Linear quadrupoles with added octopole fields. 
Two methods of adding relatively small octopole fields to the main quadrupole field of quadrupoles and linear ion traps with cylindrical rods are investigated.  The first, 'stretching' the quadrupole by moving two rods out from the axis, produces a combination of higher order fields with similar magnitudes in which the octopole field is not necessarily the greatest.  The quadrupole field strength is changed significantly and a large potential appears on the axis.  The second method uses rod pairs of different diameters.  It adds octopole components of up to several percent while all other higher order fields remain small.  An axis potential is also added, but it is only a few percent of the radio-frequency (RF) voltage and approximately equal to the strength of the octopole field.  The axis potential can be removed by moving the larger rod pair out from the axis or applying unbalanced RF to the electrodes.