Bunch compressors. ILC Accelerator School May 20 2006 Eun-San Kim Kyungpook National University Korea. Locations of bunch compressors in ILC. BCs locates between e - (e + ) damping rings and main linacs, and make bunch length reduce from 6 mm rms to 0.15 mm rms.
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ILC Accelerator School
May 20 2006
Kyungpook National University
1st stage ILC : 500 GeV
2nd stage ILC : 1 TeV
- extension of main linac
- moving of SR and BC
- Such beams with long bunch length tend to reduce effects of
beam instabilities in damping rings.
- Thus, beams are compressed after the damping rings.
- to prevent large energy spread in the linac due to the curvature of the rf.
- to reduce the disruption parameter ( ~ sz) :
(ratio of bunch length to strength of mutual focusing between colliding beams)
- Required bunch length in ILC is 0.15 mm rms.
(1) by introducing an energy-position correlation along the bunch with
an RF section at zero-crossing of voltage
(2) and passing beam through a region where path length isenergy dependent
: this is generated by bending magnets to create dispersive regions.
lower energy trajectory
center energy trajectory
higher energy trajectory
Chicanes as a Wiggler
Arc as a FODO-compressor
z : longitudinal position of a particle with respect to bunch center
krf = 2p frf/c
reference energy of the beam is changed from Eo to E1.
Initial (Ei) and final (Ef) energies of a given particle are
To first order in eVrf/Eo << 1,
In a linear approximation for RF,
In a wiggler (or chicane),
In a linear approximation R56 >> T566d1,
For frf= p/2, R66=1, the transformation matrix is sympletic,
which means that longitudinal emittance is a conserved quantitiy.
If a particle at reference energy is bent by qo, a particle with relative energy error d is bent by q = qo/ (1+d).
Path length from first to final bending magnets is
Difference in path length due to relative energy error is
By performing a Taylor expansion about d = 0
For large d, d2 and d3 terms may cause non-linear deformations of the
phase space during compression.
First-order path length dependence is
final bunch lengthis
crossing of voltage, that is R66 = 1, there is some damping
(or antidamping) of the longitudinal phase space,
associated with acceleration (or deceleration).
Radiation power P ~ N
(N : number of electrons in a bunch)
Radiation power P ~ N2
Coherent radiation forlr > sz
Overtaking length : Lo (24 sz R2)1/3
h (psz√R)2/3 hc.
(for R 2.5 m, h « 10 mm will shield a 190 mm bunch.)
When an electron emits a photon of energy u, the change in the betatron action
is given by
that is produced
A wiggler based on a chicane between each pair of quadrupoles
Each chicane contains 8 bend magnets (12 chicanes total).
- contains 24 9-cell RF cavities arranged in 3 cryomodules.
- Because the bunch is long, relatively strong focusing is used to limit emittance growth from transverse wakefields.
- contains 456 9-cell RF cavities arranged in 57 cryomodules.
- A wiggler has optics identical to the wiggler in the first BC, but with weaker wiggler.