Analysis of beam loading compensation schemes at LHC
Analysis of beam loading compensation schemes at LHC injection Ivan Karpov and Philippe Baudrenghien
![LHC beam loading compensation schemes (BLCS) Half-detuning (HD) [1] Full-detuning (FD) [2] Cavity voltage](http://slidetodoc.com/presentation_image_h2/e9f76e5f5ced14de246df3728550309f/image-2.jpg "LHC beam loading compensation schemes (BLCS) Half-detuning (HD) [1] Full-detuning (FD) [2] Cavity voltage")
LHC beam loading compensation schemes (BLCS) Half-detuning (HD) [1] Full-detuning (FD) [2] Cavity voltage Phase modulation Peak beam rf current Required power Loaded quality factor 2
![Power consumption for constant amplitude of cavity voltage Instantaneous power [2, 3] Generator current](http://slidetodoc.com/presentation_image_h2/e9f76e5f5ced14de246df3728550309f/image-3.jpg "Power consumption for constant amplitude of cavity voltage Instantaneous power [2, 3] Generator current")
Power consumption for constant amplitude of cavity voltage Instantaneous power [2, 3] Generator current rf beam current 3
rf beam current Peak rf current 4
Optimal detuning in steady-state Defining peak detuning Phase derivative in different segments: 5
BLCS 1: modulation of beam phase in the SPS Injection segment LHC is operated with optimal detuning Before injection The peak power after injection 6
BLCS 2: flattened phase in the injection segment Injection segment Detuning in the LHC is a free parameter and phase is flattened to avoid phase errors For different segments we have: 7
Minimum power for BLCS 2 The peak power 8
General case Injection segment Similarly to BLCS 2, detuning in the LHC and phase derivative in the injection segment are free parameters For different segments we have: 9
Conclusions • Different beam loading compensation schemes were analyzed and compared. • The half-detuning scheme is most simplest and optimized scheme for beam loading compensation during injection process in synchrotrons. • For other schemes a newly injected train produces strong power transients that finally require the same peak power as for the halfdetuning scheme. 10
Thank you for your attention! References: 1. Daniel Boussard. RF power requirements for a high intensity proton collider; parts 1 (chapters I, III) and 2 (chapters IV, V, VI). CERN-SL-91 -16 -RFS, page 7 p, May 1991. 2. T. Mastoridis, P. Baudrenghien, and J. Molendijk. Cavity voltage phase modulation to reduce the high-luminosity Large Hadron Collider rf power requirements. Phys. Rev. Accel. Beams, 20(10): 101003, oct 2017. 3. J. Tückmantel, Cavity-Beam-Transmitter Interaction Formula Collection with Derivation, CERN-ATS-Note-2011 -002 TECH, (2011). 11
12
13
- Slides: 13