1 / 33

Synchrotron Radiation Facilities

Synchrotron Radiation Facilities. Alessandro G. Ruggiero Brookhaven National Laboratory CINVESTAV, Mexico City, January, 24-26, 2007. World Radiation Facilities. There are 60 SR Facilities in the World listed at http://www.camd.lsu.edu/lightsourcefacilities.html SPring - 8 Hyogo, Japan

jerom
Download Presentation

Synchrotron Radiation Facilities

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  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 Alessandro G. Ruggiero Brookhaven National Laboratory

  3. 3rd-Generation Facilities and Brookhaven Number of Periods Alessandro G. Ruggiero Brookhaven National Laboratory

  4. Linac Booster Storage Ring Beam Lines Typical SR Facility Undulator - Wiggler e-Source Insertion Devices Bending Magnet Energy, E Circumference, 2πR No. of Periods, M Beam Current, I Bending Radius,  Number of Beam Lines Alessandro G. Ruggiero Brookhaven National Laboratory

  5. a2 = H + ()2b2 = V  = E/E = π a    a Quadrupoles Dipoles Alessandro G. Ruggiero Brookhaven National Laboratory

  6. F B D B F 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 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 LengthL 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/2π 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 QuadrupoleK = (G/B)1/2Length 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    betatron  ’ dispersion H V tunes c momentum compaction factor = Magnet Errors & Misallignment -- H-V Coupling Chromaticity d H,V / d  -- Sextupoles -- Non-linearities Alessandro G. Ruggiero Brookhaven National Laboratory

  7. Lattice Functions Alessandro G. Ruggiero Brookhaven National Laboratory

  8. Lattice Functions Alessandro G. Ruggiero Brookhaven National Laboratory

  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 = (55/32√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 Alessandro G. Ruggiero Brookhaven National Laboratory

  10. P()  c 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 [ K2/32() + 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 E2[GeV] I[Amp] y2K2/32(y/2)  /  • photons/sec/mrad/mrad • Integrating over  dN / d = 2.457 x 1016 E[GeV] I[Amp] y (∫y∞K5/3(x)dx)  /  • photons/sec/mrad • dP/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) Alessandro G. Ruggiero Brookhaven National Laboratory

  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 voltageVRF • 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 Alessandro G. Ruggiero Brookhaven National Laboratory

  12. b a Abet Vacuum Chamber and Beam Cross-Section ARF RF Bucket and e-Bunch 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 Alessandro G. Ruggiero Brookhaven National Laboratory

  13. Damping Time75 msLifetime180 min Number of RF Buckets 1560 Number of Bunches 1280 Alessandro G. Ruggiero Brookhaven National Laboratory

  14. Helical Undulator • Field Configuration (NU is the number of periods) • B = Bu[cos(kuz) x + sin(kuz) y] kU = 2π / U • Radiated WavelengthWiggler Parameter • () = U(1 + K2 + 22) / 2 2K = eBU / mckU < 1 • Spectral and Angular Distribution ( = 0) photons/sec/steradian • dN / d = 2 NU22K2 (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 Alessandro G. Ruggiero Brookhaven National Laboratory

  15. Planar Undulator (1) • Field Configuration (NU is the number of periods) • B = Bucos(kuz) y kU = 2π / U • Radiated WavelengthUndulator Parameter • n() = U(1 + K2/2 + 22) / 2n2K = 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 Alessandro G. Ruggiero Brookhaven National Laboratory

  16. 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] NUK2 / U[cm] Alessandro G. Ruggiero Brookhaven National Laboratory

  17. 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] NWK2 / W[cm] Alessandro G. Ruggiero Brookhaven National Laboratory

  18. Klystron AC - to -RF Conversion Efficiency ~ 50-60 % Alessandro G. Ruggiero Brookhaven National Laboratory

  19. Free Electron Laser (1) • The FEL has three components: • - e-beam with E and I -> 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 / mckUkU = 2π / U •  = (K / )[ cos(kUz) x – sin(kUz) y ] + 0z • 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 Alessandro G. Ruggiero Brookhaven National Laboratory

  20. Free Electron Laser (2) • Plane wave propagating along the Undulator axis k = 2π /  • E = E0 [ cos(kz - t + ) x + sin(kz - t + ) y ] • Energy TransferPonderomotive 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 ds / dt = ec E0 (K / s) sins • Other Particle mc2 d / dt = ec E0 (K /  ) sin Alessandro G. Ruggiero Brookhaven National Laboratory

  21. /B s = 0 30o 45o 60o  s = 90o 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 mc2E0K 2 / kU Phase Oscillation Frequency  = eE0K kU cos s / m 4 Alessandro G. Ruggiero Brookhaven National Laboratory

  22. FEL Amplification • Small-Signal Gain (Meady’s Formula) • (few %) Undulator Length < Gain Length • G = 4 √2 π cK2 (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] Alessandro G. Ruggiero Brookhaven National Laboratory

  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 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] BU2[T] LU[m] • 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 x10–4 E[GeV] BU2[T] LU[m] = 0.3 Alessandro G. Ruggiero Brookhaven National Laboratory

  24. Which Accelerator? Alessandro G. Ruggiero Brookhaven National Laboratory

  25. Procedure • -Talk to the User’s 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 Alessandro G. Ruggiero Brookhaven National Laboratory

  26. 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] Alessandro G. Ruggiero Brookhaven National Laboratory

  27. Circumference, Beam Current and RF Power • U0 =Energy Loss / Turn • Isomagnetic Storage Ring • Packing Factor = Bending Radius  / Average RadiusR = 0.20 • rms Energy Spread = E / E = (Cq 2 / JE )1/2 Cq = 3.84 x 10–13 m Alessandro G. Ruggiero Brookhaven National Laboratory

  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 < 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 Alessandro G. Ruggiero Brookhaven National Laboratory

  29. Facilities Comparison L, Horizantal ~ 1 m 10% coupling Alessandro G. Ruggiero Brookhaven National Laboratory

  30. Brightness -- Spring-8 & APS Alessandro G. Ruggiero Brookhaven National Laboratory

  31. Brightness -- ESRF Alessandro G. Ruggiero Brookhaven National Laboratory

  32. Brightness -- NSLS Alessandro G. Ruggiero Brookhaven National Laboratory

  33. Damping and Quantum Fluctuation  = emittance or energy spread • d / dt = –  /  + DQ = 0 • Equilibrium ∞ =  DQ • It takes 3 or 4 Damping • Times  to reach • Equilibrium. • Usually • initial > ∞ > source / ∞ ∞ t /  Alessandro G. Ruggiero Brookhaven National Laboratory

More Related