Synchrotron Radiation Facilities

1
Synchrotron Radiation Facilities

• Alessandro G. Ruggiero
• Brookhaven National Laboratory
• CINVESTAV, Mexico City, January, 24-26, 2007

2
World Radiation Facilities

• There are 60 SR Facilities in the World listed at
• http//www.camd.lsu.edu/lightsourcefacilities.html
  
• SPring - 8 Hyogo, Japan
• Advanced Photon Source Argonne, IL, United
  States
• European Synchrotron Radiation Facility Grenoble,
  France
• National Synchrotron Light Source Brookhaven,
  NY, United States

3
3rd-Generation Facilities and Brookhaven
Energy Circumfer. Linac/Booster Beam Current Emittance m-rad
SPring-8 8 GeV 1436 m
APS 7 GeV 1104 m / 40 450 MeV 0.822 x 10-8
ESRF 6 GeV 844 m / 16 200 MeV 0.2 Amp 0.695 x 10-8
NSLS-Xray 2.5 GeV 170 m / 8 120/750 MeV 0.5 Amp 0.102 x 10-6
NSLS-VUV 750 MeV 51 m / 4 120/750 MeV 1.0 Amp 0.138 x 10-6
Number of Periods
4
Typical SR Facility
Undulator - Wiggler
e-Source
Insertion Devices
Bending Magnet
Energy, E Circumference, 2pR No. of Periods,
M Beam Current, I Bending Radius, ? Number of
Beam Lines
5
a2 ??H (??)2 b2 ??V ?
?E/E ? p a?
?
?
?
a
Dipoles
Quadrupoles
6
Lattice Design Period
Equations of Motion x radial and y vertical
displacement from reference orbit x, y are
angles that electron trajectory makes with
reference orbit. ? d / ds s ?
longitudinal coordinate x' KH(s) x
h(s) ? h(s) curvature 1 / ? ?
?E/E y' KV(s) x 0 KH,V(s)
focusing function G / B?

• Drift Length L
• 1 L 0 0 0 0
• 0 1 0 0 0 0
• 0 0 1 L 0 0
• 0 0 0 1 0 0
• 0 0 0 0 1 0
• 0 0 0 0 0 1

• Total Period Matrix M H or V
• cos? ?sin? ?sin?
• -?sin ? cos? ?sin?
• ?H Np?/2p

• Dipole Bending Angle ? Radius ?
• cos? sin? 0 0 0 ?(1- cos?)
• -?-1sin? cos? 0 0 0 sin?
• 0 0 1 ?? 0 0
• 0 0 0 1 0 0
• sin? ?(1- cos?) 0 0 1 ?(? - sin?)
• 0 0 0 0 0 1

• Quadrupole K (G/B?)1/2 Length L Strength
  ? LK
• cos? K-1sin? 0 0 0 0
• -Ksin? cos? 0 0 0 0
• 0 0 cosh? K-1sinh? 0 0
• 0 0 Ksinh? cosh? 0 0
• 0 0 0 0 1 0
• 0 0 0 0 0 1
• For QF Invert 2x2 H with 2x2 V for QD

• x m11 m12 0 0
  0 m16 x
• x' m21 m22 0 0
  0 m26 x'
• y 0 0 m33 m34
  0 0 y
• y' 0 0 m43 m44
  0 0 y'
• s -m26 -m16 0 0
  1 m56 s
• ? 2 0 0 0 0
  0 1 ? 1

? ? ? betatron ? ? dispersion ?H ?V
tunes ?c momentum compaction
factor

Magnet Errors Misallignment -- H-V
Coupling Chromaticity d ?H,V / d ? --
Sextupoles -- Non-linearities
7
Lattice Functions
8
Lattice Functions
9
Radiation Integrals

