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

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