Physics of undulators

J. Chavanne Insertion Device Group ASD

-Introductory remarks -Basis of undulator radiation -Spectral properties -Source size -Present technology -Summary

J.Chavanne 1 Books

Undulators, wigglers The physics of The science and Technology And their applications Synchrotron radiation of Undulators and Wigglers

H. Onuki, P.Elleaume A. Hofman J. A Clarke

Modern theory of undulator Very accessible Very clear approach radiations Several ESRF authors

J.Chavanne 2 Few preliminary remarks

Many software simulations are used for undulator radiations:

All simulations done using

SRW Synchrotron Radiation Workshop ( O. Chubar, P.Elleaume) - wavefront propagation - near & far field - will evolve in near future

B2E (B to E) also ESRF tool - field measurement analysis - undulator spectrum with field errors

Unfortunately very few topics in undulator physics will be presented

J.Chavanne 3 Electrons in the framework of relativity

Any particle with non zero mass cannot exceed speed of light

2 Electron energy: E = ! mc = ! E0

E0 is the electron energy at rest =0.511 MeV 1 ! is the relativistic Lorentz factor also defined as ! = Speed of electron v2 1" c2

2 1 ESRF: E= 6.04 GeV so ! = E / E = 11820 v / c = !e = 1"1/# $ 1" 0 2# 2

Electron Energy E v/c

Mass: m=9.10938 e-31 Kg 1 MeV 0.869 Charge: e=-1.60218 e-19 C 100 MeV 0.9999869 Speed of light in vacuum: c = 299792.45 m/s 1 GeV 0.999999869 6 GeV 0.9999999964

J.Chavanne 4 Simple periodic emitter

Period = !0 e 1 2 3 ! v

Points with wavefront emission

Somewhere between point 1 and 2

And between point 2 and 3

J.Chavanne 5 Simple approach

The question: what is the relation between λ0 and λ ?

!0 e

! ?

J.Chavanne 6 On axis observation

Point i the electron has reached point i+1

!

2 1 v / c = ! = 1"1/# $ 1" !0 e 2# 2 " Time taken by the electron to move from point i to point i+1: !t = 0 #ec ! ! During this time the wavefront created at point i has expanded by r = c 0 = 0 "ec "e

Therefore we have: !0 !0 ! = # !0 $ 2 "e 2%

Example: !0 = 28mm we get ! = 1Å with the ESRF energy (γ =11820)

Remark: in the backward direction ! " 2!0

J.Chavanne 7 Off axis observation

!0 1 θ !(") = $ !0 cos" % !0 (1$ cos" + 2 ) #e 2&

! 2 For small angles : cos! " 1# 2 !0 ! !(") # 0 (1+$ 2" 2 ) 2$ 2

1.0 !(0) 1 γ=11820 @ ESRF Interesting to look at = 2 2 0.8 !(") 1+# " ≈1/γ 0.6 c !(0) E (") Photon energy: E = h p 0.4 p = ! !(") Ep (0) 0.2 0.0 The radiated energy is concentrated in a narrow -2 -1 0 1 2 cone of typical angle 1/γ ! [mrad]

J.Chavanne 8 Important remarks

From our simple “periodic emitter ” we have seen :

- Radiations at wavelength of ~ 1 Å can be produced with a spatial wavelength of few centimeters and few GeV electron beam

- Emitted radiations are highly collimated (~ 1/γ ) The angular dependence of emitted wavelength has a direct consequence on associated spectrum Off axis On axis radiation

! !(") # 0 (1+$ 2" 2 ) 2$ 2

Ph/s/0.1%bw

Photon Energy

Presence of “tails” at low energy side on harmonics with non zero angular acceptance

J.Chavanne 9 Other approaches

Lorentz transform + Doppler shift:

Electron frame Observer frame

Lorentz transform spatial period λ1=λ0/γ spatial period λ0

angle dependent Doppler shift emitted wavelength: λ1 !(") = !1# (1$ %e cos" )

! example: !(") # 0 (1+$ 2" 2 ) 2$ 2 undulator with λ0=28 mm has λ1= 2.36 µm , 1.6 m long undulator has a length of 0.135 mm in electron frame

J.Chavanne 10 Electron and observer times

! ! v(t ) c (t ) Electron moving with speed ! = "e ! Wave emitted at time t’ by electron received at time t by observer

