\preprint{MUC-NOTE-COOL\_THEORY-288}
\preprint{Muon Tech. Note MU-053}
\title{Behavior of Kinematic Invariants of Beams with Large Energy Spread}
\author{J.~Gallardo}\email[]{gallardo@bnl.gov}
\author{R.~Fernow}\email[]{fernow@bnl.gov}
Abstract
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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