Theoretical calculation of the antenna impedance and shot noise at low-frequencies: application to Parker Solar Probe

The voltage power spectral density measured around the ambient plasma frequency in space is not affected by spacecraft perturbations that impact traditional plasma analysers. The spectroscopy of this noise, produced by the quasi-thermal motion of ambient charged particles, is thus an efficient tool for measuring in situ plasma properties in space. In contrast, the spectrum at lower frequencies, which is determined by the parallel antenna resistance due to electric currents, depends on the spacecraft local environment. Recently, \citet{zhe26} erroneously estimated this resistance from Parker Solar Probe (PSP) data. We hereby present a theoretical calculation of this resistance, which determines the shot noise and the receiver gain at low frequencies, and provide a preliminary comparison to PSP/FIELDS data. We also show that this resistance can change the receiver gain in the frequency range used for QTN spectroscopy during PSP inner orbits.