Fermilab AD Accelerator Physics Center MARS 15 Energy

Fermilab AD / Accelerator Physics Center MARS 15 Energy Deposition Modeling and Quench Stability of the APS USC 0 Undulator Yu. Eidelman and N. Mokhov Fermilab RESMM’ 15 East Lansing, MI May 10 -14, 2015

Advanced Photon Source (APS) Undulator Super. Conducting-0 (USP 0) RESMM'15, East Lansing, May 10 -14, 2015 APS USC 0 Undulator - N. Mokhov 2

MARS 15 Model Al beam pipe 2 x 41 SC Coils Front View SC Coil RESMM'15, East Lansing, May 10 -14, 2015 APS USC 0 Undulator - N. Mokhov 3

Materials of SC Coils SC wire: 52. 6% Nb. Ti + 47. 4% Cu Epoxy EPOXY 87 K Element Z A r (g/cm 3) Weight fraction Nb 41 92. 906 8. 57 0. 261 Ti 22 47. 867 4. 54 0. 134 Cu 29 63. 564 8. 92 0. 355 Ca 20 40. 078 1. 55 0. 0263 Si 14 28. 086 2. 33 0. 0368 Na 11 22. 990 0. 971 0. 0303 C 6 12. 011 2. 25 0. 0934 O 8 15. 999 1. 4 e-3 0. 0546 H 1 1. 008 9. 0 e-5 0. 0086 Average density of the coil (g/cm 3) RESMM'15, East Lansing, May 10 -14, 2015 WF total Partial r (g/cm 3) 75% 6. 012 25% 0. 366 6. 378 APS USC 0 Undulator - N. Mokhov 4

Magnetic Field and Beam Parameters RESMM'15, East Lansing, May 10 -14, 2015 APS USC 0 Undulator - N. Mokhov 5

Beam Loss Model • Grazing Angle: 2 and 4 mrad • Beam hits edge or center of Undulator RESMM'15, East Lansing, May 10 -14, 2015 APS USC 0 Undulator - N. Mokhov 6

Shower Development Particle tracks above 100 ke. V in showers induced in SCU 0 by ten 7 Ge. V electrons of the APS beam started at z = -10 cm at 3 s from the beam pipe No photons and electron All tracks RESMM'15, East Lansing, May 10 -14, 2015 APS USC 0 Undulator - N. Mokhov 7

Energy Deposition x-y Profiles (beam at 2 mrad) “Target”: Center RESMM'15, East Lansing, May 10 -14, 2015 “Target”: Edge APS USC 0 Undulator - N. Mokhov 8

Energy Deposition x-s Profiles 2 mrad “Target”: Center RESMM'15, East Lansing, May 10 -14, 2015 2 mrad “Target”: Edge 4 mrad “Target”: Edge APS USC 0 Undulator - N. Mokhov 9

From Energy Deposition to Beam Loss Limit To calculate the relative quench stability, energy deposition averaged over the coil width were used to find dependence of absorbed energy on inside the SC winding at the hottest spot at the downstream end of the undulator. Averaging gives and power density. Parameters 2 mrad, Center 2 mrad, Edge 4 mrad, Edge (mm) 0. 6383 0. 6392 0. 6351 1. 48 e+04 4. 40 e+04 8. 79 e+04 4. 1 e+09 1. 2 e+10 2. 4 e+10 (m. J/cm 3/pulse) RESMM'15, East Lansing, May 10 -14, 2015 APS USC 0 Undulator - N. Mokhov 10

Fast Beam Loss Limits The beam loss limits can be estimated from the values and the quench limits for the Nb. Ti based coils operated at a certain subcriticality I/IC, where IC = 827 A is the SCU 0 critical current. The quench limits Equench for the SCU 0 coils are derived from the dedicated experiments and the experience with the Nb. Ti coils of Tevatron dipole magnets for fast beam losses. The “fast” beam loss is that impacting the Nb. Ti SC coils during the time of shorter than about 350 msec. For the APS, with the beam revolution time of 3. 7 msec, it corresponds to anything between 1 and 100 turns. The beam loss limits for these two extremes are defined as a fraction of the beam (of one pulse of 24 bunches) lost on the undulator that quenches it. These are given in the following table for three irradiation cases. I/Ic I (A) Equench (m. J/cm 3) 0. 544 450 8. 30 0. 604 500 7. 66 0. 79 650 3. 83 0. 9 744 3. 20 RESMM'15, East Lansing, May 10 -14, 2015 Beam loss duration (turns) 1 100 2 mrad, center 2 mrad, edge 4 mrad, edge 5. 61 e-4 5. 61 e-2 5. 18 e-4 5. 18 e-2 2. 59 e-4 2. 59 e-2 2. 16 e-4 2. 16 e-2 1. 90 e-4 1. 90 e-2 1. 75 e-4 1. 75 e-2 8. 76 e-5 8. 76 e-3 7. 32 e-5 7. 32 e-3 9. 44 e-5 9. 44 e-3 8. 72 e-5 8. 72 e-3 4. 36 e-5 4. 36 e-3 3. 64 e-5 3. 64 e-3 APS USC 0 Undulator - N. Mokhov 11

Summary The limits of fast beam loss for various coil currents and beam loss duration are found. For the case of losses during 100 turns, a few percent loss can result in a quench in the windings. For the case of loss during one turn, the limit is much tighter. RESMM'15, East Lansing, May 10 -14, 2015 APS USC 0 Undulator - N. Mokhov 12