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Sponsored by the Center for Science and Technology Development of the Ministry of Education
Supervised by Ministry of Education of the People's Republic of China
In a free-electron devices such as the free-electron laser and the electron cyclotron maser, the electric and magnetic fields generated by a relativistic electron beam substantially affect the electrons' motion and consequently the performance of the device. In this paper the expressions are analytically derived by means of the conservation of particle number for both the electric and magnetic fields generated by a solid electron beam with Gaussian profile, where the situations inside and outside regions of the electron beam are included, and all the explicit expressions are written in terms of the macroscopical radius, current and drifting velocity of the electron beam.