Transition from ion-cyclotron to ion-acoustic longitudinal waves in a Maxwellian plasma

The roots k perpendicular-to versus omega and k parallel-to of the electrostatic dispersion relation in a magnetized Maxwellian plasma in the frequency range that covers the first few ion-cyclotron harmonics, are followed when the external magnetic field is decreased down to arbitrarily low values and compared with the roots of the non-magnetic dispersion relation (the ion-acoustic roots). It is found that the "forward" branch of the magnetic case tends to the less damped ion-acoustic root and that the whole series of backward Bernstein waves become, in the limit, the second, third, etc., less damped waves in the ion-acoustic series.