1

AcceleratorsWe’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

2

AcceleratorsCirca 2000

3

AcceleratorsA brief history

4

Accelerators

A brief history Electrostatic (Cockcroft-Walton, van

de Graaf) Linac (linear accelerator) Circular (cyclotron, betatron,

synchrotron) Development of strong focusing Colliding beams (present day) Plasma wakefield, ???

5

Accelerators“Moore’s law” ~ e+t/C

6

Accelerators“Moore’s

law”

7

LinacLinac = linear

acceleratorApplications in both high

energy physics and radiation therapy

8

LinacLinacs 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

9

LinacBrief history

Invented by Wideroe (Germany) in 1928 Accelerated potassium ions to 50 keV using 1 MHz AC

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)

10

LinacWideroe’s linac

11

LinacAlvarez drift tube linac

First stage of Fermilab linac

12

LinacA 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

13

LINAC

Medical linacs can be either type

14

Waveguides

occurcannot mode

0 mode

0 mode

solutions of sets h twodistinguis We

wallmetal at the 0

apply conditionsboundary following thecavity, metal aIn

0 and 0

mediadifferent between boundary aAt

and 0

equations sMaxwell' of some Recall

||

2||

1||

21

TEM

BTE

ETM

BE

EEBB

adBdt

dldEadB

z

z

T

TT

SLS

15

WaveguidesCyclindrical wave guide

dimensions waveguideby the determined is r wavenumbecutoff The

llyexponentia off falls wave theimaginary, is If

propagates wave thereal, is If

have also We

functions Bessel theof szero' at the are boundaries metallic The

,E

bygiven is field E theofcomponent The

0B modes TM heConsider t

a radius of guide wavelcylindrica aConsider

222222

0z

z

c

z

z

zczyx

mkzticm

k

k

k

kkkkkk

erkJEr

z

16

TM Modes

TM01 mode

17

Waveguides

ccdk

dv

cv

ckk

v

kv

cgr

zph

ph

2/1

possible ison accelerati noin that problem a is But there

ed transmittisenergy or n informatio no

since that problem No

by given is velocity phase The

18

WaveguidesPhase and group velocity

19

WaveguidesPhase and group velocity

velocitygroup with thepropagated isenergy or n Informatio

is velocity group The

constant remains that so propagated is term thisof phase the

again and envelope thedefines termsecond The

is velocity phase The

constant is that so propagated is first term theof phase The

,,2

cossin2

sinsin

210

0

00

dk

dv

tdxdk

kv

tkx

txftxfEE

tddkxtkxEE

tdwxdkkEtdwxdkkEE

g

p

20

WaveguidesThe 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

Conducting irises in a waveguide in TM0,1 mode act as discrete capacitors with separation d in parallel with C0

00

1

CLvph

dCCLvph

/

1

00

21

Waveguides

Disc loaded waveguide

22

Traveling Wave LinacNotes

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

23

Traveling Wave Linac

24

Standing Wave LinacNotes

In this case one terminates the waveguide with a conducting disc thus causing a /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

25

Standing Wave Linac

26

Standing Wave Linac

Side coupled cavities

27

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

28

RF GenerationMagnetron

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

29

RF Generation

Magnetron

30

RF Generation

Magnetron

31

RF GenerationKlystron

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

32

RF Generation

Klystron

33

Medical Linac

Block diagram

Pulse modulator

Klystron or magnetron

Bendingmagnet

Electronsource

Accelerating structure

Treatmenthead

34

Medical Linac

35

Medical Linac

36

CyclotronThe 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

37

CyclotronPrinciple of operation

Particle acceleration is achieved using an RF field between “dees” with a constant magnetic field to guide the particles

38

CyclotronPrinciple of operation

c approaches vas cancelt won'

momentum and velocity in vsince relativityby Limited

222

daccelerate is particle the

asconstant remainsfrequency that theNote

for 2

m

eB

mv

eBvvf

e

p

e

mvB

cvmv

qvB

39

CyclotronWhy don’t the particles hit the pole

pieces? The fringe field (gradient) provides vertical

and (less obviously) horizontal focusing

40

CyclotronTRIUMF in Canada has the world’s largest

cyclotron

41

CyclotronTRIUMF

42

CyclotronNSCL cyclotron at Michigan State

43

Cyclotron

44

BetatronSince 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

45

Betatron

Principle of operation

Bguide = 1/2 Baverage

CoilSteel

Vacuum chamber

<B>B0

46

BetatronPrinciple of operation

orbit

orbit

eRBBeR

p

dt

BdeR

dt

dpF

dt

BdRE

dt

BdRRE

dt

BdA

dt

dEmf

BB

2

2

thenis electron theon force The2

2

2

is betatron theof field Bfor thet requiremen A

2

47

TM Modes

48

TE Modes

Dipole mode Quadrupole mode used in RFQ’s

49

Waveguides

GHz.fcmλ cma

aac

ka

c

imc

151 and 26 ,10For

h wavelengt thedetermines radiuscavity theSo

61.2405.2

22 Thus

405.2 note Also

propagateslonger no wave theand

imaginary is then, whenNote

c

0,1

2

2,22