1 brookhaven science associates parametric optimization of in-vacuum undulators; segmented...

1 BROOKHAVEN SCIENCE ASSOCIATES

Parametric Optimization of In-Vacuum Undulators; Parametric Optimization of In-Vacuum Undulators; Segmented “Adaptive-Gap Undulator” ConceptSegmented “Adaptive-Gap Undulator” Concept

O. Chubar, with contributions from T. Tanabe, C. Kitegi, G. Rakowsky, A. Blednykh, J. Bengtsson, Y. Q. Cai, S. Hulbert, Q. Shen, and S. Dierker (Photon Sciences Directorate, BNL)

NSLS-IINSLS-IIεεxx= 0.55 nm = 0.55 nm

E = 3 GeV, I = 0.5 AE = 3 GeV, I = 0.5 A

ICFA Workshop on Future Light SourcesICFA Workshop on Future Light SourcesJLAB, March 5-9, 2012 JLAB, March 5-9, 2012


OutlineOutline

1. Approved NSLS-II Beamlines and IDs

2. Parametric Optimization of In-Vacuum Undulators

3. Some Details of Undulator Emission(inspired by discussions at this Workshop)

4. Segmented Adaptive-Gap Undulator- Concept

- Magnetic Design Issues

- Spectral Performance

5. Conclusions

NSLS-II “Project”NSLS-II “Project”,, NEXTNEXT, and , and ABBIX (NIH)ABBIX (NIH) Beamlines and IDsBeamlines and IDs

BL ID straight

typeID type, incl. period

(mm)Length Kmax FE type† # of ID's

(base scope)# FE's Project

CSX lo-β EPU49 (PPM) x2 4m (2 x 2m) 4.34 canted (0.18) 2 1 NSLS-II

IXS hi-β IVU22 (H) x2 6m (2 x 3m) 1.52 std 1 1 NSLS-IIHXN lo-β IVU20 (H) 3m 1.83 std 1 1 NSLS-IICHX lo-β IVU20 (H) 3m 1.83 std 1 1 NSLS-IISRX lo-β IVU21 (H) 1.5m 1.79 canted (2.0) 1 1 NSLS-II

XPD hi-β DW100 (H) 6.8m (2x3.4m) ~16.5 DW 0 1 NSLS-II

ESM hi-β EPU56 (PPM) & EPU180 (EM)

3m4m

3.646.8 canted (0.5) 2 1 NEXT

SIX hi-β EPU49 (PPM) x2 7m (2 x 3.5m) 3.5 std 1 1 NEXT

ISR hi-β IVU23 (H) 3.0m 1.6-2.07* canted** 1 1 NEXTSMI lo-β IVU22 (H) 1.3m 2.05 canted 1 1 NEXTISS hi-β DW100 (H) 6.8m (2x3.4m) ~16.5 DW 0 1 NEXTFXI hi-β DW100 (H) 6.8m (2x3.4m) ~16.5 DW 0 1 NEXTFMX lo-β IVU21 (H) 1.5m 1.79 canted (2.0) 1 1 NIH

AMX lo-β IVU21 (H) 1.5m 1.79 canted (2.0) 1 0 (joint w/FMX) NIH

LIX hi-β IVU23 (H) 3.0m 1.6-2.07* canted** 1 1 NIH

PPM: Pure Permanent-MagnetEM: Electro-MagnetH: Hybrid magnetic design

† For canted IDs/FEs, ( ) shows canting angle in mrad * Depending on location within ID straight section** Off-center canting magnet location in ID straight section

S. Dierker, Q. Shen, S. Hulbert


Hybrid In-Vacuum Undulator Magnetic Performance,Hybrid In-Vacuum Undulator Magnetic Performance,Required Gaps and Acceptable Lengths Required Gaps and Acceptable Lengths

IVU Parameters IVU Parameters Reference Geometry:Reference Geometry: Pole Width: 40 mm Pole Height: 25 mm Pole Thickness: 3 mm (for λu = 20 mm)

Magnet Width: 50 mmMagnet Height: 29 mm

Materials:Materials: Pole: Va Permendur NEOMAX Magnet: NdFeB, PrFeB

RADIA Model (central part)RADIA Model (central part)

βy0 = 3.4 m

βy0 = 1.06 m

IVU Lengths Satisfying Vertical IVU Lengths Satisfying Vertical “Stay Clear” Constraints in Low- “Stay Clear” Constraints in Low- and High-Beta Straight Sectionsand High-Beta Straight Sections

Fundamental Photon Energy vs GapFundamental Photon Energy vs Gapfor Different IVU Periods (E = 3 GeV)for Different IVU Periods (E = 3 GeV)

Max. Lengthin Lo-β Sect.

Max. Lengthin Hi-β Sect.

