This paper describes the contents of a general "four-dimensional" computer code for the transient thermal blooming of multi-pulse laser beam propagation. The solutions of the scalar wave equation in Fresnel approximation and the hydrodynamic equations are obtained by means of the discrete Fourier transform method. Based upon the scalar wave equation and the equations of hydrodynamics, the paper makes a model for collimated multi-pulse laser, simulates the transient thermal blooming numerically, and gives the laser beams irradiance distribution by changing respectively the value of the propagation distance, the pulse-repetition rate, the power, and the time. Besides, we simulate the thermal blooming of cw in order to make a contrast with multi-pulse laser. The results show multi-pulse lasers minimize thermal-blooming; if the pulse-repetition rate decreases, thermal blooming decrease, and the quality of the beam is better.Keyword list: Laser propagation in atmosphere; transient thermal blooming; multi-pulse; numerical simulation 1.INTRODUCTIONThe research of High Energy Laser (HEL) propagation in atmosphere is becoming a hotspot, due to its potential application in military affairs. HEL is not only affected by the linear effects [1] , including the absorption of atmospheric molecule, scattering and atmospheric turbulance, but also affected by nonlinear effects. Thermal blooming is one of the most serious nonlinear problems when the laser propagates in atmosphere and, consequently, developing the thermal blooming research is propitious to the application and the development of HEL [2] .

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This paper analyzes the effects of thermal blooming on the Far-Field Irradiance Distribution, based upon the steady-state thermal blooming model, which is introduced by Wallace. It uses the method of numerical simulation and gives the relativity between thermal blooming and these parameters, including initial power,the radius and wavelength.The result reveals that a new void dimensional parameter can describe the extent of thermal blooming. When this dimensional parameter decreases, thermal blooming effect becomes more serious. The result can provide theoretic analysis of thermal blooming effect on the Far-Field. In addition, when the wavelength or the radius changes, the result of Wallace model does not accord with the fact. The contradiction reveals the shortcoming of this model.