • Determine the lowest frequency allowed in • A cylindrical (A) has the a cubic of linear dimension (K) along its axis. • Magnetic field is directed along the of a=30 cm. n=1 axis of the cylinder • Magnetic field bends the electron A. 0.1 GHz n=2 2a = n trajectory, and accelerating electron B. 0.2 GHz n =1 n=3 emits energy in microwave range C. 0.5 GHz At low magnetic fields, the electron • The magnetic field has to be high  = 2x30 = 60cm paths’ are bent, but the electrons still D. 1 GHz reach the anode. At a field Bc, the enough to provide electron  = c /  = 31010 / 60 = 5108 = 0.5 GHz electron paths’ just graze the anode. For collection, but low enough to avoid E. 5 GHz higher fields, individual electrons are unable to reach the anode. electron accumulation at K

P.J. Biggs, AAPM Review course 2010 19 20

Magnetron Magnetron Resonant cavities • The circulating electrons induce a charge distribution between adjacent segments of the anode • This, in turn, perturbs the electron orbits shaping the distribution into a form resembling the spokes of a wheel • The resonant cavities gain energy • Current between anode and cathode is not used in a power from the orbiting electrons which source are slowed and eventually spiral • If it stops the magnetron is blocked due to electron into the anode, leading to anode accumulation around the cathode current

P.J. Biggs, AAPM Review course 2010 P.J. Biggs, AAPM Review course 2010 21 22

Magnetron Klystron

• The dc field extends radially from adjacent anode segments to the cathode (shown in red); the ac fields extend between adjacent segments (blue lines), their magnitude changes with the RF oscillations occurring Field-free region in the cavities • Klystron is a microwave amplifier • Rotating space-charge wheel • Low-power signal is supplied to the “buncher” cavity, its E- results in continuously field modulates velocities of electrons, which then merge into delivered energy to sustain the bunches going through the drift tube RF filed • Amplified signal is collected from “catcher” cavity, where Twelve- http://www.radartutorial.eu/08.transmitters/pic/mag06.big.gif electrons decelerate emitting at the same resonant frequency

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Waveguides Klystron Traveling wave Standing wave • The electron gun 1 produces electrons • The bunching cavities 2 regulate the speed of the electrons (ac field accelerates slow electrons and slows down fast ones) so that they arrive in bunches at the output cavity • The bunches of electrons decelerate and excite microwaves in the output cavity 3 (E- filed of the same frequency but polarity opposite to that applied in bunching cavities) • The amplified microwaves flow into 4, to the accelerating structure • The electrons are absorbed in the beam stop 5 • Usually klystrons have multiple amplifying http://www2.slac.stanford.edu/ cavities vvc/accelerators/klystron.html 25 26

Waveguides Waveguides

• The velocity of the wave • Cavities in an accelerating waveguide serve dual is matched with the purpose: accelerate electrons (those that are at the velocity of the electron at accelerating polarity) and transfer microwave time of injection power to the next cavity (coupling) • Disk spacing is gradually • In standing wave configuration half of cavities have increased to correspond essentially zero E-field (no acceleration); those are to velocity v down the moved off-axis thus making the waveguide shorter waveguide • Traveling waveguides (E~80kV/cm) are longer The length of the accelerating waveguide depends on the than standing waveguides (E~150kV/cm) final electron E: ~30 cm at 4 MeV; ~150 cm at 25 MeV

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Accelerating waveguides Example 5

Cut-away of standing • What is the minimum size of a cubical cavity in a wave accelerating standing wave waveguide for 3000 MHz  structure: 30cm long microwaves? with 5 accelerating cavities (from Karzmark/ A. 2 cm Podgorzak)  c 31010 cm/s d = = = = 5 cm B. 3 cm 6 C. 5 cm 2 2 2300010 /s • Most linacs use waveguides operating at 3000 MHz D. 10 cm (S-band microwaves) • Compact waveguides (used in CyberKnife, Tomotherapy) operate at 9000 MHz (X-band)

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Medical linacs Medical linacs • Most use isocentric mounts with the distance of 100 (80) cm to the axis of rotation • The center of the tumor is positioned at the axis

Source: Podgorsak, E.B., Radiation Oncology Physics Handbook, IAEA 2005, Chapter 5 31 32

Medical linacs Tomotherapy

• Various components • A linac is mounted on a serve a purpose of CT-like ring gantry delivering flat (or not) – Conformal treatment (MLC) beam with pre-defined – Image guidance (MV imaging) field sizes and • The source can move either adequate shielding through a set of discrete beyond the target angular positions or • Ion chamber is used to helically monitor the output • First patient treated in 2002

Conceptual drawing of a helical tomotherapy unit in the first tomotherapy paper (Mackie et al 1993).

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Summary Additional reading

• P.J. Biggs, AAPM Review course 2010, available at • Particle accelerators: circular and linear https://www.aapm.org/meetings/2010AM/documents/biggs2.pdf • High energy x-ray machines use electron (updated in 2014) accelerator and a target • C.J. Karzmak, R.J. Morton, A primer on theory and operation of linear accelerators in , Med. Phys. Publishing • Using electromagnetic wave rather than a corp., 1989 static potential difference allows for higher • E.B. Podgorsak, Radiation Physics for Medical Physicists, 2nd beam energies and intensities edition, Springer 2010, Chapters 13-14 (book available online through UT library) • Podgorsak, E.B., Radiation Oncology Physics Handbook, IAEA 2005, Chapter 5 (available online)

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