Integrable Optics for High Intensity Beams Jeffrey Eldred Sasha Valishev UChicago Workshop Nonlinear amp Collective Effects 28 Oct 2017 2 2 Jeffrey Eldred An RCS with Integrable Optics for the Fermilab PIPIII Upgrade ID: 710873
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Slide1
Advanced Proton Booster Design(Integrable Optics for High Intensity Beams)
Jeffrey Eldred
, Sasha
Valishev
UChicago
Workshop Nonlinear & Collective Effects
28 Oct 2017Slide2
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Jeffrey Eldred |
An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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Fermilab
Proton Accelerator FacilitySlide3
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(Proposed) PIP-III Intensity Upgrade
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An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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Rapid-Cycling Synchrotron Design
Modern RCS design calls for several features:
Dispersion-free drifts
, for RFLow momentum compaction factor, to avoid transition.
Low beta functions, for maximum emittance per aperture.Mitigation of collective instabilities, throughout the ramp.Integrable optics design is a promising innovation to provide significant nonlinear focusing with two invariants of motions.But first, it is necessary to demonstrate integrable optics is still helpful in the presence of strong space-charge forces.
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Nonlinear kick separable in elliptic coordinates:
Danilov-
Nagaitsev
Integral Design
Time-independent kick:
V. Danilov, S.
Nagaitsev
“Nonlinear Lattices with One or Two Analytic Invariants” PRST-AB 2010.Slide6
6
Integral Design with Periodicity
...
Multiple Periodic Cells:
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An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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Periodicity:
6
Circumference:
542 m
Bend-radius rho: 15.4 mMax Beta function:
35 mInsertion length: 11.2 mBetatron Tune: 16.8Insert Phase-Advance: 0.3Nonlinear t-value: 0.15Minimum c-value: 3 cmBeta at insert center: 4 mCorrected Chromaticity:
-7.7Natural Chromaticity: -33Second-order Chromaticity: -132
iRCS
v2 Lattice ParametersSlide8
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Synergia
Simulation
of Halo formed by
Beam Mismatched
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Jeffrey Eldred |
An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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Coasting proton beam with 3D PIC space-charge.Injection energy of
0.8 GeV
.Initial normalized emittance 20 mm mrad.2D Waterbag beam initially distributed along equipotential contours except with a 20% mismatch.500 revolutions of iRCS (3000 iterations of periodic cell).Phase advance through insert dΦ = 0.3Nonlinear strength parameter t = 0.31 Conventional Design, Low Intensity Beam (dQ = -0.05)2 Integrable Design, Low Intensity Beam (dQ = -0.05)3 Conventional Design, High Intensity Beam (dQ = -0.20)4 Integrable Design , High Intensity Beam (dQ = -0.20)
Simulation ParametersJeffrey Eldred | An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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RMS Beam Size
1 Conventional, Low Int.
2 Integrable, Low Int.
3 Conventional, High Int.
4 Integrable, High Int.
Jeffrey Eldred |
An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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Transverse Beam Halo
1 Conventional, Low Int.
2 Integrable, Low Int.
3 Conventional, High Int.
4 Integrable, High Int.Slide12
12
Cell
Betatron
Tune Distribution
1 Conventional, Low Int.
2 Integrable, Low Int.
3 Conventional, High Int.
4 Integrable, High Int.
Jeffrey Eldred |
An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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Ring
Betatron
Tune DistributionDescription90% Horizontal Tune Spread90% Vertical Tune Spread1 Conventional, Low Int.0.0440.0442 Integrable, Low Int.0.120.183 Conventional, High Int.0.160.16
4 Integrable, High Int.
0.150.25
Nonlinear ParametersSpace-charge tune shift dQ = -0.05, -0.20Phase advance through Insert dΦ = 0.3Nonlinear strength parameter t = 0.3
Jeffrey Eldred | An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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Mismatched
Waterbag
with Chromatic Tune Shift
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An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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Chromaticity doesn’t have to be zero, it just has to be matched between horizontal and vertical.Webb, Bruhwiler, Valishev
,
Nagaitsev, Danilov “Chromatic and Dispersive Effects in Nonlinear Integrable Optics” PR-AB (Submitted).Nominal momentum spread based on zero-charge longitudinal simulation of RF capture of injected beam.Chromaticity (matched horiz. & vert.): -33Chromatic tune-shift (nominal): 0.25%2 Integrable Design, Low Intensity, σp = 0 (Monoenergetic)5 Integrable Design, Low Intensity, σp = 0.250% (Nominal)Simulation Parameters
Jeffrey Eldred | An RCS with Integrable Optics for the Fermilab PIP-III Upgrade15
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6 Integrable WB, x20
σ
p
2 Integrable WB,
σ
p = 0
RMS Beam Size
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An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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5 Integrable WB, Nominal
σ
p
2 Integrable WB,
σ
p = 0
Transverse Beam Halo
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An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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5 Integrable WB, Nominal
σ
p
2 Integrable WB,
σ
p = 0
Cell
Betatron
Tune Distribution
The chromatic tune-shift occurs diagonally and the amplitude tune-spread occurs off-diagonally.
No evidence particles are bound by the resonance lines.
Jeffrey Eldred |
An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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Higher Periodicity Lattice,
Higher charge
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Jeffrey Eldred |
An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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Periodicity:
6
Circumference:
542 m
Bend-radius rho: 15.4 mMax Beta function:
35 mInsertion length: 11.2 mBetatron Tune: 16.8Insert Phase-Advance: 0.3Nonlinear t-value: 0.15Minimum c-value: 3 cmBeta at insert center: 4 mCorrected Chromaticity:
-7.7Natural Chromaticity: -33Second-order Chromaticity: -132
iRCS
v2 Lattice ParametersSlide21
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Periodicity:
12
Circumference:
636 m
Bend-radius rho: 15.4 mMax Beta x,y function: 25 mMax Dispersion function: 0.22 mRF Insertion length:
7.2 m, 2x 1.4mNL Insertion length: 12 mInsert Phase-Advance: 0.3Minimum c-value: 3 cmBeta at insert center: 2.2 mBetatron Tune: 21.6Natural Chromaticity: -74
iRCS v3 Lattice ParametersSlide22
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6 Periodicity 12,
dQ
= 0.4
4 Periodicity 6,
dQ
= 0.2
Cell
Betatron
Tune Distribution
Jeffrey Eldred |
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6 Periodicity 12,
dQ
= 0.4
4 Periodicity 6,
dQ
= 0.2
RMS Beam Size
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6 Periodicity 12,
dQ
= 0.4
4 Periodicity 6,
dQ
= 0.2
Transverse Beam Halo
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An RCS with Integrable Optics for the Fermilab PIP-III Upgrade
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Summary:Integrable optics provide a large nonlinear tune-spread
without introducing new resonances and can be used to
mitigate the formation of beam halo.Integrable optics is reasonably tolerant to space-charge and chromatic phase-errors.New lattice will examine advantages of high periodicity.Upcoming Work:Analyze particles trajectories to better understand the physics.Use random quad errors to break periodicity and investigate effects of integrable optics.Bunched beam with RF and 3D space-charge forces.Summary & Upcoming Work
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