advanced beam manipulation, cooling, damping and stability 223
This method is primarily intended for the beams that have
significant asymmetries between phase planes. In particular,
flat beams are often generated in accelerators. For example,
SR rings naturally have y emittance much smaller than the x
emittance.
It has been shown by Derbenev that a triplet of skew
quadrupoles can transform such a flat beam to a vortex, as
illustrated in Fig. 10.51.
The beam with vortex-like phase space distribution can
be transformed further, noting that an edge of the solenoid
also creates a vortex-like phase space portrait for an initially
parallel beam.
Therefore, sending the vortex beam created by the skew
triplet into the solenoid with appropriate strength will result
in creating a round beam with zero angles — as shown in the
final step in Fig. 10.51.
The transformation described above can be used in many
accelerator systems. A particular example 21 uses this transformation to reduce space charge effects of flat beams in
damping rings with long straight sections by employing flatto-round and round-to-flat transformations at the beginnings
and exits of each section, respectively. The round beam in
straight sections will have lower space charge effects, improving the beam stability.
21 R. Brinkmann, Ya. Derbenev and K. Floettmann, Phys. Rev. ST Accel.
Beams 4, 053501 (2001).
This method is primarily intended for the beams that have
significant asymmetries between phase planes. In particular,
flat beams are often generated in accelerators. For example,
SR rings naturally have y emittance much smaller than the x
emittance.
It has been shown by Derbenev that a triplet of skew
quadrupoles can transform such a flat beam to a vortex, as
illustrated in Fig. 10.51.
The beam with vortex-like phase space distribution can
be transformed further, noting that an edge of the solenoid
also creates a vortex-like phase space portrait for an initially
parallel beam.
Therefore, sending the vortex beam created by the skew
triplet into the solenoid with appropriate strength will result
in creating a round beam with zero angles — as shown in the
final step in Fig. 10.51.
The transformation described above can be used in many
accelerator systems. A particular example 21 uses this transformation to reduce space charge effects of flat beams in
damping rings with long straight sections by employing flatto-round and round-to-flat transformations at the beginnings
and exits of each section, respectively. The round beam in
straight sections will have lower space charge effects, improving the beam stability.
21 R. Brinkmann, Ya. Derbenev and K. Floettmann, Phys. Rev. ST Accel.
Beams 4, 053501 (2001).