Analytic properties of the whistler dispersion function

The analytic properties of the dispersion function of a whistler are investigated in the complex frequency plane. It possesses a pole and a branch point at a frequency equal to the minimum value of the electron gyrofrequency along the path of propagation. An integral equation relates the dispersion function to the distribution of magnetospheric electrons along the path and the solution of this equation is obtained. It is found that the electron density in the equatorial plane is very simply related to the dispersion function. A discussion of approximate formulas to represent the dispersion shows how particular terms can be related to attributes of the electron density distribution, and a new approximate formula is proposed.