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)