On the dispersion law of low-frequency electron whistler waves in a multi-ion plasma

A new and simple dispersion law for extra-low-frequency electron whistler waves in a multi-ion plasma is derived. It is valid in a plasma with finite ratio ωc/ωpe of electron gyro-to-plasma frequency and is suitable for wave frequencies much less than ωpe but well above the gyrofrequencies of most heavy ions. The resultant contribution of the ions to the dispersion law is expressed by means of the lower hybrid resonance frequency, the highest ion cutoff frequency and the relative content of the lightest ion. In a frequency domain well above the ions' gyrofrequencies, this new dispersion law merges with the "modified electron whistler dispersion law" determined in previous works by the authors. It is shown that it fits well to the total cold plasma electron whistler dispersion law, for different orientations of the wave vectors and different ion constituents, including negative ions or negatively charged dust grains