New Magnet Design for FCC- ee Attilio Milanese, CERN 26 Oct presented by Frank Zimmermann

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

These arc lattices – by Katsunobu Oide – were taken to define the bending and focusing strengths 175 GeV per ring) 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 75.4 m QFQDBEND QF with combined function bending magnets 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 55.8 m QFQDBEND QF with pure dipoles 380 less quadrupoles

We propose this modification to the lattice with pure dipoles, to make it compatible with a twin quadrupole (F/D) layout 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) QFQDBEND QF with pure dipoles – modified for twin quadrupoles 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 QFQDBEND QF with pure dipoles – original QFBENDQDBENDQF QDBENDQFBENDQD pending a full beam physics study

We propose this modification to use (partially) twin quads for the lattice with combined function bending magnets 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) QFBEND with combined function bending magnets – modified for twin quadrupoles 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 with combined function bending magnets – original QF QDBEND QFQDBEND QF QDBEND QF QDBEND QFQD pending a full beam physics study

Assumptions have been made on physical aperture, good field region and inter-beam distance – to be validated Aperture (from impedance / vacuum considerations) bending magnets90 mm vert. × 120 mm horiz. quadrupoles88 mm diameter Good field region (from beam dynamics and the small beam size) 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

/4 - arc dipoles

The proposed layout for the main dipoles features a twin aperture yoke and busbars to provide the Ampere-turns 450 mm 320 mm 120 mm 90 mm 210 mm I = 3570 A, B = 50 mT 00.5 T1.0 T 60×80 mm

This same layout can provide a combined function bending magnet, obtained shaping the pole tips I = 3570 A, B = 50 mT, B’ = ± 0.17 T/m 00.5 T1.0 T 450 mm 120 mm 86 mm 320 mm 210 mm defocusing quad for both beams inside ring outside ring

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

The expected field homogeneity is good, considering the small extent of the good field region (10 mm radius) dipolecombined function energy[GeV] B1B1 [mT] / 1350 / 50 b2b2 [10 -4 ] / / b3b3 [10 -4 ] / 0.2 b4b4 [10 -4 ] / -0.1 b5b5 [10 -4 ] / -0.1 b6b6 [10 -4 ] / -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.

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) –possible recycling of raw material –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

/4 - arc quadrupoles (only twin layout shown)

Also for the quadrupoles a twin design with a 50% power saving is possible, with an F/D polarity constraint T1.5 T NI = A (287 A × 47 turns) B’ = 8.71 T/m 320 mm 640 mm 520 mm 88 mm dia

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

/4 - power estimates

The resistive power depends on aperture, field strength, size and material of the coils (and layout, for twin savings) Ppower per unit length  resistivity, depending whether Cu or Al is used NIAmpere-turns, depending on field strength and aperture jcurrent 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).

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

The resistive power for the quadrupoles is about of factor of two lower if the combined function lattice is used 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 at 175 GeV current density [A/mm 2 ] total power, 2 apertures [MW] (modified) pure dipole lattice (modified) combined function lattice (7.8 twins single)

thank you