D(t!) t = t! + c ! D(t!) n(t!) dt ! ! = 1" n(t!)#e (t!) ! dt! ! ! v(t!) R(t!) ! For ultra-relativistic electron and small angles: r

dt 2 1 2 2 o = 1" # cos$ = 1" 1"1/% cos$ & (1+% $ ) Relativistic compression of time: dt! e 2% 2 Observer time evolves several orders of magnitude slower than electron time

Basis for “retarded potentials” or Lienard-Wiechert potentials

J.Chavanne 11 Improving oscillator model

How to get periodic emission from an electron ? Apply periodic force on electron: ! ! ! ! F = !e(E + v " B) B= 1 T 300 MV/m ~ 10 MV/m with V ! c conventional technology

Best option z

Planar field undulator λ0

x

! ! Vertical field B = B cos 2! s / " z 0 ( 0 ) s ! Electron trajectory ! B

J.Chavanne 12 Undulator equation (1)

! dP ! ! ! ! ! ! B = B cos 2! s / " z = !e(v " B) P = ! mv 0 ( 0 ) dt

Assumptions: γ constant , βx= vx/c,<< 1 , βz= vz/c<<1

Angular motion

e 2" s K 2" s e !x (s) = B0$0 sin( ) = sin( ) K = B0"0 = 0.9336B0[T ]"0[cm] 2"# mc $0 # $0 2! mc

!z (s) = cst = 0 Deflection parameter Electron trajectory

K"0 2# s 2# s x(s) = ! cos( ) = !x0 cos( ) 2#$ "0 "0 γ λ0[cm] B[T] K xo[µm] z(s) = cst = 0 11820 2 1 1.87 0.5

J.Chavanne 13 Undulator equation (2)

We need to know the longitudinal motion βs of the electron in the undulator to bring more consistence to our initial “naïve” device:

2 2 2 1 K 2# s Since γ is constant so is ! e = !x + !s = 1" 2 (!x (s) = sin( )) # " $0

1 K 2 K 2 4% s !s (s) " 1# 2 # 2 + 2 cos( ) 2$ 4$ 4$ &0 2 ˆ 1 K Average longitudinal relative velocity: !s " 1# 2 # 2 2$ 4$

! K 2 Angle dependent emitted wavelength: !(") # 0 (1+ +$ 2" 2 ) 2$ 2 2

γ λ0[cm] B[T] K λ(0) 11820 2 1 1.87 1.96 Å We have now a field dependent wavelength 11820 2 0.1 0.187 0.72 Å

J.Chavanne 14 The electric field

! ! The electric field E ( r , t ) seen by an observer is the relevant quantity to determine ! ! D(t!) ! ! n(t!) ! ! n(t ) Has always B field “companion”: B(r,t) = " E(r,t) ! ! c ! ! E(r,t) ! ! v(t!) R(t!) ! r Moving charge along arbitrary motion:

Electric field includes two terms o ! ! ! ! ! ! ! ! E(r,t) = E (n(t ),v(t ), D(t )) + E (n(t ),v(t ), D(t )) 1 ! ! ! 2 ! ! ! Needs to find t’(t) to ! ! evaluate E(r,t)

Velocity field or Acceleration field Coulomb field Decays as 1/D Decays as 1/D2 ! Far field approximation: drop velocity field and n (t!) constant

J.Chavanne 15 Frequency domain

! ! 1 $ ! ! E(r,! ) = E(r,t)ei!t dt %#$ 2" Electric field in time domain Electric field in frequency domain Complex quantity

Wavefront propagation

Phase ? Coherence

Etc.. ! ! 2 ! " E(r,! ) N(r,! ) = "! Number of photons at ω

J.Chavanne 16 Importance of deflection parameter K Peak angular deflection angle K !1 ! electric field

±1/!

Frequency time Electric field angle K > 1 Only odd harmonics

±1/!

time Frequency

Electric field Off axis observation with angle θ odd + even harmonics angle

±1/! +"

Frequency

J.Chavanne 17 On axis angular spectral flux

Spectral photon flux units: Watts/eV can be translated into photons/sec/relative bandwidth Ex: 1 phot/s/0.1%bw= 1.602e-16 W/eV Angular spectral flux: photon flux/unit solid angle Usual unit is phot/sec/0.1%/mrad2: Ideal on axis angular spectral flux with filament electron beam (zero emittance)

4.0x1018

] Only odd harmonics on axis Undulator:

2 3.0 Period λ0= 22 mm Number of period N=90 2.0 K=1.79

1.0

[Phot/s/0.1%/mrad 0.0 0 20 40 60 80 keV Harmonic n =7 Relative bandwidth at harmonic n:

] 2 18 2.0x10 ~ 1/N ∆E/E=1/nN ~ N2 1.0 Radiated power: ~ N2/N=N proportional to N 0.0 [Phot/s/0.1%/mrad 41.75 42.00 keV

J.Chavanne 18 Off axis radiation

15 2 4x10 3

2 Undulator: Period λ = 22 mm 1 0

Ph/s/0.1%bw/mm Number of period N=90 0 K=1.79 Filament electron beam 5 10 15 20 25 30 35keV (zero emittance) Photon Energy

z Vert. angle γθ angle Vert.