• I1 ? ? ds / ? all integrals are over
  Dipoles
• I2 ? ds / ?2
• I3 ? ds / ?3
• I4 ? (1-2n) ? ds / ?3 n - (? / B) dB /
  dx (Field Index)
• I5 ? H ds / ?3 H
  ?2 (? ?' - ?' ? / 2) / ?
  (horizontal)
• Momentum Compaction ?c (E / C)
  dC / dE I1 / C
• Energy Loss per Turn U0 2re E4
  I2 / 3 (mc2)3
• Damping Partition Factors JH 1
  - I4 / I2 and JE 2 I4 / I2
• Energy Spread ?E2 (55/32v3) (h /
  mc) (E/mc2)2 I3 / (2 I2 I4)
• Emittance ?
  (55/32v3) (h / mc) (E/mc2)2 I5 (I2 - I4)
• F(?H, lattice) E2GeV
  / JH NDipoles
• gt 7.84 mm-mrad
• Damping Times ?i ms Cm ?m /
  13.2 Ji E3 GeV
• E.D. Courant and H.S. Snyder, Theory of
  Alternating Gradient Synchrotron, Annals of
  Physics, 3, 1-48 (1958)
• M. Sands, The Physics of Electron Storage Rings.
  An Introduction, SLAC-121, Nov.ember 1970

10
Synchrotron Radiation from a Dipole Magnet

• Critical Photon Energy ?c h ?c 3 h c
  ?3 / 2 ?
• ?c keV 0.665 BT E2 GeV
• ?c Ao 18.64 / BT E2 GeV
• dN / d? (photons spectral and
  angular distribution)
• (3 ? ?6 / 4 p2) y2 (?2 ?-2)2 K2/32(?)
  K1/32(?) ?2 / (?2 ?-2) (I / e) ?? / ?
• ? / ? vertical / horizontal opening angle
• ? y (1 ?2 ?2)3/2 / 2
• y ?c / ? ? / ?c
• At ? 0 dN / d? 1.325 x 1016 E2GeV
  IAmp y2 K2/32(y/2) ?? / ?
• photons/sec/mrad?/mrad?
• Integrating over ? dN / d? 2.457 x 1016
  EGeV IAmp y (?y8K5/3(x)dx) ?? / ?
• photons/sec/mrad?
• dP/d? mW/mrad? 8.73 x 103 E4GeV
  IAmp y2 (?y8K5/3(x)dx) ?? / ? ?m
• Total Power PTkW U0keV IAmp 88.5
  E4GeV IAmp / ?m
• J. Schwinger, Phys. Rev. 97, 470 (1955)

11
RF Acceleration

• Because of the energy loss U0 to Synchrotron
  Radiation, the Beam is continuously
• re-accelerated with a RF system of cavities at
  the frequency fRF and peak voltage VRF
• The revolution Frequency f0 c / C (? 1)
• The Harmonic Number h fRF / f0
• The Synchronous Phase ?s arcsin 1/q
  
• q eVRF / U0
• The RF acceptance ?RF 2 U0
  (q2 - 1)1/2 - arccos (1/q) / p ?c h E1/2
• Synchrotron Tune ?s fs / f0 eVRF
  ?c h cos ?s / 2p E1/2
• rms Bunch Length ?L c ?c ?E / 2 p fs

12
Beam Lifetime

• Gas Scattering (elastic)
• 1/?scat 4re2Z2p d c lt?Hgt ?Hmax / a2
  lt?Vgt ?Vmax / b2 / 2 ?2
• Bremstrahlung
• 1/?brem (16/411)re2Z2 d c ln183
  Z-1/3-ln ARF - 5/8
• Touschek
• 1/?T vp re2 c N C(?) / ?H' ?3 (Aacc)2
  V V 8p3/2 ?H ?V ?L Aacc
  lt Abet or ARF
• C(?) -3 e-? / 2 ? ??8 e-u ln u du / 2
  u (3 ? - ? ln ? 2) ??8 e-u du / u
• ? (Aacc / ? ?H')2
• Quantum Lifetime
• ?q ?E e? / 2 ? ? ARF2 / 2
  ?E2

13
Damping Time 75 ms
Lifetime 180 min Number
of RF Buckets 1560 Number of
Bunches 1280
14
Helical Undulator

• Field Configuration (NU is the number of
  periods)
• B Bucos(kuz) x sin(kuz) y kU 2p /
  ?U
• Radiated Wavelength Wiggler Parameter
• ?(?) ?U(1 K2 ?2?2) / 2 ?2
  K eBU / mckU lt 1
• Spectral and Angular Distribution (? 0)
  photons/sec/steradian
• dN / d? 2? NU2 ?2 K2 (I/e) (sin x / x)2 (??
  /?) / (1 K2)2
• Resonance and Width x pNU(? - ?r) / ?r
• ?r 2 c kU ?2 / (1 K2) ?? /?r 1 /
  NU

