Parametric Optimization of In-Vacuum Undulators;
Segmented “Adaptive-Gap Undulator” Concept
NSLS-II
εx= 0.55 nm
E = 3 GeV, I = 0.5 A
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)
ICFA Workshop on Future Light Sources
JLAB, March
1 5-9, 2012
BROOKHAVEN SCIENCE ASSOCIATES
Outline
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
2
BROOKHAVEN SCIENCE ASSOCIATES
NSLS-II “Project”, NEXT, and ABBIX (NIH)
Beamlines and IDs
ID type, incl. period
(mm)
EPU49 (PPM) x2
Length
Kmax
CSX
ID straight
type
lo-β
4.34
# of ID's
# FE's
(base scope)
canted (0.18)
2
1
4m (2 x 2m)
NSLS-II
IXS
HXN
CHX
SRX
hi-β
lo-β
lo-β
lo-β
IVU22 (H) x2
IVU20 (H)
IVU20 (H)
IVU21 (H)
6m (2 x 3m)
3m
3m
1.5m
1.52
1.83
1.83
1.79
std
std
std
canted (2.0)
1
1
1
1
1
1
1
1
NSLS-II
NSLS-II
NSLS-II
NSLS-II
XPD
hi-β
6.8m (2x3.4m)
3m
4m
7m (2 x 3.5m)
~16.5
3.64
6.8
3.5
DW
0
1
NSLS-II
canted (0.5)
2
1
NEXT
hi-β
DW100 (H)
EPU56 (PPM)
& EPU180 (EM)
EPU49 (PPM) x2
ESM
hi-β
SIX
std
1
1
NEXT
ISR
SMI
ISS
FXI
FMX
hi-β
lo-β
hi-β
hi-β
lo-β
IVU23 (H)
IVU22 (H)
DW100 (H)
DW100 (H)
IVU21 (H)
3.0m
1.3m
6.8m (2x3.4m)
6.8m (2x3.4m)
1.5m
1
1
0
0
1
NEXT
NEXT
NEXT
NEXT
NIH
AMX
lo-β
IVU21 (H)
1.5m
1.79
canted (2.0)
1
LIX
hi-β
IVU23 (H)
3.0m
1.6-2.07*
canted**
1
1
1
1
1
1
0 (joint
w/FMX)
1
BL
PPM: Pure Permanent-Magnet
EM: Electro-Magnet
H:
Hybrid magnetic design
FE type†
1.6-2.07* canted**
2.05
canted
~16.5
DW
~16.5
DW
1.79 canted (2.0)
Project
NIH
NIH
† 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,
Required Gaps and Acceptable Lengths
RADIA Model (central part)
IVU Parameters
Reference Geometry:
Materials:
Pole Width: 40 mm Magnet Width: 50 mm
Pole Height: 25 mm Magnet Height: 29 mm
Pole Thickness: 3 mm
(for λu = 20 mm)
Fundamental Photon Energy vs Gap
for Different IVU Periods (E = 3 GeV)
Pole: Va Permendur NEOMAX
Magnet: NdFeB, PrFeB
IVU Lengths Satisfying Vertical
“Stay Clear” Constraints in Lowand High-Beta Straight Sections
βy0 = 3.4 m
βy0 = 1.06 m
4
Max.
Length
in Lo-β
Sect.
Max.
Length
in Hi-β
Sect.
BROOKHAVEN SCIENCE ASSOCIATES
Hybrid In-Vacuum Undulator Magnetic Performance:
Halbach Scaling Law
Planned SCU
for DIAMOND
(J. Clarke)
Following P. Elleaume, J. Chavanne, B. Faatz, NIM-A 455 (2000), 503-523
Spectral Brightness and Flux at Odd Harmonics
of Various IVU in Low-Beta Straight
NSLS-II, Low-Beta Straight Section
I = 0.5 A; εx = 0.55 nm; εy = 8 pm; σE/E = 8.9x10-4
Magnet Material: NdFeB, Br = 1.12 T
Brightness
Flux
6
BROOKHAVEN SCIENCE ASSOCIATES
Spectral Flux of Different IVUs – IXS “Candidates” –
Satisfying E-Beam Vertical “Stay Clear” Constraint
Maximal Spectral Flux through 100 μrad (H) x 50 μrad (V) Aperture
E-Beam
Energy: 3 GeV
Current: 0.5 A
NSLS-II
High-Beta (Long)
Straight Section
~9.13 keV
~9.13 keV
7
BROOKHAVEN SCIENCE ASSOCIATES
Spectral Flux of Room-Temperature & Cryogenic IVUs
Satisfying E-Beam Vertical “Stay Clear” Constraint
IXS Beamline (High-Beta Straight Section; 100 μrad H x 50 μrad V Ap.)
