![fieldlines zero electric potential fieldlines zero electric potential](http://image1.slideserve.com/1587338/checkpoint-motion-of-point-charge-electric-field-n.jpg)
In this paper, theoretical tools are developed to determine ionospheric electromagnetic fields and their effects on ion and electron velocities. Dynamo regions on some parts of Mars occur at altitudes where plasma transport has a significant effect on plasma densities. Magnetic field strength and direction vary on lengthscales of hundreds of kilometers, much smaller than the planetary radius. The effects of these problems are more obvious on Mars, which has a weak crustal magnetic field. Vertical transport of plasma is only important at higher altitudes.
![fieldlines zero electric potential fieldlines zero electric potential](https://image.slidesharecdn.com/expspa-currentofelectricity-151027030823-lva1-app6892/95/exp-spa-chp-17-current-of-electricity-20-638.jpg)
This is not generally considered a problem for terrestrial ionospheric studies because plasma transport has a negligible effect on plasma densities in the dynamo region. Therefore existing theory offers only an incomplete description of the vertical motion of plasma in a dynamo region. The conductivity equation, which assumes that the effects of gravity and pressure gradients on charged particles are negligible, can predict the electric field in an ionosphere, but its assumptions fail where plasma motion is not horizontal. Ambipolar diffusion, which assumes that no current flows through the ionosphere, can predict the electric field below the dynamo region, but not within the dynamo region. Theoretical approaches to determining the electric field include ambipolar diffusion and the conductivity equation. Empirical electric field models that are based on direct observations exist only for Earth. An ionospheric model must have a realistic representation of the electric field, which also accelerates charged particles, if it is to describe the motion of ionospheric plasma accurately. The intermediate region between 75 and 130 km is known as the dynamo region, within which currents flow. In the mid-latitude terrestrial ionosphere, electrons and ions are “frozen-in” to fieldlines above 75 km and 130 km, respectively.
![fieldlines zero electric potential fieldlines zero electric potential](https://i.ytimg.com/vi/ZXjRQsA2SZY/maxresdefault.jpg)
If the effects of magnetic fields are stronger than the effects of collisions and other forces, then charged particles cannot cross magnetic fieldlines. Moving charged particles are accelerated by magnetic fields. This relationship is valid for the terrestrial ionosphere replacing J = E′ with J = Q + E′ in terrestrial models may alter some of their predictions. In this model, ion and electron velocities transition smoothly from moving across fieldlines below the dynamo region to moving along fieldlines above the dynamo region. The relationship J = Q + E′ is applied to a one-dimensional ionospheric model to study ion velocities, electron velocities, currents, electric fields, and induced magnetic fields simultaneously and self-consistently. This has prevented models from accurately describing how vertical plasma transport affects plasma densities in the martian ionosphere. Neither J = E′ nor ambipolar diffusion can describe the vertical motion of plasma in a dynamo region, a region where electrons are tied to fieldlines, but ions are not. If J = 0, this reduces to ambipolar diffusion. If pressure gradients and gravity are neglected, this reduces to the well-known J = E′, where is the conductivity tensor. A relationship between J, the current density, and E′, the electric field measured in the frame of the neutral wind, is derived for a planetary ionosphere: J = Q + E′.