Analytic models for a rapidly spinning spherical satellite charging in sunlight

[i] We present elementary analytic models for a fast-spinning, dielectric-coated, spherical spacecraft charging in sunlight. The models are based on a multipole expansion of Laplacian potentials external to the spacecraft surface. We assume azimuthal symmetry about the spin axis, and the spin period must be short compared with surface differential charging times. There are three parameters in the models: the monopole potential, the relative strength of the dipole/quadrupole components with respect to the monopole, and a mixing angle. The combination of monopole potentials along with the dipole or quadrupole contributions produce potential barriers which form at the satellite surface. These barriers can act to block escaping photoelectrons and lead to current balance, allowing sunlight charging to high negative levels. The sunlit side charges less (negatively) than the shade side and the ratio of Sun to shade potentials is near its threshold value for high-level charging. We have calculated more general cases with various values of Sun angle relative to the spin axis by combining the dipole and quadrupole components. The potential barrier shape and area vary for different cases and the maximum barrier approximately follows the Sun angle. We stress that for physical interpretation of data obtained on board, one should take into account the potential distribution and where the instrument is located.