Abstract

The interaction between beam dynamics and the radio frequency (rf) station in circular colliders is complex and can lead to longitudinal coupled-bunch instabilities at high beam currents. The excitation of the cavity higher order modes is traditionally damped using passive devices. But the wakefield developed at the cavity fundamental frequency falls in the frequency range of the rf power system and can, in theory, be compensated by modulating the generator drive. Such a regulation is the responsibility of the low-level rf (llrf) system that measures the cavity field (or beam current) and generates the rf power drive. The Large Hadron Collider (LHC) rf was designed for the nominal LHC parameter of 0.55 A DC beam current. At 7 TeV the synchrotron radiation damping time is 13 hours. Damping of the instability growth rates due to the cavity fundamental (400.789 MHz) can only come from the synchrotron tune spread (Landau damping) and will be very small (time constant in the order of 0.1 s). In this work, the ability of the present llrf compensation to prevent coupled-bunch instabilities with the planned high luminosity LHC (HiLumi LHC) doubling of the beam current to 1.1 A DC is investigated. The paper conclusions are based on the measured performances of the present llrf system. Models of the rf and llrf systems were developed at the LHC start-up. Following comparisons with measurements, the system was parametrized using these models. The parametric model then provides a more realistic estimation of the instability growth rates than an ideal model of the rf blocks. With this modeling approach, the key rf settings can be varied around their set value allowing for a sensitivity analysis (growth rate sensitivity to rf and llrf parameters). Finally, preliminary measurements from the LHC at 0.44 A DC are presented to support the conclusions of this work.

Highlights

  • The high currents employed in modern light sources and circular accelerators lead to strong coupling of the bunch motion with the cavity impedance, which can overcome Landau and/or synchrotron radiation damping and cause coherent instabilities

  • Longitudinal coupled-bunch instability growth rates due to the cavity fundamental impedance were estimated for Large Hadron Collider (LHC) beams in the HiLumi era and for realistic cavity configurations using the experience from LHC operation

  • Significant stability margins are anticipated with the HiLumi beam, even with the oneturn feedback (OTFB) off

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Summary

INTRODUCTION

The high currents employed in modern light sources and circular accelerators lead to strong coupling of the bunch motion with the cavity impedance, which can overcome Landau and/or synchrotron radiation damping and cause coherent instabilities. A model approach is preferred to study the beam dynamics interaction with the rf system, estimate stability margins, and evaluate the sensitivity to system parameters. Such an approach has been used before at PEP-II. The sensitivity of beam instabilities to individual llrf parameters, the effectiveness of alternative operational algorithms, and the possible tradeoffs between rf loop and beam stability were studied [3,4,5]. Estimates of longitudinal coupled-bunch instabilities for the HiLumi LHC are presented [9]. X includes preliminary LHC measurements of instability growth rates used to validate the formalism presented in this work

LLRF LOOPS
FUNDAMENTAL IMPEDANCE ESTIMATION
STABILITY THRESHOLD
GROWTH RATE ESTIMATION
GROWTH RATE SENSITIVITY TO LLRF PARAMETERS
Optimizing the llrf system in the presence of beam
VIII. BEAM CURRENT THRESHOLD ESTIMATION
GROWTH RATE SENSITIVITY TO BUNCH LENGTH
MEASUREMENTS OF LONGITUDINAL COUPLED-BUNCH INSTABILITIES
CONCLUSIONS
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