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The high-luminosity LHC (HiLumi LHC) upgrade with planned operation from 2025 onward has a goal of achieving a tenfold increase in the number of recorded collisions thanks to a doubling of the intensity per bunch (2.2e11 protons) and a reduction of β Ã to 15 cm. Such an increase would significantly expedite new discoveries and exploration. To avoid detrimental effects from long-range beam-beam interactions, the half crossing angle must be increased to 295 microrad. Without bunch crabbing, this large crossing angle and small transverse beam size would result in a luminosity reduction factor of 0.3 (Piwinski angle). Therefore, crab cavities are an important component of the LHC upgrade, and will contribute strongly to achieving an increase in the number of recorded collisions. The proposed crab cavities are electromagnetic devices with a resonance in the radio frequency (rf) region of the spectrum (400.789 MHz). They cause a kick perpendicular to the direction of motion (transverse kick) to restore an effective head-on collision between the particle beams, thereby restoring the geometric factor to 0.8 [K. Oide and K. Yokoya, Phys. Rev. A 40, 315 (1989).]. Noise injected through the rf/low level rf (llrf) system could cause significant transverse emittance growth and limit luminosity lifetime. In this work, a theoretical relationship between the phase and amplitude rf noise spectrum and the transverse emittance growth rate is derived, for a hadron machine assuming zero synchrotron radiation damping and broadband rf noise, excluding infinitely narrow spectral lines. This derivation is for a single beam. Both amplitude and phase noise are investigated. The potential improvement in the presence of the transverse damper is also investigated.

a b s t r a c tThe Large Hadron Collider (LHC) relies on Landau damping for longitudinal stability. To avoid decreasing the stability margin at high energy, the longitudinal emittance must be continuously increased during the acceleration ramp. Longitudinal blowup provides the required emittance growth. The method was implemented through the summer of 2010. Band-limited RF phase-noise is injected in the main accelerating cavities during the whole ramp of about 11 min. Synchrotron frequencies change along the energy ramp, but the digitally created noise tracks the frequency change. The position of the noiseband, relative to the nominal synchrotron frequency, and the bandwidth of the spectrum are set by predefined constants, making the diffusion stop at the edges of the demanded distribution. The noise amplitude is controlled by feedback using the measurement of the average bunch length. This algorithm reproducibly achieves the programmed bunch length of about 1.2 ns 2 , at flat top with low bunch-tobunch scatter and provides a stable beam for physics coast. The noise can be injected either in the beam phase loop or directly in the cavity voltage set point. These two different technical implementations are presented and their respective advantages analyzed. The performance of the algorithm and its further applications are also presented in this paper.

Radio frequency (rf) accelerating system noise can have a detrimental impact on the Large Hadron Collider (LHC) performance through longitudinal motion and longitudinal emittance growth. A theoretical formalism has been developed to relate the beam and rf station dynamics with the bunch length growth [T. Mastorides et al., Phys. Rev. ST Accel. Beams 13, 102801 (2010)]. Measurements were conducted at LHC to determine the performance limiting rf components and validate the formalism through studies of the beam diffusion dependence on rf noise. As a result, a noise threshold was established for acceptable performance which provides the foundation for beam diffusion estimates for higher energies and intensities. Measurements were also conducted to determine the low level rf noise spectrum and its major contributions, as well as to validate models and simulations of this system.

The LHC Bunch Clock is one of the most important accelerator signals delivered to the experiments. Being directly derived from the Radio Frequency driving the beams in the accelerator by a simple division of its frequency by a factor of 10, the Bunch Clock signal represents the frequency at which the bunches are crossing each other at each experiment. It is thus used to synchronize all the electronics systems in charge of event detection. Its frequency is around 40.079 MHz, but varies with beam parameters (energy, particle type, etc) by a few hundreds of Hz.The present paper discusses the quality of this Bunch Clock signal in terms of jitter. It is in particular compared to typical requirements of electronic components of the LHC detectors and put in perspective with the intrinsic jitter of the beam itself, to which this signal is related.