1. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 1 Numerical Studies for Proton Improvement Plan (PIP) at Fermilab Leonid Vorobiev Muons, Inc., Batavia, IL 60510, USA

2. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 2 Introduction For several years I’ve been developing software and did accelerator designs for Fermilab and Muons Inc., related to : - Project X - Mu2e - Booster upgrade - Electron Cloud in Main Injector - Electron Lens (hollow e-beam) for collimation in LHC - Space Charge for HL-LHC - EGun, SRF Booster linac for FEL and other projects Now FNAL may be interested in continuing the work, in relation to PIP and PIP-II

3. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 3 List of Topics for PIP-II 1. Non-linear lattices with SC. Resonance extraction. 2. Multi-turn injection painting 3. Stripping foil heating/survival 4. Transition crossing. Acceleration scenarios. 5. Momentum stacking. Beam loading. Feedback. 6. Beam notching during injection into Booster 7. Linac/FEL. Electrons/Ions. SRF. Dynamics, Back- bombardment, 3D Space Charge, etc. 8. ECloud

4. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 4 1. Non-linear lattices with SC. Resonance extraction. Non-linear lattices in ORBIT: third-order resonance compared to pure linear lattice Ref.: http://beamdocs.fnal.gov/AD/DocDB/0034/003474/006/APC_meeting_Oct_14_09_final.pdf

5. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 5 1. Non-linear lattices with SC. Resonance extraction. Ref.: http://beamdocs.fnal.gov/AD/DocDB/0034/003474/006/APC_meeting_Oct_14_09_final.pdf

6. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 6 2. Multi-turn injection painting (MI) Horizontal (up), Vertical (bottom) Stripping Foil Kickers + Bumps Longitudinal Painting from 325 MHz Linac into 52.8 MHz Main Injector Ref.: http://beamdocs.fnal.gov/AD-public/DocDB/ShowDocument?docid=4134

7. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 7 3. Stripping foil issues Hits on the Foil Scenario A (582-turn injection) Particle hit number on the foil during 1st, 4th, and 6th cycles are: 62067, 162470, and 284034, respectively. The total hit number is 948322. Average number of interactions with foil =33 (for each injected particle). Hit density at the maximum of the distribution =1.31e+14 proton/mm^2 at 2.52e+11 particles injected at every turn. Ref.: http://journals.aps.org/prstab/pdf/10.1103/PhysRevSTAB.15.011002

8. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 8 4. Transition crossing. Acceleration scenarios. Rapid-cycling synchrotron FNAL Booster 20,000 turns acceleration ramp Synch. phase – self-consistent Works for Main Injector CERN SC 2013: http://beamdocs.fnal.gov/AD-public/DocDB/ShowDocument?docid=4340

9. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 9 5. Momentum stacking. Beam loading. Feedback. Mu2e Exp. at Fermilab: Extinction interval for mu2e detector: NO STRAY PROTONS Long. dynamics w/o (left), with (cent) Beam Loading. Histogram (right) CERN SC 2013: http://beamdocs.fnal.gov/AD-public/DocDB/ShowDocument?docid=4340

10. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 10 6. Beam notching during injection. Acceleration, Transition, Extraction. Notched beam presumably facilitate extraction. Survival during acceleration, Transition, 3D SC, Wakes Beam Loading, Synchro-beta res. CERN SC 2013: http://beamdocs.fnal.gov/AD-public/DocDB/ShowDocument?docid=4340

11. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 11 7. Linac/FEL e - /p/ions. DTL & SRF Back-bombardment, 3D SC, etc PIP – for protons Example FEL – for electrons – serve as software demo for PIP-2: RFQ, DTL normal-conducting/SRF. SuperFish 3D SC & Geometry EGun (z=0) + 3SRF Cavities + Undulator (z>120 cm, not shown)

12. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 12 7. FEL parameters Setup: EGun + SRFs + Undulator RF EGun: bore rad. =1.75 cm + SRF Cavity: cell 10.52 2. 1 0.0 7.0 1 5. -1 0 0 0 + Solenoid: POISSON -20..88 0 0 0 0 0 1 + cell 21.79 2. 1 0.0 7.0 2 5. -1 0 0 0 + cell 21.66688 2. 1 0.0 7.0 3 5 -1 0 0 0 + cell 16.02312 2. 1 0.0 7.0 4 5 -1 0 0 0 + Undulator (omitted) Credits: Parameters from S. Kurennoy, LANL

13. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 13 7. FEL e - BB, 3D SC, etc X (red),Y (blue) dynamics vs Z. Halo formation. FEL 700MHZ, X&Y Dynamics Particle densities contour lines (up), 3D (down) vs Z in phase units (degrees). Halo formation observed. Important: self-consistent synchronous phase σ impulse is made very long to demonstrate Back-Bombardment. In real FELs – shorter!

14. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 14 7. FEL e - BB, 3D SC, etc FEL 700MHZ, dynamics Energies (blue) and Current (green) vs Z in phase units (degrees). Longitudinal impulse is very long for sake of back-bombardment (BB) demonstration.

15. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 15

16. Muons, Inc. Numerical studies for PIP-2, Aug. 25, 2014L.G.Vorobiev 16 Summary of new work to be done 1.PIP-II Booster, Main Injector with Multi-Bunch + Nonlinear Lattice + 3D SC + Wakes -Injection, notching, acceleration, stripping -Painting, foil, transition X-ing, extraction -Beam Loading, Feedback -ECloud (trial, errors) 2. PIP-II Linacs with 3D SC, Real 3D Geometry + Synch. Phase - Ion Source, RFQ, DTL Linac, SRF,… 3. Additional PIP-II needs …