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Neutrino Factory/Muon Collider Document 71-v1

Beam Envelope Equations in a Solenoidal Field

Document #:
NFMCC-doc-71-v1
Document type:
MuCool Note
Submitted by:
John Urish
Updated by:
John Urish
Document Created:
23 Dec 1999, 12:00
Contents Revised:
23 Dec 1999, 12:00
Metadata Revised:
07 Nov 2010, 14:49
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Abstract:
Revision 1:
In addition to minor corrections, the three cooling channel examples
have been changed; they are now presented consistently, and adjusted
to have similar performance.

Ionization cooling of muons requires strong focussing of beams
at the absorbers; solenoid magnets are required for cooling
channels designed to use this mechanism. Assuming a cylindrically
symmetric beam and using the single particle equations of motion,
a set of transverse beam envelope equations are derived in the
paraxial approximation. These equations incorporate the main
factors in ionization cooling: interactions with material,
acceleration by radio frequency (RF) cavities, and the possible
accumulation of canonical angular momentum. The dominant
nonlinear effect is the mirror force, which leads to estimates
of beam correlation parameters for a matched beam. This formalism,
analogous to the Courant-Snyder notation for systems of quadrupole
lenses, allows for an analysis of lattice configurations beginning
with thin lenses and then progressing to lattices of extended
magnets. A categorization of lattice types connects this analysis
with previous descriptions of cooling channels, including a
"phase diagram" of lattice properties versus magnetic field
profile. Scaling laws for channel performance are derived and
exhibit good agreement with realistic lattice designs.

Posted muc0071.pdf to WWW
This is revision # 1
Posted by Penn

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COOL_THEORY
Notes and Changes:
G. Penn
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