Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 1Muons, Inc.

Numerical Studies for Proton Improvement Plan (PIP) at Fermilab

Leonid Vorobiev

Muons, Inc., Batavia, IL 60510, USA

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

IntroductionFor 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

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 3Muons, Inc.

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

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 4Muons, Inc.

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

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 5Muons, Inc.

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

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 6Muons, Inc.

2. Multi-turn injection painting (MI)Horizontal (up), Vertical (bottom)

StrippingFoilKickers +Bumps

LongitudinalPainting from

325 MHz Linac into52.8 MHz

Main Injector

Ref.: http://beamdocs.fnal.gov/AD-public/DocDB/ShowDocument?docid=4134

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 7Muons, Inc.

3. Stripping foil issuesHits 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

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 8Muons, Inc.

4. Transition crossing. Acceleration scenarios.

Rapid-cycling synchrotron

FNAL Booster

20,000 turns acceleration ramp

Synch. phase –

self-consistentWorks for Main Injector

CERN SC 2013: http://beamdocs.fnal.gov/AD-public/DocDB/ShowDocument?docid=4340

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 9Muons, Inc.

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

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 10Muons, Inc.

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

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 11Muons, Inc.

7. Linac/FEL e-/p/ions. DTL & SRF Back-bombardment, 3D SC, etc

PIP – for protonsExample FEL – for electrons – serve as software

demo for PIP-2: RFQ, DTL normal-conducting/SRF.

SuperFish3D SC &Geometry

EGun (z=0) + 3SRF Cavities + Undulator (z>120 cm, not shown)

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 12Muons, Inc.

7. FEL parametersSetup: 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

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 13Muons, Inc.

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 Zin 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!

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 14Muons, Inc.

7. FEL e- BB, 3D SC, etcFEL 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.

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

Numerical studies for PIP-2, Aug. 25, 2014 L.G.Vorobiev 16Muons, Inc.

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 …