4 Impedance and Collective Effects
143
multiplication happening over the falling edge of the bunch can reach levels as to
render the beam unstable. Even coasting beams are not immune from electron cloud
problems. The electrons produced from residual gas ionization remain trapped in the
transverse potential of the uniform beam and tend to accumulate to very high central
density values. The electrons created at the chamber walls (e.g. from beam loss) are
accelerated and decelerated in the beam field and eventually hit the chamber with the
same energy with which they were emitted. Multipacting can play here a role, since
electrons can gain energy and create secondaries when hitting the wall, if the beam
line density is perturbed. The interaction of the coasting beam with the electrons can
make noise evolve into an unstable coupled oscillation, called e–p instability, which
was widely studied already at the beginning of the 70s [138, 139]. While the singlebunch instability described earlier in this section can be treated separately from the
build-up of the electron cloud that causes it, in all other cases the two processes are
coupled together and need to be solved with a joint model.
Electron cloud instabilities for short bunches have been observed in form of
emittance growth and beam loss at the KEKB LER, at the CERN PS, SPS and
LHC, and at the PEP-II LER. At the KEKB LER a blow-up of the vertical beam
size was already observed at the early commissioning time [140]. This blowup was not accompanied by any coherent beam motion, which could be easily
suppressed by transverse feedback and chromaticity, and the blow-up was only
seen in multi-bunch operation with a narrow bunch spacing. The single-bunch
two-stream instability provided a plausible explanation of the observed beam
blow-up [141]. This explanation has since been reinforced by the simultaneous
observation of a tune shift along the bunch train, which appears for the same bunches
exhibiting vertical size blow-up. Also the experimental evidence that the installation
of solenoids around the ring could increase the instability threshold in regular
operation shows the relation between electron cloud and the instability. At the
CERN SPS the electron cloud has been observed since the ring has been regularly
operated with LHC-type bunch trains [142] and it has been held responsible for
strong transverse instabilities. In the horizontal plane a low order coupled bunch
instability develops within a few tens of turns after injection. In the vertical plane,
a single-bunch head tail instability rises on a much shorter time. The reason of the
different behavior in the two transverse planes is ascribed to the confinement of the
electron cloud mostly in dipole regions, which can limit the intra-bunch electron
pinching in the horizontal plane and therefore inhibit the single-bunch mechanism
for instability. The horizontal (coupled-bunch) instability is cured by means of a
transverse feedback system. Similar to the situation at the KEKB LER, running the
SPS at high positive chromaticity can cure the vertical instability [143]. Upstream
from the SPS, when the nominal LHC beam was generated by the PS machine,
one of the standard signatures of the electron cloud was observed shortly before
extraction: a baseline drift in electrostatic devices. However, the beam resided too
shortly in the machine to become unstable, even if a dedicated experiment proved
the onset of an electron cloud instability on the short bunches, if they are kept in
the machine for a sufficiently long time. In the LHC, transverse beam instabilities
affecting the last bunches of long 25 ns trains in both transverse planes have been
143
multiplication happening over the falling edge of the bunch can reach levels as to
render the beam unstable. Even coasting beams are not immune from electron cloud
problems. The electrons produced from residual gas ionization remain trapped in the
transverse potential of the uniform beam and tend to accumulate to very high central
density values. The electrons created at the chamber walls (e.g. from beam loss) are
accelerated and decelerated in the beam field and eventually hit the chamber with the
same energy with which they were emitted. Multipacting can play here a role, since
electrons can gain energy and create secondaries when hitting the wall, if the beam
line density is perturbed. The interaction of the coasting beam with the electrons can
make noise evolve into an unstable coupled oscillation, called e–p instability, which
was widely studied already at the beginning of the 70s [138, 139]. While the singlebunch instability described earlier in this section can be treated separately from the
build-up of the electron cloud that causes it, in all other cases the two processes are
coupled together and need to be solved with a joint model.
Electron cloud instabilities for short bunches have been observed in form of
emittance growth and beam loss at the KEKB LER, at the CERN PS, SPS and
LHC, and at the PEP-II LER. At the KEKB LER a blow-up of the vertical beam
size was already observed at the early commissioning time [140]. This blowup was not accompanied by any coherent beam motion, which could be easily
suppressed by transverse feedback and chromaticity, and the blow-up was only
seen in multi-bunch operation with a narrow bunch spacing. The single-bunch
two-stream instability provided a plausible explanation of the observed beam
blow-up [141]. This explanation has since been reinforced by the simultaneous
observation of a tune shift along the bunch train, which appears for the same bunches
exhibiting vertical size blow-up. Also the experimental evidence that the installation
of solenoids around the ring could increase the instability threshold in regular
operation shows the relation between electron cloud and the instability. At the
CERN SPS the electron cloud has been observed since the ring has been regularly
operated with LHC-type bunch trains [142] and it has been held responsible for
strong transverse instabilities. In the horizontal plane a low order coupled bunch
instability develops within a few tens of turns after injection. In the vertical plane,
a single-bunch head tail instability rises on a much shorter time. The reason of the
different behavior in the two transverse planes is ascribed to the confinement of the
electron cloud mostly in dipole regions, which can limit the intra-bunch electron
pinching in the horizontal plane and therefore inhibit the single-bunch mechanism
for instability. The horizontal (coupled-bunch) instability is cured by means of a
transverse feedback system. Similar to the situation at the KEKB LER, running the
SPS at high positive chromaticity can cure the vertical instability [143]. Upstream
from the SPS, when the nominal LHC beam was generated by the PS machine,
one of the standard signatures of the electron cloud was observed shortly before
extraction: a baseline drift in electrostatic devices. However, the beam resided too
shortly in the machine to become unstable, even if a dedicated experiment proved
the onset of an electron cloud instability on the short bunches, if they are kept in
the machine for a sufficiently long time. In the LHC, transverse beam instabilities
affecting the last bunches of long 25 ns trains in both transverse planes have been