Accelerators
We’ve seen a number of examples of
technology transfer in particle detector
development from HEP (basic science)
to industry (medical, …)
Particle accelerators provide another
such example

There are currently more than 30,000
particle accelerators in use throughout the
world with only a small fraction being used
in HEP/nuclear research
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Accelerators
 Circa 2000
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Accelerators
 A brief history
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Accelerators
A brief history

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Electrostatic (Cockcroft-Walton, van de
Graaf)
Linac (linear accelerator)
Circular (cyclotron, betatron, synchrotron)
Development of strong focusing
Colliding beams (present day)
Plasma wakefield, ???
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Accelerators
 “Moore’s law” ~ e+t/C
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Accelerators
 “Moore’s
law”
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Linac
 Linac = linear accelerator
 Applications in both high
energy physics and
radiation therapy
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Linac
 Linacs are single pass accelerators for
electrons, protons, or heavy ions

Thus the KE of the beam is limited by length of
the accelerator
 Medical (4-25 MeV) – 0.5-1.5 m
 SLAC (50 GeV) – 3.2 km
 ILC (250 GeV) - 11 km
 Linac – static field, induction (time varying B
field), RF



Operate in the microwave region
Typical RF for medical linacs ~ 2.8 GHz
Typical accelerating gradients are 1 MV/m – 100
MV/m
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Linac
 Brief history

Invented by Wideroe (Germany) in 1928
 Accelerated potassium ions to 50 keV using 1 MHz AC


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First realization of a linac by Sloan (USA) in 1931
No further progress until post-WWII when high
power RF generators became available
Modern design of enclosing drift tubes in a cavity
(resonator) developed by Alvarez (USA)
 Accelerated 32 MeV protons in 1946 using 200 MHz 12 m
long linac

Electron linac developed by Hansen and Ginzton
(at Stanford) around the same period
 Evolved into SLAC laboratory and led to the birth of
medical linacs (Kaplan and Varian Medical Systems)
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Linac
 Wideroe’s linac
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Linac
 Alvarez drift tube linac
 First stage of Fermilab
linac
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Linac
A linac uses an oscillating EM field in a
resonant cavity or waveguide in order
to accelerate particles

Why not just use EM field in free space to
produce acceleration?
We need a metal cavity (boundary
conditions) to produce a configuration
of waves that is useful


Standing wave structures
Traveling wave structures
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LINAC
Medical linacs can be either type
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Waveguides
Recall some of Maxwell's equations
 
 
d  
SB  da  0 and LE  dl   dt SB  da
At a boundary between differentmedia
BT1  BT2  0 and E||1  E||2  0
In a metalcavity,thefollowingboundary conditionsapply
E||  BT  0 at themetalwall
We distinguish two sets of solutions
TM mode E z  0 
TE mode Bz  0
TEM mode cannotoccur
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Waveguides
 Cyclindrical wave guide
Consider a cylindrical wave guide of radius a
Consider the T M modes B z  0 
T he z componentof t heE field is given by
E z r ,    E0 J m kc r e i t  kz m 
T hemet allicboundariesare at t hezero's of t heBessel funct ions
We also havek 2  k x2  k y2  k z2  k c2  k z2
If k z is real, t he wave propagat es
If k z is imaginary,t he wave falls off exponent ia
lly
T hecut off wavenumber k c is det erminedby t hewaveguide dimensions
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TM Modes
TM01 mode
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Waveguides
T hephase velocityis given by v ph 
v ph 

kz


k

k
c
No problem thatv  c since
no information or energyis transmitted
But thereis a problemin thatno acceleration is possible
d
2
vgr 
 c 1  c /    c
dk
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Waveguides
 Phase and group velocity
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Waveguides
 Phase and group velocity
E  E0 sink  dk x  w  d t   E0 sink  dk x  w  d t 
E  2 E0 sinkx  t cosdkx  dt 
E  2 E0 f1 x, t  f 2 x, t 
T hephaseof thefirst termis propagatedso thatkx  t is constant
T hephase velocityis v p 

k
T hesecond termdefines theenvelopeand again
the phaseof this termis propagatedso that xdk  td remainsconstant
d
T hegroup velocityis v g 
dk
Informatio
n or energyis propagatedwith thegroup velocity
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Waveguides
 The phase velocity can be slowed by fitting the
guide with conducting irises or discs
 The derivation is complicated but alternatively
think of the waveguide as a transmission line
1
v ph 
L0C0
 Conducting irises in a waveguide in TM0,1
mode act as discrete capacitors with
separation d in parallel with C0
1
v ph 
L0 C0  C / d 
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Waveguides
Disc loaded waveguide
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Traveling Wave Linac
 Notes

