Deformation method for electromagnetic magnetospheric fields: 1. Theory

摘要

In this paper the deformation method for magnetospheric magnetic fields is generalized to electric fields. It has been previously shown that an initial magnetic field configuration can be deformed to another configuration given in original coordinates by expressing the initial field in terms of the deformed coordinates and by multiplying this field by a deformation matrix. The method introduced here can be used in constructing model three-dimensional electric fields consistent with model magnetic fields, and, most importantly, the electric field contributions induced by temporal variations of the magnetic field are globally modeled. The generalization is done by introducing a deformation matrix (M) of the vector potential consistent with the deformation matrix (T) of the magnetic field. These two types of deformations termed as M-type and T-type have different properties. Most importantly, the M-type deformation conserves the curl-free properties of an initial potential field, whereas the T-type deformation introduces a curl to an initial potential field. It is shown that as previously shown for the magnetic field, no explicit Euler potentials are required for the deformation of the electric field that corresponds to frozen-in plasma convection. This is a result of central importance for electromagnetic field modeling when only fields are initially known. Presently, the method assumes a gauge of zero magnetic helicity, and it is valid only for simply connected magnetic fields.