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 Design Review Jun. 6, 2014 1

2. Integrated Design Review, Jun. 6, 2014 Undulator Layout 2 Undulator period = 19.0 mm, gap = 8.0 mm Peak field requirement B eff = 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 pole Nb 3 Sn to NbTi joints at the end of the undulator Single Wire Winding Electron Beam Joint Section

3. Integrated Design Review, Jun. 6, 2014 Simulation Tools 3 Opera 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 ModelEnd Design Model

4. Integrated Design Review, Jun. 6, 2014 Coil Optimization 4 Find 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 μm Scaling relation used with Jc = 2000 A/mm 2 @ 12 T 5 layers is sufficient to operate below 80 % Modest gains margin can be obtained by adding more layers Number of layers Number of turns per layer Load Line Margin 8 turns per layer

5. Integrated Design Review, Jun. 6, 2014 Operating Current 5 Operating 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 margin Can increase length of conductor to reduce the risk of stability problems Operating current for B 0 = 1.86 TLoad Lines 8 by 5 8 by 7 8 by 9 On-Axis Field Peak Conductor Field Design Point

6. Integrated Design Review, Jun. 6, 2014 End Design 6 Want zero net displacement and steering due to the ends Even 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 +δ -δ Steering + Displacement Displacement Only Ideal

7. Integrated Design Review, Jun. 6, 2014 End pattern 7 Odd poles/even coils Binomial 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 μT  m, I2 (end) < 50 μT  m 2 0 +1/4 -3/4 +1 -1 +1/8 -1/2 +7/8 -1 Yoke Poles Coils Y Z # turns: potential:

8. Integrated Design Review, Jun. 6, 2014 Non-Ideal End Effects 8 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 field xxx xxx xxx xxx 12 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

9. Integrated Design Review, Jun. 6, 2014 Dipole Corrector End corrector #1 (dipole) 9 Wound on top of the main coil in the remaining pocket on each end Adds both a dipole and end kicks  Used to correct the dipole first Second Field Integral

10. Integrated Design Review, Jun. 6, 2014 End corrector #2 (kick) 10 Wound in a separate yoke on each end Decoupled 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

11. Integrated Design Review, Jun. 6, 2014 Correction Current as a Function of Undulator Current 11 0.56 T 0.83 T 1.12 T 1.48 T 1.86 T Corrector #1Corrector #2 Required Max current [A]Sensitivity [A] 1 st corrector2.20.004 2 nd corrector13.10.01 * Sensitivity based on dipole field < 10 μT * Sensitivity based on end kick < 1 μTm

12. Integrated Design Review, Jun. 6, 2014 Conclusions 12 Magnetic design for the periodic and end sections is complete End 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