Considering 3rd3rd order solenoid transport from Ref.  we obtained 90 keV PF-477736 trajectories as shown in Fig. 2, from r=0.08 mm (paraxial) to r=8 mm (most off-axis) for two coil loops corresponding to field type at points c and b in Fig. 1, given by g=1.384Rc, NI=444.25 A–Turns and g=Rc, NI=420 A–Turns, scaled to same focusing strength. Here Rc=0.01 m so that incoming beam size is 80% of aperture. The two sets of trajectories are almost identical. The zoomed focal region in Fig. 2 shows the minor difference. Finding the focal distance f for the most off-axis particle and fo for paraxial particle from Fig. 2 and using Eq. (4) we find Cs=0.026 cm−2 for the helmholtz case b (g=Rc) and Cs=0.022 cm−2 for optimum slot separation case c (g=1.384Rc). These agree very well with points b and c in Fig. 1 having Cs=0.026 cm−2 and Cs=0.023 cm−2 respectively. Thus, the lowest aberration case with a minor dip in peak field can be used practically. But caution is needed if such a pair is repeated contiguously. It is known that for bunched charged particle beams, periodically modulated unidirectional solenoidal fields can give rise to instabilities . It is well known that a shielded solenoid with a small ratio of slot-size s to aperture diameter Da is equivalent to a current loop of diameter same as aperture diameter for the slot . Hence by using two air slots in a single shielded solenoid orgasm should be possible to overlap the fields from the two air slots like a pair of current carrying loops and reduce the spherical aberration.