8 Accelerator Engineering and Technology: Accelerator Technology
347
The interaction between a moving charge and the magnetic field is described by
the so called Lorentz force, which in the macroscopic form for a wire carrying a
current I is referred as Laplace force:
F = I l × B,
(8.12)
where the length l is oriented towards the direction of the current flow. For
example 1.5 m of straight coil immerged in an average magnetic field component
perpendicular to the coil of 0.5 T, carrying a total current of 60,000 ampere-turns, is
subjected to a force of F = 60,000 · 1.5 · 0.5 = 45 kN.
8.1.2.3 Yoke
The magnet yoke has the function of directing and shaping the magnetic field
generated by the coils. While magnets operated in persistent mode can be built
either with solid or with laminated steel, the yokes of cycled magnets are composed
of laminations electrically insulated from each other to reduce the eddy currents
generated by the change of magnetic field with time. This electrical insulation can
be inorganic (oxidation, phosphating, Carlite) or organic (epoxy). Epoxy coating in
a B-stage form can be used to glue laminations together, a technique widely used for
small to medium magnets, possibly reinforced by welded bars on the yoke periphery.
The magnetic properties of steel depend on the chemical composition and
on the temperature/mechanical history of the material. Important parameters for
accelerator magnets are the coercive field H c and the saturation induction. The
coercive field has an impact on the reproducibility of the magnetic field at
low currents. A typical requirement for the steel used in accelerator magnets is
H c < 80 A/m. Tighter constraints (H c < 20 A/m) apply when the operation covers
a large field factor starting from low field inductions (few hundred gauss). The
saturation induction is highest with low carbon steel (carbon content in the final
state <0.006%). It is common to specify points along the normal magnetization
curve, with the condition that the magnetic induction B shall exceed specification
values at given field levels H.
To increase its electrical resistivity and at the same time narrow the hysteresis
cycle, laminated steel used in cycled magnets usually contains 2 . . . 3% of silicon.
With 3% of Si the electrical resistivity increases from ρ = 2 · 10 −7 m to
ρ = 5 · 10 −7 m.
The work performed during the hysteresis cycle and the eddy currents produce
losses in cycled magnets. An estimate of hysteresis losses can be obtained by the
Steinmetz law:
P
W
kg
= η · f · B
1.6 ,
(8.13)
347
The interaction between a moving charge and the magnetic field is described by
the so called Lorentz force, which in the macroscopic form for a wire carrying a
current I is referred as Laplace force:
F = I l × B,
(8.12)
where the length l is oriented towards the direction of the current flow. For
example 1.5 m of straight coil immerged in an average magnetic field component
perpendicular to the coil of 0.5 T, carrying a total current of 60,000 ampere-turns, is
subjected to a force of F = 60,000 · 1.5 · 0.5 = 45 kN.
8.1.2.3 Yoke
The magnet yoke has the function of directing and shaping the magnetic field
generated by the coils. While magnets operated in persistent mode can be built
either with solid or with laminated steel, the yokes of cycled magnets are composed
of laminations electrically insulated from each other to reduce the eddy currents
generated by the change of magnetic field with time. This electrical insulation can
be inorganic (oxidation, phosphating, Carlite) or organic (epoxy). Epoxy coating in
a B-stage form can be used to glue laminations together, a technique widely used for
small to medium magnets, possibly reinforced by welded bars on the yoke periphery.
The magnetic properties of steel depend on the chemical composition and
on the temperature/mechanical history of the material. Important parameters for
accelerator magnets are the coercive field H c and the saturation induction. The
coercive field has an impact on the reproducibility of the magnetic field at
low currents. A typical requirement for the steel used in accelerator magnets is
H c < 80 A/m. Tighter constraints (H c < 20 A/m) apply when the operation covers
a large field factor starting from low field inductions (few hundred gauss). The
saturation induction is highest with low carbon steel (carbon content in the final
state <0.006%). It is common to specify points along the normal magnetization
curve, with the condition that the magnetic induction B shall exceed specification
values at given field levels H.
To increase its electrical resistivity and at the same time narrow the hysteresis
cycle, laminated steel used in cycled magnets usually contains 2 . . . 3% of silicon.
With 3% of Si the electrical resistivity increases from ρ = 2 · 10 −7 m to
ρ = 5 · 10 −7 m.
The work performed during the hysteresis cycle and the eddy currents produce
losses in cycled magnets. An estimate of hysteresis losses can be obtained by the
Steinmetz law:
P
W
kg
= η · f · B
1.6 ,
(8.13)