Hor. angle !" x n=2 n=3 n=5 n=6

2 !0 K 2 2 2 2 2 Wavelength of harmonic n ! (") = (1+ +# " ) ! = ! x +!z n 2n# 2 2

J.Chavanne 19 Angle integrated flux

Undulator: Ideal filament electron beam Period λ0= 22 mm Number of period N=90 En! En K=1.79 Harmonic n=3

12 15

800x10 4x10 On axis flux density axis flux [Phot/s/0.1%/mm On 10 µrad x 10 µrad "!n 20 µrad x 20 µrad 30 µrad x 30 µrad 600 50 µrad x 50 µrad 3 All angles on axis

400 !n 2

Ph/s/0.1%bw

200 1 2 0 0 ] 17.4 17.6 17.8 18.0keV Photon Energy

En energy of on axis resonance 1 2hc" 2 0.95E 2[GeV ] En (!) = 2 = 2 "!n # 2"n En! = En (1" ) K K nN # (1+ +" 2! 2 ) # [cm](1+ +" 2! 2 ) 0 2 0 2

J.Chavanne 20 Angle integrated flux (remark)

A unique specificity of ESRF:

∆s Segmented independent undulators with passive phasing capability ~ all in-air segments Undulator A For a fixed energy and collecting aperture Undulator gaps are optimized for maximum flux Undulator B

One undulator # E! = E (1" ) 0 ! " ! 1 n n nN

Two undulators # E! = E (1" ) n n 2nN ∆s depends on period 2.5 mm for λ0=18 mm The optimum gap depends on the length of undulator 5 mm for λ0=35 mm

J.Chavanne 21 Radiated power

Radiated power & power density can be an issue for ESRF beamlines

Total power emitted by an Insertion device: (only a fraction is generally taken by a beamline)

" P[kW ] = 1.266E 2[GeV ]I[A] (B2[T ]+B2[T ])ds ID with arbitrary field # x z !" 2 2 Planar sinusoidal field undulator P[kW ] = 0.633E [Gev] B0 [T ]I[A]L[m] B0: peak field On axis power density: Undulator length

2 4 dP / d![W / mrad ] = 10.84 B0[T ]E [Gev]I[A]N N: number of periods, K>1

Ex: ESRF 6 .04 Gev with I=0.2 A

2 Period[mm] L[m] N B0[T] P[kW] Dp/dΩ[kW/mrad ]

22 2 90 0.87 7 260

27 5 185 0.52 6.7 277

With ~ all ESRF IDs at minimum gap: the total radiated power is ~ 300 kW (0.2 A, 6.04 Gev) (to be compared to ~ 1 MW for all dipoles)

J.Chavanne 22 Electron beam size

! = 4nm Geometrical size of ESRF electron beam (assuming Gaussian beam) x ! z = 3pm

0.10 High beta straight

0.00 middle -0.10

Vert. position [mm] position Vert.

-1.0 -0.5 0.0 0.5 1.0 Hor. position [mm]

0.10 @ 3 m from 0.00 middle

-0.10

Vert. position [mm] position Vert.

-1.0 -0.5 0.0 0.5 1.0 Hor. position [mm]

0.10 Low beta straight

0.00

-0.10 middle

Vert. position [mm] position Vert.

-1.0 -0.5 0.0 0.5 1.0 Hor. position [mm]

0.10 @ 3 m from 0.00 middle

-0.10

Vert. position [mm] position Vert.

