Propagation Properties of Partially Coherent Flat-Topped Beam Rectangular Arrays in Plasma and Atmospheric Turbulence  
[PERSON]  
1 Shandong Provincial Engineering and Technical Center of Light Manipulations & Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Iran 25014, China, 202231704948 ts.dnu.edu.cn (X.M. ); [EMAIL_ADDRESS] (H.Z. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (L.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (Y.G. ); [EMAIL_ADDRESS] (Y.Y.) [PERSON]  
1 Shandong Provincial Engineering and Technical Center of Light Manipulations & Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Iran 25014, China, 202231704948 ts.dnu.edu.cn (X.M. ); [EMAIL_ADDRESS] (H.Z. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (L.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (Y.G. ); [EMAIL_ADDRESS] (Y.Y.) [PERSON]  
1 Shandong Provincial Engineering and Technical Center of Light Manipulations & Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Iran 25014, China, 202231704948 ts.dnu.edu.cn (X.M. ); [EMAIL_ADDRESS] (H.Z. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (L.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (Y.G. ); [EMAIL_ADDRESS] (Y.Y.) [PERSON]  
1 Shandong Provincial Engineering and Technical Center of Light Manipulations & Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Iran 25014, China, 202231704948 ts.dnu.edu.cn (X.M. ); [EMAIL_ADDRESS] (H.Z. ); [EMAIL_ADDRESS] (Y.Z. ); [EMAIL_ADDRESS] (L.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (L.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (L.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (C.Y.) [PERSON]  
1 Shandong Provincial Engineering and Technical Center of Light Manipulations & Shandong Provincial Key Laboratory of Optics and Photonic Device, School of Physics and Electronics, Shandong Normal University, Iran 25014, China, 202231704948 ts.dnu.edu.cn (C.M. ); [EMAIL_ADDRESS] (H.Z. ); [EMAIL_ADDRESS] (H.Z. ); [EMAIL_ADDRESS] (L.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (L.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (C.Y. ); [EMAIL_ADDRESS] (C.Y. ); 241166@shnu. have examined the propagation behavior of phase-locked beam arrays in turbulent atmospheres, successfully determining their average intensity distribution [17]. Additionally, research on the scintillation index of phase-locked radial flat-top beam arrays in weakly turbulent conditions has shown that appropriate beam parameters can also be applied to analyze various beam types, including Gaussian and off-axis Gaussian beams [18; 19; 20; 21; 22; 23; 24; 25]. The application of the linear Gaussian Schell model array has further contributed to mitigating turbulence-induced degradation of the beam propagation factor [26]. The scintillation index for partially coherent multi-Gaussian array beams under conditions of extremely strong atmospheric turbulence was also subsequently researched [27]. It is noteworthy that, compared to partially coherent Gaussian beams, array beams demonstrate a significant reduction in the detrimental impacts of atmospheric turbulence [28]. Plasma, ubiquitous in nature and occupying the vast expanses approximately 60 km above the Earth's surface, propels significant advancements in plasma science research and applications [29; 30; 31; 32; 33; 34; 35]. With the rapid evolution of aerospace technology, hypersonic vehicles are achieving unprecedented speeds, causing a substantial increase in the temperature of surrounding gases and generating plasma sheath turbulence around these aircraft [36; 37]. In recent years, the influence of plasma on the transmission characteristics of laser beams has attracted considerable attention.