  We study the formation of non-linear structures in Warm Dark Matter (WDM)
models and in a Long-Lived Charged Massive Particle (CHAMP) model. CHAMPs with
a decay lifetime of about 1 yr induce characteristic suppression in the matter
power spectrum at subgalactic scales through acoustic oscillations in the
thermal background. We explore structure formation in such a model. We also
study three WDM models, where the dark matter particles are produced through
the following mechanisms: i) WDM particles are produced in the thermal
background and then kinematically decoupled; ii) WDM particles are fermions
produced by the decay of thermal heavy bosons; and iii) WDM particles are
produced by the decay of non-relativistic heavy particles. We show that the
linear matter power spectra for the three models are all characterised by the
comoving Jeans scale at the matter-radiation equality. Furthermore, we can also
describe the linear matter power spectrum for the Long-Lived CHAMP model in
terms of a suitably defined characteristic cut-off scale k_{Ch}, similarly to
the WDM models. We perform large cosmological N-body simulations to study the
non-linear growth of structures in these four models. We compare the halo mass
functions, the subhalo mass functions, and the radial distributions of subhalos
in simulated Milky Way-size halos. We study the models with k_{cut}=51, 410,
820 h/Mpc, and confirm that these statistics are indeed similar between the
different WDM models and the Long-Lived CHAMP model. The result suggests that
the cut-off scale k_{cut} not only characterises the linear power spectra but
also can be used to predict the non-linear clustering properties. The radial
distribution of subhalos in Milky Way-size halos is consistent with the
observed distribution for k_{cut}~50-800 h/Mpc; such models resolve the
so-called "missing satellite problem".