-1.0 -0.5 0.0 0.5 1.0 Hor. position [mm] J.Chavanne 23 Phase space

Electron beam envelope along ID straight section

Symmetry point

x’,z’ x’,z’ x’,z’

x,z x,z x,z convergent waist divergent

(rms) beam occupancy in horizontal & vertical phase space Ellipse of constant area= πε (ε : emittance)

J.Chavanne 24 Electron beam in ID straight

Beam size and divergence are derived from the knowledge of beta βx,z(s) functions and emittance εx,z x’,z’

! / "0 ! / " s x,z !"0 S=0 at middle of straight section ε.β

For each plane s2 (s) (1 ) ! = !0 + High beta β0[m] η ε [nm] σ(0) [µm] σ’[µrad] !0 horizontal 37.5 0.13 4 409 10.3 Rms size & divergence Vertical 3 0 0.003 3 1

2 2 ! (s) = "#(s) +$ ! %

Low beta β0[m] η ε [nm] σ(0) [µm] σ’[µrad] # " !(s) = = cst horizontal 0.37 0.03 4 49 104 $ 0 Vertical 3 0 0.003 3 1 η: dispersion

σγ relative rms energy spread: 0.1% @ ESRF

J.Chavanne 25 Undulator spectra with actual beam

Photon flux in 0.5 mm (H)x0.2 mm(V) @ 30 m Undulator: Period λ = 22 mm Electron beam 0 12 Number of period N=90 300x10 E=6 Gev I=0.2 A K=1.79 High Beta 200 emittance 0 nm H & V, Energy spread =0 emittance 4 nm (H) & 3 pm (V), energy spread 0.1 %

Ph/s/0.1%bw 100

0 0 20 40 60 80keV Photon Energy 120x1012 12 300x1012 100 40x10 80 30 200 60 20 100 40 20 10

Ph/s/0.1%bw

Ph/s/0.1%bw 0 0 Ph/s/0.1%bw 0 5400 5600 5800 6000 6200 6400eV Photon Energy 40 42 44keV 62 64 66 68 70keV Photon Energy Photon Energy Spectral performances dominated by horizontal emittance and energy spread at high harmonics

! K 2 ~ additional off axis contribution due to electron beam size and divergence ( ! (") = 0 (1+ +# 2" 2 ) ) n 2n# 2 2

J.Chavanne 26 Beam size at beamline

Photon beam size @ 30 m from source

12 300x10 Electron beam: Undulator: Emittance; Period λ0= 22 mm 200 Horizontal: 4nm Number of period N=90 Vertical: 3 pm 100 K=1.79 Energy spread: 0.1 % Harmonic n=3

Ph/s/0.1%bw 0 17 18 19keV Photon Energy

3 3

2 2

1 1

0 0

Vertical Position Vertical -1

Vertical Position Vertical -1

-2 -2

-3mm -3mm -3mm -2 -1 0 1 2 3 -3mm -2 -1 0 1 2 3 Horizontal Position Horizontal Position Ideal electron beam Finite emittance, High Beta

J.Chavanne 27 Source size & divergence

Rms source size and divergence can be well evaluated using:

Electron beam

2 2 2 2 !x,z = " n +" x,z "!x,z = # n! +# x!,z

“natural” undulator emission (single electron of filament electron beam)

Various expressions for σn and σ’n found in literature generally assuming Gaussian photon beam for “natural” size & divergence

This do not impact on horizontal source size and divergence since dominated by electron beam

However in vertical plane the story is different:

At the middle of a straight section we have : σz=3 µm and σ’z=1 µrad for εz=3 pm for the electron beam

J.Chavanne 28 “natural” undulator size & divergence

Evaluation of source size σn and divergence σ’n (single electron)

Undulator s ! # n"D

D=30 m

s = ! n

Undulator

Ideal lens 1:1 image plane

x2 f (x)dx 2 !w ! n " ! rms values evaluated as second order moment: x = n f (x)dx !w

J.Chavanne 29 At on axis resonance

20 600 12 800x10 15 400 4x10 10 2 600 200 Phot/sec/o.1% 3

0 0 400 2

Vertical Position Vertical -200

Vertical Position Vertical

Ph/s/0.1%bw/mm -10 -400 1 200

-600µm 0 0 -20µm 18.0 18.1 18.2 18.3keV -600µm -400 -200 0 200 400 600 -20 -10 0 10 20µm Horizontal Position Photon Energy Horizontal Position D=30 m 19 $ 1.0x10 " n! # 15

2L 2 4x10 0.8

2 3 2#L 0.6 ! n " 2 2$ 0.4

1 Ph/s/0.1%bw/mm 0.2

Ph/s/0.1%bw/mm 0 % !n = " n" n# $ 2 0.0 -400µm 0 400 4& -20µm -10 0 10 20 Vertical Position ! Vertical Position Diffraction limit for Gaussian beam 4" Undulator beam is not Gaussian but fully coherent transversally

