An Analogue Solution of the Continuity Equation of the Ionospheric F Region

It is shown that the continuity equation for the electron density in the F region of the ionosphere can be solved by the use of an electrical analogue. The equation which is solved in this way takes account of the rates of production and loss of electrons, and of vertical diffusion, but other types of movement are not included. The rates of production, loss and diffusion are assumed to vary with height in a manner appropriate to a particular model of the atmosphere, based on rocket and satellite data. The analogue computer is first used to find how the electron density at a series of heights varies with time due to the diurnally varying rate of production. The time of maximum production is at noon, but the time of maximum electron density occurs some time after noon, and the variation of this time lag with height is studied. Near noon, the electron density is found to be a maximum at a height of 250 km. In the evening, the height of the maximum rises to about 300 km, and remains constant during the night. Above the level of the maximum, the ionization is controlled by diffusion and the ionization density falls off exponentially with increasing height; its time variation follows closely the time variation at the maximum. In other experiments, the production function is modified so as to represent a solar eclipse which occurs near noon. Diurnal curves of electron density are obtained at a series of heights, and the results show how the time of maximum electron density and the percentage decrease of electron density vary with height. In another type of experiment, the diffusion and recombination of a slab of ionization introduced at a fixed height are studied. It is shown that the slab spreads out to form a `layer' which eventually assumes a certain fixed shape with a maximum at a fixed height of 300 km, and that this `shape-preserving' layer then decays with a time constant determined by the rate of recombination at the level of maximum ionization density. The final form of the layer is independent of the height at which the slab of ionization is introduced. These results may be relevant to the behaviour of the F layer at night when production is absent, and diffusion and recombination are the controlling factors.