Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T....

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Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated Design Review Jun. 6, 2014 1

Transcript of Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T....

Page 1: Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated.

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Magnetic Design

S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL)

Superconducting Undulator Integrated Design Review

Jun. 6, 2014

Page 2: Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated.

Integrated Design Review, Jun. 6, 2014

Undulator Layout

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Undulator period = 19.0 mm, gap = 8.0 mmPeak field requirement Beff = 1.86 T

Single wire winding– 0.6 mm diameter wire– 60 μm thick s-glass braid insulation

Wire turns around at the end of the poleNb3Sn to NbTi joints at the end of the undulator

Single Wire WindingElectron Beam

Joint Section

Page 3: Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated.

3Integrated Design Review, Jun. 6, 2014

Simulation ToolsOpera 2D– Coil pack optimization of periodic design– Initial end design calculations

Opera 3D– 3D verification for periodic design (load line calculation)– End design– Calculation of force and stored energy (inductance)

¼ Period Model End Design Model

Page 4: Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated.

4Integrated Design Review, Jun. 6, 2014

Coil OptimizationFind optimal number of turns per layer and total layers necessary to meet peak field requirement (1.86 T @ λ = 19.0 mm, g = 8.0 mm)Wire diameter = 0.6 mm, insulation thickness = 60 μmScaling relation used with Jc = 2000 A/mm2 @ 12 T5 layers is sufficient to operate below 80 %Modest gains margin can be obtained by adding more layers

Number of layers

Num

ber o

f tur

ns p

er la

yer Load Line Margin Load Line Margin

8 turns per layer

Page 5: Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated.

5Integrated Design Review, Jun. 6, 2014

Operating CurrentOperating current is reduced as the number of layers is increased (operate at higher conductor peak field)Need to perform short-sample tests on the candidate conductors in order to understand the stability marginCan increase length of conductor to reduce the risk of stability problemsOperating current for B0 = 1.86 T Load Lines

8 by 5

8 by 7

8 by 9

On-Axis Field

Peak Conductor Field

Design Point

Page 6: Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated.

Integrated Design Review, Jun. 6, 2014

End Design

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Want zero net displacement and steering due to the endsEven or Odd number of poles– Even – zero net steering, non-zero net displacement– Odd – zero net displacement, non-zero net steering

Even number of poles

δ+K

-K

Odd number of poles

+K +K

+δ -δ

Steering + Displacement

Displacement Only

Ideal

Page 7: Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated.

7Integrated Design Review, Jun. 6, 2014

End pattern

Odd poles/even coilsBinomial expansion pattern– Poles: 0, +1/4, -3/4, +1, -1,…– Coils: +1/8, -4/8, +7/8, -1, +1,…

7 x 8 turns/pocket:– Turns/coil: 7, 28, 49, 56, 56,…

Requirements:I1 (end) < 40 μTm, I2 (end) < 50 μTm2

0 +1/4 -3/4 +1 -1

+1/8 -1/2 +7/8 -1

Yoke

Poles Coils

Y

Z# turns:

potential:

Page 8: Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated.

8Integrated Design Review, Jun. 6, 2014

Non-Ideal End Effects

Non-ideal effects due to finite permeability and differential saturation of end poles– End kick is dependent on the undulator field– Dipole field is generated by unbalanced yoke

fieldx x x

xx x

x x x

xx x

1 2

Magnetic Field (one period filter)

As field is ramped:Pole 2 saturates before 1

Second Field Integral

End Kick

Curvature due to dipole field

End Kick

Non-zero offset

Page 9: Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated.

9Integrated Design Review, Jun. 6, 2014

Dipole Corrector

End corrector #1 (dipole)

Wound on top of the main coil in the remaining pocket on each endAdds both a dipole and end kicks Used to correct the dipole first

Second Field Integral

Page 10: Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated.

10Integrated Design Review, Jun. 6, 2014

End corrector #2 (kick)

Wound in a separate yoke on each endDecoupled from the main yoke Add only end kicks

Used to cancel the exit kick once the 1st coil is tuned

Kick Corrector

Second Field Integral

Page 11: Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated.

11Integrated Design Review, Jun. 6, 2014

Correction Current as a Function of Undulator Current

0 200 400 600 800 1000 1200 1400 1600 18000

5

10

15

20

25

30

35

Undulator Current Density [A/mm2]

Corr

ecto

r Cur

rent

Den

sity

[A/m

m2]

0 200 400 600 800 1000 1200 1400 1600 18001.0

1.5

2.0

2.5

3.0

Undulator Current Density [A/mm2]

Corr

ecto

r Cur

rent

Den

sity

[A/m

m2]

0.56 T

0.83 T1.12 T

1.48 T1.86 T

Corrector #1 Corrector #2

Required

Max current [A] Sensitivity [A]

1st corrector 2.2 0.004

2nd corrector 13.1 0.01* Sensitivity based on dipole field < 10 μT* Sensitivity based on end kick < 1 μTm

Page 12: Magnetic Design S. Prestemon, D. Arbelaez, S. Myers, R. Oort, M. Morsch, E. Rochepault, H. Pan, T. Ki, R. Schlueter (LBNL) Superconducting Undulator Integrated.

12Integrated Design Review, Jun. 6, 2014

Conclusions

Magnetic design for the periodic and end sections is completeEnd corrector summary– Correctors of type # 1 (dipole correctors) at each end are wired

in series (1 power supply) – Correctors of type # 2 (end kick correctors) at each end are

independent to allow entrance and exit kick adjustment (2 power supplies)

One master power supply controls the undulator field and three slave power supplies provide end corrections