Synchrotron Radiation Facilities
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Transcript of Synchrotron Radiation Facilities
Synchrotron Radiation Facilities
Alessandro G. RuggieroBrookhaven National Laboratory
CINVESTAV, Mexico City, January, 24-26, 2007
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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
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3rd-Generation Facilities and Brookhaven
Energy Circumfer. Linac/Booster Beam Current Emittancem-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
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Typical SR Facility
Linac Booster Storage Ring
Beam Lines
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Bending Magnet
Undulator - Wiggler
e-Source
Energy, E
Circumference, 2πR
No. of Periods, M
Beam Current, I
Bending Radius,
Number of Beam Lines
Insertion Devices
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a2 = H + ()2 b2 = V = E/E = π a
a
DipolesQuadrupoles
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Lattice Design Period
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
F B D B F
=
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 = 0KH,V(s) = focusing function = G / B
betatron
’ dispersion
H V tunes
c momentum compaction factor
Magnet Errors & Misallignment -- H-V Coupling
Chromaticity d H,V / d -- Sextupoles -- Non-linearities
Dipole Bending Angle Radius
cos sin 0 0 0 (1- cos) --1sin cos 0 0 0 sin 0 0 1 0 00 0 0 1 0 0sin (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 00 0 Ksinh cosh 0 00 0 0 0 1 0 0 0 0 0 0 1For QF Invert 2x2 H with 2x2 V for QD
Drift Length L
1 L 0 0 0 00 1 0 0 0 00 0 1 L 0 00 0 0 1 0 00 0 0 0 1 00 0 0 0 0 1
Total Period Matrix M H or V
cos + sin sin … … -sin cos – sin … … … … … … … … H = Np/2π
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Lattice Functions
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Lattice Functions
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Radiation Integrals
I1 = ds / all integrals are over DipolesI2 = 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 / CEnergy Loss per Turn U0 = 2re E4 I2 / 3 (mc2)3
Damping Partition Factors JH = 1 - I4 / I2 and JE = 2 + I4 / I2 Energy Spread E
2 = (55/32√3) (h / mc) (E/mc2)2 I3 / (2 I2 + I4)Emittance = (55/32√3) (h / mc) (E/mc2)2 I5 (I2 - I4)
= F(H, lattice) E2[GeV] / JH NDipoles > 7.84 mm-mrad
Damping Times i [ms] = C[m] [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
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Synchrotron Radiation from a Dipole Magnet
Critical Photon Energy c = h c = 3 h c 3 / 2
c [keV] = 0.665 B[T] E2 [GeV] c [Ao] = 18.64 / B[T] E2 [GeV]
dN / d = (photons spectral and angular distribution)(3 6 / 4 π2) y2 (2 + -2)2 [ K2/3
2() + 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 E2[GeV] I[Amp] y2 K2/32(y/2) /
photons/sec/mrad/mradIntegrating over dN / d = 2.457 x 1016 E[GeV] I[Amp] y (∫y∞K5/3(x)dx) /
photons/sec/mraddP/d [mW/mrad] = 8.73 x 103 E4[GeV] I[Amp] y2 (∫y
∞K5/3(x)dx) / [m]Total Power PT[kW] = U0[keV] I[Amp] = 88.5 E4[GeV] I[Amp] / [m]
J. Schwinger, Phys. Rev. 97, 470 (1955)
P()
c
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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)] / π c h E]1/2
Synchrotron Tune s = fs / f0 = [eVRF c h cos s / 2π E]1/2
rms Bunch Length L = c c E / 2 π fs
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Beam Lifetime
Gas Scattering (elastic)
1/scat = 4re2Z2π d c [<H> Hmax / a2 + <V> Vmax / b2 ] / 2 2
Bremstrahlung
1/brem= (16/411)re2Z2 d c ln[183 Z-1/3][-ln ARF - 5/8]
Touschek
1/T = √π re2 c N C() / H' 3 (Aacc)2 V V = 8π3/2 H V L Aacc < Abet or ARF
C() = -3 e- / 2 + ∫∞ e-u ln u du / 2 u + (3 - ln + 2) ∫∞ e-u du / u
= (Aacc / H')2
Quantum Lifetime
q = E e / 2 = ARF2
/ 2 E2
RF Bucket and e-Bunch
ARF
ab
Vacuum Chamber and
Beam Cross-Section
Abet
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Damping Time 75 ms Lifetime 180 min
Number of RF Buckets 1560 Number of Bunches 1280
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Helical Undulator
Field Configuration (NU is the number of periods)
B = Bu[cos(kuz) x + sin(kuz) y] kU = 2π / U
Radiated Wavelength Wiggler Parameter
() = U(1 + K2 + 22) / 2 2 K = eBU / mckU < 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 = πNU( - r) / r
r = 2 c kU 2 / (1 + K2) /r = 1 / NU
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Planar Undulator (1)
Field Configuration (NU is the number of periods)
B = Bucos(kuz) y kU = 2π / U
Radiated Wavelength Undulator Parameter
n() = U(1 + K2/2 + 22) / 2n2 K = eBU / mckU < 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 = πNUn( - n) / n
n = 2 nc kU 2 / (1 + K2/2) n /n = 1 / nNU
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Planar Undulator (2)
Form Factor
Fn(K) = [nK / (1 + K2/2)]2 [J(n+1)/2 (u) - J(n-1)/2 (u) ]2
n = 1, 3, 5, …. u = n K2/(4 + 2K2)
Total Power Radiated
PT[W] = 7.26 E2[GeV] I[Amp] NU K2 / U[cm]
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Planar Wiggler
The Insertion is a Wiggler when K >> 1 (with NW periods)
Critical Energy
c() = c0 [1 - ( / K)2]1/2
c0[keV] = 0.665 B[T] E2[GeV]
K = 0.934 B[T] w[cm]
Flux = 2 NW x equivalent arc source flux of same c
Total Power Radiated
PT[W] = 7.26 E2[GeV] I[Amp] NW K2 / W[cm]
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Klystron
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AC - to -RF
Conversion
Efficiency
~ 50-60 %
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Free Electron Laser (1)
The FEL has three components:- e-beam with E and I -> P = E x Ia 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 = 2π / U
= (K / )[ cos(kUz) x – sin(kUz) y ] + 0 z
0 = [1 – (1 + K2) / 2]1/2
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A Coherent Source of Tunable Radiation
If e-Bunch length >> c then Prad ~ N
If e-Bunch length <~ c then Prad ~ N2
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Free Electron Laser (2)
Plane wave propagating along the Undulator axis k = 2π /
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 -> = c
Otherwise d / dt = k (z / 0 – 1) -> … bunching ...