~9.13 keV
SRX Beamline (one of two Canted Undulators in Low-Beta Straight Sect.; 150 μrad H x 50 μrad V Ap.)
~4.7 keV
8
BROOKHAVEN SCIENCE ASSOCIATES
Effect of Electron Beam Energy Spread
on Spectral Flux of IXS IVU22-6 m
I = 0.5 A, High-Beta straight section
100 μrad (H) x 50 μrad (V) Aperture
20 x 20 μrad2 Aperture
Single-Electron Undulator Radiation
Intensity Distributions “in Far Field” and “at Source”
UR “Single-Electron” Intensity and “Multi-Electron” Flux
E-Beam Energy: 3 GeV
Current: 0.5 A
Undulator Period: 20 mm
Undulator
H5
Intensity Distributions at 30 m from Undulator Center
Intensity Distributions in 1:1 Image Plane
“Phase-Space Volume” Estimation for Vertical Plane
(RMS sizes/divergences calculated for the portions of intensity distributions containing 95% of flux)





 y y '  7.7
9 .2
1 .5
1 .9
3 .3
4
4
4
4
4
Ideal
Lens
1:1
Image
Plane
Vertical Cuts (x = 0)
X-Ray Beam Angular Divergence and “Source Size” from
Partially-Coherent Wavefront Propagation Simulations
IVU20-3m Spectral Flux
through 100 μrad (H) x 50 μrad (V) Aperture
at K~1.5 providing H5 peak at ~10 keV
Electron Beam:
Hor. Emittance: 0.9 nm
Vert. Emittance: 8 pm
Energy Spread: 8.9x10-4
Current: 0.5 A
Low-Beta Straight
Test Optical Scheme
Ideal Lens 1:1 Image Plane
IVU20
Intensity Distributions at ~10 keV
At 30 m from Undulator
Horizontal Cuts (y = 0)
 x x '  97
Vertical Cuts (x = 0)
In 1:1 Image Plane
Horizontal Cuts (y = 0)


;  y y '  5.7
…very far from Coherent Gaussian Beam !
4
4
Vertical Cuts (x = 0)
RMS sizes/divergences calculated for
the portions of intensity distributions
containing 95% of flux
Comparison of IVU Spectral Flux (per Unit Surface)
for IXS Locations in Low- and High-Beta Straights
Spectral Flux of different IVU providing H5 peak at ~9.1 keV
E-Beam
Energy: 3 GeV
Current: 0.5 A
Flux per Unit Surface (Intensity) Distributions at 20 m from IVUs (ε = 9.13 keV)
IVU20-3m in Low-Beta
Straight Section
IVU22-6m in High-Beta
Straight Section
Horizontal Cuts (y = 0)
12
Vertical Cuts (x = 0)
BROOKHAVEN SCIENCE ASSOCIATES
IVU22 – 6 m Spectral Flux (per Unit Surface)
Near Harmonic Peak
Spectral Flux at K~1.5 Providing H5 at ~9.1 keV
E-Beam
Energy: 3 GeV
Current: 0.5 A
High-Beta (Long)
Straight Section
Flux per Unit Surface (Intensity) Distributions at 20 m from Undulator Center
Horizontal Cuts (y = 0)
13
Vertical Cuts (x = 0)
BROOKHAVEN SCIENCE ASSOCIATES
Possible Next Step on IVU Optimization:
Segmented “Adaptive-Gap Undulators”
Magnetic Field (NSLS-II IXS BL Example)
IVU22
λu = 22 mm
K ≈ 1.5
G ≈ 7 mm
λu≈ 22.87 mm 20.98 mm
K ≈ 1.45
1.57
G ≈ 7.74 mm 6.23 mm
19.74 mm
1.66
5.32 mm
Basic Points about Segmented AGU:
● All segments
are tuned to the same
Resonant Photon Energy
● Vertical Gaps in segments satisfy “StayClear” and Impedance Constraints
● Undulator Period may vary from
segment to segment (however it is
constant within one Segment)
λu≈ 22.54 mm 21.26 mm 20.24 mm 19.64 mm
K ≈ 1.47
1.62
1.66
1.55
G ≈ 7.46 mm 6.45 mm 5.68 mm 5.25 mm
λu≈ 22.87 mm
K ≈ 1.45
G ≈ 7.74 mm
19.59 mm
1.67
5.21 mm
(1  K i2 2)u i
1 
 const
2 ²
Gi  a zi2  b
14
BROOKHAVEN SCIENCE ASSOCIATES
Parameters of AGU “Candidates” for IXS Beamline
