## 2 System and Theoretical Model
### Amplitude Fluctuations Variance Model  
Solar wind erupts from the Sun stochastically, and it fluctuates in space and time. The study of solar wind belongs to the field of space physics. Exploring solar wind plasma theory is not only related to human understanding of physical processes, such as stellar particle acceleration, stellar energy transport, space weather change, and magnetic reconnection, but it is also related to ensuring the safety of human outer space and the normal communication between deep space detectors and earth observation stations. In recent years, electromagnetic studies on optical signal propagation have been concerned by researchers [21; 22; 23]. As the main factor affecting the relationship between the Sun and the Earth, the research on the variation of solar wind has gradually attracted the attention of space physics and received extensive research. The accurate solar wind model does not yet exist. However, the spatial spectrum of solar wind can be used to describe the irregularity of its turbulence. When ignoring coronal mass ejections, the turbulent vortices of solar wind plasma in a certain region is considered to be locally uniform. The observed data indicates that the changes in the internal structure of solar wind turbulence is not pronounced within a wave period, and the turbulence at this time is usually regarded as \"frozen\", so that \"[PERSON]'s freezing theory\" might be applied [24]. According to this theory, the coronal turbulence is regarded as a locally homogeneous frozen random medium moving at a constant solar wind velocity. The hypothesis is reasonable and has been widely used in radio astronomy research [25]. Moreover, based on long-term observations, the coronal spectrum has been proved to be  
Figure 1: Geometric diagram for deep space communication during superior conjunction. close to the non-Kolmogorov spectrum [26]. Therefore, we set the value of the spectral index \(p\) as \(3<p<4\), and then the spatial power spectrum of the density fluctuations in corona is characterized by the generalized von Karman turbulence spectrum and the generalized exponential spectrum as:  
\[\Phi_{N}\ (\kappa,z)=C_{N}^{2}(z)\kappa^{-p},\kappa_{i}<\kappa<\kappa_{o}, \tag{2}\]  
where \(C_{N}^{2}\) is the structural constant of the solar wind coronal turbulence, which is obtained from [25] as follows:  
\[C_{N}^{2}(z)= \begin{cases}(2\pi)^{(-3/2)}\frac{(p-3)\Gamma(\frac{r}{2})\kappa_ {o}(p-3)}{\Gamma\left(\frac{p-1}{2}\right)}\delta(N_{e}(r))_{r}^{2}\ for\ 3<p<4\\ 4\pi\ln\left(\frac{2\kappa_{o}}{\kappa_{i}}\right)\delta(N_{e}(r))^{2},\ for\ p=3\end{cases} , \tag{3}\]  
where \(\kappa_{o}=2\pi/l_{o}\), \(\kappa_{i}=2\pi/l_{i}\). \(l_{o}\) and \(l_{i}\) are the outer and inner scales of the coronal turbulence, respectively. \(\Gamma(\cdot)\) is the Gamma function. Using the empirical formula in [27] for the solar wind plasma density, the electron density is obtained as a function of the heliocentric distance \(r\):  
\[N_{e}(r)=2.21\times 10^{14}\bigg{(}\frac{r}{R_{sun}}\bigg{)}^{-6}+1.55\times 10^{ 12}\bigg{(}\frac{r}{R_{sun}}\bigg{)}^{-2.3}. \tag{4}\]  
Moreover, the irregularities of solar wind plasma density are usually assumed proportional to the plasma density as \(\delta N_{e}(r)=\eta N_{e}(r)\), and \(\eta\) is solar wind plasma density relative fluctuation factor [25]. As we discussed in Section 1, when the optical signal approaches the solar region, it is scattered by the turbulent medium in the Fresnel region, which results in the amplitude and phase fluctuation of the electromagnetic wave through the solar wind turbulent vortex in the coronal region. These fluctuations are commonly referred to as solar scintillation [28]. Here we only consider the effect of solar scintillation on the amplitude fluctuations of optical waves. Since the amplitude fluctuations usually distribute around their mean levels, the variance of the signal \(\chi^{2}\) is an important parameter to characterize its variation.