Figure 3577 shows an octupole design. The optical axis, along which the electrons travel, is into the page. indicates the direction of the electron beam. The blue curves represent the magnetic field lines, while the red and plum arrowed lines represent the Lorentz force on the electrons. An octupole can be used to adjust a square distortion to the beam. Furthermore, from Equation 4313, we can know the field in the octupole system can be given by,
Namely, it varies by r3, which acts directly as third order aberrations, increasing with distance from the optical axis. However, its lack of cylindrical symmetry can not lead to 3rd-order Cs when the paraxial optics is spherically symmetric, i.e. created by solenoid lenses. In other words, an octupole always generates parasitic aberrations because it has cubic radial dependence together with four-fold azimuthal symmetry (four-fold astigmatism).
Figure 3577. The octupole design for spherical aberration (Cs) correction.
arrows show focusing function, while the red arrows show defocusing function.