Room-Temperature AGU
E1= 1.824 keV (E5= 9.12 keV)
Magnetic Field
Room-Temperature AGU
E1= 3.04 keV (E3= 9.12 keV)
Magnetic Field
Br = 1.12 T
Nper = 331
Br = 1.12 T
Nper = 394
λu≈ 19.64 mm 20.24 mm 21.26 mm 22.54 mm
1.55
1.47
K ≈ 1.66
1.62
G ≈ 5.25 mm 5.68 mm 6.45 mm 7.46 mm
λu≈ 16.61 mm 17.07 mm 17.85 mm 18.82 mm
K ≈ 1.177
1.138
0.994
1.072
G ≈ 5.25 mm 5.68 mm 6.45 mm 7.46 mm
Electron Trajectory (after correction)
Cryo-Cooled AGU
E1= 3.04 keV (E3= 9.12 keV)
Magnetic Field
Br = 1.5 T
Nper = 423
λu≈ 15.38 mm 15.84 mm 16.63 mm 17.58 mm
K ≈ 1.287
1.244
1.095
1.175
G ≈ 5.25 mm 5.68 mm 6.45 mm 7.46 mm
“Kick” Angle between AGU Segments
The large magnetic susceptibility of
poles changes the kick angle
3.0
30
2.5
25
2.0
20
1.5
[rad]
Kick Angle [Gm]
Max. electron deflection in Part i Ki/
Max. electron deflection in Part i+1 Ki+1/
Kick Angle at the interface (Ki+1- Ki)/
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
15
1.0
10
0.5
5
0.0
0
2000
2400
2800
3200
Fundamental Energy [eV]
Ch. Kitegi
16
BROOKHAVEN SCIENCE ASSOCIATES
Possible AGU Active Correction Scheme
Part i
Part i +1
Part i
Part i +1
Correction with coils in entrant Ports
Keep coil in air
Compatible with CPMU
Ch. Kitegi
Horizontal Traj [mm]
Initial Trajectory
Horizontal Traj [mm]
Kick due to Coils
17
BROOKHAVEN SCIENCE ASSOCIATES
AGU Field and Electron Trajectories
Segment
junction
Segment
junction
Spectral Flux of AGU and IVU “Candidates” for
NSLS-II IXS Beamline
Spectral Flux through
On-axis Spectral Flux per Unit Surface
100 μrad (H) x 50 μrad (V) Aperture
from Filament Electron Beam
from Finite-Emittance Electron Beam
at 20 m Observation Distance
Ee = 3 GeV, Ie = 0.5 A; NSLS-II High-β (Long) Straight
Approximate (!) Estimation of Spectral Flux at Odd
Harmonics of AGU and IVU “Candidates” for IXS
Ee = 3 GeV, Ie = 0.5 A; NSLS-II High-β (Long) Straight
Estimation of Spectral Performances of (cryo-)AGU
and (cryo-)IVU in Low-Beta Straight of NSLS-II
Spectral Flux in 100 μrad (H) x 50 μrad (V) Aperture
Ee = 3 GeV, Ie = 0.5 A; NSLS-II Low-β (Short) Straight
Examples of AGU Radiation Intensity Distributions
for a Room-Temperature, 7 x 1 m AGU with E1 = 3.04 keV
Ee = 3 GeV, Ie = 0.5 A; NSLS-II High-β (Long) Straight
Intensity Distributions at 20 m
Spectral Flux at 3rd Harmonic
Aperture: 100 μrad (h) x 50 μrad (v)
Horizontal Cuts (y = 0)
Vertical Cuts (x = 0)
Shapes of all distributions are very similar to those of a regular undulator…
2D Impedance Analysis of Segmented AGU
for NSLS-II Long Straight Section by A. Blednykh
Geometries Considered
“Constant Gap”
“Linear Gap Variation”
“Stepped Gap Variation”
Longitudinal Short-Range Wakepotential
Vertical Short-Range Wakepotential
20
0.2
0
0.15
-20
Wy, V/m
W||, V
0.1
0.05
0
-0.05
Constant Gap
Linear Gap Variation
Stepped Gap Variation
-0.1
-0.15
-10
0
10
s, mm
20
30
-60
-80
Constant Gap
Stepped Gap Variation
Linear Gap Variation
-100
-120
-0.2
-0.25
-20
-40
40
-140
-30
-20
-10
0
10
s, mm
20
30
40
Estimated Longitudinal Loss Factors, Power Losses, and Transverse Kick Factors
Discussion 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 Cryocooled, 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.
