Evolution of current loops in space

Ampere's law requires that every magnetic field have an associated current. The analysis of magnetic fields in this paper begins with that current in a circular loop and calculates the forces that make the loop evolve. A circular current generates a dipole field; and a second-order, ordinary differential equation represents the evolving magetic field. The theory describes cases where the conductor shrinks as the loop increases in size. The temperature of the conducting ions and electrons then decreases. The theory also describes cases where the conductor grows as the loop grows. Then the conducting particles heat up.Analysis shows that the magnetic clouds in the solar wind belong to the first type. In the provisional model adopted, the Klein-Burlaga clouds at one astronomical unit have a toroidal shape, centered on the sun, with a conductor radius of .125 au, and temperature (same for conducting electrons and protons) of 10⁵ K. After 26 days the toroid has a radius of 7.1 au, the conductor radius is .025 au, and the temperature is 2600 K.