Insertion Devices

CERN Accelerator School, Chios 2011 Intermediate Level Course, 26.09.11

Markus Tischer, DESY, Hamburg

Outline

• Generation and Properties of

• 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 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 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 or undulator with length L=N : (typ.: 50kW) 2 U Bz 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

13.056 cm K 2 0.950 E 2 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 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. at PETRA III or sFLASH)

M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 19 Magnet Technology

Magnetic force

2 superconducting B L W F 0 40

hybrid Area L x W of magnet structure permanent magnets + poles [T]

0 5 2 B F[N] 210 B0 [T] L[m] W[m]

ppm pure permanent magnet Peak Field Peak Peak field

2 electro- g g magnetic b c U U B0 a e

for ~ 0.1 g/U 1 P. Elleaume et al., NIM A 455 (2000) 503-523

Gap / Period g/U M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 20 Permanent Magnet Technology

Hybrid design Pure permanent magnet (ppm) • higher field • simpler to compute and to correct • field quality limited by • field quality limited by -mechanical tolerance of poles -block errors -block errors

Pole (Steel, CoFe) Magnet (NdFeB, SmCo)

Magnet materials PM issues: Remanence Permeability CoercitivityT-Koeff •Magneticerrorsimprintedduringpressing Material Br [T] µr,|| µr, Hc,j [kA/m] [%/°C] (Br, angular errors, N/S-effect)

SmCo5 0.9–1.01 1.05 2400–1500 –0.04 •Radiation hardness

Sm2Co17 1.04–1.12 1.05–1.08 2100–800 –0.03 •Temperatureresistivity( SmCo)

Nd2Fe14B1.0–1.45 1.03–1.06 1.12–1.17 3000–900 –0.11 •Machining(NdFeBis a littlelessbritle)

Latest development: Vapor diffusion of Dy into grain •Expensive (both) boundaries of NdFeB Hcj increase by >300kA/m ! M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 21 In-Vacuum Undulators

Widely used at many SR sources Originally developed at NSLS, SPring-8, ESRF Minimum magnetic gap of 3-6mm

SACLA -XFEL(SPring-8) IVU

L=18x5m, U=18mm

Flexible taper transitions SLS require careful design M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 22 Cryogenic In-Vacuum Undulator

• Increased coercivity at cryogenic temperatures (~130K)

choice of high Br material, high resistance against demagnetization • Increased remanent field (Br) at low temperatures higher fields at same period length, i.e. larger energy tunability • Modification of mechanical design (thermal deformation, therm. Isolation), use of cryo-coolers • Development of magnetic measurements and tuning techniques at cryogenic temperatures • Some IDs already built or in operation (ESRF, SLS, Diamond, Soleil)

7 1.6 53CR 5000 6 1.5 50BH

5 4000 ~30% 1.4 i H c

4 (kA/m) 53CR (T) 50BH 3000 c 35EH 1.3 H i

0 3 Br (T) 2000 1.2 2 35EH 1000 1 1.1 240HR

0 0 1.0 100 150 200 250 300 100 150 200 250 300 Temperature (K) Temperature (K)

T. Hara, T. Tanaka, SPring-8, PRST-AB 7 (2004) M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 23 Helical / Elliptical Undulators

Permanent magnet devices Electromagnetic devices

K.J.Kim Cornell APS Elettra / SLS Spring8 ESRF Soleil

H.Onuki

• Apple2 design: highest field + fast helicity change most popular + mechanically simpler Elettra, ESRF –weak fields –restricted to long periods –not invisible to other users –not hysteresis-free

M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 24 Apple2 Undulator: Principle

Split magnet rows (movable along the beam) • variable polarization • high field • planar structure

Shift = 0 horizontal linear polarization Shift = /2 vertical linear polarization

Parallel motion circular/ellipt. polarization Antiparallel motion 45deg linear polarization

Beff Beff By

By Bx Bx

By But: Transverse field profiles have a Bx large horizontal field roll-off with x significant impact on beam dynamics -20 20mm M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 25 APPLE2 – UE65 at PETRA III

L = 5 m, U = 65.6 mm, gap = 11 mm

Beff=1.04T, Keff=6.4 (circ.mode) circ E1 = 245eV ~ C K-edge

2 Ptot = 13 kW, dP/d = 0.12 W/µrad (very low!)

• Additional large transverse and longitudinal magnetic forces in antisymm. mode • Requires detailed optimization of mechanical support • with 4-axes drive: deformation can be partly HZB-DESY collaboration compensated (J.. Bahrdt et al., conf. proc. SRI09)

