Problems
Sextupolar fields are non-linear (i.e. they depend on the product of the sizes of the transverse displacements), and have terms which depend on both the horizontal and vertical offsets (i.e. they are coupled).
This leads to equations of motion that cannot be solved for the general case, thus requiring approximations to be used when calculating their effects on the beam.
In addition, the quadrature dependence of the sextupole kick on the transverse offset of the beam, can lead to high amplitude particles being kicked far from the beam axis and being lost on the beam-pipe walls. Due to this mechanism, the addition of sextupole fields to an accelerator lattice will limit the dynamic aperture or acceptance of the accelerator.
Read more about this topic: Sextupole Magnet
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