Random matrix a (m, n) and by means of the inverse Fourier transform towards the discretized phase screen as follows [27]: (m, n) =m =1 n =NxNya (m, n)0.479 -5/6 -11/6 k r L x Lyexp jmm nn + Nx Ny,(18)where L x and Ly are side lengths, and Nx and Ny would be the number of grids. Moreover, the third harmonic strategy is utilized to compensate for the low frequency inadequacy. Lastly, the total phase S(r, z), such as the low and high frequency elements, modulates the light field. Hence, the resolution of Equation (10) is expressed as [28] E(r, z + z) = exp exactly where expi 2k z+z zi 2kz+z zd exp[iS(r, z)] E(r, z),(19)d is triggered by vacuum diffraction.3.two. Simulation parameters This simulation study involves laser characteristics, atmospheric properties, and sodium layer features. All relevant parameters are listed in Table 1 [2]. When = 30 and B = 0.228 Gs, the scale aspect of depolarization f m = 0.8466. Particularly, a laser with TEM00 mode is launched at collimation.Atmosphere 2021, 12,7 ofTable 1. Numerical simulation parameters.Variable Names Laser parameters Center wavelength of laser Linewidth of continuous wave laser Laser polarization Laser beam excellent factor Diameter of laser launch Zenith of laser launch Angle between directions of laser beam and geomagnetic field vector Sodium parameters Linewidth of sodium atomic distributions at sodium layer Life time of excited sodium atoms Backscattering coefficient of excited sodium atoms Column density of sodium layer Cycle time of sodium atomic collisions Altitude of sodium layer centroid Atmospheric, magnetic field parameters Atmospheric transmissivity Mesospheric magnetic field 4. Final results and Analysis four.1. Recoil and Linewidth BroadeningSymbols L v D + D v D CNa T L T0 BValues 589.159 nm 0.0 GHz circular 1.1 40 cm 30 30 1.0 GHz 16 ns 1.5 four 1013 cm-2 35 92 km 0.8 0.228 GsThe continuous wave laser is single-mode having a 0 or 2.0 MHz linewidth. For the 2.0 MHz linewidth laser, its intensity distribution is expressed as Equation (five). The total intensity of your laser is taken as I = 150 W/m2 . It is actually assumed that sodium atoms are excited just about every 32 ns as a consequence of the cycle time of excited LY267108 custom synthesis states. The tens of nanoseconds inside the ascending stage are ignored just before steady states. For the 0 MHz laser, the normalized distributions of sodium atoms immediately after recoil are simulated at t = 10 , 20 , and 35 as in Figure two. As a way to study the effects of linewidth broadening around the mitigation of recoil, the linewidth of your continuous wave laser is taken to become two.0 MHz in Equation (5). Soon after t = 10 , 20 , and 35 , the normalized distributions of the sodium atoms are presented in Figure three.Figure two. Normalized distributions of sodium atoms with recoil at t = 10 , 20 , and 35 for 0 MHz linewidth.Atmosphere 2021, 12,eight ofFigure three. Normalized distributions of sodium atoms with linewidth broadening at t = 10 , 20 , and 35 .From Figure 2, a single can see that recoil benefits inside the accumulation of sodium atoms at greater and Fluticasone furoate Biological Activity larger Doppler shifts as time goes on. Compared with Figure 2, right after linewidth broadening is employed, the peaks of recoil considerably drop in Figure four, plus the corresponding 3 sodium atomic distributions are coincident. As well as this, the laser intensity also influences recoil, as is shown in Figure 4. With all the similar linewidth broadening system as the above, after t = 35 for I = 50 W/m2 , one hundred W/m2 , and 150 W/m2 , the conditions of mitigated recoil are shown in Figure 5.Figure 4. Normalized dist.
