A Stokes parameter description is developed for synchrotron radiation from a group of ultrarelativistic electrons with any specified distribution of positions, energies and directions of motion. This description is used to study the radiation from a shell of ultrarelativistic electrons trapped in a dipole field. It is found that the polarization observed for the 31 cm radiation from Jupiter could be obtained from such shells provided a large number of the electrons have relatively flat helices.
The problem of obtaining high energy , flat-helix electrons in a planetary magnetic field is considered. In particular, the effects of large scale magnetic disturbances on trapped particles are studied by following the particle guiding center motions through a disturbance. The guiding center motions of relativistic particles are determined by using relativistically correct drift velocity expressions obtained by application of an asymptotic approximation method of Bogolyubov and Zubarev. It has been found that these magnetic disturbances might lead to a high density of high energy, flat helix electrons; however, many disturbances are required for appreciable diffusion to occur. Magnetic activity at Jupiter must be very great if this type of mechanism is to provide the relatively flat helix electrons required for the decimeter radiation from Jupiter to be synchrotron radiation.
