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The propagation of the Gaussian laser beam through the atmosphere is one of the most important features for military, scientific, industry and medical applications. this paper presents a theoretical study to simulate the effect of turbulence attenuation on propagation of laser beam and calculation of lossy power and divergence beam. A simulation of laser production within the X-ray region showed that the wavelength (0.0985 nm) used in the research could be obtained using the energy of the electron beam of (320 PJ). There are three important parameters in calculating the wavelength in the free electron laser (undulator period, relativistic factor, undulator parameter), and they appear through simulations when the laser power depends greatly on the undulator length and we can dispense with the resonator and increasing the undulator length. The divergence beam was increased with altitude and equals (0.0195003m) in (H= 11km). From the attenuation calculations, the power absorbed (lost) is directly proportional to the radius of the laser beam and inversely proportional to the laser wavelength. From the attenuation calculations, the power absorbed (lost) is directly proportional to the radius of the final laser beam and inversely proportional to the laser wavelength. As for the atmosphere turbulence, it is intense at sea level and decreases with altitude, the structure refractive index C n 2 in MSL equal 3.92 × 10 − 13 m 2 3 and indicates the severe of turbulence. Fried Parameter ro is directly proportional with altitude and (ro=0.7485 μm) in sea level and indicates to severe turbulence and decreases with altitude. Therefore, the attenuation operation and atmospheric turbulence are affected by temperature fluctuations and altitude. [ABSTRACT FROM AUTHOR]

Gaussian beam propagation of the Free Electron Laser (FEL) through the atmosphere is a very important topic for many vital applications in the military, scientific, and medical fields, where laser beam spot size and final power are extremely important requirements in most laser applications. The propagation of a Gaussian laser beam in the atmosphere is subject to attenuation processes that affect the laser beam. From the results, simulations of the free electron laser system showed that an X-ray laser with a wavelength of 0.50418 nm can be produced with an energy beam of 200 PJ. The M2 quality factor will increase with the propagation distance, determining the final laser spot size. As a result of the attenuation processes, there is a slight loss in the final energy of the laser as well as divergence in the laser beam that reaches the target. The amount of attenuation is highly dependent on the density of the atmosphere and the size of the laser spot. When the laser beam propagates in the near-field (less than 20 m) or mid-field (20–100 m) horizontally and vertically at sea level, the values of the attenuation coefficient when propagating in the horizontal direction are greater compared to the propagation in the vertical direction. [ABSTRACT FROM AUTHOR]