Hybrid In-Vacuum Undulator Magnetic Performance: Hybrid In-Vacuum Undulator Magnetic Performance: Halbach Scaling LawHalbach Scaling Law

Following P. Elleaume, J. Chavanne, B. Faatz, NIM-A 455 (2000), 503-523

Planned SCU for DIAMOND(J. Clarke)


Spectral Brightness and Flux at Odd Harmonics Spectral Brightness and Flux at Odd Harmonics of Various IVU in Low-Beta Straight of Various IVU in Low-Beta Straight

NSLS-II, Low-Beta Straight SectionI = 0.5 A; εx = 0.55 nm; εy = 8 pm; σE/E = 8.9x10-4

Magnet Material: NdFeB, Br = 1.12 T

BrightnessBrightness FluxFlux


Spectral Flux of Different IVUs – IXS “Candidates” – Spectral Flux of Different IVUs – IXS “Candidates” – Satisfying E-Beam Vertical “Stay Clear” ConstraintSatisfying E-Beam Vertical “Stay Clear” Constraint

E-Beam Energy: 3 GeVCurrent: 0.5 A

NSLS-IIHigh-Beta (Long) Straight Section

Maximal Spectral Flux through 100 Maximal Spectral Flux through 100 μμrad (H) x 50 rad (H) x 50 μμrad (V) Aperturerad (V) Aperture

~9.13 keV

~9.13 keV


Spectral Flux of Spectral Flux of Room-TemperatureRoom-Temperature & & CryogenicCryogenic IVUs IVUs Satisfying E-Beam Vertical “Stay Clear” ConstraintSatisfying E-Beam Vertical “Stay Clear” Constraint

~9.13 keV

~4.7 keV

IXS Beamline IXS Beamline (High-Beta Straight Section; (High-Beta Straight Section; 100 100 μμrad H x 50 rad H x 50 μμrad V Ap.rad V Ap.))

SRX Beamline SRX Beamline (one of two Canted Undulators in Low-Beta Straight Sect.; (one of two Canted Undulators in Low-Beta Straight Sect.; 150 150 μμrad H x 50 rad H x 50 μμrad V Ap.rad V Ap.))

Effect of Electron Beam Energy SpreadEffect of Electron Beam Energy Spreadon Spectral Flux of IXS IVU22-6 mon Spectral Flux of IXS IVU22-6 m

I = 0.5 A, High-Beta straight sectionI = 0.5 A, High-Beta straight section100 100 μμrad (H) x 50 rad (H) x 50 μμrad (V) Aperturerad (V) Aperture 20 x 20 20 x 20 μμradrad22 Aperture Aperture

E-Beam Energy: 3 GeV Current: 0.5 AUndulator Period: 20 mm

Vertical Cuts (x = 0)Vertical Cuts (x = 0)

Intensity Distributions in 1:1 Image PlaneIntensity Distributions in 1:1 Image Plane

UR “Single-Electron” Intensity and “Multi-Electron” FluxUR “Single-Electron” Intensity and “Multi-Electron” FluxUndulator

Ideal

Lens

1:1 Image Plane

47.7'yy

4

3.3

49.1

45.1

42.9

““Phase-Space Volume” Estimation for Vertical PlanePhase-Space Volume” Estimation for Vertical Plane(RMS sizes/divergences calculated for the portions of intensity distributions containing 95% of flux)

H5

Intensity Distributions at 30 m from Undulator CenterIntensity Distributions at 30 m from Undulator Center

Single-Electron Undulator Radiation Single-Electron Undulator Radiation Intensity Distributions “in Far Field” and “at Source”Intensity Distributions “in Far Field” and “at Source”

At 30 m from UndulatorAt 30 m from Undulator

Horizontal Cuts (y = 0)Horizontal Cuts (y = 0) Vertical Cuts (x = 0)Vertical Cuts (x = 0)

IVU20 Ideal Lens 1:1 Image Plane

IVU20-3m Spectral Flux IVU20-3m Spectral Flux through 100 μrad (H) x 50 μrad (V) Aperture

at K~1.5 providing H5 peak at ~10 keV

In 1:1 Image PlaneIn 1:1 Image Plane

Test Optical Scheme Test Optical Scheme


Intensity Distributions at ~10 keVIntensity Distributions at ~10 keV

4' 5.7yy

Electron Beam: Hor. Emittance: 0.9 nm Vert. Emittance: 8 pm Energy Spread: 8.9x10-4 Current: 0.5 A Low-Beta Straight

;4

' 97xx …very far from Coherent Gaussian Beam !