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
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Injection energy of electrons at 50 kV (v=0.4c)
The electrons become relativistic in the first
portion of the waveguide
The first section of the waveguide is described as
the buncher section where electrons are
accelerated/deaccelerated
The final energy is determined by the length of
the waveguide
In a traveling wave system, the microwaves must
enter the waveguide at the electron gun end and
must either pass out at the high energy end or be
absorbed without reflection
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Traveling Wave Linac
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Standing Wave Linac
 Notes



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In this case one terminates the waveguide with a
conducting disc thus causing a p/2 reflection
Standing waves form in the cavities (antinodes
and nodes)
Particles will gain or receive zero energy in
alternating cavities
Moreover, since the node cavities don’t contribute
to the energy, these cavities can be moved off to
the side (side coupling)
The RF power can be supplied to any cavity
Standing wave linacs are shorter than traveling
wave linacs because of the side coupling and also
because the electric field is not attenuated
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Standing Wave Linac
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Standing Wave Linac
Side coupled cavities
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Electron Source
 Based on thermionic
emission
 Cathode must be insulated
because waveguide is at
ground
 Dose rate can be regulated
controlling the cathode
temperature


Direct or indirect heating
The latter does not allow
quick changes of electron
emission but has a longer
lifetime
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RF Generation
Magnetron


As seen in your microwave oven!
Operation
 Central cathode that also serves as filament
 Magnetic field causes electrons to spiral
outward
 As the electrons pass the cavity they induce a
resonant, RF field in the cavity through the
oscillation of charges around the cavity
 The RF field can then be extracted with a short
antenna attached to one of the spokes
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RF Generation
Magnetron
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RF Generation
Magnetron
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RF Generation
 Klystron


Used in HEP and > 6 MeV medical linacs
Operation – effectively an RF amplifier
 DC beam produced at high voltage
 Low power RF excites input cavity
 Electrons are accelerated or deaccelerated in
the input cavity
 Velocity modulation becomes time
modulation during drift
 Bunched beam excites output cavity
 Spent beam is stopped
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RF Generation
Klystron
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Medical Linac
Block diagram
Electron
source
Bending
magnet
Accelerating structure
Pulse
modulator
Klystron or
magnetron
Treatment
head
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Medical Linac
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Medical Linac
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Cyclotron
 The first circular accelerator was the cyclotron

Developed by Lawrence in 1931 (for $25)
 Grad student Livingston built it for his thesis

About 4 inches in diameter
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Cyclotron
 Principle of operation

Particle acceleration is achieved using an RF field
between “dees” with a constant magnetic field to
guide the particles
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Cyclotron
 Principle of operation
qvB 
m v2

for v  c
mv p
B 

e
e
Note t hat thefrequency remainsconstantas
the part icleis accelerat ed
v
v eB
eB
f 


2p 2p m v 2pm
Limitedby relat ivitysince v in velocit yand momentum
won' t cancelas v approachesc
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Cyclotron
 Why don’t the particles hit the pole pieces?

The fringe field (gradient) provides vertical and (less
obviously) horizontal focusing
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Cyclotron
 TRIUMF in Canada has the world’s largest
cyclotron
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Cyclotron
 TRIUMF
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Cyclotron
 NSCL cyclotron at Michigan State
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Cyclotron
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Betatron
 Since electrons quickly become relativistic
they could not be accelerated in cyclotrons

Kerst and Serber invented the betatron for this
purpose (1940)
 Principle of operation


Electrons are accelerated with induced electric
fields produced by changing magnetic fields
(Faraday’s law)
The magnetic field also served to guide the
particles and its gradients provided focusing
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Betatron
Principle of operation
Steel

Coil
<B>
B0
Vacuum
chamber
Bguide = 1/2 Baverage
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Betatron
 Principle of operation
A requirement for theB field of thebetatronis
B
Borbit 
2
d
dB
Em f 
A
dt
dt
2 dB
E 2pR  pR
dt
R dB
E
2 dt
T heforceon theelectronis then
dp eR dB
F

dt
2 dt
eRB
p
 eRBorbit
2
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TM Modes
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TE Modes
Dipole mode
Quadrupole mode used in
RFQ’s
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Waveguides

, thenk is imaginary
Note when    
 a
2
2
c
2
m ,i
2
and the wave no longer propagates
Also note 0,1  2.405
2pa
 2.61a

T husc 
c 2.405
2pc
So thecavityradius determinesthe wavelength
For a  10 cm, λ  26 cm and f  1.15 GHz
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