THIRD ORDER TRANSFER MATRICES FOR THE FRINGING FIELD OF MAGNETIC AND ELECTROSTATIC QUADRUPOLE LENSES.

Abstract Third order transfer matrices are derived for the fringing field of magnetic and electrostatic quadrupole lenses. All ion optical effects of the fringing field are reduced to a simple transformation at the ideal field boundary. The dominant third order elements are independent of the distribution of the fringing field. The other third order and the first order elements can be evaluated using the distribution function of the field gradient. The calculations are done in an effective fourth order approximation under the assumption that the extension of the fringing field is of about the same size as the beam diameter.