Title: Correcting Quadrupole Roll in Magnetic Lenses with Skew Quadrupoles

Quadrupole rolls (i.e. rotation around the magnet axis) are known to be a significant source of image blurring in magnetic quadrupole lenses. These rolls may be caused by errors in mechanical mounting of quadrupoles, by uneven radiation-induced demagnetization of permanent-magnet quadrupoles, etc. Here a four-quadrupole ×10 lens with so-called ”Russian” or A -B B-A symmetry is used as a model problem. Existing SLAC 1/2 in. bore high-gradient quadrupoles are used in the design. The dominant quadrupole roll effect is changes in the first-order part of the transfer map (the R matrix) from the object to the image plane (Note effects on the R matrix can be of first order in rotation angle for some R-matrix elements and second order in rotation angle for other elements, as shown below). It is possible to correct roll-induced image blur by mechanically adjusting the roll angle of one or more of the quadrupoles. Usually, rotation of one quadrupole is sufficient to correct most of the combined effect of rolls in all four quadrupoles. There are drawbacks to this approach, however, since mechanical roll correction requires multiple entries into experimental area to make the adjustments, which are made according to their effect on images. Anmore » alternative is to use a single electromagnetic skew quadrupole corrector placed either between two of the quadrupoles or after the fourth quadrupole (so-called “non-local” correction). The basic feasibility of skew quadrupole correction of quadrupole roll effects is demonstrated here. Rolls of the third lens quadrupole of up to about 1 milliradian can be corrected with a 15 cm long skew quadrupole with a gradient of up to 1 T/m. Since the effect of rolls of the remaining three lens quadrupoles are lower, a weaker skew quadrupole can be used to correct them. Non-local correction of quadrupole roll effects by skew quadrupoles is shown to be about one-half as effective as local correction (i.e. rotating individual quadrupoles to zero roll angle or placing skew quadrupole correctors in the bores of main quadrupoles).« less