Synchrotron Radiation Facilities

Synchrotron Radiation Facilities

Alessandro G. RuggieroBrookhaven National Laboratory

CINVESTAV, Mexico City, January, 24-26, 2007

Mexico City January 24-26, 2007

Alessandro G. Ruggiero Brookhaven National Laboratory

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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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http://www.camd.lsu.edu/lightsourcefacilities.html



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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



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



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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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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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 /

∞

Synchrotron Radiation Facilities

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