4 Impedance and Collective Effects
145
A number of simulation tools have been developed over the years in order to
study the electron cloud single-bunch instability for short bunches via direct particle
tracking. The simulations of electron cloud build-up are generally treated separately,
since they make use of a weak-strong approach, in which the beam is rigid
and is approximated by bunches with static transverse and longitudinal Gaussian
distributions, while the electrons are macroparticles. Build-up simulations need to
be run prior to the instability simulations, because they provide the necessary input
on the transverse distribution of the electron cloud density at saturation just before
the arrival of a bunch. A variety of simulation codes are presently available for this
purpose [150]. Fully self-consistent computations, in which the cloud generation
over a bunch train around the ring as well as the resulting bunch instabilities, are
treated by a single program are still under development. The existing simulation
programs to study the electron cloud instabilities model the interaction of a single
bunch with an electron cloud on successive turns. The cloud is always assumed to
be generated by the preceding bunches, and can be considered initially uniform or
the distribution is imported from a build-up code. The electrons give rise to a headto-tail wake field, which amplifies any initial small deformation in the bunch offset,
e.g. due to the finite number of macroparticles in the simulation. All simulation
tools that have been developed for this study are essentially of the strong–strong
type, since the purpose is to investigate how the bunch particles are affected by
the electron cloud via the continuous interaction. In particular, electrons are always
modeled as macroparticles either concentrated at one or several locations along
the ring or uniformly smeared along the axis of the machine. The bunch consists
of macroparticles or of microbunches with a fixed transverse size. The bunch is
then subdivided into slices, which interact in sequence with the electrons of the
cloud, creating the distortion of the initially uniform cloud distribution that can
affect the body and tail of the bunch. The electric fields of the electrons and of
the beam acting mutually on each other are calculated by means of a ParticleIn-Cell (PIC) algorithm. The transformation of the 6D phase-space vectors of the
beam particles between two kick points is achieved using the appropriate transport
matrices or nonlinear tracking. The field of the electron cloud acting on itself can
be optionally included, but in general does not seem to play a significant role in
this type of mechanisms and hence it is neglected. For the purpose of studying the
interplay of electron cloud instability with other mechanisms, the simulation codes
contain synchrotron motion, chromaticity and usually additional options to model
the action of an independent impedance source beside the electron cloud, as well as
space charge and detuning with amplitude.
4.5.3 Mitigation and Suppression
There are at least three possible actions to reduce, or even suppress, the electron
cloud: (i) reducing the production rate of primary electrons or confining their motion
to a region where they are not likely to do any harm; (ii) eliminating the possibility
145
A number of simulation tools have been developed over the years in order to
study the electron cloud single-bunch instability for short bunches via direct particle
tracking. The simulations of electron cloud build-up are generally treated separately,
since they make use of a weak-strong approach, in which the beam is rigid
and is approximated by bunches with static transverse and longitudinal Gaussian
distributions, while the electrons are macroparticles. Build-up simulations need to
be run prior to the instability simulations, because they provide the necessary input
on the transverse distribution of the electron cloud density at saturation just before
the arrival of a bunch. A variety of simulation codes are presently available for this
purpose [150]. Fully self-consistent computations, in which the cloud generation
over a bunch train around the ring as well as the resulting bunch instabilities, are
treated by a single program are still under development. The existing simulation
programs to study the electron cloud instabilities model the interaction of a single
bunch with an electron cloud on successive turns. The cloud is always assumed to
be generated by the preceding bunches, and can be considered initially uniform or
the distribution is imported from a build-up code. The electrons give rise to a headto-tail wake field, which amplifies any initial small deformation in the bunch offset,
e.g. due to the finite number of macroparticles in the simulation. All simulation
tools that have been developed for this study are essentially of the strong–strong
type, since the purpose is to investigate how the bunch particles are affected by
the electron cloud via the continuous interaction. In particular, electrons are always
modeled as macroparticles either concentrated at one or several locations along
the ring or uniformly smeared along the axis of the machine. The bunch consists
of macroparticles or of microbunches with a fixed transverse size. The bunch is
then subdivided into slices, which interact in sequence with the electrons of the
cloud, creating the distortion of the initially uniform cloud distribution that can
affect the body and tail of the bunch. The electric fields of the electrons and of
the beam acting mutually on each other are calculated by means of a ParticleIn-Cell (PIC) algorithm. The transformation of the 6D phase-space vectors of the
beam particles between two kick points is achieved using the appropriate transport
matrices or nonlinear tracking. The field of the electron cloud acting on itself can
be optionally included, but in general does not seem to play a significant role in
this type of mechanisms and hence it is neglected. For the purpose of studying the
interplay of electron cloud instability with other mechanisms, the simulation codes
contain synchrotron motion, chromaticity and usually additional options to model
the action of an independent impedance source beside the electron cloud, as well as
space charge and detuning with amplitude.
4.5.3 Mitigation and Suppression
There are at least three possible actions to reduce, or even suppress, the electron
cloud: (i) reducing the production rate of primary electrons or confining their motion
to a region where they are not likely to do any harm; (ii) eliminating the possibility