SYNCHROTRON RADIATION - CERN · Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS...

Lenny Rivkin

Ecole Polythechnique Federale de Lausanne (EPFL)

and Paul Scherrer Institute (PSI), Switzerland

SYNCHROTRON RADIATION

CERN Accelerator School: Introduction to Accelerator Physics

November 5, 2012, Granada, Spain

Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS Granada, Spain, November 2012

Useful books and references

A. Hofmann, The Physics of Synchrotron Radiation Cambridge University Press 2004

H. Wiedemann, Synchrotron Radiation Springer-Verlag Berlin Heidelberg 2003

H. Wiedemann, Particle Accelerator Physics I and II Springer Study Edition, 2003

A. W. Chao, M. Tigner, Handbook of Accelerator Physics and Engineering, World Scientific 1999


Synchrotron Radiation and Free Electron Lasers

Grenoble, France, 22 - 27 April 1996 (A. Hofmann’s lectures on synchrotron radiation) CERN Yellow Report 98-04

Brunnen, Switzerland, 2 – 9 July 2003 CERN Yellow Report 2005-012

http://cas.web.cern.ch/cas/Proceedings.html

CERN Accelerator School Proceedings

GENERATION OF


Swiss Light Source, Paul Scherrer Institute, Switzerland

Curved orbit of electrons in magnet field

Accelerated charge Electromagnetic radiation

Crab Nebula

6000 light years away

First light observed

1054 AD


1947

GE Synchrotron

New York State


Synchrotron radiation: some dates

1873 Maxwell’s equations

1887 Hertz: electromagnetic waves

1898 Liénard: retarded potentials

1900 Wiechert: retarded potentials

1908 Schott: Adams Prize Essay

... waiting for accelerators …

1940: 2.3 MeV betatron,Kerst, Serber

Maxwell equations (poetry)

War es ein Gott, der diese Zeichen schrieb

Die mit geheimnisvoll verborg’nem Trieb

Die Kräfte der Natur um mich enthüllen

Und mir das Herz mit stiller Freude füllen. Ludwig Boltzman

Was it a God whose inspiration

Led him to write these fine equations

Nature’s fields to me he shows

And so my heart with pleasure glows. translated by John P. Blewett

THEORETICAL UNDERSTANDING

1873 Maxwell’s equations

made evident that changing charge densities would

result in electric fields that would radiate outward

1887 Heinrich Hertz demonstrated such waves:

….. this is of no use whatsoever !

1898 Liénard:

ELECTRIC AND

MAGNETIC FIELDS

PRODUCED BY A POINT

CHARGE MOVING ON AN

ARBITRARY PATH

(by means of retarded potentials … proposed first by Ludwig Lorenz in 1867)

1912 Schott:

COMPLETE THEORY OF


IN ALL THE GORY DETAILS

(327 pages long)

… to be forgotten for 30 years

(on the usefulness of prizes)

Donald Kerst: first betatron (1940)

"Ausserordentlichhochgeschwindigkeitelektronen

entwickelndenschwerarbeitsbeigollitron"


Synchrotron radiation: some dates

1946 Blewett observes energy loss

due to synchrotron radiation

100 MeV betatron

1947 First visual observation of SR

70 MeV synchrotron, GE Lab

1949 Schwinger PhysRev paper

…

1976 Madey: first demonstration of

Free Electron laser


A larger view

Crab Nebula

6000 light years away


1054 AD


1947

GE Synchrotron

New York State

Storage ring based

synchrotron light source


Charge at rest: Coulomb field, no radiation

Uniformly moving charge

does not radiate

Accelerated charge

Why do they radiate?

v = const.

But! Cerenkov!

Bremsstrahlung

or

“braking” radiation


t =

1

40

q

r 1 – n ret

A t =

q

40c

2

v

r 1 – n ret

A +

1

c2

t= 0

B = A

E = – –A

t

and the electromagnetic fields:

(Lorentz gauge)

