LHC Radio Frequency Swing P. Baudrenghien AB/RF

Frequency Program for Synchrotrons LHC conceptual design 1995 B is the guide field in T: 0.539 T to 8.386 T finf = 400.789 662 MHz with h=35640 and 2pR=26658.883m r is the bending radius r = 2784.32 m E0 is the rest energy of the particle/ion being accelerated (in eV) q is the number of elementary charges in the particle/ion 15 December 2003 LEADE meeting

Proton acceleration E0 = 938.26 x106 eV We have: q = 1 The RF frequency ramps from 400.788 790 MHz at injection (0.539 T) to 400.789 658 MHz at top energy (8.386 T) N.B.: The bunch frequency @ 40 MHz is 1/10 times the above RF frequency. 15 December 2003 LEADE meeting

Ions Acceleration E0 = rest energy of ion = sum of energy of protons, neutrons (and electrons) minus binding energy q = number of protons (minus number of electrons) In all cases E0/q will be larger than the case of proton. Ions are less relativistic at injection and the frequency swing is larger. 15 December 2003 LEADE meeting

Lead ion acceleration For fully stripped lead Pb20882+ we have: q = 82 (82 protons) E0 = 193.683 956 GeV considering the 82 p and 126 n with mp = 938.259 MeV, mn = 939.553 MeV and a binding energy of 7.87 MeV/nucleon E0/q= 2.362 x109 (to be compared to 0.93826 x 109 for protons) The RF frequency ramps from 400.784 139 MHz at injection (0.539 T) to 400.789 639 MHz at top energy (8.386 T) 15 December 2003 LEADE meeting

Other ions ? Considering only fully stripped ions: for In11549+ we get E0 = 107.08 GeV and E0/q= 2.185 x109 for Kr8436+ we get E0 = 78.215 GeV and E0/q= 2.173 x109 for Ar4018+ we get E0 = 37.24 GeV and E0/q= 2.069 x109 for Sn12050+ we get E0 = 111.74 GeV and E0/q= 2.235 x109 for O168+ we get E0 = 14.90 GeV and E0/q= 1.862 x109 In all cases the frequency swing is smaller than with Pb20882+ (E0/q= 2.362 x109) N.B.: The above figures for E0 are approximations using the 7.87 MeV/nucleon figure for binding energy. Exact for Pb only. 15 December 2003 LEADE meeting

Remarks In theory the frequency swing is not relevant to the experiment since you are only concerned by the RF during collisions We do not guarantee any meaningful RF when no beam is in the machine (degaussing, access, shutdown,…) 15 December 2003 LEADE meeting