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A system of dusty plasma, containing negatively charged dust particles, Boltzmann distributed electrons and ions, is considered in a cylindrical set up and electrostatic wave modes have been studied in the presence of an external magnetic field. The dust particles are of two different sizes such that small grains are present in significant amount. Using Fourier transformation along temporal and azimuthal directions, linear dispersion relation is derived, which indicates the existence of two distinct wave modes for the stable case. Among the breathing and rotation modes, density profiles have been observed numerically for the rotation mode corresponding to the stable case. The density fluctuation of small grains is noticed to be more prominent than that of the big grains. In the presence of external magnetic field, large grains contribute very negligible magnitude of dust number density in those regions, where voids are generated by the small grains only. The effect of mode number on the dust density fluctuation as well as on the structure of density profile is observed. The magnetic field effect on dust void formation is also studied.

The electrostatic wave modes and formation of dust voids in an externally magnetized cylindrical dusty plasma