THEORY OF HIGH FREQUENCY ELECTROSTATIC WAVES IN A NON-UNIFORM PLASMA IN PRESENCE OF A MAGNETIC FIELD

High frequency ( omega << omega ci, omega pi) electrostatic waves propagated in a non-uniform plasma in the presence of a uniform magnetic field are described. The analysis is carried out in cylindrical geometry and both perfectly conducting and vacuum boundary conditions are included. Solutions of the dispersion relation corresponding to waves propagating perpendicularly (even for a uniform plasma column) and obliquely to the magnetic field are obtained. For oblique propagation there are two branches to the dispersion relation for a given value of mod l mod where l is the azimuthal mode number. The relationship of these waves to the low frequency ( omega << omega ci) drift waves of a non-uniform plasma and to the lower branch of the modes discussed by Trivelpiece and Gould (1959) is considered. The attenuation of the waves due to collisions is computed. The validity of the electrostatic approximation is examined.