Dispersion relations for the lower hybrid frequency range

The hot plasma electrostatic dispersion relation for the lower hybrid frequency range has been cast into a form without any sums using the method of steepest descents. This new form of the dispersion relation with the exact resonance term, which is valid for general complex wavenumber and each term of which is identified according to its role of representing physical waves, is shown to be accurate and to be reducible to an expression obtained by Brambilla [Plasma Phys. 18, 699 (1976)] when some approximations are taken. A very simple dispersion relation is also obtained without singular terms near the high ion cyclotron harmonics that are encountered by lower hybrid waves propagating in inhomogeneous magnetic fields. Finally, the damping rate in space is numerically calculated using the equation derived and compared with the result from the unmagnetized ion dispersion relation.