The circumstances under which certain plasma dispersion equations may be used in electrostatic ray tracing problems connected with studies of ionospheric topside plasma resonances are investigated. Three plasma ‘models’ of increasing complexity are compared with each other. The models are based on the assumption of: (i) an adiabatic process with a scalar pressure, (ii) a fully adiabatic process (Buneman 1961), and (iii) an electrostatic kinetic description. It is found that near fN, and within 10° of the static magnetic field, all three models may be used with good accuracy, and collisionless damping is very small. Near fT, and for propagation nearly across the field, only the second model (ii) gives tolerably accurate results as judged by the kinetic equation. For frequencies within 10 kc s-1 of fT such as are encountered in ray tracing, collisionless damping may be neglected within a cone of ∽ 10° about the perpendicular to the field for fT < 2fH, and within ∽ 20° whenfT ≫ 2fH Model (iii) may be used to examine the dispersion equation near the electron gyroharmonics: this topic is discussed in Andrews & Fang (1971).