A model for the electron temperature variation along geomagnetic field lines and its effect on electron density profiles and VLF paths

A realistic model for the temperature variation along geomagnetic field lines is described. For high altitudes (>1500 km) the temperature is taken to increase as the nth power of radial distance (n−2), giving temperatures consistent with those measured in situ by high altitude satellites. For realistic temperatures at low altitude an extra term is included. The temperature gradient along the field line is then 0.9–1.6° km⁻¹ during the day and 0.5–0.7° km⁻¹ during the night at 1000 km, reducing to about half these values at 2000 km, for the latitude range 35–50°. This is consistent with calculations made from nearly simultaneous satellite measurements at 1000 and 2500 km. It is shown that assuming diffusive equilibrium, including the new temperature model, more realistic equatorial electron density profiles result than for isothermal field lines.The temperature gradient model is also purposely formulated to be of a form that enables the temperature modified geopotential height to be obtained without numerical integration. This renders the model particularly suitable for ray-tracing calculations. A ray-tracing model is developed and it is shown that unducted ray paths are significantly altered from the corresponding paths in an equivalent isothermal model; there is greater refraction and magnetospheric reflection takes place at lower altitudes. For summer day conditions, an inter-hemispheric unducted ray path becomes possible from 26° latitude that can reach the ground at the conjugate.