The Delta Undulator
*Work has been supported by NSF grant DMR 0225180 and PHY-013150
A. Temnykh, CLASSE, Cornell University, Ithaca, New York, USA
Concept Two adjustable phase undulators*
assembled in one device**30 cm long model built in Cornell
*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)
1. Compact box-like frame (prototype has dimensions ~150mmx150mm)2. Full polarization control3. 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.
Delta undulator installed in BL2 ATF.
5300nm wavelength radiation as function of the electron beam energy.Signal confirmed 1.28T peak field in undulator
Beam test in BNL (ATF)
4520nm (bottom) and 3600nm (right) wavelength radiations versus beam energy. Both data confirmed 0.93T field amplitude.
Model in vacuum vessel Transport from Cornell to BNLFirst harmonics in planar and helical mode
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.
1 2
4
3
5
1 – Rectangular frame2 - Linear bearings3 – Movable plates4 – copper holders
5 – PM (NdFeB) blocks
Two 1.65m long sections connected together
Magnet array mover(electrical cylinder)
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
Source http://www.cy-magnetics.com
Br as function of coercivity
Progress in PM material development
NdFeB – is the best chose
NdFeB grade
PM materials NdFeB 40SH or N40UH seem a reasonable compromise between magnetization strength and stability. UH – is more stable, but ~3X more expensive
Material TypeResidual Flux
Density(Br)
Coercive Force(Hc)
Intrinsic Coercive Force
(Hci)
Max.Energy Product(BH)max
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
Source http://www.kjmagnetics.com/specs.asp
Source http://www.cy-magnetics.comSource http://www.electronenergy.com/media/N40SH.pdf
N40SH N40UH
Undulator Period definition(result of 3D magnetic field modeling)
Period [mm]
Peak field in helical mode
[G]
Peak field in planar mode
[G]
Khelical
Kplanar
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
Model parameters: Br = 12.6kG (low limit), bore diameter = 6.4mm
22 1][][
56.130)( KGeVEm
nm p
For wavelength calculation in helical mode used:
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
Bx_min = 5.3kGs => reverse field -7.3kOe, T_demag ~150degC for 40SH T demag ~ 180degC for 40UH
By_min=5.1kGs => reverse field -7.5kOeT_demag ~145degC for 40SH T demag ~ 175degC for 40UH
Single V-block
Undulator mode H-blockBx_min[kG]
V-blockBy_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
Helical “zero” field -1.795 5.82 70 110
Undulator demagnetization temperature (reverse field effect) for various modes
*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
The measured correlation between radiation dose (high energy electrons) and demagnetization temperature
For 100degC demagnetization temperature the critical dose (1% demagnetization) ~ 1Mrad
Radiation damage consideration
Copy from paper *
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
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
Peak field on beam axis
Mechanical structure deformation under magnetic force load (stress analysis)
Base plate deformation
Helical mode
Maximum deformation ~6mm
Planar mode
Maximum deformation ~4.8mm
Frame deformation
Helical mode
Maximum deformation ~0.6mmMaximum deformation ~0.7mm
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. Single NdFeB (40SH) PM block, T_demag ~ 1320C2. PM block in steel jacked, T_demag ~ 2280C !
63Sn/37Pb alloy melting point 182degC(US Patent 7,896,224)
1 2
Hall probe measurement setup for Delta
http://www.lakeshore.com/mag/hs/hsts.html
Ceramic tubing
Hall probe sensor
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)
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