In this paper, we present a simulation of the dynamic procedure of the photon storage in a practical supercavity (R = 99.99%) pumped by a circular symmetric Gaussian beam. The Fox-Li technique has been used to numerically calculate the field distribution, the diffraction losses, and the round-trip phase shift of TEM(0n) modes. A concept of an effective Fresnel number is put forward. Details of the Fox-Li type calculation are introduced along with the discussions of the convergence in solutions of the iterative equations. The effects of the refraction index of the e-beam and the loss of Compton backscattering by the e-beam inside the cavity are discussed. [References: 5]
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