Calculation of aberration coefficients up to sixth order of multipole focusing elements

A method and a computer code have been developed to calculate the aberration coefficients, up to sixth order, for a focusing device consisting of magnetic or electric multipoles. The method is based on the calculation of the ray coordinates at the exit of a focusing device using the RAYTRACE code which provides the magnetic and electric multipole fields necessary for the integration of the equation of motion of the charged particles moving into the focusing device. Subsequently, the exit ray coordinates are considered as a Taylor series expansion, about the origin, in terms of the ray coordinates at the entrance. The coefficients of expansion are the aberration coefficients. The method to calculate the aberration coefficients is discussed further in the text. 5 refs., 1 fig., 1 tab