Post on 10-Jan-2022
transcript
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!