simplified modeling of space charge losses in booster at injection alexander valishev june 17, 2015

Simplified Modeling of Space Charge Losses in Booster at InjectionAlexander ValishevJune 17, 2015

A.Valishev - IOTA/FAST update2

Motivation and Outline

6/12/15

• Another look at incoherent Space Charge effect in Booster at injection aiming toa) 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 MeVSC Linac

2/11/2015V.Shiltsev | FNAL Institutional review, 02/10-13/2015

new 8-12 GeV “smart” RCSi-Booster

120 GeV RCSMain Injector

8 GeV Recycler

?>2 MWtarget


Approach and Previous Work

6/12/15

• 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


Modeling Tools

6/12/15

• 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.


Booster Parameters in Simulation

6/12/15

Energy 400 MeV (β=0.713, γ=1.426)URF 0.7 MV

Qs 0.078 (ωs=35 kHz)

Bucket size 4.2×10-3

Energy spread 2.1×10-3 (σz=1.26 m)

Transverse emittance

15 mm×mrad (95% normalized)

Aperture Ax=2.86 cm, Ay=2.08 cmNp 0.42×1013 in 84 bunches

SC tuneshift ΔQx=-0.197, ΔQy=-0.307

Betatron tunes Qx=6.70, Qy=6.80

Chromaticity Cx=-20, Cy=-14


Lattice Used in Simulation

6/12/15

a) 24-cell fully symetrical FODO (V.Kapin)b) 24-cell with 10% beta-beatc) 24-cell with 20% beta-beatd) Actual Booster (C.Y.Tan)

– Chromaticity (-30, +13)?


Results – FMA (a)

6/12/15


Results – FMA (a) As=0

6/12/15


Results – FMA (a) As=1

6/12/15


Results – FMA (b) As=1

6/12/15


Results – FMA (c) As=1

6/12/15


Results – Multiparticle Tracking

6/12/15

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 4×1012 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 update

simplified modeling of space charge losses in booster at injection alexander valishev june 17, 2015

Documents