The Delta Undulator
A. Temnykh, CLASSE, Cornell University,
Ithaca, New York, USA
*Work has been supported by NSF grant DMR 0225180 and PHY-013150
Concept
Two adjustable phase undulators*
assembled in one device**
30 cm long model built in Cornell
1. Compact box-like frame (prototype has dimensions ~150mmx150mm)
2. Full polarization control
3. Sqrt(2) stronger field in planar mode and ~2X stronger in helical mode in compare with conventional
Apple II type undulators.
Project was motivated by the Cornell ERL needs.
*R. Carr, Adjustable phase insertion devices as X-ray sources, Nucl. Instr. And Meth. A 306(1991) 391-396
**A. Temnykh, Delta undulator for Cornell energy recovery linac , Phys. Rev. ST Accel. Beams 11, 120702 (2008)
Beam test in BNL (ATF)
Model in vacuum vessel
Transport from Cornell to BNL
Delta undulator installed in BL2 ATF.
First harmonics in planar and helical mode
5300nm wavelength radiation as function of the electron
beam energy.
Signal confirmed 1.28T peak field in undulator
4520nm (bottom) and 3600nm (right) wavelength
radiations versus beam energy. Both data
confirmed 0.93T field amplitude.
A. Temnykh, et al., Delta undulator model: Magnetic field and beam test results. Volume 649, Issue 1, 1 September
2011, Pages 42-45
Delta Undulator for SLAC
(development underway)
Four movable magnet arrays
mounted inside box like frame.
Two 1.65m long sections connected together
Magnet array mover
(electrical cylinder)
4
5
3
1
2
1 – Rectangular
4 – copper holders
frame
5 – PM (NdFeB)
2 - Linear bearings blocks
3 – Movable plates
Basic Parameters
•
•
•
•
•
•
Bore diameter - 6.4mm*
PM material - NdFeB 40SH (or 40UH)
Period - 32mm*
Two sections 1.65m each (3.3m total)*
Full polarization control
Peak field in helical mode 0.898 T, peak field in
planar mode 1.270 T
* Under discussion
PM material chose
Br as function of coercivity
Source http://www.cy-magnetics.com
NdFeB – is the best chose
Progress in PM material development
NdFeB grade
Material Type
Residual Flux
Density
(Br)
Intrinsic
Coercive Force
Coercive Force
(Hc)
(Hci)
N40SH
12.6-12.9 KGs
>11.4 KOe
>20 Koe
38-40 MGOe
N40UH
12.6-12.9 KGs
>11.4 KOe
>25 KOe
38-40 MGOe
N40SH
Source http://www.electronenergy.com/media/N40SH.pdf
Max.Energy
Product
(BH)max
Source
http://www.kjm
agnetics.com/sp
ecs.asp
N40UH
Source http://www.cy-magnetics.com
PM materials NdFeB 40SH or N40UH seem a reasonable compromise between
magnetization strength and stability. UH – is more stable, but ~3X more
expensive
Undulator Period definition
(result of 3D magnetic field modeling)
Model parameters: Br = 12.6kG (low limit), bore diameter = 6.4mm
Period
[mm]
Peak field in
helical mode
[G]
Peak field in
planar mode
[G]
K
helical
K
planar
Resonance wavelength in
helical mode for 4.3GeV
beam [nm]
29
8696
12298
2.355
3.331
1.341
30
8802
12448
2.466
3.488
1.500
31
8900
12587
2.577
3.644
1.672
32
8978
12697
2.683
3.795
1.853
33
9048
12796
2.789
3.944
2.045
For wavelength calculation in helical mode used:
 ( nm )  130 . 56
 p [m ]
E [ GeV ]
1  K 
2
2
We need 1.5nm wavelength in helical mode (K=2.466) and K=3.5 in planar.
For 32mm period there will be ~10% margin for the field strength
Magnetic field properties (field on beam axis)
Bx,y,z in helical mode
Bx,y,z in planar mode
Magnetic field properties (field roll-off)
For 100mm trajectory offset in helical mode dB/B ~1.7e-4 and in planar mode ~1.0e-4
Reverse field effect analysis
Single H-block
Single V-block
Bx_min = 5.3kGs => reverse field -7.3kOe,
T_demag ~150degC for 40SH
T demag ~ 180degC for 40UH
By_min=5.1kGs => reverse field -7.5kOe
T_demag ~145degC for 40SH
T demag ~ 175degC for 40UH
Undulator demagnetization temperature (reverse field effect) for various modes
Undulator mode
H-block
Bx_min[kG]
V-block
By_min[kG]
T dmg [C]
N40SH
T dmg [C]
N40UH
Planar, max peak field
5.20
5.00
180
180
Planar, “zero” field
-2.68
3.80
60
100
Helical, max peak field
3.99
9.00
150
175
-1.795
5.82
70
110
Helical “zero” field
Radiation damage consideration
The measured correlation between radiation dose (high energy electrons) and
demagnetization temperature
Copy from paper *
For 100degC demagnetization temperature
the critical dose (1% demagnetization) ~
1Mrad
*A. Temnykh, Measurement of NdFeB permanent magnets demagnetization induced by high energy electron
radiation, NIMA Volume 587, Issue 1, 11 March 2008, Pages 13-19
Peak field on beam axis
Along beam axis
Transverse
Comment
Helical, max peak field
0
0.898T
Helical field
Planar, max field peak
0
1.269T
Planar field
Helical, zero field
1.0338 T
0
0
Planar, zero field
1.3651 T
0
0
Magnetic Forces for 1 period / for 51 periods
Per quadrant per
period/total
Fx[N]
Along beam axis
Fy[N]
Transverse
Fz[N]
Transverse
Helical, max peak field
0
-39/-1989
0
Planar, max field peak
0
-39/-1989
-179/-4029
Helical, zero field
-200/-10200
46 / 2346
0
Planar, zero field
0
224
0
Mechanical structure deformation under magnetic force load
(stress analysis)
Base plate deformation
Helical mode
Frame deformation
Helical mode
Maximum deformation ~0.6mm
Maximum deformation ~0.7mm
Planar mode
Maximum deformation ~4.8mm
Maximum deformation ~6mm
Conclusion
Project is feasible
Acknowledge
Many thanks to Jim Welch, Heinz-Dieter Nuhn, Zack
Wolf, Yurii Levashov and other people for interest in
this project, invitation to work in SLAC and help.
PM block soldering technique
1
2
1. Single NdFeB (40SH) PM block, T_demag ~ 1320C
2. PM block in steel jacked, T_demag ~ 2280C !
63Sn/37Pb alloy melting point 182degC
(US Patent 7,896,224)
Hall probe measurement setup for Delta
http://www.lakeshore.com/mag/hs/hsts.html
Hall probe sensor
Ceramic tubing
CHESS Compact Undulator
PPM structure, 24.4mm period, 1.1T peak field, 5mm constant gap . Dimensions: 1m
x 152mm x 146mm, Weight - 83kg (with driver attached)