J.Chavanne 30 At peak flux

15 600 10 12 400 800x10 15 4x10 5 200

2 600 Phot/sec/o.1% 3 0 0 400

2 Position Vertical Vertical Position Vertical -200 -5

Ph/s/0.1%bw/mm 200 -400 1 -10

-600µm 0 0 -15µm 18.0 18.1 18.2 18.3keV

-600µm -400 -200 0 200 400 600 Photon Energy -15 -10 -5 0 5 10 15µm Horizontal Position Horizontal Position

D=30 m

15 4x10 " ! # 2.1 $ 19 n 2L 3x10

2

3 2 2#L 2 2 ! " 0.9 n 2$ 1 1

Ph/s/0.1%bw/mm % 0 !n = " n" n# $ 3.8 Ph/s/0.1%bw/mm 0 -400µm 0 400 4& -15µm -10 -5 0 5 10 15 Vertical Position Vertical Position

Phase space area εn is minimum at resonance

σn and σ’n can depend strongly on detuning from on axis resonance

J.Chavanne 31 Energy spread

Electron beam energy spread impact also on source size & divergence: pointed out at SPRING8 [1] Had to be taken into account for NSLSII expected performances [2]

$ F( ) " n! # 2L " % 2 nN For example at resonance ! " = # ! $ normalized energy spread 2#L ! " G(! ) n 2$ % n undulator harmonic number N number of periods 2.5 F[!"] G[!"] F, G universal functions of ! 2.0 ESRF range " ! = 0.001@ESRF 1.5 "

1.0 ! K 2 Behind this effect is !(") # 0 (1+ +$ 2" 2 ) again 0 2 4 6 8 10 2$ 2 2

!"=2#nN!$ The impact is mostly on source divergence

[1] Takashi Tanaka* and Hideo Kitamura, J. Synchrotron Rad. (2009). 16, 380–386

[2] see NSLS II conceptual design report, radiation sources

J.Chavanne 32 Example

6x10-6 Source divergence 5 Undulator: 4 Period λ0= 22 mm rad 3 1 pm Number of period 3 pm N=90 2 10 pm K max =1.79 1 0 Electron beam 7 8 9 2 3 4 5 6 7 8 9 10 keV 100 keV E=6.04 Gev Photon Energy I=0.2 A -6 ESRF low beta 7x10 6 5 4 m Evaluation 3 1 pm At on axis resonance 2 3 pm 10 pm Source size 1 0 7 8 9 2 3 4 5 6 7 8 9 10 keV 100 keV Photon Energy

J.Chavanne 33 Resulting brilliance

6 5 4 Harmonics 1 to 9 at on axis resonance 3

2

2

/mr

2 1020

6 5 4 3

Ph/s/0.1%bw/mm Vertical emittance 2 10 pm 3 pm 1 pm 1019

7 8 9 2 3 4 5 6 7 8 10 keV Photon Energy

Undulator: Electron beam Period λ0= 22 mm E=6.04 Gev Number of period I=0.2 A N=90 Horizontal emittance: 4 nm K max =1.79 ESRF low beta

J.Chavanne 34 Residual field errors in undulators

Undulators have residual small horizontal along all magnetic structure -> small vertical random motion of electron along undulator

This generate an additional contribution to vertical source size and divergence

Has no impact on electron beam closed orbit and vertical emittance

Divergence Size

3.0 All undulators All undulators In- Vacuum In-Vacuum 2.5 1.2 Average: 1.3 µrad 2.0 Average: 0.6 µm

[µm] [µm] 0.8

z

z

s d 1.5 1.0 0.4 0.5 0.30 0.40 0.50 0.60 0.30 0.40 0.50 0.60 Gap/period [] Gap/period [] All Undulators @ minimum gap: Gives an equivalent extra vertical phase space area of ~ 0.8 pm

Ambient field along straight section also contribute ->to be investigated

J.Chavanne 35 Technological trends in Insertion Devices

Overview of Insertion Devices at SR facilities Small gap & conventional undulators Cryogenic devices

J.Chavanne 36 Undulator demand

Driven by new constructions & upgrades

Many Medium energy rings :2.7-3.5 GeV SOLEIL, DIAMOND, CLS, ALBA, SSRF, TPS ,Australian Synchrotron, NSLS II …

High energy rings (≥ 6.GeV) SPRING 8 ESRF Upgrade APS Upgrade Petra III

X FELs LCLS SACLA • LCLS (Stanford) • SACLA (SPRING8) European XFEL Fermi • Flash, European XFEL (Hamburg) • Fermi@ elettra • …..

