Transformations of space electromagnetic fields in different non-inertial reference frames and their applications

How to transform an electromagnetic field across non-inertial frames of reference is a common challenge encountered in electromagnetic space measurements and analyses. Finding clear and precise ways to evaluate transformation formulas can be difficult. This study presents results of a thorough theoretical investigation that has yielded universal transformation formulas; these transformations are successfully applied to two specific scenarios. We find that, for space plasmas, if the relative velocities of structures are significantly lower than the speed of light, Galilean transformations are suitable. The transformations presented in this paper are applicable, in low speed situations, to electromagnetic fields, electric potentials and magnetic vector potentials, and to charge density and current density, measured in various non-inertial reference frames. Truncation errors associated with these simplified transformations are calculated and shown to be acceptable. These findings have broad implications for space physics measurements and analyses. We address two key issues related to non-inertial frame transformations: first, how to derive a general formula for the rotational electric potential of planets with intrinsic magnetic fields; second, how to verify rigorously the calculation of charge density from MMS (Magnetospheric Multiscale) electrostatic field measurements. We suggest that, due to the validity of the Coulomb gauge, the Poisson equation can be applied in situations of low-speed motion, allowing MMS measurement data to be used to calculate minimal-error charge density.