LHC Radio Frequency Swing

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 0.539 T to 8.386 T
• finf 400.789 662 MHz with h35640 and
  2pR26658.883m
• 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

3
Proton acceleration

• We have
• E0 938.26 x106 eV
• 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 _at_ 40 MHz is 1/10 times
  the above RF frequency.

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.
5
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)
6
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.

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,)