Abstract
The motional electric field of the solar wind as seen by the Earth is examined theoretically and with spacecraft measurements. As it flows outward from the sun, the solar-wind plasma carries a spatially structured magnetic field with it. To calculate the motional electric field of the solar wind the spatially structured magnetic field is Lorentz transformed; for a full physical understanding, it is also necessary to Lorentz transform the current densities and charge densities in the solar wind. Referring to Maxwell’s equations, two related questions are asked: 1) Is the source of the solar-wind motional electric field charge density in the solar wind, time derivatives of current densities in the solar wind, or both? 2) Is the solar-wind motional electric field at Earth an electrostatic field, an induction field, or a superposition of the two? A Helmholtz decomposition of the motional electric field of the solar wind is made into a divergence-origin (electrostatic) and a curl-origin (induction) electric field. The global electric field associated with the outward advection of the global Parker-spiral magnetic field is found to be electrostatic with its origin being a distributed charge density in the solar-wind plasma. The electrostatic versus induction nature of the time-varying electric field associated with the advection of mesoscale magnetic structure varies with time as differently shaped magnetic structures in the solar-wind plasma pass the Earth; the mesoscale structure of the solar-wind plasma contains sheets of space charge and sheets wherein the current density has nonzero time derivatives.
Highlights
The solar wind is a magnetized collisionless plasma comprised of ions and electrons. (Collisionless means that inter-particle collisions that would disrupt the ion or electron orbits in the magnetic and electric fields are rare.) The solar-wind plasma flows at a high velocity radially outward from the Sun, in the range 250 km/s to 1000 km/s
A Helmholtz decomposition of the motional electric field in the solar wind was made and the electrostatic versus induction nature of the field was analyzed as was the charge-density origin versus the time-varying-currentdensity origin of the field
Just as the transformation of the motional electric field E from B is important at non-relativistic solar-wind velocities, the transformation of the charge density ρq from the current density j is important at non-relativistic velocities
Summary
The solar wind is a magnetized collisionless plasma comprised of ions (mostly protons) and electrons. (Collisionless means that inter-particle collisions that would disrupt the ion or electron orbits in the magnetic and electric fields are rare.) The solar-wind plasma flows at a high velocity radially outward from the Sun, in the range 250 km/s to 1000 km/s. The sign of this interplanetary electric field is outward along the magnetic field lines, accelerating ions away from the Sun and retarding the outward electron flux This interplanetary electrostatic potential is responsible for the observed statistical increase of the bulk speed of the solar wind vsw between 0.3 AU and 1 AU. We will define a purely induction electric field Eind as a solenoidal field having its origin in regions where the curl ∇ × E is nonzero. From this and from expression (3) it follows that ∇ ⋅ E = ∇ ⋅ Ees and that ∇ × E = ∇ × Eind. In this paper more care will be taken with the “induction” nomenclature
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