X-Ray Beam Angular Divergence and “Source Size” from X-Ray Beam Angular Divergence and “Source Size” from Partially-Coherent Wavefront Propagation SimulationsPartially-Coherent Wavefront Propagation Simulations

RMS sizes/divergences calculated for the portions of intensity distributions containing 95% of flux


Comparison of IVU Spectral Flux (per Unit Surface)Comparison of IVU Spectral Flux (per Unit Surface)for IXS Locations in for IXS Locations in Low-Low- and and High-Beta StraightsHigh-Beta Straights

E-Beam Energy: 3 GeVCurrent: 0.5 A

Spectral Flux of different IVU providing H5 peak at ~9.1 keVSpectral Flux of different IVU providing H5 peak at ~9.1 keV

Flux per Unit Surface (Intensity) Distributions at 20 m from IVUs (Flux per Unit Surface (Intensity) Distributions at 20 m from IVUs (εε = 9.13 keV) = 9.13 keV)

Horizontal Cuts (y = 0) Vertical Cuts (x = 0)IVU20-3m in Low-Beta

Straight SectionIVU22-6m in High-Beta

Straight Section


IVU22 – 6 m Spectral Flux (per Unit Surface) IVU22 – 6 m Spectral Flux (per Unit Surface) Near Harmonic PeakNear Harmonic Peak

Spectral Flux at K~1.5 Providing H5 at ~9.1 keVSpectral Flux at K~1.5 Providing H5 at ~9.1 keVE-Beam Energy: 3 GeVCurrent: 0.5 A

High-Beta (Long) Straight Section

Flux per Unit Surface (Intensity) Distributions at 20 m from Undulator CenterFlux per Unit Surface (Intensity) Distributions at 20 m from Undulator CenterHorizontal Cuts (y = 0) Vertical Cuts (x = 0)


Possible Next Step on IVU Optimization: Possible Next Step on IVU Optimization: Segmented “Adaptive-Gap Undulators”Segmented “Adaptive-Gap Undulators”

λu≈ 22.87 mmK ≈ 1.45G ≈ 7.74 mm

19.59 mm1.675.21 mm

λu≈ 22.54 mmK ≈ 1.47G ≈ 7.46 mm

19.64 mm1.665.25 mm

20.24 mm1.625.68 mm

21.26 mm1.556.45 mm

λu≈ 22.87 mmK ≈ 1.45G ≈ 7.74 mm

19.74 mm1.665.32 mm

20.98 mm1.576.23 mm

λu = 22 mmK ≈ 1.5G ≈ 7 mm

Magnetic Field (NSLS-II IXS BL Example)Magnetic Field (NSLS-II IXS BL Example)

IVU22

constK iui

²2

)21( 2

1

bzaG ii 2

Basic Points about Segmented AGU:Basic Points about Segmented AGU:

● ● All segments are tuned to the same Resonant Photon Energy

● ● Vertical Gaps in segments satisfy “Stay-Clear” and Impedance Constraints

● ● Undulator Period may vary from segment to segment (however it is constant within one Segment)

17.58 mm1.0957.46 mm

λu≈ 15.38 mmK ≈ 1.287G ≈ 5.25 mm

15.84 mm1.2445.68 mm

16.63 mm1.1756.45 mm

Magnetic FieldMagnetic FieldBr = 1.5 TNper = 423

λu≈ 19.64 mmK ≈ 1.66G ≈ 5.25 mm

20.24 mm1.625.68 mm

21.26 mm1.556.45 mm

Magnetic FieldMagnetic Field 22.54 mm1.477.46 mm

Br = 1.12 TNper = 331

18.82 mm0.9947.46 mm

λu≈ 16.61 mmK ≈ 1.177G ≈ 5.25 mm

17.07 mm1.1385.68 mm

17.85 mm1.0726.45 mm

Electron Trajectory (after correction)Electron Trajectory (after correction)

Magnetic FieldMagnetic FieldBr = 1.12 TNper = 394

Parameters of AGU “Candidates” for IXS BeamlineParameters of AGU “Candidates” for IXS BeamlineRoom-Temperature AGURoom-Temperature AGUEE11= 1.824 keV (E= 1.824 keV (E55= 9.12 keV)= 9.12 keV)

Room-Temperature AGURoom-Temperature AGUEE11= 3.04 keV (E= 3.04 keV (E33= 9.12 keV)= 9.12 keV)

Cryo-Cooled AGUCryo-Cooled AGUEE11= 3.04 keV (E= 3.04 keV (E33= 9.12 keV)= 9.12 keV)


““Kick” Angle between AGU SegmentsKick” Angle between AGU Segments

Part i with Peak Field Bi

and period i

Part i+1 with Peak Field Bi+1

and period i+1

Max. electron deflection in Part i Ki/Max. electron deflection in Part i+1 Ki+1/Kick Angle at the interface (Ki+1- Ki)/

The large magnetic susceptibility of poles changes the kick angle

3.0

2.5

2.0

1.5

1.0

0.5

0.0

Kic

k A

ngle

[G

m]

3200280024002000

Fundamental Energy [eV]

30

25

20

15

10

5

0

[ra

d]

Analytical model (K1-K2)/ (K2-K3)/ (K3-K4)/

kick computed with RADIA Part 1 to Part 2 Part 2 to Part 3 Part 3 to Part 4

Ch. Kitegi


Possible AGU Active Correction SchemePossible AGU Active Correction Scheme

Correction with coils in entrant PortsKeep coil in airCompatible with CPMU

Hor

izon

tal T

raj [

mm

]

