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Neutrino Factory/Muon Collider Document 257-v1

Muon Cooling Channels

Document #:
Document type:
MuCool Note
Submitted by:
John Urish
Updated by:
John Urish
Document Created:
07 Oct 2002, 12:00
Contents Revised:
07 Oct 2002, 12:00
Metadata Revised:
07 Oct 2002, 12:00
Actually Revised:
14 Sep 2006, 13:35
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A procedure uses the equations that govern ionization
cooling, and leads to the most important parameters of a muon
cooling channel that achieves assumed performance parameters. First,
purely transverse cooling is considered, followed by both transverse
and longitudinal cooling in quadrupole and solenoid channels.
Similarities and differences in the results are discussed in
detail, and a common notation is developed. Procedure and notation
are applied to a few published cooling channels. The parameters of
the cooling channels are derived step by step, starting from assumed
values of the initial, final and equilibrium emittances, both
transverse and longitudinal, the length of the cooling channel, and
the material properties of the absorber. The results obtained
include cooling lengths and partition numbers, amplitude functions
and limits on the dispersion at the absorber, length, aperture and
spacing of the absorber, parameters of the RF system that achieve
the longitudinal amplitude function and bucket area needed. Finally,
I compute the merit factor that describes the enhancement of the
density in 6D phase space. The consequences of changes in the input
parameters are discussed. The lattice parameters needed to achieve
the assumed performance are summarized. The design proper of such a
lattice, i.e. finding the precise arrangement of magnets, RF cavities,
absorbers, etc., which has these properties, is well beyond the scope
of this document.

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