8 Accelerator Engineering and Technology: Accelerator Technology
343
8.1.2.1 Magnetic Design
Transfer function (the ratio of the magnetic field intensity in the magnet aperture
to the supply current) and inductance can be computed starting from the Ampere’s
law and considering the relationship between magnet inductance (L), current (I) and
energy (E) as E = ½·LI 2 .
In practical cases the theoretical transfer function of an ideal magnetic circuit
is reduced by an “efficiency” η, typically of the order of η = 0.95 . . . 0.98, which
depends on the length, stacking factor and working conditions of the magnetic yoke.
The formulas in Table 8.2 provide an analytical formulation of the inductance values
for different magnet configurations.
The inductance depends on how the pole geometry is trimmed (shims, tapered
poles, chamfers) and on saturation. For quadrupole and sextupole magnets different
tapering of the poles can strongly modify the inductance. For such magnets these
simplified formulas can cover only standard designs.
The field homogeneity typically required by an accelerator magnet within its
good field region is of the order of few parts in 10 −4 . Transfer line and corrector
magnets may be specified with lower homogeneity.
Field quality in a given volume is determined by several factors:
• the size of the magnet aperture with respect to the good field region
• the shape of the iron poles
• manufacture and assembly tolerances
• the position of active conductors (coils), in particular in window-frame magnets
• the ferromagnetic properties at the working conditions of the steel used for the
yoke
• dynamic effects
Optimizing field quality is achieved considering all above aspects. In particular
magnets operating below 2 T, as the ones treated in this chapter, are also described
as iron dominated magnets because the shape of the magnetic field induction is
dominated by the shape of the ferromagnetic poles. At the interface between the
magnet aperture and the poles, i.e. between steel and air, the component of the
magnetic field induction B ⊥ perpendicular to the interface surface is the same
on both media. The tangential component of the magnetic field H t also remains
the same in case no surface currents are present: this corresponds to a change of
the tangential components B t of the field induction by the ratio of the magnetic
permeability between the two media. As a result, in case of infinite permeability the
direction of the magnetic field induction in the air at the exit of a magnet pole is
always perpendicular to the pole surface.
An example of trimming field quality with pole shims in a dipole magnet is
shown in Fig. 8.3.
343
8.1.2.1 Magnetic Design
Transfer function (the ratio of the magnetic field intensity in the magnet aperture
to the supply current) and inductance can be computed starting from the Ampere’s
law and considering the relationship between magnet inductance (L), current (I) and
energy (E) as E = ½·LI 2 .
In practical cases the theoretical transfer function of an ideal magnetic circuit
is reduced by an “efficiency” η, typically of the order of η = 0.95 . . . 0.98, which
depends on the length, stacking factor and working conditions of the magnetic yoke.
The formulas in Table 8.2 provide an analytical formulation of the inductance values
for different magnet configurations.
The inductance depends on how the pole geometry is trimmed (shims, tapered
poles, chamfers) and on saturation. For quadrupole and sextupole magnets different
tapering of the poles can strongly modify the inductance. For such magnets these
simplified formulas can cover only standard designs.
The field homogeneity typically required by an accelerator magnet within its
good field region is of the order of few parts in 10 −4 . Transfer line and corrector
magnets may be specified with lower homogeneity.
Field quality in a given volume is determined by several factors:
• the size of the magnet aperture with respect to the good field region
• the shape of the iron poles
• manufacture and assembly tolerances
• the position of active conductors (coils), in particular in window-frame magnets
• the ferromagnetic properties at the working conditions of the steel used for the
yoke
• dynamic effects
Optimizing field quality is achieved considering all above aspects. In particular
magnets operating below 2 T, as the ones treated in this chapter, are also described
as iron dominated magnets because the shape of the magnetic field induction is
dominated by the shape of the ferromagnetic poles. At the interface between the
magnet aperture and the poles, i.e. between steel and air, the component of the
magnetic field induction B ⊥ perpendicular to the interface surface is the same
on both media. The tangential component of the magnetic field H t also remains
the same in case no surface currents are present: this corresponds to a change of
the tangential components B t of the field induction by the ratio of the magnetic
permeability between the two media. As a result, in case of infinite permeability the
direction of the magnetic field induction in the air at the exit of a magnet pole is
always perpendicular to the pole surface.
An example of trimming field quality with pole shims in a dipole magnet is
shown in Fig. 8.3.