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Neutrino Factory/Muon Collider Document 23-v1

Stability of alternating solenoid lattice solutions

Document #:
Document type:
MuCool Note
Submitted by:
John Urish
Updated by:
John Urish
Document Created:
12 Feb 1999, 12:00
Contents Revised:
12 Feb 1999, 12:00
Metadata Revised:
12 Feb 1999, 12:00
Actually Revised:
14 Sep 2006, 13:35
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We examine the stability of particle orbits in alternating solenoid lattices. We show that the
equations of motion reduce to a form of the Mathieu equation. Stable orbits are determined by
particular values of the parameters of the Mathieu equation. These parameters are then related to
the momentum of the particle and the field strength and period of the alternating solenoid lattice.
Stability predictions are shown to agree exactly for a perfect sinusoidally-varying magnetic field.
The stability predictions do not work for the alternating solenoid magnetic field pattern used in
the muon collider, except for the fundamental resonance condition.
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Notes and Changes:
R.C. Fernow
Publication Information:
BNL Muon Tech Note 026
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