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Insertion Devices Insertion Devices CERN Accelerator School, Chios 2011 Intermediate Level Course, 26.09.11 Markus Tischer, DESY, Hamburg Outline • Generation and Properties of Synchrotron Radiation • Undulator Technology • Interaction of IDs with e-Beam • Magnet Measurements and Tuning In memoriam Pascal Elleaume Countless contributions to FELs … Insertion Devices … Accelerator physics Major share in the establishment of permanent magnet based undulators Development of several new ID concepts and related components 1956-2011 Development and refinement of new ID technologies like in-vacuum undulators Realization of diverse new measurement and shimming techniques Elaboration of various simulation and analysis software Investigation of interaction of IDs with the e-beam Contributions to SR diagnostics M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 2 Insertion Device Alternating magnetic field Radiation e-beam Idea • Oscillating magnetic field causes a wiggling trajectory Emission of synchrotron radiation • So-called „Undulators“ or „Wigglers“ are often „inserted“ in straight sections of storage rings „Insertion Device“ • Period length ~15 400mm, magnetic gap as small as possible (5 40mm) Purpose • Intense synchrotron radiation source in electron storage rings • Emittance reduction in light sources (NSLS II, PETRAIII) • Beam damping in colliders (LEP, ) M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 3 Undulators in PETRA III at DESY PU10 PU08 / PU09 PU04: APPLE II M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 4 Synchrotron Radiation Sources & Brilliance Spectral characteristics of different SR-sources Development of brilliance: 15 orders of magnitude FEL: Peak-brilliance another ~8 orders [B] = photons/sec/mm2/mrad2/0.1%bw Brilliance = Photon flux at energy E within 0.1% bandwidth normalized to beam size and divergence n B (often used as figure of merit) 4 2 x y x y M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 5 Principle of Synchrotron Radiation Acceleration of charged particle • Accelerated charge emits electromagnetic radiation Lorentz-Transformation • Angular distribution like for e– Rest frame Lab frame electric Dipole Acceleration Acceleration • Acceleration induced by Lorentz force dp dv 90° F m0 ev B 1 dt dt Detector i.e. transverse acceleration in a storage ring Opening angle of SR • Radiated power • natural opening angle ~1/ = 0.06-0.5mrad e2c E 4 P e.g. ESRF, PETRA3: 1/(1957x4.5[GeV]) = 85µrad 2 4 60 m0c M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 6 Dipole Radiation 2 1 1 t t t sin 2 1 3 c 3c 1 1 • Due to the narrow opening cone (=1/) t 6 3 the observer will see only a short light d 2 1 s 2 t1 sin t2 (v c) pulse with duration t ~ /c3 c c v c • This results in a broad continuous Fourier spectrum with a characteristic frequency 3 2 c ~ c / ~ Ee ·B (~1019 Hz ~1Å) or “critical” energy Ec 2 Ec [keV] = 0.665Ee [GeV] B0 [T] (ESRF, PETRA: E ~20keV) c Ec M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 7 Dipole Radiation •Spectral Intensity Distribution • Linearly polarised in orbit plane (Schwinger equation) 2 d 3 I E 2 2 (E,) 2 e 1 2 2 K 2 K 2 2 2 / 3 2 2 1/ 3 d 4 e Ec 1 with E 3 / 2 1 2 2 2Ec Ec • Flux density, emitted in orbit plane =0 [phot./sec/mrad2/0.1%bw] 13 2 d/d(E)|=0 = 1.3310 Ee [GeV] Ie[A] h(E/Ec) • Flux, integrated over all vertical angles [phot./sec/mrad/0.1%bw] 13 2 d/d(E) = 2.4610 Ee [GeV] Ie[A] g(E/Ec) M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 8 Electron Trajectory in an Insertion Device dv Lorentz force F m ev B 0 dt 1 v with , 1 2 c Assume small angular deflections vx , vy vz ~ c Equations of motion: d 2 x e dx dx dz x B yB with x xz , z c const, 1 2 y z dt dz dt dz m0c d 2 y e y 2 x Bz Bx dz m0c For a sinusoidal vertical field (0, By , 0) : 2 By B0 sin z U with the so-called Deflection Parameter K K 2 e x cos z Angular deflection K B0 U 0.934 B0 [T] U [cm] U 2 m0c K 2 Displacement x U sin z Maximum angular deflection angle = K/ 2 U K is a measure for the strength of the insertion device M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 9 Wigglers Permanent magnets Poles Intensities of all poles add up (incoherently) FluxWiggler = 2N FluxDipole (for equal Ec) Magnetic field High intensities e- trajectory Emitted SR z High photon energies Gap Critical energy: 2 Ec [keV] = 0.665Ee [GeV] B0[T] • AlternatinG magnetic field Emitted total power of a wiggler or undulator with length L=N : (typ.: 50kW) 2 U B z B sin z 0 P = 0.633 B 2 [T] L [m] E 2 [GeV] I [A] U tot 0 e e Period length U (typ. 10-30cm) Peak field B (typ. >1.5T) 0 Polarisation of wiggler radiation: Number of periods N=L/ (typ. 5-100) U linearly polarised in the orbit plane =0, unpolarised out of plane • K-parameter: K >> 1, typ. K > 10 Opening angle of the emitted SR = K/ spatial power distribution (typ. ~mrad) M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 10 Undulator Radiation Consider K<<1: Lorentz contraction: u u •Maximum angular deflectionismuchsmaller than the opening angle of the radiation cone Doppler effect: u 1 2 2 u 2 •Observer canfullyfollowthesinusoidaltrajectory 2 2 Combined: u 1 R 2 2 •Wavelengthoftheemittedlight R ~ U is drastically shortened due to relativistic effects: 7 For ~GeV machines: 10 , U ~mm R ~Å Time for the e- to travel one period: U c z In this time the wavefront from P will propagate: U z Constructive interference for: d U z U cos nR K 2 U 1 2 2 2 2 R 2 x y 2n 2 2 13.056 cm K 2 0.950 E GeV Å U 1 or E keV e R 2 1 2 (on-axis) E GeV 2 U cm 1 K 2 typically: K = 1 3, U = 1 5 cm R ~ nm Å M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 11 Higher Undulator Harmonics •Constant propagation velocity along trajectory s •Drift velocity along the averaged propagation direction z does vary •Electron motion in its rest frame corresponds to a figure 8 e- rest frame •Larger K-parameter stronger modulation of vz •The modulation of vz is the reason for the occurance of higher undulator harmonics (usually highly desired!) z M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 12 Odd and Even Undulator Harmonics e- rest frame laboratory frame Transverse oscillation Odd harmonics Longitudinal oscillation Even 2 longitudinal oscillations for harmonics 1 transverse twice the frequency Transverse oscillation Odd harmonics on-axis emission Longitudinal oscillation Even harmonics off-axis radiation M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 13 Undulator ... … Wiggler Discrete spectrum Continuous spectrum characteristic quantity: E1 K-parameter characteristic quantity: Ec 15 Ec larger K-Parameter more higher harmonics fundamentale E1 spacing of harmonics … overlap of harmonics quasi-continuous spectrum = wiggler M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 14 Spectral and Spatial Distribution of SR (for a filament e-beam) d 2 sin 2 x n 0 2 H , with x N N 1 2 2 N H n , Fn K n 2 d d n1,3,5... x 1 10 10 x, y 0 1 23 Spectral dependence H(,=0) Angular intensity distribution (Energy domain) (Spatial domain) of an undulator harmonics along beam axis 1 Spectral width Natural source size and divergence (~ 1% ... 0.1%) nN 2 L , ' but Gaussian approx. R 4 R 2L not always accurate (typically 1-10µm 1-10µrad) M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 15 Undulator: Photon Flux Fn On-axis flux density [phot./sec/mrad2/0.1%bw] in practical units: d n 1.7441014 N 2 E 2 GeV I A F K , (n 1,3,5...) d e n x, y 0 Integrated over the „central cone“ Flux 14 [phot./sec/0.1%bw]: n 1.43110 N I e A Qn M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 16 Tuning of Photon Energy 3. 1. min. gap 5. 3. 7. 1. constant Gap! max. gap Change of photon energy by: • (variation of electron energy ) K 2 • variation of K-parameter by changing the gap U 1 gap B K = E R 2 R ph 2n 2 Kmax > 2 : fully tunable Kmax = 1.3 : tunable only above 3rd harmonic M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 17 Emittance Effects Spatial Effects: e-Beam emittance x, y x, y x, y •Enlargementof size and divergence of the •Broadeningofundulator harmonics emitted photon beam •Intensityreduction 2 2 ' 2 2 (Light sources: x ~ 1-450 nm rad, coupling =y/x ~1%) x,y x,y R , x,y 'x,y 'R Spectral Effects: Spectral intensity distribution (at fixed gap!), • Red shift with a low energy tail integrated over different apertures: • Even harm. of off-axis electrons get visible on-axis 2525µrad2, 5050µrad2, 100100µrad2 and 200200µrad2 •Symmetricbroadeningdue toenergy spread / of electrons (typ. ~0.1%) M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 18 Undulator Technology: Support Structure 2 or 4-axes drive, electronic gears Various requirements: Minimum girder deformation Gear box & motor Changing magnetic forces up to ~100kN Gap accuracy of ~1µm (1µm 1 Gs) Magnet girder Possibility for taper up to ~1mm Temperature insensitivity Magnet modules e-Beam Hard stop, limit switches Gap measurement Drive train with system fully decoupled rail, carriaGe, and from load support ball bearing leadscrew Support frame (installed e.g.
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