24
BROOKHAVEN SCIENCE ASSOCIATES
Conclusions 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.
25
BROOKHAVEN SCIENCE ASSOCIATES
Computer Codes
RADIA and SRW were started at ESRF in 1996
These codes are updated from time to time on the ESRF Web site:
http://ftp.esrf.fr/pub/InsertionDevices/
Tracy was started at LBNL in 1990
Tracy-3 is the most recent version available from J. Bengtsson (NSLS-II)
Acknowledgments




J.-L. Laclare, P. Elleaume
J. Chavanne (ESRF)
M.-E. Couprie, A. Nadji (SOLEIL)
NSLS-II ID and Accelerator Physics Group
Effects of Different IVUs on Electron Beam Dynamics:
“2nd-Order Kicks”
From Baseline IVU20 at E = 3 GeV (Radia)
15 μrad
Horizontal Kick
10
In Horizontal Median Plane
Theory: P. Elleaume, EPAC-92
wpole =
Tracy-2 Particle Tracking J. Bengtsson
Simulation Results for NSLS-II:
5
wpole≥ 40 mm is OK for Low-Beta Straight Section
wpole≥ 60 mm is OK for High-Beta Straight Section
0
-5
The baseline magnetic design, which assumed
the use of IVUs in Low-Beta Straight Sections,
can hardly be applied for the High-Beta Sections
-10
Horizontal Position [mm]
From IXS Beamline “Candidate” IVUs
In Horizontal Median Plane
In Vertical Median Plane
28
BROOKHAVEN SCIENCE ASSOCIATES
APPLE-II Undulator Period Choice
Radia Model (reduced number of periods)
Invented by S. Sasaki
Minimal (11.5 mm Gap) and Maximal Photon Energies
of the Fundamental Harmonic vs Undulator Period for E = 3 GeV
Br = 1.25 (NdFeB)
29
CSX beamline
choice:
λu= 49 mm
BROOKHAVEN SCIENCE ASSOCIATES
APPLE-II Effect on Electron Beam
Linear Vertical Polarization Mode
Horizontal Magnetic Field “Roll-Off”
In Horizontal Median Plane (Radia)
Passive and active compensation schemes
of APPLE-II “natural” focusing effects are
under investigation based on ESRF,
BESSY-II and SOLEIL experiences
Tune Shift from 2-nd Order Kick:
 x ( y ) ( x, y ) 
1
 x ( y )  x ( y )  x ( y ) ( x, y )
4
Horizontal Tune Shift in Low- and
Horizontal 2nd Order Kick at E = 3 GeV High-Beta Straight Sections of NSLS-II
30
BROOKHAVEN SCIENCE ASSOCIATES
Compensation of APPLE-II Dynamic Focusing Effects
Idea: I. Blomqvist
RADIA EPU Model with Strips
by Current Strips Implementation at BESSY: J. Bahrdt
in Linear Vertical
Polarization Mode
Equivalent Vertical Field Integrals
Compensating Currents
in Lower Strips
Field Integral (at y=0)
from Current Densities:
I  QJ
Matrix
calculated
by Radia
J  (QTQ)1 QTI
Since the Dynamic Effects
are Anti-Symmetric vs x:
Jupper ( x)  Jlower ( x)
Horizontal Position [mm]
Horizontal Position [mm]
Electron Trajectory in 3D Magnetic Field
Without and With Correction
Horizontal Trajectory
x0=0, y0=0 before Undulator
Number of Strips used: 2 x 20
Strip Dims: 2 mm x 0.3 mm x 2 m
Horizontal Gap bw Strips: 1 mm
Vertical Gap bw Strips: 10.7 mm
Max. Current obtained: ~ 2.3 A
APPLE-II Vertical Gap: 11.5 mm
Horizontal Trajectory
x0= 4 mm, y0=0 before Undulator
x0= -4 mm, y0=0 before Undulator
Longitudinal Position [mm]
Horizontal Position [μm]
Vertical Trajectory
Horizontal Position [μm]
Horiz. Position [μm]
Using Least-Squares Linear Fit
