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Table 8.2 Basic magnets: approximate pole shape, transfer function and inductance
Magnet type
Descriptions
Pole shape
Transfer function Inductance
C-type dipole
w: pole width
g: distance between
poles
NI: total ampereturns
l: yoke longitudinal
length
y = ± g/2
B = ημ 0 NI/g
L = ημ 0 N 2 A/g
A~(w + 1.2g)
(l + g)
H-type dipole
w: pole width
g: distance between
poles
NI: total amperturns
l: yoke longitudinal
length
y = ± g/2
B = ημ 0 NI/g
L = ημ 0 N 2 A/g
A~(w + 1.2g)
(l + g)
Window-frame
d: aperture between
coils
t: coil width
g: physical vertical
aperture
NI: total ampereturns
l: yoke longitudinal
length
y = ± g/2
B = ημ 0 NI/g
L = ημ 0 N 2 A/g
A~(d + 2/3t)
(l + g)
Window-frame
d: aperture between
coils
t: coil width
g: physical vertical
aperture
NI: ampereturns on
one leg
l: yoke longitudinal
length
y = ± g/2
B = ημ 0 NI/g
L = η2μ 0 N 2
A/gA~(d + 2/3t)
(l + g)
Quadrupole
R: radius at pole tip
d: distance
centre-inner coil
NI: ampere-turns per
pole
l: yoke longitudinal
length
2xy = R 2
|B|(r) = Gr
G = η2μ 0 NI/R 2
L = 8πμ 0 N 2
l m
√
d/R
l m = (l + 2/3R)
Sextupole
R: radius at pole tip
d: distance
centre-inner coil
NI: ampere-turns per
pole
l: yoke longitudinal
length
3x 2 y − y 3 = R 3 |B|(r) = Sr 2
S = B ” /2
S = η3μ 0 NI/R 3
L = 12πμ 0 N 2
l m
√
d/R
l m = (l + 1/2R)