1. Arc magnet designs Attilio Milanese 13 Oct. 2016

2. magnet layouts & lattices aperture and good field region
- 1/4 -
magnet layouts & lattices
aperture and good field region

3. with combined function bending magnets
These arc lattices – by Katsunobu Oide – were taken to define the bending and focusing strengths 175 GeV per ring)
with combined function bending magnets QF
BEND QD
BEND QF
75.4 m
BEND: 50 mT & T/m × 33.9 m, 2124 units per ring
QF: 7.71 T/m × 3.5 m = 27.0 T, 1062 units per ring
QD: T/m × 1.4 m = T, 1062 units per ring
380 less quadrupoles
with pure dipoles QF
BEND QD
BEND QF
55.8 m
BEND: 52 mT × 23.9 m, 2884 units per ring
QF: 8.77 T/m × 3.5 m = 30.7 T, 1442 units per ring
QD: T/m × 1.8 m = 30.4 T, 1442 units per ring

4. We propose this modification to the lattice with pure dipoles, to make it compatible with a twin quadrupole (F/D) layout
with pure dipoles – modified for twin quadrupoles QF
BEND QD
BEND QF QD
BEND QF
BEND QD
BEND: 54 mT × 22.9 m, 2884 twin units
QF: 8.73 T/m × 3.5 m = 30.6 T, 2884 twin units
QD: T/m × 3.5 m = 30.6 T, 2884 twin units (combined with the QF)
pending a full beam physics study
with pure dipoles – original QF
BEND QD
BEND QF QF
BEND QD
BEND QF
BEND: 52 mT × 23.9 m, 2884 units per ring
QF: 8.77 T/m × 3.5 m = 30.7 T, 1442 units per ring
QD: T/m × 1.8 m = 30.4 T, 1442 units per ring

5. We propose this modification to use (partially) twin quads for the lattice with combined function bending magnets
with combined function bending magnets – modified for twin quadrupoles QF
BEND QD
BEND QF QD
BEND QF
BEND QD
BEND: 52 mT & T/m × 32.4 m, 2124 twin units
QF: 7.71 T/m × ( ) m = 27.0 T, 2124 twin units (shorter) units per ring
QD: T/m × 2.2 m = T, 2124 twin units (combined with the twin QF)
pending a full beam physics study
with combined function bending magnets – original QF
BEND QD
BEND QF QF
BEND QD
BEND QF
BEND: 50 mT & T/m × 33.9 m, 2124 units per ring
QF: 7.71 T/m × 3.5 m = 27.0 T, 1062 units per ring
QD: T/m × 1.4 m = T, 1062 units per ring

6. Assumptions have been made on physical aperture, good field region and inter-beam distance – to be validated
Aperture (from impedance / vacuum considerations)
bending magnets 90 mm vert. × 120 mm horiz.
quadrupoles 88 mm diameter
Good field region (from beam dynamics and the small beam size)
10-4 field homogeneity in ±10 mm horiz., not counting quad term
Inter-beam distance (assumed, not a constraint)
320 mm
down to ≈250 mm is likely achievable for the proposed magnets layouts

7. - 2/4 -
arc dipoles

8. The proposed layout for the main dipoles features a twin aperture yoke and busbars to provide the Ampere-turns
I = 3570 A, B = 50 mT
320 mm
90 mm
210 mm
120 mm
60×80 mm
450 mm
0.5 T
1.0 T

9. defocusing quad for both beams
This same layout can provide a combined function bending magnet, obtained shaping the pole tips
defocusing quad for both beams
I = 3570 A, B = 50 mT, B’ = ± 0.17 T/m
320 mm
86 mm
210 mm
120 mm
inside ring
outside ring
450 mm
0.5 T
1.0 T

10. Trims can provide a few % tunability of the strengths of the two apertures, as well as introduce skew low order term
4 trims powered
0.50 mT in right aperture
-0.50 mT in left aperture
1 trim powered
skew dipole (and quad) in right aperture
left aperture unaffected

