Calibration of electrically short antennas using the l = 2 spherical harmonic expansion coefficients of the radio brightness distribution on the sky between 0.5 and 6.8 MHz

Abstract

A space-borne radio-frequency antenna is typically located in the vicinity of a conductive spacecraft body that influences its beam. Also, at wavelengths that greatly exceed the sizes of such an antenna and spacecraft, the antenna is expected to have the beam of an equivalent short dipole. This type of beam varies with direction as sin²(ζ), where ζ is the polar angle relative to the antenna's electrical axis. We describe a Markov Chain Monte Carlo method for fitting for this axis and apply it to measurements from Parker Solar Probe's four whip antennas. Depending on how the antennas are connected to the spacecraft's radio receiver, their voltages are processed individually for “monopole” measurements or differenced for “dipole” measurements. We find with a reduced χ² = 1.01 that the electrical axes of the dipoles deviate from the whip axes by 0° — 4°. A byproduct of this fit is a measurement of the l = 2 spherical harmonic expansion coefficients of the brightness distribution on the sky. We utilize this measurement to in turn determine the electrical axes of the monopoles from a much smaller data set. These are found to be deflected ≈ 27° away from the whips. Rheometric calibration and computational electromagnetic simulations of the antenna system corroborate the fits. All of the analyzed data were captured with the spacecraft solar array deployed, which perturbs the electrical axes of the antennas by a few degrees.