Liénard-Wiechert potentials


E t =q

40

n –

1 – n 3 2

1r 2

ret

+

q

40c

n n –

1 – n 3 2

1r

ret

B t =

1

cn E

Fields of a moving charge


Transverse acceleration

v a

Radiation field quickly separates itself from the Coulomb field


v

a

Radiation field cannot separate itself from the Coulomb field

Longitudinal acceleration

Moving Source of Waves

Electron with velocity emits a wave with period Temit

while the observer sees a different period Tobs because

the electron was moving towards the observer

The wavelength is shortened by the same factor

in ultra-relativistic case, looking along a tangent to the

trajectory

since

Time compression

obs = 1

22

emit

emitobs TT )1( βn

n

emitobs )cos1(

1 – =

1 – 2

1 + 1

22


Radiation is emitted into a narrow cone

v << c vc

v ~ c

e = 1

e


Sound waves (non-relativistic)

v

e

v

=

vsvs|| + v =

vsvs||

11 + v

vs

e 1

1 + vvs

Angular collimation

Doppler effect (moving source of sound)

s

emittedheardv

1v


Synchrotron radiation power

P E2B2

C = 4

3re

mec2 3

= 8.858 10– 5 mGeV 3

Power emitted is proportional to:

2

4

2

EcCP


2

4

2

EcCP

The power is all too real!


Synchrotron radiation power

P E2B2

C = 4

3re

mec2 3

= 8.858 10– 5 mGeV 3

U0 = C

E 4

U0 = 43hc

4

= 1

137

hc = 197 Mev fm

Power emitted is proportional to:

Energy loss per turn:

2

4

2

EcCP

2

42

3

2

cP


Typical frequency of synchrotron light

Due to extreme collimation of light observer sees only a small portion of electron trajectory (a few mm)

l ~

2

t ~ l

c– l

c = lc

1 –

/1

Pulse length: difference in times it takes an electron and a photon to cover this distance

t ~

c

12 2

~ 1

t~ 30


Spectrum of synchrotron radiation

• Synchrotron light comes in a series of flashes every T0 (revolution period)

• the spectrum consists of harmonics of

• flashes are extremely short: harmonics reach up to very high frequencies

• At high frequencies the individual harmonics overlap

time

T0

0

0

1

T

0

3 typ

continuous spectrum !

! Hz10~

4000 ~

MHz1~

16

typ

0

Wavelength continuously tunable !


0.001

0.01

0.1

1

0.001 0.01 0.1 1 10x = c

50%

~ 2.1x

13

13

~ 1.3 xe

– x

G1 x = x K5 35 3

x dxx

ceV = 665 E

2GeV B T

dP

d=

Ptot

c

S

c

c=

3

2

c3

Ptot =2

3hc

2

4

2

S x =

9 3

8x K5

35

3x dx

x

S x dx

0

= 1


A useful approximation

spectral Flux G1

0.001

0.01

0.1

1

0.001 0.01 0.1 1 10x

G1

Spectral flux from a dipole magnet with field B

Fluxphotons

s mrad 0.1%BW= 2.4610

13E[GeV] I[A]G1 x

Approximation: G1 ≈ A x1/3 g(x)

SN

Lx

xxg

1

])(1[()(

A = 2.11 , N = 0.848

xL = 28.17 , S = 0.0513

Werner Joho, PSI


109

1010

1011

1012

1013

Flu

x [p

hoto

ns/s

/mra

d/0.

1%B

W]

101

102

103

104

105

106

107

Photon energy [eV]

20 GeV

50 GeV

100 GeVLEP Dipole FluxI = 1 mA

Synchrotron radiation flux for different electron energies

Angular divergence of radiation

The rms opening angle R’

• at the critical frequency:

• well below

• well above

= c R 0.54

« c

R 1

c

13

13

0.4

13

13

independent of !

» c

R 0.6

c

12

12

Electron in a storage ring:

TOP VIEW

TILTED VIEW

SIDE VIEW

Polarisation

Synchrotron radiation observed in the plane of the particle orbit is horizontally polarized, i.e. the electric field vector is horizontal

Observed out of the horizontal plane, the radiation is elliptically polarized

E

E

Polarisation: spectral distribution

xSxSP

xSP

d

dP

c

tot

c

tot

x

SS8

7

SS8

1

3:1

Angular divergence of radiation

•at the critical frequency

•well below

•well above

c 2.0

c 2


Seeing the electron beam (SLS)

visible light, vertically polarised X rays

mx 55~


Seeing the electron beam (SLS)

Making an image of the electron beam using the vertically

polarised synchrotron light


High resolution measurement

Wavelength used: 364 nm

For point-like source the

intensity on axis is zero

Peak-to-valley intensity ratio

is determined

by the beam height

Present resolution: 3.5 m

SYNCHROTRON RADIATION - CERN · Synchrotron Radiation Basics, Lenny Rivkin, EPFL & PSI, CAS...

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