4 Impedance and Collective Effects
169
4.6.10.1 Electron Lenses
The basic principle of a compensation of proton–proton (or antiproton) collisions
with an “electron lens” implies that the proton (antiproton) beam travels through
a counter-rotating high current electron beam (“electron lens”) [189, 190]. The
negative electron space charge can reduce the effect from the collision with the
other proton beam.
An electron beam with a size much larger than the proton beam can be used to
shift the tune of the proton beam (“linear lens”). When the current in the electron
bunches can be varied fast enough, the tune shift can be different for the different
proton bunches, thus correcting PACMAN tune shifts.
When the electron charge distribution is chosen to be the same as the counterrotating proton beam, the non-linear focusing of this proton beam can be compensated (“non-linear lens”). When it is correctly applied, the tune spread in the beam
can be strongly reduced.
Such lenses have been constructed at the Tevatron at Fermilab [190] and
experiments are in progress.
4.6.10.2 Electrostatic Wire
To compensate the tune spread from long-range interactions, one needs a non-linear
lens that resembles a separated beam. At large enough separation, the long-range
force changes approximately with 1/r and this can be simulated by a wire parallel
to the beam [191].
In order to compensate PACMAN effects, the wires have to be pulsed according
to the bunch filling scheme. Tests are in progress at the SPS to study the feasibility
of such a compensation for the LHC.
4.6.10.3 Möbius Scheme
The beam profiles of e + e − colliders are usually flat, i.e. the vertical beam size is
much smaller than the horizontal beam size. Some studies indicate that the collision
of round beams, even for e + e − colliders, show more promise for higher luminosity
since larger beam–beam parameters can be achieved. Round beams can always be
produced by strong coupling between horizontal and vertical planes. A more elegant
way is the so-called Möbius lattice [192, 193]. In this lattice, the horizontal and
vertical betatron oscillations are exchanged by an insertion. A horizontal oscillation
in one turn becomes a vertical oscillation in the next turn and vice versa. Tests with
such a scheme have been done at CESR at Cornell [193].
169
4.6.10.1 Electron Lenses
The basic principle of a compensation of proton–proton (or antiproton) collisions
with an “electron lens” implies that the proton (antiproton) beam travels through
a counter-rotating high current electron beam (“electron lens”) [189, 190]. The
negative electron space charge can reduce the effect from the collision with the
other proton beam.
An electron beam with a size much larger than the proton beam can be used to
shift the tune of the proton beam (“linear lens”). When the current in the electron
bunches can be varied fast enough, the tune shift can be different for the different
proton bunches, thus correcting PACMAN tune shifts.
When the electron charge distribution is chosen to be the same as the counterrotating proton beam, the non-linear focusing of this proton beam can be compensated (“non-linear lens”). When it is correctly applied, the tune spread in the beam
can be strongly reduced.
Such lenses have been constructed at the Tevatron at Fermilab [190] and
experiments are in progress.
4.6.10.2 Electrostatic Wire
To compensate the tune spread from long-range interactions, one needs a non-linear
lens that resembles a separated beam. At large enough separation, the long-range
force changes approximately with 1/r and this can be simulated by a wire parallel
to the beam [191].
In order to compensate PACMAN effects, the wires have to be pulsed according
to the bunch filling scheme. Tests are in progress at the SPS to study the feasibility
of such a compensation for the LHC.
4.6.10.3 Möbius Scheme
The beam profiles of e + e − colliders are usually flat, i.e. the vertical beam size is
much smaller than the horizontal beam size. Some studies indicate that the collision
of round beams, even for e + e − colliders, show more promise for higher luminosity
since larger beam–beam parameters can be achieved. Round beams can always be
produced by strong coupling between horizontal and vertical planes. A more elegant
way is the so-called Möbius lattice [192, 193]. In this lattice, the horizontal and
vertical betatron oscillations are exchanged by an insertion. A horizontal oscillation
in one turn becomes a vertical oscillation in the next turn and vice versa. Tests with
such a scheme have been done at CESR at Cornell [193].