The impedance for a monopole antenna is derived and compared with the cases for wire dipole and double-sphere antennas. This derivation produces a new expression for the monopole antenna response function, $F_{m1}(x)$. The monopole, wire dipole, and double-sphere response functions are compared by modeling an antenna in Earth's ionospheric plasma (i.e. electrostatic and collisionless) and predicting the antenna capacitance and voltage power spectra for quasi-thermal noise (QTN) and shot noise. The monopole antenna current distribution is assumed to be a half-triangular current distribution (considering only the positive half of the triangular distribution). The predictions for the shot noise and capacitance presented problems, as the integral over wavenumber-space or $k$-space did not converge for large values of $k$. The derived expression therefore remains a current problem and necessitates future work to determine a more general expression. In this paper we bring the problem of an appropriate analytic monopole antenna response function to the attention of the community and outline a number of tests that can be used to verify any future expression.

中文翻译：

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暖等离子体中单极天线的阻抗和电压功率谱 - 推导和在立方体卫星上的应用

导出了单极天线的阻抗，并与线偶极天线和双球天线的情况进行了比较。此推导为单极天线响应函数 $F_{m1}(x)$ 生成了一个新表达式。通过对地球电离层等离子体（即静电和无碰撞）中的天线进行建模并预测准热噪声 (QTN) 和散粒噪声的天线电容和电压功率谱，比较了单极子、线偶极子和双球体响应函数。单极天线电流分布假定为半三角形电流分布（仅考虑三角形分布的正半部分）。散粒噪声和电容的预测存在问题，因为在波数空间或 $k$-空间上的积分对于 $k$ 的大值没有收敛。因此，派生表达式仍然是一个当前的问题，需要未来的工作来确定更一般的表达式。在本文中，我们将适当的解析单极天线响应函数的问题提请社区注意，并概述了一些可用于验证任何未来表达式的测试。