Current Densities
from Field Integral:
Current [A]
Vertical (Equivalent)
Field Integral [G.cm]
from Dynamic Focusing and from the Current Strips
Vertical Position [μm]
Efficient Solving for Currents
Longitudinal Position [mm]
Longitudinal Position [mm]
Compensation of APPLE-II Dynamic Focusing Effects
by Current Strips in Linear Tilted (45˚) Polarization Mode
Equivalent Field Integrals
dynam. effect
current strips
Compensating Currents
in Lower Strips
“Current Strips” are
efficient, however
require dedicated
additional “FeedForward” correction
tables…
Current [A]
Vertical (Equivalent)
Field Integral [G.cm]
Horizontal (Equivalent)
Field Integral [G.cm]
from Dynamic Focusing and from the Current Strips
Horizontal
Vertical
dynam. effect
current strips
Horizontal Position [mm]
Horizontal Position [mm]
Horizontal Position [mm]
Electron Trajectory in 3D Magnetic Field Without and With Correction
Longitudinal Position [mm]
Vertical Trajectory
Longitudinal Position [mm]
x0= 4 mm, y0= 0 before Undulator
Horizontal Trajectory
Vertical Position [μm] Horizontal Position [μm]
Vertical Trajectory
x0= -4 mm, y0= 0 before Undulator
Horizontal Trajectory
Vertical Position [μm] Horizontal Position [μm]
Vertical Position [μm] Horizontal Position [μm]
x0= 0, y0= 0 before Undulator
Horizontal Trajectory
Vertical Trajectory
Longitudinal Position [mm]
Spectral-Angular Distributions of Emission from
2x3.5 m Long Damping Wiggler in “Inline” Configuration
Spectral Flux per Unit Solid Angle
FWHM Angular Divergence of DW Emission
1/ ≈ 170 μrad
Angular Profiles of DW Emission
at Different Photon Energies
Horizontal Profiles
Vertical Profiles
TPW: Magnetic Field, Electron Trajectory and Spectra
(in presence of Bending Magnets)
Upstream
BM
On-Axis Magnetic Field in Dispersion Section
TPW
Downstream
BM
Average Electron Trajectory: Horizontal Angle
Average Electron Trajectory: Horizontal Position
TPW Field taken
from magnetic simulations
BM Field is taken from
magnetic measurements on
a prototype BM with “nose”
Longitudinal Position s are
approximate
On-Axis Spectral Flux per Unit Surface at 30 m from TPW
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
Spectral Flux through 1.75 mrad (H) x 0.1 mrad (V) Aperture
(centered on the axis)
34
BROOKHAVEN SCIENCE ASSOCIATES
TPW and BM Radiation Intensity Distributions (Hard X-rays)
Intensity Distributions at Different Photon Energies at 30 m from TPW
Electron Current: 0.5 A
Horizontal Cuts at y = 0
Vertical Cuts at x = 0
Angular Power Density Distributions
of Radiation from NSLS-II Insertion Devices
Undulators and Multi-Pole Wigglers
In Horizontal Mid-Plane
In Vertical Mid-Plane
Horizontal FWHM Angle:  x  1.7 K 
Vertical FWHM Angle:  y  1.3 
Three-Pole Wiggler and Bending Magnet Radiation at 30 m
In Horizontal Mid-Plane
|θX| = 4.75 mrad |θX| ≈ 2.6 mrad
θX= 0
θX= 1.5 mrad
NSLS-II: E = 3 GeV, I = 0.5 A
36
BROOKHAVEN SCIENCE ASSOCIATES
Power Density Distributions of Radiation from NSLS-II
Insertion Devices at Fixed Masks (at ~16 m)
DW100 (2 x 3.5 m)
SCW60 (1 m)
P ≈ 61 kW
