Mapping guided Alfven wave magnetic field amplitudes observed on the ground to equatorial electric field amplitudes in space

A technique for converting the magnetic field amplitudes of guided toroidal and guided poloidal waves observed on the ground into the equatorial electric field amplitudes of the waves in space is presented. Analytic solutions of the guided toroidal and guided poloidal Alfven wave equations are used to determine the ratio of the equatorial electric field amplitude to the ionospheric magnetic amplitude, E-eq/b(i). Using these solutions, we show that in general E-eq/b(i) only depends very weakly on the Pedersen conductance, Sigma(P), and is linearly proportional to the guided Alfven waves' frequency. We also present numerical solutions of the guided Alfven wave equations illustrating how the value of E-eq/b(i) varies as a function of L shell for a range of different realistic field-aligned plasma density profiles. These results can be used to determine the equatorial wave electric field amplitude, E-eq, in space using the magnetic field amplitude observed on the ground, b(g). Accurate estimates of E-eq are crucial to understanding the role and importance of ultralow frequency waves on the energization and radial transport of radiation belt electrons.