Magneto-optical Kerr effect for a dissipative plasma

Abstract

Ion collisions in plasmas cause damping of hydromagnetic modes, but also a strong Hall effect if the collision time is of the same order as the gyroperiod. This is known to be very marked in the E region of the Earth's ionosphere, but should also occur in other partially ionized space and laboratory plasmas. In this work dynamic effects of such Hall currents are investigated theoretically. The linear modes that are obtained are, for sufficiently large scales, distinctly different from ordinary damped Alfvén modes, and similar to whistler waves even when the dynamic time scale is much longer than the ion gyroperiod. The dynamics of the coupling between planetary ionospheres and magnetospheric plasmas may be viewed as a reflection of Alfvén waves at a sharp boundary. By applying the results of the linear mode analysis, it is shown that the usually employed reflection coefficient needs to be replaced by a reflection tensor for large-scale waves due to self-induction of ionospheric Hall currents. This is similar to the magneto-optical Kerr effect, which is well-known in solid state physics. In the Earth's ionosphere, variations from incident torsional modes over periods as long as several minutes, which have been observed to occur over scales of a few thousand kilometres, are predicted to cause the generation of substantial eddy electric fields and compressional flows. Consequences for the energy exchange between ionosphere and magnetosphere and possibilities to observe the effect are discussed.