HL-LHC Crab Cavity Field Regulation and Resulting RF Noise Spectrum

The HL-LHC Low Level RF (LLRF) must fulfill three requirements: it must reduce the cavity impedance at the fundamental below the instability threshold, it must regulate the crab cavity voltage precisely (amplitude and phase), and it must provide a cavity field with a spectral purity resulting in negligible degradation of the integrated luminosity due to transverse emittance growth. In this note, we present a LLRF system that fulfills these objectives. We then provide an estimate of the crab cavity RF noise spectrum for this LLRF system, a key parameter to evaluate transverse emittance growth.