Jeffrey Eldred, Sasha Valishev AAC Workshop 2016 Integrable RCS as a proposed replacement for Fermilab Booster Jeffrey Eldred, Sasha Valishev AAC Workshop 2016 1 1 1 1

Integrable Optics 2 2 2 2

Integrable Optics for High Intensity Integrable optics provides a way to provide strong nonlinear focusing while avoiding parametric resonances. Application to high-intensity proton beams: Laslett betatron tune spread can cross resonances. Landau damping mitigates collective effects. Increase beam intensity be a factor of 4-6. Integrable optics as part of a comprehensive proposal to replace the Fermilab Booster with an RCS. 3 3

Integrable Optics safdsf Integrable optics avoids parametric resonances. Integrable optics nonlinearity provides Landau damping safdsf From S. Nagaitsev 4 4

FAST/IOTA Facility FAST: Fermilab Accelerator Science and Technology 150 MeV electron superconducting Linac, serves as R&D for ILC 2.7 MeV proton RFQ IOTA ring for physics experiments IOTA: Integrable Optics Test Accelerator 5 5

Fermilab High Intensity Proton Program 6 6 6 6

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Proton Improvement Plan II (PIP-II) New 800 MeV SRF Linac Proton power at 120 GeV to increase from 700kW to 1.2MW in year 2019. Laslett Tune-shift from PIP-II 8 8

LBNF/DUNE Era at Fermilab “Long Baseline Neutrino Facility” (LBNF) beamline to produce neutrinos for the “Deep Underground Neutrino Experiment” (DUNE). P5 Report: “Form a new international collaboration to design and execute a highly capable LBNF hosted by the US. […] LBNF is the highest priority project in its lifetime.” from DUNE CDR 9 9

DUNE Neutrino Exposure Req. P5 Report: “[...] , we set as the goal a mean sensitivity to CP violation of better than 3σ [...] over more than 75% of the range of possible values of the unknown CP-violating phase δCP” Corresponds to 900 kt MW yr. Keep PIP-II Proton Power: 1.2MW, 50kt -> 15 years Upgrade Proton Power: 5MW, 20kt -> 9 years from DUNE CDR 10 10

Limitations of Fermilab Booster Fermilab Booster is over 45 years old! Reliability concerns. RF cavities will not sustain a ramp rate beyond 20 Hz. Impedance problem at Transition Energy: No beampipe in magnets, impedance problem. ~200kV deceleration during transition crossing. Booster beam is slip-stacking in the Fermilab Recycler which may not be possible at higher intensity. Slip-stacking is an accumulation technique which doubles the number of Booster batches that can be stored in the Main Injector. 11 11

Siting for Booster Replacement 12 Siting for Booster Replacement Image credit Steve Dixon 12 12 12 12 12

Integrable RCS Design 13 13 13 13

RCS Lattice Requirements Standard Requirements: Bounded beta functions. Chromaticity correction. Modern RCS Design: No transition crossing. Long dispersion-free drifts. Separate function magnets. Integrable optics Removes parametric resonances, provides Landau damping Beam intensity may increase by a factor of 4-6. 14 14

Lattice Requirements for IO Integrable lattices are composed of: Arcs with pi-integer betatron phase-advance. Dispersion-free drifts, with horizontal and vertical beta functions matched. Special nonlinear octupole magnets in those drifts. The horizontal and vertical chromaticity should match. From S. Nagaitsev 15 15

iRCS Example Lattice 16 16

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Other Considerations Drift space provides ample sufficient space for 1.2 MV and 20Hz ramp rate. Room to upgrade in the future. Switch from parallel-biased ferrite cavities to perpendicular-biased ferrite cavities Active R&D effort on perpendicular-biased Yttrium-Iron-Garnet cavities. Resonant-circuit sinusoidal magnet ramp Longitudinal emittance after capture of 0.08 eVs Requires a 1-2ms fill time from a 5mA linac. Requires adiabatic capture or aggressive chopping. Harmonic cavity could be used to further control emittance. 18 18

Future Work on iRCS Design General High-Intensity RCS Research Harmonic cancellation of sextupoles. H- stripping and chicane design. Target design for 2-5 MW beams. High-Intensity Integrable Optics Synergia simulation with both space-charge forces and integrable optics. Transverse phase-space painting scheme. Lattice optimization incorporated with Synergia simulation. 19 19

Thank you! 20 20 20 20

Traditional Approach: Transverse Focusing Four degrees of freedom: x, x’, y, y’ Betatron Oscillations: 21 21

The Problem is Parametric Resonances octupole If the betatron frequency is a rational multiple of the revolution frequency, there is a parametric resonance. The orbit errors accumulate over many revolutions and lead to particle loss. 22 22

Tune Diagram The betatron tunes are carefully picked to avoid parametric resonances. As the beam intensity increases, the betatron tune spread increases and losses become unavoidable. 23 23

Nonlinear Magnet 24 24

Novel Features of IOTA: Nonlinear Magnets for Integrable Optics Electron Lens for space-charge compensation Optical Stochastic Cooling 25