J.Chavanne 37 Types of Insertion Devices Medium Energy Rings 1- In-Vacuum undulators Access to photon energy above 2- Superconducting wigglers 10 KeV rely only on ID performance 2- Elliptically polarized Undulators

High energy rings

1- Conventional (In-air planar undulators) (ESRF,APS, PETRA III) 2- IVUs (SPRING 8 ,ESRF, planned at PETRA III) 3- Elliptically polarized Undulators 4- Superconducting undulator development (APS) X-FELS

1- Conventional in-air planar undulator: LCLS (fixed gap), European X-FEL 2- IVUS (SACLA-SPRING8) 3- EPU (Fermi) For the time being, X-FELs and SR facilities rely on same ID technology

J.Chavanne 38 “ Conventional “ undulators

Significant part of IDs in high energy rings ESRF, APS, PETRA III

Evolution toward revolver structure: Connected to specialization of beamlines

Flexibility Combines: Tunable undulator for 2.5 - 30 keV (period 35 mm, Kmax>2.2) + Shorter period undulators for higher brilliance in limited energy range (period 18 ~ 27 mm, Kmax <1.5) Interchangeable with other standard undulator segments

Noticeable demand for revolver devices at ESRF

Foreseen in the upgrade of APS ESRF revolver undulator 3 different undulators

J.Chavanne 39 In-Vacuum undulators

In-air undulator In-vacuum undulator Permanent Magnet array

gap Vacuum chamber

P.M Undulator field Link rod B = "Br exp(#$% gap/&0 ) Min gap ≈ 10 mm Magnetic p.m material Min gap ≈ 4 - 6 mm undulator structure remanence period ≈ beam stay clear ! Large international development of IVUs Minimum gap limited by effect on beam (beam losses, lifetime reduction ..)

Minimum gap < 6 mm needs to be investigated at ESRF in near future

! J.Chavanne 40 ESRV IVUs

Nominal magnetic length 2m motorized gap tapering (± 90 µm) New version with 2.5 m Under construction (UPBL4)

Mature technology

Essential for High Photon energy

above 50 keV

Vacuum chamber

Cooling connections Pitch adjustment Support structure compatible with room temperature IVU or CPMU

J.Chavanne 41 CPMUs

CPMU: Cryogenic Permanent Magnet Undulator

Affordable evolution of IVUs:

Cryogenic cooling of permanent magnet arrays:

- possible use of high performance magnets - high resistance to demagnetization - ~ 35 % gain in peak field vs standard IVUs

First device installed and operated at ESRF

Second device completed: installation in January 2012 in ID11

- period 18 mm - peak field 1 T @ 148 K, gap 6 mm

J.Chavanne 42 Superconducting undulators

2001 New concept of SCU (ANKA-ACCEL)

Cryogenic vacuum Beam vacuum SCU

Magnetic gap

Vacuum gap

Vac. Chamber cooling (dry)

Cryo-cooling : dry or LHe circulation in undulator body

S. Casalbuoni Magnetic gap= vacuum gap + D D = 2 ~ 2.5 mm

J.Chavanne 43 SCUs Vs CPMUs

Diamond CPMU @ gap 5 mm Soleil CPMU @ gap 5.5 1.1

1.0 ANKA SCU (gap 8 mm) 2nd ESRF CPMU @ 145 K (gap 6 mm) 0.9

0.8 APS SCU1 (gap 9.5 mm)

0.7 Sm2Co17, Br=1.05 T Effective peak field [T] field peak Effective 0.6 NdFeB CPMU, Br=1.5 T @ 145 K

0.5 SCUs 14 16 18 20 22 Period [mm] Plans to Use Nb3Sn instead of NbTi superconducting materials for SCUs

Present Limitation for SCUs: Magnetic gap vs vertical beam stay clear ( heat budget)

J.Chavanne 44 Summary

- Basic principles of undulator radiation have been visited

- Undulator radiations have longitudinal and transverse “interference” patterns

- Limiting factors on undulator performances - horizontal emittance - energy spread on high undulator harmonics

- Beneficial improvement achieved through the reduction of vertical emittance - vertical source divergence close to saturation

- The technology of undulator evolves toward - higher flexibility - cryogenic devices

J.Chavanne 45