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Neutrino Factory/Muon Collider Document 288-v1

Behavior of Kinematic Invariants of Beams with Large Energy Spread

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MuCool Note
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John Urish
Updated by:
John Urish
Document Created:
06 Feb 2004, 12:00
Contents Revised:
06 Feb 2004, 12:00
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07 Nov 2010, 15:08
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\preprint{Muon Tech. Note MU-053}

\title{Behavior of Kinematic Invariants of Beams with Large Energy Spread}



The well known kinematic moment invariants, emittance $\epsilon_N=\mathbf{det}(\Sigma)$ and $I_N=-0.5\mathbf{Tr}(J \Sigma J \Sigma )$~\cite{ref1} in linear beam dynamics are computed using ICOOL~\cite{ref2} for a simple drift problem. We show that they are not constant for a non-paraxial beam with significant energy spread ($> 5\% $). This fact may have implications for the MICE experiment.

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