1. Simplified Modeling of Space Charge Losses in Booster at Injection Alexander Valishev June 17, 2015

2. Motivation and Outline A.Valishev - IOTA/FAST update26/12/15 Another look at incoherent Space Charge effect in Booster at injection aiming to a)Understand the current limitations. b)Make projections for post-PIP-II era. c)Synergistic with IOTA program This presentation is a seed to start discussions within AD. Outline: –The approach and previous work –Modeling tools –First results –Questions, proposals and next steps

3. PIP-III “multi-MW”- Option B: 8+ GeV smart RCS 800 MeV SC Linac 2/11/2015V.Shiltsev | FNAL Institutional review, 02/10-13/20153 new 8-12 GeV “smart” RCS i-Booster 120 GeV RCS Main Injector 8 GeV ? Recycler ? >2 >2 MW target

4. Approach and Previous Work A.Valishev - IOTA/FAST update46/12/15 If one forgets about coherent instabilities, the action of direct SC on stability of single-particle motion is through the time modulation of nonlinear transverse field and consequently, betatron and synchrobetatron resonances. –Emittance growth and particle losses. Modeling can be done with following simplifying approximations: a)No self-consistency: Gaussian beam profile. b)Many thin kicks per turn instead of smooth action. This approach is usually referred to as “frozen SC”, and can be implemented with beam-beam tracking codes –Yu.Alexahin et al., Beams-doc 2609 –F.Schmidt, V.Kapin, http://cds.cern.ch/record/1703980

5. Modeling Tools A.Valishev - IOTA/FAST update56/12/15 I was using Lifetrac: –20 years of development as beam-beam tracking code (many e+e- colliders, Tevatron, LHC, HL-LHC). –Single-particle tracking, well-parallelized tracking of multiparticle distributions, Frequency Map Analysis, Dynamical Aperture. Workflow: –Start with madx lattice file. –Install thin beam-beam elements (120, 17 per betatron period). –Produce FMA (quick) and multiparticle distribution evolution (slower). Limitations: –Frozen SC with constant emittance of “strong beam”. –Synchrotron modulation not taken into account.

6. Booster Parameters in Simulation A.Valishev - IOTA/FAST update66/12/15 Energy400 MeV (β=0.713, γ=1.426) U RF 0.7 MV QsQs 0.078 (ω s =35 kHz) Bucket size4.2×10 -3 Energy spread2.1×10 -3 (σ z =1.26 m) Transverse emittance 15 mm×mrad (95% normalized) ApertureAx=2.86 cm, Ay=2.08 cm NpNp 0.42×10 13 in 84 bunches SC tuneshiftΔQ x =-0.197, ΔQ y =-0.307 Betatron tunesQ x =6.70, Q y =6.80 ChromaticityC x =-20, C y =-14

7. Lattice Used in Simulation A.Valishev - IOTA/FAST update76/12/15 a)24-cell fully symetrical FODO (V.Kapin) b)24-cell with 10% beta-beat c)24-cell with 20% beta-beat d)Actual Booster (C.Y.Tan) –Chromaticity (-30, +13)?

8. Results – FMA (a) A.Valishev - IOTA/FAST update86/12/15

9. Results – FMA (a) A s =0 A.Valishev - IOTA/FAST update96/12/15

10. Results – FMA (a) A s =1 A.Valishev - IOTA/FAST update106/12/15

11. Results – FMA (b) A s =1 A.Valishev - IOTA/FAST update116/12/15

12. Results – FMA (c) A s =1 A.Valishev - IOTA/FAST update126/12/15

13. Results – FMA (c) A s =1 A.Valishev - IOTA/FAST update136/12/15

14. Results – Multiparticle Tracking A.Valishev - IOTA/FAST update146/12/15

15. Summary and Questions With known limitations, the method allows for very fast evaluation of options The half-integer resonance seems to be the limiting factor –At intensity of 4×10 12 the core particles cross 1/2 Well known “standard” way to mitigate SC-like (beam-beam) issues in colliders is to operate very near integer or half- integer in order to reduce tune shift –Why Booster working point is near integer? SBRs don’t allow to come closer than 0.2 –Can the tune be put just below 0.5, e.g. 0.45? This would allow ×3 intensity! –Requires good optics correction (control of β-beating for both on- and off-momentum, e.g. Tevatron second-order chroma correction). 6/12/15A.Valishev - IOTA/FAST update15