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Neutrino Factory/Muon Collider Document 27-v1

General moment model of beam transport

Document #:
NFMCC-doc-27-v1
Document type:
MuCool Note
Submitted by:
John Urish
Updated by:
John Urish
Document Created:
06 Jun 1999, 12:00
Contents Revised:
06 Jun 1999, 12:00
Metadata Revised:
07 Nov 2010, 15:13
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Abstract:
Using the Hamiltonian structure of the Vlasov equation, we develop a
general, relativistic, three-dimensional model of beam transport based on
phase space moments of the beam particle distribution. Evolution equations
for these moments are derived from the non-canonical Poisson bracket for
the Vlasov equation. In this model, the beam centroid experiences the full
non-linear forces in the system while the higher order moments are coupled
to both the centroid and to various spatial derivatives of the applied
fields. For example, when moments up to second order are retained, the
physics content is similar to considering linearized forces. Given the
large number of equations (there are 27 equations when all second order
moments are kept) and their algebraic complexity, the use of symbolic
computation in the derivation was critical to ensuring the correctness of
the equations. This approach also allows for analytical verification of
conservation laws associated with the model. The initial
investigations [1] have considered only externally applied
fields, however in principle space-charge forces can also be included. We
discuss the necessary extensions to the basic theory needed to model
ionization cooling for the muon collider [2].
Posted muc0027.pdf to WWW
This is revision # 2
Posted by Shadwick
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Keywords:
COOL_THEORY
Notes and Changes:
B.A. Shadwick, J.S. Wurtele
Publication Information:
submitted to PAC99
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