Maximum forces and torques

units: kN, kNm Fx Fy Fz Tx Ty Tz hor. linear 0 73 0 0 0 0

inclined, 16.4 mm 54 0 12 6.4 0.75 22.5 M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 26 Asymmetric & Elliptical Wiggler

R L R

Photon Factory / KEK

DESY, ESRF SPring-8

• mechanically simpler • 2 source points (on-axis: 1) • magnetically delicate (large field integrals) M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 27 High Field Devices

Permanent magnet devices Superconducting devices

• Hybrid Wiggler (DESY) • 3.5T Wiggler (Elettra, MAX-Lab)

B=2T, U=11cm, K=21, L=4m, Ec=27keV, U=61mm, gap=10.2mm, 46 poles

• Superbends (ALS, BESSY, SLS) : B=3-9T

• 10T Wavelength Shifter (Spring8)

• Multipole Wiggler (HMI, BESSY) B=7T, K=92, 13 poles, P=56kW !

• Asymmetric Wiggler (ESRF)

B=3.1T, U=378mm, 11mm gap M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 28 Superconducting Undulators

Goal: Short period, higher field, harder X-ray spectrum IVU CPMU SCU Technology: NbTi or Nb3Sn, cold bore, cryo-coolers (mm) 21 18 15 iron poles contribute to the field by ~1/3 u N95111133 Challenges: • Preservation of accuracies towards low temperatures gap (mm) 6 6 7 field errors due to therm. expansion, winding errors and large forces on conductor B (T) .75 .88 .98

• Magn. measurements & tuning mechanisms K1.471.481.37 • Cryo losses development of special diagnostics for SR and image current effects

Developments at various labs LBNL: Nb3Sn U=30mm, gap~10mm, ANKA: NbTi j=6.1kA/m2, B=3.2T full devices (1.5m) built, to be installed Daresbury: NbTi pushing new technologies, shimming strategies, „cold bench“ helical prototypes and full length study YBCO diagnostics built to study cryo losses device, planar prototypes APS: NbTi large R&D program, several prototypes

M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 29 Figure-8 Undulator

Goal: Reduction of high on-axis power density Other alternative: 2 Helical undulator B B sin z y y0 (SPring-8) U Bx Bx0 sin z U

Reduction of on-axis power density to ~few % for only ~30% decrease in 1st harm. flux

(Occurence of half integer odd harmonics) M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 30 Quasi-Periodic Undulator

Shift of the higher harmonics towards Concept non-integer multiples •Likefordiffractionfroma quasi-crystal S.Sasaki et al., Rev. Sci. Instrum. 66 (1995) 1953 • Position of poles follow a •Suppression of higher order radiation so-called Fibonacci sequence •realized by modification of distinct magnets •Easierrealizedbyverticalpole displacements •cleaner photon spectrum ! at destinct locations (because monochromator usually transmits higher harmonics) •In operationatvariousSR facilities

Example: U=31.4mm, gap=9.5mm, L=2m

J. Bahrdt

E1=2.6keV (13keV) Ê5=12keV

Ê3=6.7keV

(7.8keV)

M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 31 Interaction of IDs with e-Beam

> In terms of beam dynamics, an insertion device should be “transparent” to the machine, i.e. behave like drift space. But there are

> Intrinsic effects Betatron tune shifts, focusing effects induced by the nominal field of the ID For high field devices: Change of emittance, energy spread growth, reduction of damping time

> Effects due to field errors of the ID Closed Orbit Distortions (by dipole errors, gap dependent) Coupling (induced by skew-quad errors) Reduction of dynamic aperture (decrease of life time and injection efficiency)

> Most of these effects can be avoided or corrected by careful design and manufacture, passive field shimming and active adjustments

just as a remark > Also vice versa: The ID might be affected by radiation background in the tunnel Any electronics must be shielded Permanent magnets may partly be demagnetized Corrosion of permanent magnets or poles due to radio chemistry

M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 32 Impact of IDs: COD, Tune shift

COD are caused by gap-dependent residual Focussing properties of an ID field integrals (kick and displacement) d 2 x e x B yB N S N Compensation by feed-forward of small 2 y z dz m0c z corrector coils at the ends of the ID 2 d y e S N S y xB B dz 2 m c z x Example: Read-out of all BPMs around the 0 machine while closing the undulator gap Close to the mid plane: Bz Bz dy y By dzy Without feed-forward vert: 50µm Vertical focussing: Any vertically displaced e- will experience a longitudinal field which bends it back towards the horizontal plane. The vertical focussing parameter is given by

gap: max min – min max 2 e B2 1 k y With feed-forward vert: 5µm y 2 m0c 2 2 2 1 e B2 k dz y L y Fy m0c 2

