## 1. Introduction

[2] For several decades, the impedance of antennas immersed in plasmas has received a great deal of attention. The precise knowledge of the impedance of antennas aboard scientific spacecraft is essential, e.g., for the data calibration required in plasma wave observations and some plasma diagnostic techniques such as the impedance probe. The precise impedance knowledge is also useful for the circuit matching of antenna systems used in space missions.

[3] Various methods for the evaluation of antenna impedance in plasma have been developed by using theoretical approaches. Because of the complexity of the plasma dynamics around the antenna, most of the methods have introduced certain assumptions and approximations to simplify the antenna modeling and calculation of the antenna impedance. As a pioneering work in this field, *Balmain* [1964] theoretically derived a formulation of the input impedance of short dipole antennas in magnetized plasma with an assumption of cold plasma. Analyses of short antenna impedance in kinetic plasma have also been performed for some limited models [e.g., *Kuehl*, 1966, 1967; *Schiff*, 1970; *Nakatani and Kuehl*, 1976]. In those theories, an assumption of a triangular current on the antenna surface was used in order to avoid the complexity of deriving the real form of the current distribution. Although it has been considered that the assumption is valid for antennas with length sufficiently smaller than applicable wavelength, a more self-consistent method without any assumptions on the current distribution is necessary for the precise evaluation of antenna impedance. Recently, several studies have been performed to derive the real form of the current distribution in cold plasma [e.g., *Bell et al.*, 2006]. However, there are no studies that derived a self-consistent form of the current distribution by kinetic plasma approaches.

[4] Another important point to be considered in the antenna analysis is the inhomogeneous plasma environment around the antenna. In absence of any effects of particle emission from an antenna surface, an electron-sparse region called an ion sheath is created around the surface with a floating potential. The dynamics and the detailed properties of the ion sheath have been exhaustively studied particularly in the field of active experiments [e.g., *Calder et al.*, 1993]. In aspect of the ion sheath effect on antenna impedance, however, it has been simply regarded as a vacuum layer in a frequency range in which ions are assumed to be immobile. It has been reported that such a vacuum layer may contribute prominently to antenna impedance, and rocket and satellite observations have indicated that the the sheath impedance is important [*Oya and Obayashi*, 1966]. However, the inclusion of the inhomogeneous plasma effect caused by the ion sheath leads to complication in theoretical derivation of antenna impedance. Therefore, several theoretical analyses of the sheath impedance have been conducted for much simplified sheath configuration such as planar [*Oya*, 1965; *Balmain and Oksiutik*, 1969] and cylindrical [*Aso*, 1973] structures. *Béghin and Kolesnikova* [1998] proposed a numerical approach using the surface-charge distribution (SCD) method, which can consider all of the boundary surfaces involving ion-sheath interfaces around the antenna and satellite bodies with complex geometry. In the SCD method, the ion-sheath interfaces were given as parameters of the numerical tool.

[5] Recently, numerical simulations have been recognized as a powerful tool as the theoretical and experimental approaches. In the field of antenna characteristics, extensive analyses have been conducted using numerical simulations via the Finite-Difference-Time-Domain (FDTD) method [*Taflove*, 1995] in free-space cases. The FDTD method was also applied to plasma simulations by treating the plasma as an anisotropic and dispersive dielectric [e.g., *Cummer*, 1997]. The advantage of the FDTD simulations lies in the ability to treat realistic antenna geometries without too simplified approximations of the antenna current distribution. Using the FDTD simulation with the fluid-plasma description, the nontriangular antenna current distribution was suggested to have caused the deviation of impedance value from that obtained by the assumption of triangular current distribution [*Ward et al.*, 2005]. However, in order to analyze the impedance including the plasma kinetic effects, the plasma must be modeled as particles in the FDTD simulations.

[6] In the present study, by applying the three-dimensional Electromagnetic Particle-In-Cell (EM-PIC) simulation, we developed a numerical tool for the antenna analysis in kinetic plasma environment. The developed tool enables us to perform simulation analysis including plasma kinetic effects on the antenna impedance, e.g., the existence of finite resistance below the electron plasma frequency and a change of an impedance resonance signature due to damping of plasma kinetic waves [*Kuehl*, 1967; *Meyer-Vernet and Perche*, 1989]. In addition, we incorporated the numerical model of the conducting surfaces of an antenna as inner boundaries and a boundary treatment for plasma particles on the surfaces in the simulation tool. With these treatments, we can simulate sheath dynamics in a self-consistent manner throughout the antenna analysis and evaluate antenna impedance without any assumptions on the sheath structure.

[7] The present paper presents simulation results obtained for the impedance of an electrically short dipole antenna covered with an electron-sparse region. The major motivation of this work is to demonstrate the application of PIC simulation techniques to the analysis of the antenna characteristics. We particularly focus on the impedance of a low-power transmitting antenna. The impedance calculation is fundamental and useful for the validation of the EM-PIC method. The transmitted power is small enough not to disturb the boundary environment of the simulation box so that numerical errors caused by the boundary effects are minimized. We consider a very simple situation in which a set of dipole antenna is immersed in Maxwellian, unmagnetized, and collisionless plasma. The plasma is so dense and low-temperature that the Debye length becomes smaller than the antenna length. First, we validate the developed EM-PIC simulation tool by examining the impedance without considering any effects of an ion sheath and comparing obtained results to the conventional kinetic theories [e.g., *Schiff*, 1970; *Meyer-Vernet and Perche*, 1989]. After that, we analyze the impedance characteristics of antennas covered with an ion sheath, which is created under the condition that an antenna has a floating potential. We focus on the impedance dependence on the ratio of the antenna length to the Debye length. We also discuss the dependence of sheath capacitance on the sheath thickness by the simulations with different bias potentials.