Part i Part i +1

Part i Part i +1

Hor

izon

tal T

raj [

mm

] Initial Trajectory

Kick due to Coils

Ch. Kitegi

AGU Field and Electron TrajectoriesAGU Field and Electron TrajectoriesSegment junction

Segment junction

Spectral Flux of AGU and IVU “Candidates” for Spectral Flux of AGU and IVU “Candidates” for NSLS-II IXS BeamlineNSLS-II IXS Beamline

Spectral Flux through Spectral Flux through 100 μrad (H) x 50 μrad (V) Aperture100 μrad (H) x 50 μrad (V) Aperturefrom Finite-Emittance Electron Beamfrom Finite-Emittance Electron Beam

On-axis Spectral Flux per Unit SurfaceOn-axis Spectral Flux per Unit Surfacefrom Filament Electron Beamfrom Filament Electron Beamat 20 m Observation Distanceat 20 m Observation Distance

Ee = 3 GeV, Ie = 0.5 A; NSLS-II High-β (Long) Straight

Approximate (!) Estimation of Spectral Flux at Odd Approximate (!) Estimation of Spectral Flux at Odd Harmonics of AGU and IVU “Candidates” for IXSHarmonics of AGU and IVU “Candidates” for IXS


Estimation of Spectral Performances of (cryo-)AGU Estimation of Spectral Performances of (cryo-)AGU and (cryo-)IVU in Low-Beta Straight of NSLS-IIand (cryo-)IVU in Low-Beta Straight of NSLS-II

Ee = 3 GeV, Ie = 0.5 A; NSLS-II Low-β (Short) Straight

Spectral Flux in 100 Spectral Flux in 100 μμrad (H) x 50 rad (H) x 50 μμrad (V) Aperturerad (V) Aperture

Examples of AGU Radiation Intensity DistributionsExamples of AGU Radiation Intensity Distributionsfor a Room-Temperature, 7 x 1 m AGU with Efor a Room-Temperature, 7 x 1 m AGU with E11 = 3.04 keV = 3.04 keV


Intensity Distributions at 20 mIntensity Distributions at 20 m Spectral Flux at 3Spectral Flux at 3rdrd Harmonic HarmonicAperture: 100 Aperture: 100 μμrad (h) x 50 rad (h) x 50 μμrad (v) rad (v)


Shapes of all distributions are very similar to those of a regular undulator…

-20 -10 0 10 20 30 40-0.25

-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

0.2

s, mm

W||,

V

Constant Gap Linear Gap Variation Stepped Gap Variation

-30 -20 -10 0 10 20 30 40-140

-120

-100

-80

-60

-40

-20

0

20

s, mm W

y, V

/m

Constant Gap Stepped Gap Variation Linear Gap Variation

Geometries ConsideredGeometries Considered

2D Impedance Analysis of Segmented AGU 2D Impedance Analysis of Segmented AGU for NSLS-II Long Straight Section for NSLS-II Long Straight Section by A. Blednykhby A. Blednykh

Longitudinal Short-Range WakepotentialLongitudinal Short-Range Wakepotential Vertical Short-Range WakepotentialVertical Short-Range Wakepotential

Estimated Longitudinal Loss Factors, Power Losses, and Transverse Kick FactorsEstimated Longitudinal Loss Factors, Power Losses, and Transverse Kick Factors

“Constant Gap” “Stepped Gap Variation” “Linear Gap Variation”


Discussion on AGUDiscussion on AGU

● Segmented Adaptive-Gap Undulators (AGUs) allow for most efficient use of space available in (long) Straight Sections of modern Storage Ring sources;

● According to estimations, Room-temperature AGU can offer better spectral performance in Medium-Energy Electron Storage Rings than “standard” Room-temperature IVUs, and even Cryo-cooled IVUs (depending on magnet lattice);

● AGU concept is applicable to ~any magnet technology: AGUs can possibly be made Cryo-cooled, and maybe even Superconducting;

● AGU effects on electron beam seem to be tolerable: “stay-clear” constraint is satisfied “by definition”, impedance seems to be within acceptable limits; heat load on magnet arrays can be tolerable as well;

● AGUs seem to be feasible (at least room-temperature version), from the points of view of magnetic and mechanical designs;

● Production cost of AGU segments can be not very high: assembly and shimming of short segments is simpler than longer ones; mechanics doesn’t need to withstand large forces; overall undulator dimensions can be smaller.


Conclusions on Undulator OptimizationConclusions on Undulator Optimization

The described insertion device design and optimization activity, which is based on high-accuracy calculations in different areas:

- (3D) magnetostatics- accelerator physics - synchrotron radiation- thermal and mechanical stress analysis

allows to find most appropriate ID parameters for experimental program of every NSLS-II beamline, taking into account all existing constraints and maximally profiting from available magnet technologies and unique features of the NSLS-II storage ring.

