Based on the equivalence principle and the reciprocity theorem, the multiple scattering up to $N$th-order by adjacent multi-particles is considered in this study. It is well known that the first-order solution can easily be obtained by calculating the scattered field from isolated targets when illuminated by a plane wave/Gaussian beam. However, due to the difficulty in formulating the couple scattered field, it is very difficult to find an analytical solution for the higher-order of the scattered field with considering the multiple scattering even for multi-canonical geometries, such as spheres, spheroids, and cubes. In order to overcome this problem, in this present work, the higher-order solutions of electromagnetic scattering for multi-particles are derived by employing the technique based on the reciprocity theorem and the equivalence principle. In specific, using the formulas of the composite scattering field obtained in this work, the bi-static scattering of plane wave/Gaussian beam by adjacent multi-spheres is calculated and the results are compared with those obtained from the numerical computations by the Time Domain Integral Equation Method (TDIEM).
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