Second-order theory of helical hexapole lens of infinite length

Expressions which can be used to calculate the focusing coefficients applicable to the interior regions (no fringe fields) of magnetic helical hexapole lenses of infinite length have been derived through second-order. It is shown that the helical hexapole has better focusing properties than the non-helical case. Expressions for the aberration coefficients are derived and, for appropriate value of the twisted angle, the helical hexapole reduces aberrations compared to the non-helical case. The numerical examples of a magnetic helical hexapoles in the case of a 25 MeV proton and 250 GeV electron beams are performed.