Linear quadrupoles with added hexapole fields are described. The shifts in ion oscillation frequency caused by the addition of a hexapole field are calculated within the effective potential model. Methods to construct linear quadrupoles with added hexapole fields with exact electrode geometries and with round rods are discussed. A quadrupole with added hexapole field can be constructed with round rods by rotating two rods (say the y rods) towards an x rod. Computer simulations are used to investigate the possibility of mass analysis with quadrupoles with added hexapole fields. We find that a quadrupole with an added hexapole field in the range 2-12% can provide mass analysis provided the dc is applied with the correct polarity and value. When a rod set is constructed with round rods, other multipoles in the potential degrade the peak shape, resolution and transmission. The largest of these after the quadrupole and hexapole are a dipole and octopole term. With round rod sets, the peak shape can be improved by using different diameters for the x and y rod pairs to minimize the octopole term in the potential and by injecting ions at the field center where the dipole term is zero. Calculations of the boundaries of the stability diagram for this case show the boundaries move out, relative to those of a pure quadrupole field, but remain sharp.
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