Acknowledgments Acknowledgments J.-L. Laclare, P. ElleaumeJ.-L. Laclare, P. Elleaume J. Chavanne (ESRF)J. Chavanne (ESRF) M.-E. Couprie, A. Nadji (SOLEIL)M.-E. Couprie, A. Nadji (SOLEIL) NSLS-II ID and Accelerator Physics GroupNSLS-II ID and Accelerator Physics Group

Computer Codes Computer Codes RADIA and SRW were started at ESRF in 1996These codes are updated from time to time on the ESRF Web site:

http://ftp.esrf.fr/pub/InsertionDevices/http://ftp.esrf.fr/pub/InsertionDevices/

TracyTracy was started at LBNL in 1990Tracy-3Tracy-3 is the most recent version available from J. Bengtsson (NSLS-II)


Effects of Different IVUs on Electron Beam Dynamics:Effects of Different IVUs on Electron Beam Dynamics:““2nd-Order Kicks”2nd-Order Kicks”

Theory: P. Elleaume, EPAC-92

From Baseline IVU20 at E = 3 GeV (Radia) From Baseline IVU20 at E = 3 GeV (Radia) In Horizontal Median PlaneIn Horizontal Median Plane

In Vertical Median PlaneIn Vertical Median Plane

wpole≥ 40 mm is OK for Low-Beta Straight Section

Tracy-2 Particle Tracking Tracy-2 Particle Tracking Simulation Results for NSLS-II:Simulation Results for NSLS-II:

wpole≥ 60 mm is OK for High-Beta Straight Section

From IXS Beamline “Candidate” IVUs From IXS Beamline “Candidate” IVUs In Horizontal Median PlaneIn Horizontal Median Plane

wpole =

Horizontal Position [mm]

15 μrad

10

5

0

-5

-10

Hor

izon

tal K

ick

The baseline magnetic design, which assumed the use of IVUs in Low-Beta Straight Sections, can hardly be applied for the High-Beta Sections

J. Bengtsson


Radia Model (reduced number of periods) Radia Model (reduced number of periods)

APPLE-II Undulator Period ChoiceAPPLE-II Undulator Period Choice

Invented by S. Sasaki

Br = 1.25 (NdFeB)

CSX beamline CSX beamline choice: choice:

λλuu= 49 mm= 49 mm

Minimal (11.5 mm Gap) and Maximal Photon Energies Minimal (11.5 mm Gap) and Maximal Photon Energies of the Fundamental Harmonic vs Undulator Period for E = 3 GeVof the Fundamental Harmonic vs Undulator Period for E = 3 GeV


APPLE-II Effect on Electron BeamAPPLE-II Effect on Electron BeamLinear Vertical Polarization ModeLinear Vertical Polarization Mode

Tune Shift from 2-nd Order Kick: Tune Shift from 2-nd Order Kick:

),(4

1),( )()()()( yxyx yxyxyxyx

Horizontal Magnetic Field “Roll-Off” Horizontal Magnetic Field “Roll-Off” In Horizontal Median Plane (Radia)In Horizontal Median Plane (Radia)

Horizontal 2Horizontal 2ndnd Order Kick at E = 3 GeV Order Kick at E = 3 GeV

Passive and active compensation schemes Passive and active compensation schemes of APPLE-II “natural” focusing effects are of APPLE-II “natural” focusing effects are under investigation based on ESRF, under investigation based on ESRF, BESSY-II and SOLEIL experiencesBESSY-II and SOLEIL experiences

Horizontal Tune Shift in Low- and Horizontal Tune Shift in Low- and High-Beta Straight Sections of NSLS-II High-Beta Straight Sections of NSLS-II

Compensation of APPLE-II Dynamic Focusing Effects Compensation of APPLE-II Dynamic Focusing Effects by Current Strips by Current StripsRADIA EPU Model with StripsRADIA EPU Model with Strips Idea: I. Blomqvist

Implementation at BESSY: J. BahrdtVe

rtica

l (Eq

uiva

lent

) F

ield

Inte

gral

[G.c

m]


Curre

nt [A

]


in Linear Vertical in Linear Vertical Polarization ModePolarization Mode

Equivalent Vertical Field Integrals Equivalent Vertical Field Integrals from Dynamic Focusing and from the Current Stripsfrom Dynamic Focusing and from the Current Strips

Compensating Currents Compensating Currents in Lower Stripsin Lower Strips

Electron Trajectory in 3D Magnetic FieldElectron Trajectory in 3D Magnetic FieldWithout and With CorrectionWithout and With Correction

Horizontal TrajectoryHorizontal Trajectory

Longitudinal Position [mm]Longitudinal Position [mm]

xx00=0, y=0, y00=0 before Undulator =0 before Undulator

Vertical TrajectoryVertical Trajectory

Horiz

. Pos

ition

[Ho

riz. P

ositio

n [ μμ

m]

m]

