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A variational calculus approach for improving the field quality in Glaser magnets

Glaser magnets used for focusing low-energy charged particle beams show appreciable spherical aberration causing an increase in the beam emittance. By using the variational method we have shown that the spherical aberration can be minimized if the axial field in the magnet follows a cosine-squared form. We have shown that by shaping the pole pieces one can make the field have a shape closer to the cosine-squared function.