IMPASS - A Computer Program for Calculations of Impedances of Periodic Axially Symmetric Smooth Structures (Bellows)

The computer program IMPASS approximately solves an infinite system of linear algebraic equations for the expansion coefficients of the general solution of the Maxwell equations derived in Ref. 1. The coefficients are found by inverting the matrix, cut to a certain finite size. The values of longitudinal and transverse impedances, for a given frequency and for a given number (e.g. m=0 or m=1) of the azimuthal Fourier harmonic of the bunch density, are proportional to the zeroth coefficients of the solutions. Standard FFT routines are used to speed up the calculations of the matrix elements and terms in the right hand side of the equations. The stability of the solution, with respect to the matrix size and to the precision of the equation terms, is studied. The CPU time on a CYBER 875 computer, needed to find both the longitudinal and the transverse impedances of bellows for one value of the frequency, is of the order of a second.