Verti

cal P

ositio

n [

Verti

cal P

ositio

n [ μμ

m]

m]

Horizontal TrajectoryHorizontal Trajectoryxx00= -4 mm, y= -4 mm, y00=0 before Undulator =0 before Undulator xx00= 4 mm, y= 4 mm, y00=0 before Undulator =0 before Undulator


Horiz

onta

l Pos

ition

[Ho

rizon

tal P

ositio

n [ μμ

m]

m]


Horiz

onta

l Pos

ition

[Ho

rizon

tal P

ositio

n [ μμ

m]

m]

Efficient Solving for CurrentsEfficient Solving for CurrentsUsing Least-Squares Linear FitUsing Least-Squares Linear Fit

QJI

Field Integral (at y=0) from Current Densities:

IQQQJ T1T )(

Current Densitiesfrom Field Integral:

Number of Strips used: 2 x 20Strip Dims: 2 mm x 0.3 mm x 2 mHorizontal Gap bw Strips: 1 mmVertical Gap bw Strips: 10.7 mmMax. Current obtained: ~ 2.3 AAPPLE-II Vertical Gap: 11.5 mm

)()( xx lowerupper JJ

Since the Dynamic Effectsare Anti-Symmetric vs x:

Matrix calculated

by Radia

Compensation of APPLE-II Dynamic Focusing Effects Compensation of APPLE-II Dynamic Focusing Effects by Current Strips in Linear Tilted (45˚) Polarization Modeby Current Strips in Linear Tilted (45˚) Polarization Mode

Equivalent Field Integrals Equivalent Field Integrals from Dynamic Focusing and from the Current Stripsfrom Dynamic Focusing and from the Current Strips Compensating Currents Compensating Currents

in Lower Stripsin Lower Strips

Electron Trajectory in 3D Magnetic Field Without and With CorrectionElectron Trajectory in 3D Magnetic Field Without and With Correction

HorizontalHorizontal VerticalVertical


Curre

nt [A

]

“Current Strips” are efficient, however require dedicated additional “Feed-Forward” correction tables… Ho

rizon

tal (

Equi

vale

nt)

Fie

ld In

tegr

al [G

.cm

]


dynam. effect

current strips


Verti

cal (

Equi

vale

nt)

Fie

ld In

tegr

al [G

.cm

]

dynam. effect

current strips



xx00= 0, y= 0, y00= 0 before Undulator = 0 before Undulator

Horiz

onta

l Pos

ition

[Ho

rizon

tal P

ositio

n [ μμ

m]

m]

Verti

cal P

ositio

n [

Verti

cal P

ositio

n [ μμ

m]

m] Vertical TrajectoryVertical Trajectory

xx00= -4 mm, y= -4 mm, y00= 0 before Undulator = 0 before Undulator


Horiz

onta

l Pos

ition

[Ho

rizon

tal P

ositio

n [ μμ

m]

m]

Verti

cal P

ositio

n [

Verti

cal P

ositio

n [ μμ

m]

m]



xx00= 4 mm, y= 4 mm, y00= 0 before Undulator = 0 before Undulator

Horiz

onta

l Pos

ition

[Ho

rizon

tal P

ositio

n [ μμ

m]

m]

Verti

cal P

ositio

n [

Verti

cal P

ositio

n [ μμ

m]

m]




Spectral-Angular Distributions of Emission from Spectral-Angular Distributions of Emission from 2x3.5 m Long 2x3.5 m Long Damping Wiggler Damping Wiggler in “Inline” Configurationin “Inline” Configuration

Angular Profiles of DW Emission at Different Photon Energies

1/ ≈ 170 μrad

FWHM Angular Divergence of DW Emission

Spectral Flux per Unit Solid Angle Horizontal Profiles

Vertical Profiles


TPW Field taken from magnetic simulationsBM Field is taken from magnetic measurements on a prototype BM with “nose”

Longitudinal Position s are approximate

Electron Energy: 3 GeV Current: 0.5 A Hor. Emittance: 0.9 nm Vert. Emittance: 8 pm

Initial Conditions: <x> = 0, <x’>= 0 in TPW Center

Upstream BM

Downstream BMTPW

On-Axis Magnetic Field in Dispersion SectionOn-Axis Magnetic Field in Dispersion Section

Spectral Flux through 1.75 mrad (H) x 0.1 mrad (V) Aperture Spectral Flux through 1.75 mrad (H) x 0.1 mrad (V) Aperture (centered on the axis)(centered on the axis)

On-Axis Spectral Flux per Unit Surface at 30 m from TPW On-Axis Spectral Flux per Unit Surface at 30 m from TPW

Average Electron Trajectory: Horizontal Angle Average Electron Trajectory: Horizontal Angle

Average Electron Trajectory: Horizontal Position Average Electron Trajectory: Horizontal Position

TPW: Magnetic Field, Electron Trajectory and SpectraTPW: Magnetic Field, Electron Trajectory and Spectra(in presence of Bending Magnets)(in presence of Bending Magnets)