15
Planar Undulator (1)

• Field Configuration (NU is the number of
  periods)
• B Bucos(kuz) y kU 2p / ?U
• Radiated Wavelength Undulator Parameter
• ?n(?) ?U(1 K2/2 ?2?2) / 2n?2
  K eBU / mckU lt 1
• Spectral and Angular Distribution (? 0)
  photons/sec/steradian
• dN / d? ? NU2 ?2 Fn(K) (I/e) (sin xn / xn)2
  (?? /?)
• Resonance and Width xn pNUn(? - ?n) / ?n
• ?n 2 nc kU ?2 / (1 K2/2) ??n /?n
  1 / nNU

16
Planar Undulator (2)

• Form Factor
• Fn(K) nK / (1 K2/2)2 J(n1)/2 (u) -
  J(n-1)/2 (u) 2
• n 1, 3, 5, . u n K2/(4 2K2)
• Total Power Radiated
• PTW 7.26 E2GeV IAmp NU K2 / ?Ucm

17
Planar Wiggler

• The Insertion is a Wiggler when K gtgt 1 (with
  NW periods)
• Critical Energy
• ?c(?) ?c0 1 - (?? / K)21/2
• ?c0keV 0.665 BT E2GeV
• K 0.934 BT ?wcm
• Flux 2 NW x equivalent arc source flux of same
  ?c
• Total Power Radiated
• PTW 7.26 E2GeV IAmp NW K2 / ?Wcm

18
Klystron
AC - to -RF Conversion Efficiency 50-60
19
Free Electron Laser (1)
A Coherent Source of Tunable Radiation If e-Bunch
length gtgt ?c then Prad N If e-Bunch length
lt ?c then Prad N2

• The FEL has three components
• - e-beam with E and I -gt P E x I
• a fraction of the beam power is converted to
  FEL power
• - Undulator (Helical) with BU and ?U
• stimulates radiation at wavelength ?c ?c
  ?U(1 K2) / 2 ?2
• - Low-Level e.m. Field at ?c (beam noise,
  external input, mirrors,.)
• creates beam self-bunching at lengths
  comparable to ?c
• Electron Orbit in Undulator K eBU / mckU kU
  2p / ?U
• ? (K / ?) cos(kUz) x sin(kUz) y
  ?0 z
• ?0 1 (1 K2) / ?21/2

20
Free Electron Laser (2)

• Plane wave propagating along the Undulator axis
  k 2p / ?
• E E0 cos(kz - ?t ?) x sin(kz - ?t
  ?) y
• Energy Transfer Ponderomotive Force Phase
• mc2 d? / dt ec E0 (K / ?) sin (? ?) ?
  (k kU) z ?t ?0
• Synchronism Condition d? / dt 0
  -gt ? ?c
• Otherwise d? / dt k (?z / ?0 1) -gt
  bunching ...
• Synchronous Particle mc2 d?s / dt ec E0 (K
  / ?s) sin ?s
• Other Particle mc2 d? / dt ec E0 (K / ?
  ) sin ?

21
Free Electron Laser (3)

• Energy Difference ? mc2 (? ?s)
• Equations of Motion
• d? / dt eE0 c (K / ?) (sin ? sin ?s)
• d? / dt ckU ? / mc2 ?3
• Hamiltonian
• H eE0 c (K / ?) (cos ? ? sin ?s) ckU
  ?2 / 2mc2 ?3
• Bucket Height
• ?B 2e mc2 E0 K ?2 / kU
• Phase Oscillation Frequency
• ? eE0 K kU cos ?s / m ?4

22
FEL Amplification

• Small-Signal Gain (Meadys Formula)
• (few ) Undulator Length lt Gain Length
• G 4 v2 p ?c K2 (I / IA) NW3 d(sinx / x)2 /
  dx / W2 (1 K2)3/2
• 17 kA (Alfven current) x
  p NW ?? /? radiation cross-section
• High-Gain
• (single pass) Undulator Length gt Gain Length
  FEL Volume Length
• Stored Energy WFEL E02 VFEL / 4p
• Power Gain d WFEL / dt 0.633 kW E2GeV IA
  BUT LUm

23
FEL Performance Evaluation (Low Gain)

• Plane Undulator
• Length LU NU ?U
• Number of Periods NU
• Period Length ?U
• Field Strength BU
• Undulator Parameter K 0.934 BUT ?Ucm
• Radiated Wavelength ?c 0.13 x 106 ?U (1
  K2/2) / E2GeV
• Radiated Power PTkW 0.633 E2GeV IAmp
  BU2T LUm
• BU 1 T 10 T
• ?U 1 cm
• E 1 GeV 3 GeV
• I 1 Amp
• LU 1 m 15 m
• ?c 19 Ao
• PT 0.633 kW
• PBeam 1 GW

