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Neutrino Factory/Muon Collider Document 205-v1

Beam parameterization and invariants in a periodic solenoidal channel

Document #:
Document type:
MuCool Note
Submitted by:
John Urish
Updated by:
John Urish
Document Created:
17 Apr 2001, 12:00
Contents Revised:
17 Apr 2001, 12:00
Metadata Revised:
07 Nov 2010, 14:56
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The standard Courant-Snyder formalism is generalized for a
solenoidal channel, for which 4D instead of 2D treatment is
required due to the cylindrical symmetry. Unlike a coupled
quadrupole channel, beam dynamics in a solenoidal channel have
unique properties. Four quadratic constants of the motion, the
canonical angular momentum plus three Courant-Snyder type
invariants, are found. Based on this, a natural set of
beam-envelope functions are introduced to parameterize the ten
independent beam moments of the 4D phase-space distribution of a
beam. General expression of an equilibrium Gaussian distribution
is given. General formalism is developed for describing the
evolution of matched and mismatched beams in periodic solenoidal
Posted muc0205.pdf to WWW
Posted by Wang
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Notes and Changes:
Chun-xi Wang and Kwang-Je Kim
Publication Information:
To be published in PRE
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