TPW and BM Radiation Intensity Distributions (Hard X-rays) TPW and BM Radiation Intensity Distributions (Hard X-rays)

Horizontal Cuts at y = 0Horizontal Cuts at y = 0

Intensity Distributions at Different Photon Energies at 30 m from TPW Intensity Distributions at Different Photon Energies at 30 m from TPW Electron Current: 0.5 A

Vertical Cuts at x = 0Vertical Cuts at x = 0


Kx 7.1 3.1 y

Angular Power Density Distributions Angular Power Density Distributions of Radiation from NSLS-II Insertion Devicesof Radiation from NSLS-II Insertion Devices

Undulators and Multi-Pole Wigglers Undulators and Multi-Pole Wigglers

Horizontal FWHM Angle: Horizontal FWHM Angle: Vertical FWHM Angle: Vertical FWHM Angle:

Three-Pole Wiggler and Bending Magnet Radiation at 30 mThree-Pole Wiggler and Bending Magnet Radiation at 30 m

In Horizontal Mid-PlaneIn Horizontal Mid-Plane In Vertical Mid-PlaneIn Vertical Mid-Plane

|θX| = 4.75 mrad |θX| ≈ 2.6 mrad θX= 0 θX= 1.5 mradIn Horizontal Mid-PlaneIn Horizontal Mid-Plane

NSLS-II: E = 3 GeV, I = 0.5 A


Power Density Distributions of Radiation from NSLS-II Power Density Distributions of Radiation from NSLS-II Insertion Devices at Fixed Masks (at ~16 m)Insertion Devices at Fixed Masks (at ~16 m)

DW100 (2 x 3.5 m)DW100 (2 x 3.5 m) SCW60 (1 m)SCW60 (1 m) TPWTPW

IVU20 (3 m)IVU20 (3 m) IVU21 (1.5 m)IVU21 (1.5 m) IVU22 (6 m)IVU22 (6 m)

EPU49 (2 x 2 m) LH modeEPU49 (2 x 2 m) LH mode EPU49 (2 x 2 m) LV modeEPU49 (2 x 2 m) LV mode EPU49 (2 x 2 m) LT-45º modeEPU49 (2 x 2 m) LT-45º mode

EPU49 (2 x 2 m) Helical modeEPU49 (2 x 2 m) Helical modeNSLS-II: E = 3 GeV, I = 0.5 AIVU, EPU power is given for min. gaps2 x EPU49 are in canted mode

P ≈ 61 kW P ≈ 40 kW P ≈ 0.4 kW

P ≈ 8.1 kW P ≈ 3.6 kW P ≈ 9.4 kW

P ≈ 10 kW P ≈ 5.7 kW P ≈ 3.7 kW

P ≈ 7.3 kW

Radiation Power Density Distributions on Straight Section Radiation Power Density Distributions on Straight Section Chamber Wall for DW90 (9.5 mm int. chamber size) and Chamber Wall for DW90 (9.5 mm int. chamber size) and

DW100 (11.5 mm int. chamber size) for “Mis-Steered” E-BeamDW100 (11.5 mm int. chamber size) for “Mis-Steered” E-BeamMagnetic FieldMagnetic Field

Horizontal Projection of Electron TrajectoryHorizontal Projection of Electron TrajectoryVertical Projection Vertical Projection

of “Mis-Steered” Electron Trajectoryof “Mis-Steered” Electron Trajectory

NSLS-II: E = 3 GeV, I = 0.5 AHigh-Beta Straight Section

“Mis-steered” electron initial conditions:y0 = 2 mm, y0’= 0.25 mrad at z0 ≈ -3.8 m

DW100 chamber wall (y = 5.75 mm)DW90 chamber wall (y = 4.75 mm)

Power Density Distributions on Chamber WallPower Density Distributions on Chamber WallDW90 (y = 4.75 mm)DW90 (y = 4.75 mm)

Horizontal Cuts Horizontal Cuts at Longitudinal Position z = 3.9 mat Longitudinal Position z = 3.9 m

Longitudinal Cuts Longitudinal Cuts at Horizontal Position x = 0at Horizontal Position x = 0

DW100 (y = 5.75 mm)DW100 (y = 5.75 mm)

P ≈ 4.05 kW P ≈ 4.05 kW P ≈ 0.51 kW P ≈ 0.51 kW

EPU49 (2 x 2m) Radiation Power (Helical Mode, 11.5 mm Min. Gap) EPU49 (2 x 2m) Radiation Power (Helical Mode, 11.5 mm Min. Gap) on Straight Section Chamber Wall at Different Vertical Offsets on Straight Section Chamber Wall at Different Vertical Offsets

and Angular Deviations of Electron Beam and Angular Deviations of Electron Beam

Electron Beam Current: 0.5 A

Power Density Distributions on Chamber WallPower Density Distributions on Chamber WallDeposited PowerDeposited Power in vertical median plane (x = 0)in vertical median plane (x = 0)

at different e-beam vertical offsetsat different e-beam vertical offsets

at different e-beam at different e-beam vertical angular deviationsvertical angular deviations(applied before undulator)(applied before undulator)

