Electron dynamics with Synchrotron Radiation - CERN · Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest Electron dynamics with Synchrotron Radiation

Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest

Electron dynamicswith

Synchrotron Radiation

Lenny Rivkin

Paul Scherrer Institute (PSI)

and

Swiss Federal Institute of Technology Lausanne (EPFL)


Click to edit Master title styleUseful books and references

H. Wiedemann, Synchrotron RadiationSpringer-Verlag Berlin Heidelberg 2003

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

A.Hofmann, The Physics of Synchrotron RadiationCambridge University Press 2004

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


Click to edit Master title style

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 2003CERN Yellow Report 2005-012

Previous CAS Schools Proceedings

CERN Accelerator School Proceedings

http://cas.web.cern.ch/cas/CAS Welcome/Previous Schools.htm


Curved orbit of electrons in magnet field

Accelerated charge Electromagnetic radiation


Electromagnetic waves

Crab Nebula

6000 light years away

First light observed

1054 AD

First light observed

1947

GE Synchrotron

New York State

GENERATION OFSYNCHROTRON RADIATION

Swiss Light Source, Paul Scherrer Institute, Switzerland


60‘000 SR users world-wide


Why do they radiate?


Synchrotron Radiation isnot as simple as it seems

… I will try to showthat it is much simpler


Charge at restCoulomb field, no radiation


Uniformly moving charge does not radiate

v = constant

But! Cerenkov!


Click to edit Master title styleFree isolated electron cannot emit a photon

Easy proof using 4-vectors and relativity

momentum conservation if a photon is emitted

square both sides

in the rest frame of the electron

this means that the photon energy must be zero.

𝑷𝑖 = 𝑷𝑓 + 𝑷𝛾

𝑷𝛾 = (𝐸𝛾 , 𝑝𝛾)

𝑚2 = 𝑚2 + 2𝑷𝑓 ∙ 𝑷𝛾+ 0 ⇒ 𝑷𝑓 ∙ 𝑷𝛾 = 0

𝑷𝑓 = (𝑚, 0)

We need to separate the field from charge

Bremsstrahlung

or

“braking” radiation

Transition Radiation

𝝐𝟏 𝝐𝟐

𝑐1 =1

𝜖1𝜇1𝑐2 =

1

𝜖2𝜇2

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

va

Radiation field quickly separates itself from the

Coulomb field

v

a

Radiation field cannot separate itself from the

Coulomb field

Longitudinal acceleration


Synchrotron RadiationBasic Properties

Moving Source of Waves

Cape Hatteras, 1999


Click to edit Master title styleTime compression

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

n

1 – =

1 – 2

1 + 1

22

obs = 1

22

emit

emitobs TT )1( βn

emitobs )cos1(

Radiation is emitted into a narrow cone

v << c v c

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 flashesevery T0 (revolution period)

• the spectrum consists ofharmonics 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 = 665E

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


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


Synchrotron light polarization

An electron in a storage ring

TOP VIEW

Polarization:

Linear in the plane of the ring

the electric field vector

SIDE VIEW

TILTED VIEW

elliptical out of the plane

E

E

Angular distribution of SR

E

E


Synchrotron light basedelectron beam diagnostics


Seeing the electron beam (SLS)

visible light, vertically polarisedX rays

mx 55~

Seeing the electron beam (SLS)

Making an image of the electron beam using the verticallypolarised synchrotron light

High resolution measurement

Wavelength used: 364 nm

For point-like source theintensity on axis is zero

Peak-to-valley intensity ratiois determined

by the beam height

Present resolution: 3.5 m

Electron dynamics with Synchrotron Radiation - CERN · Electron Beam Dynamics, L. Rivkin, Introduction to Accelerator Physics, Budapest Electron dynamics with Synchrotron Radiation

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