On the study of ion cyclotron waves in a cylindrical magnetized plasma

In this work, a general dispersion relation of waves in the region of ion cyclotron frequency in the cylindrical magnetized plasma is derived. The waves are assumed to be cylindrically symmetric oscillations of small amplitude. Analytical calculations are performed to find the plasma dielectric tensor for the plasma consisting of hot electron and multi-component cold ions fluid. The special case of a three component plasma with hot electrons in a strong magnetic field may be interesting, e.g., in the context of fusion plasma containing D+, T+ and He2+. The general dispersion relation is simplified in two solutions. Firstly, E1 wave (E2 = 0) which has an electrostatic character, and secondly E2 wave (E1 = 0) which has an electromagnetic character. The dispersion relations for both waves are described and identified as the ion acoustic and electrostatic ion cyclotron (EIC) waves for E1 wave and the torsional Alfvén, i.e. ion cyclotron (IC) waves and the compressional Alfvén wave for E2 wave. These waves are studied due to their importance in the heating of plasmas.