Impedance of electric field sensors in magnetized plasmas: particle-in-cell simulations

<jats:title>Abstract</jats:title><jats:p>To obtain both the intensities and phases of electric fields, it is necessary to calibrate the data observed by the sensor by consulting the sensor characteristics. The frequency profile of the sensor impedance obtained from the simulation is roughly consistent with that obtained from the theory. However, some differences are identified in the frequency profile of the sensor impedance obtained from the simulation compared to the theory. We conducted simulations using the particle-in-cell (PIC) simulation tool to analyze the impedance of electric field sensors immersed in magnetized space plasmas. The simulation model comprised a dipole sensor placed in a three-dimensional simulation box filled with electrons and ions. The dipole sensor was represented by perfect conductor rods. We carefully selected simulation parameters and employed an appropriate feeding technique to accurately evaluate the sensor impedance. We observed significant changes in the frequency dependence of the sensor impedance as cyclotron frequency varied. To understand the simulation results, we introduced the linear dispersion relation. By comparing the real part of the sensor impedance with the <jats:inline-formula><jats:alternatives><jats:tex-math>$$\omega-k$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>ω</mml:mi> <mml:mo>-</mml:mo> <mml:mi>k</mml:mi> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula> diagram, we found that the impedance peaks corresponded to frequencies at which branches of plasma waves were present, with <jats:inline-formula><jats:alternatives><jats:tex-math>$$k=k_{\text{half}}$$</jats:tex-math><mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"> <mml:mrow> <mml:mi>k</mml:mi> <mml:mo>=</mml:mo> <mml:msub> <mml:mi>k</mml:mi> <mml:mtext>half</mml:mtext> </mml:msub> </mml:mrow> </mml:math></jats:alternatives></jats:inline-formula>, representing half the wavelength equal to the tip-to-tip sensor length, i.e., the sensor can be assumed as the half-wavelength dipole antenna.</jats:p> <jats:p><jats:bold>Graphical Abstract</jats:bold></jats:p>