It consists of cryo modules containing a cascade of cavities and non corrugated beam tubes. For solving equations in time domain, the finite-difference method with improved characteristic of the dispersion curve in the region of minimum critical wavelength was used in the SN code. For long bunches the single-cell approximation can be used, where the bunch is assumed to keep the same field pattern in its vicinity before and after it travels through a cell. The radiation process is then identical in each cell and the total energy loss in multi-cell structures is simply the sum of the energy losses in the individual cells. However, for short bunches, the field pattern changes tremendously after a passage through a cell.
Dotted curve shows charge density distribution.
The electric force lines are almost radial for the longer bunch, as they were before the cell, whereas a lot of lines lie horizontal and do not touch the wall of the beam tube for the shorter bunch. From the frequency point of view, it means that periodic or quasi periodic accelerating structures have a limited frequency, above which no waves can be excited by a very short bunch. There is some distance, for which the wake potential is approximately constant and close to the value found at vanishing bunch length. The change in amplitude and shape with increasing number of cells can be clearly noted. The peak value of the wake is decreasing during about the first ten cells, after which new maxima appear at the tail of the bunch, which slowly move towards the bunch center.