  Actively propelled particles undergoing dissipative collisions are known to
develop a state of spatially distributed coherently moving clusters. For
densities larger than a characteristic value clusters grow in time and form a
stationary well-ordered state of coherent macroscopic motion. In this work we
address two questions: (i) What is the role of the particles' aspect ratio in
the context of cluster formation, and does the particle shape affect the
system's behavior on hydrodynamic scales? (ii) To what extent does particle
conservation influence pattern formation? To answer these questions we suggest
a simple kinetic model permitting to depict some of the interaction properties
between freely moving particles and particles integrated in clusters. To this
end, we introduce two particle species: single and cluster particles.
Specifically, we account for coalescence of clusters from single particles,
assembly of single particles on existing clusters, collisions between clusters,
and cluster disassembly. Coarse-graining our kinetic model, (i) we demonstrate
that particle shape (i.e. aspect ratio) shifts the scale of the transition
density, but does not impact the instabilities at the ordering threshold. (ii)
We show that the validity of particle conservation determines the existence of
a longitudinal instability, which tends to amplify density heterogeneities
locally, and in turn triggers a wave pattern with wave vectors parallel to the
axis of macroscopic order. If the system is in contact with a particle
reservoir this instability vanishes due to a compensation of density
heterogeneities.
