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

TL;DR

The paper tackles the low-frequency QTN regime where the spectrum is controlled by the antenna's parallel resistance rather than spacecraft perturbations. It derives a physically grounded model for the resistance $R \simeq \frac{T_{ph}}{2 e N_e}$ and the associated impedance $Z = \frac{R}{1 - i R C \omega}$, then links these to the shot-noise spectrum $V_{shot}^2 \simeq 2 e^2 N_e |Z|^2 \Gamma^2$ with receiver gain $\Gamma^2 \simeq \frac{1+R^2 C^2 \omega^2}{1+R^2 (C+C_b)^2 \omega^2}$; these relations enable a quantitative comparison with Parker Solar Probe data. When applied to PSP/FIELDS observations, the model yields plasma properties ($n$, $T$, $L_D$, $C$) and a resulting $R$, whose predicted shot-noise component matches the observed low-frequency spectrum, highlighting that $R$ can modify QTN diagnostics close to the Sun. The work provides a framework to interpret low-frequency QTN measurements, with implications for receiver design and for extending the analysis to biased antennas and broader solar-distance ranges.

Abstract

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.

Figures (1)

• Figure 1: Theoretical shot noise (in green) superimposed to the power spectrum measured in the absence of biasing on the two PSP/FIELDS dipoles (in respectively orange and blue) at heliocentric distance $\simeq 19 R_s$. The theoretical shot noise, which largely dominates the electron QTN below 100 kHz, roughly agrees with the low-frequency spectrum measured by the unperturbed dipole V3V4.