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The advent of laser-assisted ion acceleration technology promises an alternative candidate to conventional accelerator drivers used in inertial confinement fusion. The experimental generation of quasi-monoenergetic heavier ion species i.e. carbon and aluminum, applicable to fast ignition studies has been recently reported. The propagation of these energetic ions may impact on the proper ignition phase through growing of micro-instabilities of beam–plasma system. The growth of flow-aligned instabilities is much more important for heavier ions transport in the dense plasma. Here, we have presented a general non-relativistic one-dimensional dispersion relation of cold fluid model as well as corresponding kinetic theory of incident ion beam with atomic number, Z b enters into a fast ignition DT plasma. The longitudinal instabilities of some selected average energies of experimentally generated C 6+ (E C =50, 100 and 200 MeV with δ E/E ∼ 10 % ) and Al 11+ (E Al =150 and 300 MeV with δ E/E ∼ 25%) quasi-monoenergetic beams were examined and beam–plasma system stable configuration have been then derived. It has been shown that in the kinetic theory framework, carbon and aluminum ions may be completely stabilized by the combination of beam to plasma density ratio ( α b ) and plasma temperature (T p ) of ignition phase parameters. Moreover, in complete stabilization, α b parameter of aluminum beam is an order of magnitude lower than carbon. [ABSTRACT FROM AUTHOR]