Insertion Devices CERN Accelerator School, Chios 2011 - PowerPoint PPT Presentation

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 Radiation Alternating magnetic field 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 PU08 / PU09 PU10 PU04: APPLE II M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 4

Synchrotron Radiation Sources & Brilliance Development of brilliance: 15 orders of magnitude Spectral characteristics of different SR-sources FEL: Peak-brilliance another ~8 orders � [B] = photons/sec/mm 2 /mrad 2 /0.1%bw Brilliance = Photon flux at energy E within 0.1% bandwidth normalized to beam size and divergence � � B n (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 • Accelerated charge emits Acceleration of charged particle electromagnetic radiation Lorentz-Transformation • Angular distribution like for electric Dipole e – Rest frame Lab frame • Acceleration induced by Lorentz force Acceleration Acceleration � � � � d p d v � � � � � � F m e v B 90° 0 dt dt 1 � � i.e. transverse acceleration in a storage ring Detector Opening angle of SR • Radiated power 2 4 • natural opening angle ~1/ � = 0.06-0.5mrad e c E P � � � � 4 e.g. ESRF, PETRA3: 1/(1957x4.5[GeV]) = 85µrad �� 2 6 m c 0 0 M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 6

Dipole Radiation � � � � � � 2 1 1 � � � � � � � � t t t sin � � � � 2 1 � � � 3 c 3 c � � � � � t • Due to the narrow opening cone ( � =1/ � ) 1 1 � � � � 3 6 the observer will see only a short light � � � � d 2 1 s 2 � � � � � � � � t sin t ( v c ) � � pulse with duration � t ~ � /c � 3 1 � 2 � c c v c � � • This results in a broad continuous Fourier spectrum with a characteristic frequency � c ~ c � 3 / � ~ E e 2 ·B (~10 19 Hz � � ~1Å) or “critical” energy E c E c [keV] = 0.665 � E e 2 [GeV] � B 0 [T] (ESRF, PETRA: E c ~20keV) E c M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 7

Dipole Radiation • Spectral Intensity Distribution • Linearly polarised in orbit plane ( � Schwinger equation) 2 � � � � � � � � � � 2 � 2 d 3 I E � � � � � � � � � � � � � � � � � � 2 e 2 2 2 2 ( E , ) 1 K K � � � 2 / 3 1 / 3 � � 2 � � � 2 � 2 d 4 e E 1 � � � � c with � � � E 3 / 2 � � � � 2 � 2 1 2 E c E c • Flux density, emitted in orbit plane � =0 [ phot./sec/mrad 2 /0.1%bw ] d � /d � (E) | � =0 = 1.33 � 10 13 E e 2 [GeV] � I e [A] h(E/E c ) • Flux, integrated over all vertical angles � [ phot./sec/mrad/0.1%bw ] d � /d � (E) = 2.46 � 10 13 � E e 2 [GeV] � I e [A] � g(E/E c ) M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 8

Electron Trajectory in an Insertion Device � � � d v � Lorentz force � � � � F m e v B 0 dt 1 v � � � � , with c � � 2 1 Assume small angular deflections v x , v y � v z ~ c Equations of motion: 2 � � d x e dx dx dz � � � � � � � � � � � � � c � � � x B y B x � x � z , z � const , 1 with y z dt dz dt 2 � dz m c 0 2 d y e � � � � � � � � � y x B B z x 2 � dz m c 0 For a sinusoidal vertical field (0, B y , 0) : � � � 2 � � � B B sin z � � y 0 � � � U with the so-called Deflection Parameter K � � � K 2 e � � � � � � � � x cos z Angular deflection K B 0 . 934 B [ T ] [ cm ] � � � � 0 U 0 U � 2 m c � � U 0 � � � � K 2 Maximum angular deflection angle � = � K / � � � Displacement � x U sin z � � � � � 2 � � K is a measure for the strength of the insertion device U M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 9

Wigglers Permanent magnets Intensities of all poles add up (incoherently) Poles Flux Wiggler = 2 � N � Flux Dipole (for equal E c ) Magnetic field � High intensities z e - trajectory Emitted SR � High photon energies Gap Critical energy: E c [keV] = 0.665 � E e 2 [GeV] � B 0 [T] Emitted total power of a wiggler or undulator • Alternating magnetic field with length L=N �� U : (typ.: 50kW) � � � 2 � � � � � B z B sin z � � 2 [T] � L [m] � E e 2 [GeV] � I e [A] P tot = 0.633 � B 0 0 � � � U Period length � U (typ. 10-30cm) Peak field B 0 (typ. >1.5T) Polarisation of wiggler radiation: Number of periods N = L / � U (typ. 5-100) 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 � u Consider K<<1: � u � Lorentz contraction: � • Maximum angular deflection is much smaller � � � � u � � � � 1 2 2 u than the opening angle of the radiation cone Doppler effect: � 2 • Observer can fully follow the sinusoidal trajectory � � � � � � � R � 2 1 2 2 u Combined: � 2 • Wavelength of the emitted light � R ~ � U For ~GeV machines: � �� � �� 10 7 , � U ~mm � � R ~ Å is drastically shortened due to relativistic effects: � U c � Time for the e- to travel one period: z � U � In this time the wavefront from P will propagate: z � � � � � � � � d cos n Constructive interference for: U z U R � � � 2 K � 2 2 � � � � � � � � 2 � � � 2 � U 1 � � � R x y � 2 2 n 2 � � � � � � � � � � 2 � � 2 13 . 056 cm K 0 . 950 E GeV � � � � � � � � � � Å U 1 or E keV e � � � � � � � � (on-axis) R 1 2 � � 2 E GeV 2 cm 1 K 2 � � U K = 1 3, � U = 1 5 cm � � R ~ nm Å typically: 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 v z • The modulation of v z 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: E 1 characteristic quantity: E c K -parameter 15 E c larger K-Parameter �� � more higher harmonics � fundamentale E 1 � � spacing of harmonics � … � overlap of harmonics � quasi-continuous spectrum = wiggler M. Tischer | Insertion Devices | CAS Chios Sep. 2011 | Page 14