Computations of the accelerator section of the International Linear Collider (ILC), which consists of superconducting niobium cavities, are performed for conditions of the maximum energy transfer to electrons that travel along the cavity axis. A mathematical model and software packages are created for the computation of the electric characteristics and profile of a single-cell cavity. A computer-based synthesis of the cavity shape that yields the required electric characteristics is performed. The promising design variants of a single-cell cavity, with which a quality factor of 10 ~(10) is provided at a working frequency of 1.3 GHz, are found to optimize the construction and manufacture of a single-cell cavity. The electric characteristics of a chain of single-cell cavities are computed.
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