Synchronous Particle mc2 ds / dt = ec E0 (K / s) sin s
Other Particle mc2 d / dt = ec E0 (K / ) sin
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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
/B s = 0
30o
60o 45o
s = 90o
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FEL Amplification
Small-Signal Gain (Meady’s Formula)(few %) Undulator Length < Gain Length
G = 4 √2 π c K2 (I / IA) NW3 [ d(sinx / x)2 / dx] / W2 (1 + K2)3/2
17 kA (Alfven current) x = π NW / radiation cross-section
High-Gain(single pass) Undulator Length > Gain Length FEL Volume Length
Stored Energy WFEL = E02 VFEL / 4π
Power Gain d WFEL / dt = 0.633 kW E2[GeV] I[A] BU[T] LU[m]
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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 BU[T] U[cm]Radiated Wavelength c = 0.13 x 10–6 U (1 + K2/2) / E2[GeV]Radiated Power PT[kW] = 0.633 E2[GeV] I[Amp] BU
2[T] LU[m]
BU = 1 T 10 TU = 1 cmE = 1 GeV 3 GeVI = 1 AmpLU = 1 m 15 m
c = 19 Ao
PT = 0.633 kWPBeam = 1 GW
Eff[%] = 0.633 x10–4 E[GeV] BU2[T] LU[m]
= 0.3
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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
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Procedure
-Talk to the User’s Community-Determine Requirements:
Wavelength, c
Flux dN / dNumber of Beam Lines
-Chose Accelerator Type E, I, C, Lattice,…-Plan in Phases:
SR from Bending Magnets aloneInsertion DevicesFEL
-Cost and Schedule Estimate
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Performance
c [Ao] = 18.64 / B[T] E2 [GeV]
dN / d [ph/Amp sec mrad 0.1% BW] = 1.6 x 1013 E[GeV] at = c
For instance with B = 1.25 T -> 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
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Circumference, Beam Current and RF Power
U0 = Energy Loss / Turn
Isomagnetic Storage Ring
Packing Factor = Bending Radius / Average Radius R = 0.20rms Energy Spread = E / E = (Cq 2 / JE )1/2 Cq = 3.84 x 10–13 m
B = 1.25 T
C = 2π R PRF
I = 0.5 A
E E / E
400 MeV 1.07 m 34 m 1.06 kW2.12 keV
21.5 ms 0.33 x 10–3
800 MeV 2.14 m 67 m 8.5 kW17 keV
10.6 ms 0.47 x 10–3
1.5 GeV 4.00 m 125 m 56 kW112 keV
5.6 ms 0.64 x 10–3
3.0 GeV 8.00 m 250 m 450 kW900 keV
2.8 m 0.91 x 10–3
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Brightness and Beam Emittance
Flux dN / d = photons / Amp sec sterorad 0.1% BW
Brightness dN / ddS = photons / Amp sec sterorad mm2 0.1% BW
Beam Emittance = H2 / L = (JE / JH) (E / E)2 < H >Mag
Lattice Choice (Horizontal Plane, Isomagnet Storage Ring)
< H >Mag = ∫Mag { 2 + (L ' – L' / 2 )2 } ds / 2π L
≈ c R / H
To increase Brightness -> reduce beam spot size H -> reduce Emittance -> choose Low-Dispersion Lattice
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Facilities Comparison
Emittance m-rad
H Brilliance / Flux
R c H < H >Mag
ESRF 0.695 x 10–8
0.083 mm 1500 / mm2
175.7 m 0.282 x 10–3
36.2 1.37 mm
APS 0.822 x 10–8
0.091 mm 1200 / mm2
134.3 m 0.228 x 10–3
35.215 0.87 mm
NSLSXray
0.102 x 10–6
0.32 mm 98 / mm2 27.1 m 0.654 x 10–2
9.144 19.4 mm
NSLSUV
0.138 x 10–6
0.37 mm 73 / mm2 8.12 m 0.235 x 10–1
3.123 61.1 mm
L, Horizantal ~ 1 m 10% coupling
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Brightness -- Spring-8 & APS
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Brightness -- ESRF
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Brightness -- NSLS
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Damping and Quantum Fluctuation
= emittance or energy spread
d / dt = – / + DQ = 0
Equilibrium ∞ = DQ
It takes 3 or 4 DampingTimes to reach Equilibrium.
Usually
initial > ∞ > source
/ ∞
t /
∞