1

End Design Discussion

D. Arbelaez (LBNL)Oct. 7, 2014

Basic End Design Kicks (ideal)Potentials at Poles: 0, ½, -1, +1, …

01/2

-1

+1

-1 Even poles

Odd poles

# of coil turns:¼, ¾, 1 …

01/4

-3/4

+1

-1 Even poles

Odd poles

Potentials at Poles: 0, ¼, -3/4, +1, -1, …# of coil turns:1/8, ½, 7/8, 1 …

# of coil turns is given by the difference in neighboring pole potentials

End Design Including Local End Errors

3

Kick and displacement errors at the ends due to non-ideal effectsEven or Odd number of poles– Even – zero net steering, non-zero net displacement– Odd – zero net displacement, non-zero net steering

2δ

Even number of poles

δ+K

-K

Odd number of poles

+K +K

+δ -δ

Steering + Displacement

Displacement Only

Ideal

δ

Undulator Pole/Core Saturation

Saturation of the undulator core and poles leads to non-ideal effects– Pole saturation changes the local kick strength– Pole and core saturation leads to non-ideal global effects

Variation in Pole Saturation

No Core Saturation near end

Flux through the end

2D calculations are shown to demonstrate the principles For accurate results 3D calculation must be used

Global Field Effects

B

z

On-Axis Field Profile

B

z

On-Axis Field Profile

Even # of poles, Odd # of coils

Odd # of poles, Even # of coils

cw cw

ccw ccw

cw ccw

cwccw

• Number of turns are chosen to cancel these effects in an ideal case• Global field effects are present due to saturation

Scaling of Global Field Effects with Undulator Length

Magnetic field was calculated with two different length undulators (second one is twice as long)The effect of the end coil corrector is shownSlope of the distributed field scales approximately with 1/L Second field integral scales with slope*L3 ≈ L2

Slope = 0.17 G/mm

Slope = 0.28 G/mm

I2dev α slopeL3

Magnetic Field Variation First Field Integral Variation

End kick strength

Even # of polesEven # of poles

LBNL End Design Principles

2 Independent CorrectorsCorrection of global field effects– 1 corrector (coil at each end wired in series) is used for

correction of the global field effect– corrector produces both a local kick and a global field– In principle the two ends can be wired independently to produce

both a constant and linearly varying global fields

Correction of local end kick– 1 corrector at each end wired independently for entrance and

exit kick correction– This correction is decoupled from the main core and produces no

global fields– Field clamps are included for this corrector in order to avoid

interference with nearby magnetic components

Global Field Correction

Coils are wound in first and last pocket of each coreProduces a global correction + local kickStrength is chosen to cancel only global field error

Effect of end corrector

global field

local kicks

odd# of poles

Local End Kick Correction

Magnetically decoupled from main undulator coreProduces only local kicksField clamps are used to minimize stray fieldCompact design (fits under splice joint in Nb3Sn device)

Effect of end corrector

no global field

local kicks

odd# of poles

Glass Braid Insulation Update

4 braiding angles were tested on 0.6 mm diameter copper wire by New England Wire CompanySCD 450 fine filament Glass yarn was purchased from AGY The final braid thickness was 55 μm with excellent coverage

Increasing braid angle (with respect to wire axis)

Final braid test