Accelerator- and detector Physics:

Synchrotron radiation from dipole magnetsInsertion devices: Wigglers, Undulatorsinfluence on beam (later)

Lecture 5a

Søren Pape Møller

Synchrotron Radiation (SR)

• Acceleration of charged particles– Emission of EM radiation– In accelerators: Synchrotron Radiation

• Significance– Characterization and use of SR– Effect on particle/accelerator (#10)

General Electric synchrotron accelerator built in 1946, the origin of the discovery of synchrotron radiation from 70 MeV electrons. Glass beam tube.

The circle indicates the evidence of “arcing”.

SR fra ASTRID/2

Udsendelse af synkrotron stråling

Synkrotronstråling fra ASTRID

Fotonenergi (eV)

Bølgelængde (nm)

Synkrotronstrålingfra ASTRID

Sollys

Synligtlys

0.1101000100000

0.01 1 100 10000

Emission of Synchrotron Radiation

• Present lecture, see “Wille” chap 2+”8”– Details, see Jackson – “Classical Electrodynamics”– Here: Mainly key physical elements

• Acceleration of charged particles EM radiation

• Larmor: Total power v<<c

Angular distribution(Hertz dipole)

Relativistic particles

cv ≈

Linear acceleration

• Accelerator energy gain: dE/dx ≈ 15 MeV/m

– Ratio between energy lost and gain:

– η = 5 * 10-14 (for v ≈ c)

– Negligible

Circular accelerat-ion/ors

• In practice: Only SR from electrons! But …

vv⊥

dtd

Energy loss per turn

[m][GeV]5.882][

4

RE

cRPdtPkeVE ss ===∆ ∫

π

ASTRID2E=0.58 GeVR = 1 m∆E≈8 keV

Angular distribution of synchrotronradiation

Spectrum of SR• Spectrum: Harmonics of frev

• Critical SR frequency• Divide power in ½

Synkrotronstråling

[ ] [ ] [ ] [ ] [ ] [ ]GeVT864.1nm GeVT665.0keV 2

2

EBEB cc == λε

0.01 0.1 1 101E10

1E11

1E12

1E13

εc=358 eVved 580 MeVog 1.6 T

Universeltsynkrotronstrålingsspektrum

phot

ons/

s/m

rad/

0.1%

BW/G

eV

Energy/εc

ASTRID

ASTRID og synkrotronstråling

Fotonenergi (eV)

Bølgelængde (nm)

Inte

nsite

t

Synkrotronstrålingfra ASTRID

Sollys

Synligtlys

0.1101000100000

0.01 1 100 10000

cε

𝜀𝜀𝑐𝑐[𝑒𝑒𝑒𝑒] = 665𝐸𝐸2 𝐺𝐺𝑒𝑒𝑒𝑒 𝐵𝐵[𝑇𝑇]

𝜃𝜃 ≈ 1/𝛾𝛾 ≈ 1𝑚𝑚𝑚𝑚𝑚𝑚𝑚𝑚

𝛾𝛾 = 1/ 1 − 𝛽𝛽2

E.g. ASTRID (580 MeV)

Vertical angular distribution

Polarization_____ og -----

[ ] [ ] [ ]GeVT665.0keV 2EBc =ε

Spectral Brightness

1E+11

1E+12

1E+13

1E+14

1E+15

1E+16

1E+17

0.001 0.01 0.1 1 10Photon Energy (keV)

Ph/s

*mm

^2*m

rad^

2*0.

1BW

Undulator, ASTRID2

Undulator

2T 12 pol wiggler, ASTRID2

Bend, ASTRID1

Bend ASTRID2

ASTRID2 brightness• Horizontal

emittance [nm]– ASTRID2: 12.1– ASTRID: 140

• Diffraction limit!

ASTRID/2 beamstørrelse

2mm

0.1mm

ASTRID (140 nm)

0.2mm

0.01mm

ASTRID2 (10 nm)

Diffraktionsbegrænset i V og delvist i H

ε𝛾𝛾 = 𝜎𝜎𝜎𝜎𝜎 = �/4� ASTRID2εH = 10 nm → λ = 100nmεV = 0.1 nm → λ = 1nm

Synkrotron stråling : EffektEnergitab/omgang : U[keV] = 88.5*E4[GeV4]/ρ[m]Udstrålet effekt: P[kW] = U[keV]*I[A]

E [GeV] B [T] εc [keV] U [keV] P [kW]

ASTRID-200mA 0.100 0.276 0.002 0.007 0.001

ASTRID-200mA 0.580 1.6 0.36 8.3 1.7

ESRF-EBS 6 0.85 20.7 3000 1012

LEP 100 0.1 665 2950000 29000

I praksis, max 100 GeV for elektron synkrotron -> linear accelerator

200 mA

Light sources in Europe

#=18

ESRF-EBS – MAX IVESRF-Grenoble 2020 840m – 6 GeV0.133 nm

MAX IV – Lund 2017528m – 3 GeV0.300 nm

Fashion:Multi-Bend achromat

Storage rings for SR• SR – unique broad spectrum!• 0th generation: Paracitic use• 1st generation: Dedicated rings for SR• 2nd generation: Smaller beams

– ASTRID• 3rd generation: Insertion devices (straight sections), small beam

– ASTRID2• 4th generation: Multibend achromats – emittans ↓ x~100

Insertion devices

Multi-pole wiggler (MPW)

• Insertion device in straight section of storage ring• Shift SR spectrum towards higher energies by larger

magnetic fields• Gain multiplied by number of periods

• W/MPW made up to 10 T

K>>1Wiggler”wavelength shifter

Wiggler/undulatorparameterK=ΘW /(1/γ)=eBλu/(2πmec)

ASTRID2 Wiggler

ASTRID2 – MPW - 2 T

Example (ASTRID2):Multi-pole wiggler (MPW)

• B0 = 2.0 T• λ = 11.6 cm• Number of periods = 6• K = 21.7• Critical energy = 447 eV

(dipoles 238 eV)

Undulator radiationIf K <~1 : Interference - Line-spectrum with harmonics

anglen observatio

21

2

0

20

22

2,

Θ

Θ++

⋅= γ

γλλ K

nu

nw

Undulator/wiggler spektrum

ASTRID/2 Undulator

Constructiona) Electromagnet; b) permanent magnets; c) hybrid

magnets

0 50 100 150 2000.0

2.0x1014

4.0x1014

6.0x1014

8.0x1014

1.0x1015

Photo

n flux

Photon energy (eV)

K = 2.3 (25 mm gap) Integrated flux 2.02 mrad2

1.02 mrad2

0.52 mrad2

0.252 mrad2

Spectral Brightness

1E+11

1E+12

1E+13

1E+14

1E+15

1E+16

1E+17

0.001 0.01 0.1 1 10Photon Energy (keV)

Ph/s

*mm

^2*m

rad^

2*0.

1BW

Undulator, ASTRID2

Undulator

2T 12 pol wiggler, ASTRID2

Bend, ASTRID1

Bend ASTRID2

Brightness• Horizontal

emittance [nm]– ASTRID2: 10– ASTRID: 140

Insertion devices: Summary• Wiggler (K > 1, Θ > 1/γ)

– Broad broom of radiation– Broad spectrum– Stronger mag. field: Wavelength shifter (higher

energies!)– Several periods: Intensity increase

• Undulator (K < 1, Θ < 1/γ)– Narrow cone of radiation: Very high brightness

• Brightness ~ N2

– Peaked spectrum (adjustable)• Harmonics if not K<<1

– Ideal source!