[Paper Review] Flat Bunches with a Hollow Distribution for Space Charge Mitigation

Adrian Oeftiger, Hannes Bartosik+3 more|arXiv (Cornell University)|May 5, 2016

Particle Accelerators and Free-Electron Lasers6 references3 citations

TL;DR

This paper proposes using longitudinally hollow bunches with a dipolar parametric excitation in CERN's Proton Synchrotron Booster to mitigate transverse space charge effects. By modulating the RF phase to excite a 1:1 parametric resonance, the bunch core is depleted, creating a hollow phase space distribution that reduces peak line charge density. The key result is a 24.8–34.8% reduction in horizontal emittance blow-up and significantly lower space charge tune shift compared to standard parabolic bunches during the PS injection plateau.

ABSTRACT

Longitudinally hollow bunches provide one means to mitigate the impact of transverse space charge. The hollow distributions are created via dipolar parametric excitation during acceleration in CERN's Proton Synchrotron Booster. We present simulation work and beam measurements. Particular emphasis is given to the alleviation of space charge effects on the long injection plateau of the downstream Proton Synchrotron machine, which is the main goal of this study.

Motivation & Objective

• To mitigate transverse space charge effects during the 1.2 s injection plateau in CERN's Proton Synchrotron (PS), which limits high-brightness LHC beam performance.
• To develop a reliable method for creating longitudinally hollow bunches in the PSB with minimal changes to the existing operational cycle.
• To compare the impact of space charge on beam quality—specifically emittance blow-up and tune shift—between hollow and standard parabolic bunches.
• To validate that hollow bunches reduce peak line charge density and broaden momentum distributions, thereby decreasing the transverse space charge detuning effect.

Proposed method

• A dipolar parametric resonance is excited in the PSB using phase modulation of the RF phase loop, with driving frequency ω_drive ≈ 0.9ω_S,lin to deplete the bunch core.
• The excitation is applied via a phase loop feedback system that modulates the RF reference phase φ_rf(t) = φ_S + φ̂_drive·sin(ω_drive·t) around the synchronous phase.
• The 1:1 resonance condition (m:n = 1:1) is used to maximize core depletion and achieve a uniform azimuthal distribution of particles in longitudinal phase space.
• Longitudinal emittance ε_z is tuned primarily by adjusting the excitation amplitude φ̂_drive, while duration is optimized to maximize phase space coverage.
• Beam parameters are measured via tomography and wire scans at 15 ms after PS injection and 20 ms before second batch injection.
• Horizontal emittance ε_x is reconstructed by convolving the measured momentum distribution with the betatron distribution, using a least-squares fit to match the measured profile.

Experimental results

Research questions

• RQ1 Can longitudinally hollow bunches created in the PSB reduce transverse emittance growth during the PS injection plateau?
• RQ2 To what extent does the hollow bunch profile reduce the space charge tune shift compared to standard parabolic bunches?
• RQ3 How does the beam's momentum distribution in hollow bunches affect the validity of the Gaussian emittance model (Eq. 2)?
• RQ4 What is the optimal excitation amplitude and duration for maximizing phase space coverage and minimizing peak line density?
• RQ5 How does the emittance blow-up depend on brightness and bunch length for hollow versus parabolic bunches under identical RF voltage conditions?

Key findings

• Hollow bunches achieved a 90% reduction in peak line charge density compared to a theoretical ideal rectangular profile, significantly lowering space charge effects.
• The vertical emittance blow-up was reduced by 24.8–34.8% for hollow bunches compared to parabolic bunches when normalized to the same space charge tune shift.
• The real transverse space charge tune shift for hollow bunches was 12% lower than predicted by the Gaussian model due to reduced λ_max and increased σ_x.
• The Gaussian model underestimated the emittance for hollow bunches by 24.8–34.8%, confirming that Eq. (2) is invalid for non-Gaussian momentum distributions.
• For fixed RF voltage (80 kV), the emittance blow-up was consistently lower for hollow bunches across all brightness levels, demonstrating superior space charge mitigation.
• The method achieved a reliable, repeatable creation of hollow bunches with minimal changes to the PSB operational cycle, enabling transfer to the PS without disruption.