Les lentilles quadrupolaires magnetiques (I)

New method of designing pole profile in combined function magnets of high field quality

“…Figure 2 shows the profiles of the poles for C 14 ϭ0.0001. The 0.00005 C 18 1.75ϫ10 Ϫ4 C 22 2.00ϫ10 Ϫ6 C 26 1.45ϫ10 Ϫ8 C 30 4.00ϫ10 Ϫ11 quadrupole field gradient 2C 2 in the median plane is 0.12 times the dipole field C 1 . We note that out of the four poles the ones marked N are different from each other, one protrudes out a little while the other shifts away from the center.…”

“…30,31 Since we want a better field quality, we take C 6 ϭC 10 ϭ0. The main error field in a quadrupole comes due to the C 6 term and one tries to reduce this term to zero.…”

Improvement of field quality in quadrupole magnets by optimizing the pole profile consisting of plane surfaces

“…(1) where the C terms are the coefficients of the various harmonics. A pure quadrupole potential contains only the r 2 term and so the pole profile of a perfect quadrupole is given by r 2 cos(2θ) = constant (2) which is a hyperbola. However, for making a quadrupole magnet one has to place energizing coils around the poles and so the poles' width cannot be arbitrarily large.…”

“…However, a circular profile has one advantage apart from easy machinability. The radius of the circle can be so chosen that the 12-pole term becomes zero [1,2]. Grivet and Septier [2] tried various radii experimentally.…”

“…The radius of the circle can be so chosen that the 12-pole term becomes zero [1,2]. Grivet and Septier [2] tried various radii experimentally. The rule of thumb is that the radius of the circle should be 1.145-1.15 times the half-aperture of the magnet [1,2].…”