The behaviour of the ion beam is similar to that of light ray propagated through a system of lenses. Due to this analogy, a system of magnets for beam transportation is often called ion optics . At GSI a [...] operating accelerators it is extremly important to be able to simulate the beam properties. In an ion beam, the motion of the particles perpendicular to the direction of beam propagation is determined [...] a frequently used tool for simulating ion optical systems is the program MIRKO, which was developed at GSI by B.J. Franczak. MIRKO is in particular used heavily for the design of accelerators and beam transport