1. LHC Radio Frequency Swing
P. Baudrenghien AB/RF

2. Frequency Program for Synchrotrons
LHC conceptual design 1995
B is the guide field in T: T to T
finf = MHz with h=35640 and 2pR= m
r is the bending radius r = 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

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

4. 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

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

6. Other ions ? Considering only fully stripped ions:
for In we get E0 = GeV and E0/q= x109
for Kr we get E0 = GeV and E0/q= x109
for Ar we get E0 = GeV and E0/q= x109
for Sn we get E0 = GeV and E0/q= x109
for O168+ we get E0 = GeV and E0/q= x109
In all cases the frequency swing is smaller than with Pb (E0/q= 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

7. 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