CERN LHC Project Report 91 (revised) (1997)
Landau Damping, Dynamic Aperture and Octupoles in LHC
J. Gareyte, J.P. Koutchouk and F. Ruggiero
April 1997
Abstract:
Maximization of the dynamic aperture and Landau damping of the
collective instabilities are partly conflicting requirements.
On the one hand, the
non-linearities of the lattice must be minimized at large
oscillation amplitude to guarantee the stability of the single particle motion.
On the other hand, a
spread of the betatron frequencies is needed for
the stability of the collective motion of
bunches of particles; this requires non-linearities effective
at small amplitudes. We show in this note that the `natural' spread of
betatron tunes due to the field imperfections is inadequate
for Landau damping.
An octupole scheme is required to
provide collective stability at high energy. At low energy it may be used
to find the optimum between the correction of the octupolar field imperfections
and Landau damping. The solution of the stability problem taking into
account the two degrees of freedom of the transverse motion allows a
significant saving in octupole strength
even though a safety margin is included: 144 octupoles with
a magnetic length of 32 cm are
needed, leaving some reserve slots for other correctors. The present localization close
to the lattice quadrupoles is well adapted for Landau damping, but
unfavourable for the correction of the octupolar imperfection of the
dipoles. Depending on the multipolar errors in the dipoles, octupolar and skew
octupolar spool pieces may have to be envisaged.
F. Ruggiero
Sat Apr 12 17:11:35 1997