11. The expected field homogeneity is good, considering the small extent of the good field region (10 mm radius)
dipole
combined function
energy
[GeV] 45
175 B1
[mT] 15 50
13 / 13
50 / 50 b2
[10-4]
-0.7
0.1 / / b3
0.5
0.4
0.3 / 0.2 b4
-0.8
0.1 / -0.1 b5
-0.3
-0.2 / -0.1 b6
-0.1
-0.0
0.1 / -0.0
allowed multipoles at 10 mm radius
(inside / outside apertures for the combined function)
A further optimization of field quality – including 3D effects at the end of the blocks and busbar routings – is possible, though the pole width is already compatible with the field homogeity requirements.

12. This twin “I” layout for the bending magnets has several features
50% power consumption w.r.t. separate magnets
half the units to manufacture, transport, install, remove
the excitation circuit is made with (water cooled) busbars
no cost for coil manufacturing
no inter-turn insulation (reliability even with radiation)
possible recycling of raw material
individual trims on the apertures are possible
a split busbar is shown for the combined function, with an open midplane towards the outside of the ring, leaving space possibly to be used for synchrotron radiation absorption
the yoke is compact and with no dilution (not like LEP, for example)
punched thick laminations (5-6 mm, like HERA and LHC)
likely split in several blocks, with threaded busbars (like LEP and SLC)
the wide and slender pole amplifies the field in the iron of a factor > 3 – which is beneficial at low energy

13. (only twin layout shown)
- 3/4 -
arc quadrupoles
(only twin layout shown)

14. Also for the quadrupoles a twin design with a 50% power saving is possible, with an F/D polarity constraint
NI = A
(287 A × 47 turns) B’ = 8.71 T/m
320 mm
88 mm dia
520 mm
640 mm
0.75 T
1.5 T

15. This twin layout for the quadrupoles has several features
twin means 50% power consumption w.r.t. separate magnets
this comes with a polarity constraint, F/D as seen by the beams
the main quadrupoles of LHC are also F/D (as seen by the beams), and the (independent) powering circuits are run typically with 5% difference
the excitation is provided by water cooled coils
2 (simple racetrack) coils instead of 8
coils far from the midplane, hence far from synchrotron radiation
cable losses contained by the low current (< 300 A)
trims on individual apertures can be considered
the yoke is of a classical construction
punched laminations + plates and non magnetic spacers
parts of the inner inter-beam space could be possibly reserved for synchrotron radiation absorption
midplane shield for stray field
field quality similar to that of a classical quadrupole can be achieved on paper with the proper (asymmetric) poles

16. - 4/4 -
power estimates

17. The resistive power depends on aperture, field strength, size and material of the coils (and layout, for twin savings)
𝑃=𝜌 𝑁𝐼 j
P power per unit length
r resistivity, depending whether Cu or Al is used
NI Ampere-turns, depending on field strength and aperture
j current density, i.e. small coil or large coil area
An overall cost optimum shall derive from the sum of integrated operating cost (electricity consumption) and capital cost (amount of conductor, power converters).
The following estimates refer to 175 GeV only and they are based on not optimized cross sections (ex., different coil size for dipole and combined function).

18. The resistive power for the bending magnets at 175 GeV is about 15 MW
current density
[A/mm2]
total power, 2 apertures [MW]
twin pure dipole
0.7
10.1
twin combined function
0.9
12.9
Al conductor
losses in interconnects / cables to be considered, likely 20-30%
depending on arc filling factor and location of power converter(s)

19. The resistive power for the quadrupoles is about of factor of two lower if the combined function lattice is used
at 175 GeV
current density
[A/mm2]
total power,
2 apertures
[MW]
(modified) pure dipole lattice
2.3
21.5
(modified) combined function lattice
2.0
12.4
(7.8 twins single)
Cu conductor
cable losses to be added, for quadrupoles likely only a few %
if twins are not used, then the power goes up to 43 MW for the pure dipole lattice, and 20 MW for the combined function one

20. thank you