  The formation and evolution mechanism of fullerenes in the planetary nebula
or in the interstellar medium are still not understood. Here we present the
study on the cluster formation and the relative reactivity of fullerene cations
(from smaller to larger, C$_{44}$ to C$_{70}$) with anthracene molecule
(C$_{14}$H$_{10}$). The experiment is performed in the apparatus that combines
a quadrupole ion trap with a time-of-flight mass spectrometer. By using a 355
nm laser beam to irradiate the trapped fullerenes cations (C$_{60}$$^+$ or
C$_{70}$$^+$), smaller fullerene cations C$_{(60-2n)}$$^+$, n=1-8 or
C$_{(70-2m)}$$^+$, m=1-11 are generated, respectively. Then reacting with
anthracene molecules, series of fullerene/anthracene cluster cations are newly
formed (e.g., (C$_{14}$H$_{10}$)C$_{(60-2n)}$$^+$, n=1-8 and
(C$_{14}$H$_{10}$)C$_{(70-2m)}$$^+$, m=1-11), and slight difference of the
reactivity within the smaller fullerene cations are observed. Nevertheless,
smaller fullerenes show obviously higher reactivity when comparing to fullerene
C$_{60}$$^+$ and C$_{70}$$^+$.
  A successive loss of C$_2$ fragments mechanism is suggested to account for
the formation of smaller fullerene cations, which then undergo addition
reaction with anthracene molecules to form the fullerene-anthracene cluster
cations. It is found that the higher laser energy and longer irradiation time
are key factors that affect the formation of smaller fullerene cations. This
may indicate that in the strong radiation field environment (such as
photon-dominated regions) in space, fullerenes are expected to follow the
top-down evolution route, and then form small grain dust (e.g., clusters)
through collision reaction with co-existing molecules, here, smaller PAHs.