ΔΔy = 0y = 0ΔΔy‘= 0.8 mrady‘= 0.8 mrad

ΔΔy = 3.5 mmy = 3.5 mmΔΔy’ = 0y’ = 0

Results of Vacuum Chamber Heat Conductivity Analysis Results of Vacuum Chamber Heat Conductivity Analysis For “Mis-Steered” Electron Beam in EPU49 (Helical Mode)For “Mis-Steered” Electron Beam in EPU49 (Helical Mode)

1) Δy’ = 0.25 mrad, Δy = 2 mm, Eph= 220 eV

P = 1240 W, Tmax = 169.5 °C P = 580 W, Tmax = 128.5 °C

2) Δy’ = 0.25 mrad, Δy = 1.5 mm, Eph= 220 eV

P = 860 W, Tmax = 136 °C

3) Δy’ = 0.25 mrad, Δy = 2 mm, Eph= 270 eV 4) Δy’ = 0.25 mrad, Δy = 2 mm, Eph = 400 eV

P = 380 W, Tmax = 92.8 °C

ANSYScalculationscourtesy ofV. Ravindranath

Summary of Calculations of Radiation Power Density Summary of Calculations of Radiation Power Density on Straight Section Vacuum Chamber Walls on Straight Section Vacuum Chamber Walls (or IVU Ni-Cu Foils) for Different NSLS-II IDs (or IVU Ni-Cu Foils) for Different NSLS-II IDs

ID Intern. Chamber Size / IVU Gap

[mm]

Electron Beam Angular

Deviation [mrad]

Electron Beam + Chamber Posit.

Offset [mm]

Deposited Radiation Power [W] (at I = 0.5 A)

Max. Power Density

[W/mm2]

Max. Temperature

[deg. C]

DW100 11.5 0.25 2.0 500 ~0.02 75

--||-- --||-- 0.25 1.5 235 ~0.009 46

EPU49 (helical) 8.0 0.25 2.0 1240 0.5 170

--||-- --||-- 0.25 1.5 580 0.27 130

IVU20 5.0 0.25 1.5 780 2.08

--||-- --||-- 0.25 1.25 200 0.41

--||-- --||-- 0.25 1.0 65 0.11

--||-- --||-- 0 2.0 180 0.19

--||-- --||-- 0 1.5 25 ~0.02

IVU22 6.95 0.25 1.5 950 0.71

--||-- --||-- 0.25 1.25 460 0.30

--||-- --||-- 0.25 1.0 240 0.14

--||-- --||-- 0.25 0.75 130 0.067

--||-- --||-- 0.25 0.5 75 0.035

--||-- --||-- 0 2.0 70 ~0.02

--||-- --||-- 0 1.5 30 ~0.007Task Force on “Synchrotron Radiation Protection” Task Force on “Synchrotron Radiation Protection” has been recently created in ASD (headed by P. Ilinsky, has been recently created in ASD (headed by P. Ilinsky, Accelerator Physics group) - to treat questions about “mis-steering” assumptions, tolerances, equipment protection Accelerator Physics group) - to treat questions about “mis-steering” assumptions, tolerances, equipment protection schemes, precautions at ID operation, etc.schemes, precautions at ID operation, etc.


Estimated Spectral Flux and Brightness Estimated Spectral Flux and Brightness of the First Planned NSLS-II Undulatorsof the First Planned NSLS-II Undulators

Spectral Flux through Fixed Apertures Spectral Flux through Fixed Apertures ((200 200 μμrad x 200 rad x 200 μμrad for APPLE-II, 15rad for APPLE-II, 150 μ0 μrad H x 50 rad H x 50 μμrad V for IVU in Low-Beta, 100 μrad H x 50 μrad V in High-Beta Straightsrad V for IVU in Low-Beta, 100 μrad H x 50 μrad V in High-Beta Straights ))

Approximate Spectral Brightness at Odd HarmonicsApproximate Spectral Brightness at Odd Harmonics


Estimated Spectral Brightness and Flux Estimated Spectral Brightness and Flux of Main NSLS-II Radiation Sourcesof Main NSLS-II Radiation Sources

Approximate Spectral Brightness Approximate Spectral Brightness at Odd Harmonicsat Odd Harmonics

Approximate Undulator Spectral FluxApproximate Undulator Spectral Flux

Approximate Wiggler Spectral FluxApproximate Wiggler Spectral Fluxper Unit Horiz. Angleper Unit Horiz. Angle


Estimated Spectral Brightness of NSLS-II Estimated Spectral Brightness of NSLS-II Compared to Other Synchrotron SourcesCompared to Other Synchrotron Sources

1 brookhaven science associates parametric optimization of in-vacuum undulators; segmented...

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