Graphical Study of the Dispersion of Electro-Magneto-Ionic Waves

Abstract

A graphical method for approximating to all the eight roots of the equation of dispersion, corresponding to any numerically specified case, is described. This method uses curves drawn with ω and l as coordinates to give readily the following information about the waves which can exist in the medium : (i) the frequency- bands in which undamped waves or wave-groups can grow as they progress, (ii) the wave-number bands in which unattenuated waves can grow in time, (iii) the phase- and group-velocities, refractive indices, and coefficients of positive and negative attenuation and damping, (iv) the general effect of collisions between electrons and other particles on the attenuation or damping of a wave or wave-group. Several illustrative examples are given. The same method is also applied to a special case of the more comprehensive equation of dispersion which includes the effects due to the motions of the positive ions, and it is shown that there can then exist unattenuated waves which grow with the lapse of time.