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A plasma sheath enveloping a reentry vehicle would cause the failure of on-board antennas, which is an important effect that contributes to the “blackout” problem. The method of replacing the on-board single antenna with the array antennas and using beamforming technology has been proposed to mitigate “blackout” problem by many other researchers. Because the plasma sheath is a reflective medium, plasma will alter the mutual coupling between array elements and degrade the beamforming performance of array antenna. In this paper, the effects of the plasma sheath on the mutual coupling properties between adjacent array elements are studied utilizing the algorithm of finite integration technique. Results show that mutual coupling coefficients of array elements are deteriorating more seriously with the decrease of collision frequency. Moreover, when electron density and collision frequency are both large, plasma sheath improves the mutual coupling property of array elements; this conclusion suggests that replacing the on-board single antenna with the array antennas and using beamforming technology can be adopted to mitigate the blackout problem in this condition.

A spacecraft reentering the Earth’s atmosphere at a hypersonic speed is enveloped by plasma fluid because of the shock wave heating of ambient gas and ablating of heat shield, causing air molecules and heat shield material dissociated and ionized [

One of many significant effects that contribute to the “blackout” problem is the failure of on-board antenna which is affected greatly by the reentry plasma sheath [

It is well known that the degradation of on-board antenna performance would lower the RF signal strength. However, by using beamforming technology, array antennas can provide a certain amount of gain to the communication link between the spacecraft and ground stations, and the received or transmitted RF signal strength would be increased. Thus, replacing the on-board single antenna with the array antennas can be adopted to mitigate the blackout problem. The process of this mitigation method is shown as follows. First, the directions of received or transmitted wave are calculated according to the navigation results and the flight attitude information of the spacecraft. Then, using beamforming technology, on-board array antenna is adjusted to point to the calculated direction. Consequently, the antenna gain and signal strength is increased, and a certain amount of signal gain is obtained to the communication link between the spacecraft and ground station.

However, the reentry plasma sheath is a reflective medium and would change the input impedance of array element, alter the mutual coupling between array elements, and degrade the beamforming performance of array antenna [

The remainder of this paper is organized as follows. Section

In practice, the reentry plasma sheath is spatial nonuniform and variation profiles of electron density can be characterized by a bi-Gaussian function shown below [

Generally, the nonuniform plasma sheath can be modeled approximately by several adjacent uniform thin plasma slabs according to variation profiles of electron density. A stratified modeling method is described in [

Variation profile of an electron density radially outward from vehicle surface.

A square patch array antenna of four elements is designed. The array antenna is a simple 2-by-2 array, which is used to provide a representative result that reflective plasma degrades beamforming performance of array antenna in the presence of mutual coupling. The basic structure and dimensions of array element with an off-centre point feeding are shown in Figure

Basic structure and dimensions of antenna element (a) and layout of the array antenna (b).

Plasma-covered array antenna simulation models.

In this section, reflection coefficient property of an array element and mutual coupling characteristic between adjacent and diagonal array elements covered by reentry plasma sheath of different parameters are studied and calculated.

In the calculation, with respect to the typical reentry plasma generated in the RAM-C project [^{16}/m^{3}~10^{18}/m^{3},

To check the validity of this simulation method, we carry out a comparison between results using the simulation method and results using XFDTD simulation tool. In this validation, we give some typical comparison results, and the plasma parameters ^{16}/m^{3} and 0.1 GHz, 10^{17}/m^{3} and 1 GHz, and 10^{18}/m^{3} and 5 GHz, respectively. The material for plasma is determined by the Debye-Drude dispersion relation model, and the layered plasma model is also applied to model the nonuniform plasma sheath In the XFDTD simulation. The

Comparisons between the results from the analysis method and the XFDTD simulation method.

Since the plasma is a reflective medium, the beamforming of array antenna would be affected by the wave reflected back into its array element. We need to calculate the self

Because the structure of every array element is the same, the ^{16}/m^{3}, 10^{17}/m^{3}, and 10^{18}/m^{3} for each calculation, self-coupling coefficients for collision frequencies 0.1 GHz, 1 GHz, 5 GHz, and 20 GHz are shown in Figures

(a) Self-coupling coefficient (

The results indicate that self^{16}/m^{3}, 10^{17}/m^{3}, and 10^{18}/m^{3} are −24.5 dB, −10.2 dB, and −2.6 dB, respectively.

Besides, the lower the collision frequency, the more serious the deterioration of self^{17}/m^{3}, the

Moreover, for a large electron density (e.g., 10^{18}/m^{3}), the resonant frequency of the array element is adjusted to a higher frequency.

In the former calculation, the results reveal that the plasma sheath reflects EM waves back into the array antenna. Thus, the mutual coupling characteristic of adjacent elements caused by the plasma sheath is studied in this calculation.

The

(a) Mutual coupling coefficient (

The results indicate that the magnitude of mutual coupling coefficients is deteriorating more seriously with the decrease of collision frequency. In particular, for the collision frequency lower than the antenna operating frequency (Figures ^{16}/m^{3} and 10^{17}/m^{3}, whereas the mutual coupling coefficients are decreased when the ^{18}/m^{3}. For the collision frequency higher than the antenna frequency (Figures ^{16}/m^{3} and 10^{17}/m^{3}, whereas the mutual coupling coefficients are decreased when the ^{18}/m^{3}.

The results also indicate that the phase variation relative to initial phase of mutual coupling coefficients turn bigger with the increase of

The

(a) Mutual coupling coefficient (

The results indicate that when the ^{18}/m^{3} and the collision frequency is 0.1 GHz, the plasma sheath deteriorates the magnitude of mutual coupling coefficients of nonadjacent elements. As for the other plasma parameters, the mutual coupling coefficients are decreased. We can conclude that the plasma sheath improves the mutual coupling property of diagonal array elements.

This paper presents an approximate layered EM simulation model for the nonuniform reentry plasma sheath which obeys bi-Gaussian distributions from NASA’s report and utilizes the algorithm of finite integration technique to analyze the effects of the plasma sheath on the reflection coefficient property of an array element and mutual coupling property between array elements. The results indicate that reflection coefficients of an array element are deteriorating more seriously with increase of the electron density and decrease of the collision frequency. The resonant frequency of the array element is adjusted to a higher frequency by a larger electron density. The mutual coupling coefficients of array elements are deteriorating more seriously with the decrease of collision frequency. Moreover, when electron density and collision frequency are both large, plasma sheath improves the mutual coupling property of array elements, this conclusion suggests that replacing the on-board single antenna with the array antennas and using beamforming technology can be adopted to mitigate the blackout problem in this condition.

The authors declare that there is no conflict of interests regarding the publication of this paper.

This work has been supported in part by the National Basic Research Program of China under Grant 2014CB340204, in part by the National Natural Science Foundation of China under Grant 61431010, in part by the Young Scientists Fund of the National Natural Science Foundation of China under Grant 61301173, and in part by the Fundamental Research Funds for the Central Universities 72125087.