A Minus-I Quadrupole System for Containing Aberration-Correction Octupoles

Octupoles may be used to correct the third order spherical aberration of quadrupole transport systems. Crosstalk in the coupling of an octupole placed at a given point causes it to add a term with the wrong sign in the y-channel if it has the right sign in the x-channel, thus severely reducing efficiency. It is often convenient to utilize a special correcting section insertion which is seen as a +I transfer matrix by the first order focussing. Within point-to-point thin lens optics we give two-parameter systems with 16 magnets having locations with large Sx where Sy = 0 and vice versa for octupole placement.