  The asymptotic analysis of kinetic models describing the behavior of
particles interacting through alignment is performed. We will analyze the
asymptotic regime corresponding to large alignment frequency where the
alignment effects are dominated by the self propulsion and friction forces. The
former hypothesis leads to a macroscopic fluid model due to the fast averaging
in velocity, while the second one imposes a fixed speed in the limit, and thus
a reduction of the dynamics to a sphere in the velocity space. The analysis
relies on averaging techniques successfully used in the magnetic confinement of
charged particles. The limiting particle distribution is supported on a sphere,
and therefore we are forced to work with measures in velocity. As for the
Euler-type equations, the fluid model comes by integrating the kinetic equation
against the collision invariants and its generalizations in the velocity space.
The main difficulty is their identification for the averaged alignment kernel
in our functional setting of measures in velocity.
