ABCI described here is a computer program which solves the Maxwell equations directly in the time domain when a Gaussian beam goes through an axi-symmetrical structure on or off axis. Many new features have been implemented in this version of ABCI, including the "moving mesh" and Napoly's method of calculation of wake potentials. The mesh is now generated only for the part of the structure inside a window, and moves together with the window frame. This moving mesh option drastically reduces the

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... number of mesh points, and therefore allows calculation of wake potentials in very long structures and/or for very short bunches. In terms of Napoly's integration method, the calculation of transverse and longitudinal wake potentials in (}. structure such as a collimator, where parts of the cavity material come down below the beam pipe radius, can be carried out now correctly with beam pipes of short length at both ends. For the monopole wake potential, ABCI can be applied even to structures with unequal beam pipe radii. A newly installed mesh generator performs automatic circular and elliptical connections of input points just as TBCI does. In addition to the conventional method, ABCI permits the input of the structure geometry by giving the increments of coordinates from the previous positions. In this method, one can use the repetition commands to repeat input blocks when the same structure repeats many times. Plots of a cavity shape and wake potentials can be obtained in the form of a Top Drawer file. ABCI is available as a source code in the CERN IBM VM/CMS system. • This work was supported by the