First in Situ Estimates of the Sheath Resistance for the PSP/FIELD Antenna: Employing an Electron Shot Noise Model

Abstract Quasi-thermal noise is an important diagnostic tool for measuring electron density and temperature in space plasmas, with its low-frequency range being dominated by electron shot noise. However, previous missions have shown that conventional shot noise models often yield poor fits in the low frequency <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mo stretchy="false">(</mml:mo> <mml:mi>f</mml:mi> <mml:mo>&lt;</mml:mo> <mml:msub> <mml:mi>f</mml:mi> <mml:mi>p</mml:mi> </mml:msub> <mml:mo stretchy="false">)</mml:mo> </mml:math> , limiting the accurate characterization of electron parameters. To address this issue, we introduce an effective sheath resistance into the previous model, thereby establishing a calibrated shot noise model that improves measurements of electron parameters in the inner heliosphere. Methodologically, we applied the steep-descent and Levenberg–Marquardt method algorithm to determine the electron density and temperature above the plasma frequency; we then isolate the pure shot noise by subtracting other noise sources; and finally, we derive the antenna impedance using measurements below the plasma frequency ( <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msub> <mml:mrow> <mml:mi>f</mml:mi> </mml:mrow> <mml:mrow> <mml:mi>p</mml:mi> </mml:mrow> </mml:msub> </mml:math> ). Based on Parker Solar Probe (PSP) observations during PSP Encounter 4 ∼ 8 (with unbiased antennas operating in the dipole regime), we obtain an effective antenna capacitance of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:mn>8.30</mml:mn> <mml:mo>±</mml:mo> <mml:mn>0.21</mml:mn> <mml:mi>pF</mml:mi> </mml:math> and an effective resistance in the range of 0.5 ∼ 4 MΩ, with their radial of the capacitances and resistances of <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mi>r</mml:mi> <mml:mrow> <mml:mo>−</mml:mo> <mml:mn>0.072</mml:mn> <mml:mspace width="0.25em"/> <mml:mo>±</mml:mo> <mml:mspace width="0.25em"/> <mml:mn>0.001</mml:mn> </mml:mrow> </mml:msup> </mml:math> and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" overflow="scroll"> <mml:msup> <mml:mi>r</mml:mi> <mml:mrow> <mml:mn>2.57</mml:mn> <mml:mspace width="0.25em"/> <mml:mo>±</mml:mo> <mml:mspace width="0.25em"/> <mml:mn>0.02</mml:mn> </mml:mrow> </mml:msup> </mml:math> , respectively.