  In this paper, a detailed normal mode analysis is given based on the
Boltzmann equation in mutilated relaxation time approximation (RTA). Within
this linearized effective kinetic description, our analysis covers a full-order
calculation in wavenumber $k$, being a generalization of usual hydrodynamic
mode analysis to intermediate and short-wavelength region. Besides, the
proposed normal mode analysis can give a natural classification of kinetic
modes into collective modes and non-collective single particle excitations. In
the case with a scale-independent relaxation time, the so-called behavior of
hydrodynamic onset transitions is recovered \cite{Romatschke:2015gic}. However,
for a general case with a scale dependent relaxation time, a clear
classification broken down because the location of hydrodynamic modes is not
well separated from non-hydrodynamic modes.