Eff 0.633 x104 EGeV BU2T LUm
0.3
24
Which Accelerator?
Energy Peak Current Pulse Length Wavelength

Electrostatic 1-10 MeV 1-5 A 1-20 µs mm to 0.1 mm
Induction Linac 1-50 MeV 1-10 kA 10-100 ns cm to µm
Storage Ring 0.1-10 GeV 1-1000 A 30-1000 ps 1 µm to nm
RF Linac 0.01-25 GeV 100-5000 A 0.1-30 ps 100 µm to 0.1 nm
25
Procedure

• -Talk to the Users Community
• -Determine Requirements
• Wavelength, ?c
• Flux dN / d?
• Number of Beam Lines
• -Chose Accelerator Type E, I, C, Lattice,
• -Plan in Phases
• SR from Bending Magnets alone
• Insertion Devices
• FEL
• -Cost and Schedule Estimate

26
Performance

• ?c Ao 18.64 / BT E2 GeV
• dN / d? ph/Amp sec mrad? 0.1 BW 1.6 x
  1013 EGeV at ? ?c
• For instance with B 1.25 T -gt ?c Ao
  15 / E2 GeV

Energy ?c dN / d?
400 MeV 94 Ao 0.64 x 1013
800 MeV 23 Ao 1.28 x 1013
1.5 GeV 6.7 Ao 2.4 x 1013
3.0 GeV 1.7 Ao 4.8 x 1013
27
Circumference, Beam Current and RF Power

• U0 Energy Loss / Turn
• Isomagnetic Storage Ring
• Packing Factor Bending Radius ? / Average
  Radius R 0.20
• rms Energy Spread ?E / E (Cq ?2 / JE
  ?)1/2 Cq 3.84 x 1013 m

? B 1.25 T C 2p R PRF I 0.5 A ?E ?E / E
400 MeV 1.07 m 34 m 1.06 kW 2.12 keV 21.5 ms 0.33 x 103
800 MeV 2.14 m 67 m 8.5 kW 17 keV 10.6 ms 0.47 x 103
1.5 GeV 4.00 m 125 m 56 kW 112 keV 5.6 ms 0.64 x 103
3.0 GeV 8.00 m 250 m 450 kW 900 keV 2.8 m 0.91 x 103
28
Brightness and Beam Emittance

• Flux dN / d? photons / Amp sec sterorad
  0.1 BW
• Brightness dN / d?dS photons / Amp sec
  sterorad mm2 0.1 BW
• Beam Emittance ? ?H2 / ?L (JE / JH)
  (?E / E)2 lt H gtMag
• Lattice Choice (Horizontal Plane, Isomagnet
  Storage Ring)
• lt H gtMag ?Mag ?2 (?L ?' ?L' ? / 2 )2
  ds / 2p ? ?L
• ?c R / ?H
• To increase Brightness -gt reduce beam spot size
  ?H -gt reduce Emittance -gt choose
  Low-Dispersion Lattice

29
Facilities Comparison
?L, Horizantal 1 m 10 coupling
Emittance ? m-rad ?H Brilliance / Flux R ?c ?H lt H gtMag
ESRF 0.695 x 108 0.083 mm 1500 / mm2 175.7 m 0.282 x 103 36.2 1.37 mm
APS 0.822 x 108 0.091 mm 1200 / mm2 134.3 m 0.228 x 103 35.215 0.87 mm
NSLS Xray 0.102 x 106 0.32 mm 98 / mm2 27.1 m 0.654 x 102 9.144 19.4 mm
NSLS UV 0.138 x 106 0.37 mm 73 / mm2 8.12 m 0.235 x 101 3.123 61.1 mm
30
Brightness -- Spring-8 APS
31
Brightness -- ESRF
32
Brightness -- NSLS
33
Damping and Quantum Fluctuation

• ? emittance or energy spread
• d? / dt ? / ? DQ 0
• Equilibrium ?8 ? DQ
• It takes 3 or 4 Damping
• Times ? to reach
• Equilibrium.
• Usually
• ?initial gt ?8 gt ?source

? / ?8
?8
t / ?