本研究以Kirchhoff方法為基礎，發展考慮電子束大小之預輻射區渡越輻射理論，我們以此發展出的理論來研究橫向電子數大小對預輻射區渡越輻射角分布的影響。
我們使用準蒙地卡羅法來計算理論所包含的數值積分，一般來說蒙地卡羅積分比較耗時，而在本研究中我們需要計算不同角度的輻射能量來獲得輻射角分布，因此也將開發的數值積分程式平行化來減少計算時間。
我們也以二維的有限差分時域模擬來驗證發展的理論，此研究發展的理論和數值工具，可以用來預測國家同步輻射中心的太赫茲同調渡越輻射實驗之輻射特性。

Optical transition radiation (OTR) has been studied and applied on the beam diagnostics for decades. The potential implication of OTR also includes THz radiation sources. Therefore, the theoretical analysis and simulation tool become indispensable for the study
of OTR. The OTR theory for the wave zone (far-field approximation) has been widely used, and the theory for the pre-wave zone has also been proposed on the basis of single electron approximation. In this study, we developed a theory with consideration of
the electron beam structure based on the Kirchhoff’s method for studying the effect of beam transverse size on the angular distribution of OTR in pre-wave zone. The proposed formalism involves complicated convolution integral of functions and the dimension of the integrand is not the low dimension. To perform such integral, we developed a Fortran program for quasi-monte carlo method, which is robust and suitable for high dimensional integration. The disadvantage of this method is that a large amount of samplings may need to be employed to achieve good convergence. To get the radiation angular profile, we need to perform such integration for different observation angles. This is computing intensive, therefore we parallelize the program with MPI. Two-dimensional FDTD simulations were performed to verify the theoretical calculations. The proposed theory and numerical tool would be used to predict radiation properties of NSRRC THz coherent transition radiation (CTR) in the pre-wave zone.

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