IVU20 (3 m)
TPW
P ≈ 40 kW
P ≈ 0.4 kW
IVU21 (1.5 m)
P ≈ 8.1 kW
EPU49 (2 x 2 m) LH mode
IVU22 (6 m)
P ≈ 3.6 kW
EPU49 (2 x 2 m) LV mode
P ≈ 10 kW
P ≈ 9.4 kW
EPU49 (2 x 2 m) LT-45º mode
P ≈ 5.7 kW
P ≈ 3.7 kW
EPU49 (2 x 2 m) Helical mode
P ≈ 7.3 kW
NSLS-II: E = 3 GeV, I = 0.5 A
IVU, EPU power is given for min. gaps
2 x EPU49 are in canted mode
37
BROOKHAVEN SCIENCE ASSOCIATES
Radiation Power Density Distributions on Straight Section
Chamber Wall for DW90 (9.5 mm int. chamber size) and
DW100 (11.5 mm int. chamber size) for “Mis-Steered” E-Beam
Magnetic Field
NSLS-II: E = 3 GeV, I = 0.5 A
High-Beta Straight Section
Horizontal Projection of Electron Trajectory
Power Density Distributions on Chamber Wall
DW90 (y = 4.75 mm)
DW100 (y = 5.75 mm)
Vertical Projection
of “Mis-Steered” Electron Trajectory
DW100 chamber wall (y = 5.75 mm)
DW90 chamber wall (y = 4.75 mm)
Horizontal Cuts
at Longitudinal Position z = 3.9 m
“Mis-steered” electron initial conditions:
y0 = 2 mm, y0’= 0.25 mrad at z0 ≈ -3.8 m
Longitudinal Cuts
at Horizontal Position x = 0
P ≈ 4.05 kW
P ≈ 0.51 kW
EPU49 (2 x 2m) Radiation Power (Helical Mode, 11.5 mm Min. Gap)
on Straight Section Chamber Wall at Different Vertical Offsets
and Angular Deviations of Electron Beam
Power Density Distributions on Chamber Wall
in vertical median plane (x = 0)
at different e-beam vertical offsets
Deposited Power
Δy = 3.5 mm
Δy’ = 0
at different e-beam
vertical angular deviations
(applied before undulator)
Δy = 0
Δy‘= 0.8 mrad
Electron Beam Current: 0.5 A
Results of Vacuum Chamber Heat Conductivity Analysis
For “Mis-Steered” Electron Beam in EPU49 (Helical Mode)
1) Δy’ = 0.25 mrad, Δy = 2 mm, Eph= 220 eV
2) Δy’ = 0.25 mrad, Δy = 1.5 mm, Eph= 220 eV
ANSYS
calculations
courtesy of
V. Ravindranath
P = 1240 W, Tmax = 169.5 °C
3) Δy’ = 0.25 mrad, Δy = 2 mm, Eph= 270 eV
P = 860 W, Tmax = 136 °C
P = 580 W, Tmax = 128.5 °C
4) Δy’ = 0.25 mrad, Δy = 2 mm, Eph = 400 eV
P = 380 W, Tmax = 92.8 °C
Summary of Calculations of Radiation Power Density
on Straight Section Vacuum Chamber Walls
(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
~0.007
Task Force on “Synchrotron Radiation Protection” has been recently created in ASD (headed by P. Ilinsky,
Accelerator Physics group) - to treat questions about “mis-steering” assumptions, tolerances, equipment protection
schemes, precautions at ID operation, etc.
Estimated Spectral Flux and Brightness
of the First Planned NSLS-II Undulators
Approximate Spectral Brightness at Odd Harmonics
Spectral Flux through Fixed Apertures
(200 μrad x 200 μrad for APPLE-II, 150 μrad H x 50 μrad V for IVU in Low-Beta, 100 μrad H x 50 μrad V in High-Beta Straights)
42
BROOKHAVEN SCIENCE ASSOCIATES
Estimated Spectral Brightness and Flux
of Main NSLS-II Radiation Sources
Approximate Undulator Spectral Flux
Approximate Spectral Brightness
at Odd Harmonics
Approximate Wiggler Spectral Flux
per Unit Horiz. Angle
43
BROOKHAVEN SCIENCE ASSOCIATES
Estimated Spectral Brightness of NSLS-II
Compared to Other Synchrotron Sources
44
BROOKHAVEN SCIENCE ASSOCIATES