This causes a tune shift Additional contributions to COD: 1 k dz y -local distortions of the ambient field by adjacent y y y accelerator components in the tunnel 4 4 Fy -shielding effects of the support structure M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 33 Non-linear Focusing Effects

Example: APPLE2 UE65 at PETRA III in vertical mode Strong roll-off of the horizontal field causes dynamic multipole errors. Magnetic measurement is performed along a straight line but Compensation the field integral along the oscillating electron trajectory is not zero. by L-shims (J. Chavanne et al., Proc. of EPAC 2000 conf.) Dynamic kicks of a periodic magnet structure:

0 L 2 B0 B Measurements of the horizontal ()andvertical(x) U B0 x B0 y x 2(B)2 2 2 x x y x tune shifts as function of horizontal beam position before (blue) and after (red) placement of L-shims. 2 0 0 Theoretical calculations (lines) for comparison.. L U 0 Bx 0 By 4 y 2 2 Bx By f 2(B) 2 y y fxx 3.5 f fyy 3 Calculated dynamic multipoles:

2.5

0.6 UE65 energy = 6.0 GeV kHz 2 uncorrected / kHz / y f 0.4 y , f 1.5 x f

0.2 ,

x 1 f field intgeral [Tmm] 0 0.5 -0.2 0 -0.4 different shim configurations -0.5 -8 -6 -4 -2 0 2 4 6 8 -0.6 x x mm/ mm -30 -20 -10 0 10 20 30 (J. BahrdtM. Tischer et al., | InsertionProc. of DevicesIPAC 2011 | CAS conf.) Chios Sep. 2011 | Page 34 x [mm] Magnetic Measurements and Tuning

M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 35 Magnetic Measurements and Tuning

Purpose:

Measure and remove errors in the magnetic field distribution for all gaps

•OptimizetheSR emission characteristics flatten the trajectory inside the undulator and minimize the phase error

•MaketheID „transparent“ formachine operation remove residual field integrals and multipoles of the device for all gaps

Various Field Correction Mechanisms: Pole

•Initial sorting of magnets, dedicated magnet flipping or swapping •Magnet orpole height adjustment, •ApplicationofFe shims or small corrector magnets •Localcorrector coils Individual pole adjustment: height by ±0.1mm pole tilt by ±1mrad

M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 36 Hall Probe Measurement Bench

Purpose: Fast longitudinal field mapping of Hall probe sensor vertical and horizontal fields (1-3 axis) or pick-up coil Important for optical phase and trajectory shimming

Hall probe requires calibration, temperature stabilization

•platformon airbearings, drivenbylinear motor, servo drives for x, y, z axes, reproducibility ~µm •on-the-flymeasurements, max. sampling~ 200Hz •temperaturecontrolledenvironment(<0.5K)

M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 37 Field Integral Measurements

Different possibilities x/y-Stage •Single StretchedWire Purpose: Measurement of •MovingCoil(Multiturn) longitudinally integrated field integrals, • Rotating Coil i.e. transverse dependence of vertical and horizontal 1st and 2nd field integrals

Important for determination and shimming of multipoles

Much more accurate than Hall probes for determination of field integrals V

Vdt N ~ B dz x, y V

Other techniques •VibratingWire accurate determination of magnetic axis •PulsedWire longitudinally resolved field integrals

M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 38 Example: Measurement &Tuning Results

Trajectory straightness Multipoles tuned with magic fingers 2.5Tmm2 (rms), 3.1Tmm2 (rms) Variation of I1 within 25Gcm

initial

final (gap=10…150mm)

final (gap=10…150mm)

initial

PETRA III: U32, L=5m M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 39 Literature

> Books H. Onuki, P. Elleaume, Eds., Undulators, Wigglers and their Applications, Taylor & Francis, London (2003) J.A. Clarke, The Science and Technology of Undulators and Wigglers, Oxford University Press, Oxford (2004) F. Ciocci, Ed., Insertion Devices for Synchrotron Radiation and Free Electron Laser, World Scientific Pub., Singapore (2000) J.D. Jackson, Classical Electrodynamics, Wiley, New York (1975) A. Hofmann, The Physics of Synchrotron Radiation, Cambridge Monographs on Particle Physics No. 20, Cambridge University Press, Cambridge (2004) S. Krinsky, M.L. Perlman, R.E. Watson, Chapter 2 in “Handbook on Synchrotron Radiation”, Ed.: E.E. Koch, Vol. 2, North-Holland, Amsterdam (1983) andothervolumesfromthisseries

> Previous CAS Summer Schools See previous contributions e.g. from R. Walker, P. Elleaume, J. Clarke, J. Bahrdt

M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 40