Frascati, 7 th November 2007 CARE HHH APD mini-workshop IR’07 DESIGN ISSUES N U IN A 130 MM APERTURE TRIPLET F. Borgnolutti, E. Todesco Magnets Cryostats and Superconductors Group Magnets, Cryostats and Superconductors Group Accelerator Technology Department, CERN F. Borgnolutti, E. Todesco
CONTENTS Motivations for a 130 mm aperture triplet 130 mm aperture quadrupoles in Nb-Ti 130 mm aperture quadrupoles in Nb 3 Sn 130 mm aperture quadrupoles in Nb 3 Sn Conclusions Design issues in 130mm aperture quadruopoles - 2 F. Borgnolutti, E. Todesco
MOTIVATIONS FOR A 130 MM APERTURE Proposed LHC triplet lay-out for getting β ∗ =0.25 (the “symmetric” solution solution, LHC Project Report 1000 ) t 1000 ) LHC P j t R A stretched version of the present lay-out The same aperture and cross-section in Q1-Q3 To minimize cost of model, prototypes and spares, maximize interchangeability Different lengths of Q1-Q3 and Q2 but the same current g Q Q Q To minimize cost of power supply, simplify powering schemes We require β ∗ =0.25 m and additional aperture for collimation We end up with We end up with A=130 mm G ∼ 125 T/m Q1 l 2 Q3 * L(Q1)=L(Q3)=9 2 m L(Q1)=L(Q3)=9.2 m l L(Q2) =7.8 m l 1 Q2A Q2B Total triplet length 35 m with gaps 40 m with gaps, 40 m 0 25 50 Distance from IP (m) Design issues in 130mm aperture quadruopoles - 3 F. Borgnolutti, E. Todesco
MOTIVATIONS FOR A 130 MM APERTURE The study presented in LHC PR 1000 presents a parametric study of solutions having [E T d study of solutions having [E. Todesco, J. P. Koutchouk, CARE workshop Valencia06] J P K t h k CARE k h V l i 06] Triplet length from 25 to 40 m Triplet aperture from 90 to 150 mm Main features of the semi-analytical approach It is not a simple scaling It is not a simplified analytical model of the optics Triplet optics from IP to Q4 is exact, approximate matching is done Triplet optics from IP to Q4 is exact, approximate matching is done Four cases are computed, and then results are fit Obtained solutions proved to be rather close to exactly matched solutions with MAD [ solutions with MAD [R. De Maria, LIUWG meeting, October 2007] b ] A completely analytical approach on simplified model has been recently developed [R De Maria Phys Rev STAB 10 (2007)] recently developed [R. De Maria, Phys. Rev. STAB 10 (2007)] Design issues in 130mm aperture quadruopoles - 4 F. Borgnolutti, E. Todesco
MOTIVATIONS FOR A 130 MM APERTURE How to fix the relative lengths of Q1-Q3 and Q2 For each total quadrupole length there is a combination of lengths h l d l l h h b f l h that gives equal beta function in the two planes We compute four cases, We co pute ou cases, 14000 14000 0 l * and then we fit Q2 12000 0 Q1 Q3 10000 0 Betax β (m) 8000 [E. Todesco, J. P. Koutchouk, Valencia06] Betay 0 6000 0 4000 4000 2000 0 Q1-Q3 10 0 0 Q2 0 50 100 150 200 th (m) Distance from IP (m) 9 Baseline Nominal triplet l1=5.50 m l2=6.37 m p adrupole lengt 8 14000 0 l * 7 Q2 12000 0 Q1 Q3 10000 0 Betax Betax Qua ) β (m) 8000 6 Betay 0 6000 0 4000 5 2000 0 0 0 20 25 30 35 40 0 0 50 50 100 100 150 150 200 200 Total quadrupole length (m) l d l l h ( ) Distance from IP (m) Triplet l1=5.64 m l2=6.22 m Design issues in 130mm aperture quadruopoles - 5 F. Borgnolutti, E. Todesco
MOTIVATIONS FOR A 130 MM APERTURE How to fix the gradient This depends on matching conditions h d d h d We require to have in Q4 “similar” beta functions to the nominal We find an empirical fit of the four cases We find an empirical fit of the four cases 1 = G 2 + fl hl q q 250 250 200 T/m) Baseline Gradient (T 150 100 100 50 20 25 30 35 40 Total quadrupole length (m) Design issues in 130mm aperture quadruopoles - 6 F. Borgnolutti, E. Todesco
MOTIVATIONS FOR A 130 MM APERTURE What a Nb-Ti quadrupole can give as gradient vs aperture We computed three lay-outs with 2 layers of the LHC MB cable, of d h l h l f h bl f apertures 100, 120, 140 mm – agreement with the semi-analytical formula [L. Rossi, E. Todesco, Phys. Rev. STAB 9 (2006) 102401] LHC MQ, operational 400 400 LHC MQX operational LHC MQX, operational Ostojic,et al PAC05 - MQY Rossi Todesco, Wamdo06 300 T/m) (Bruning, Vale06) Gradient (T LHC cable, 2 layers 200 100 100 80% of Nb-Ti 0 0 0 50 50 100 100 150 150 200 200 250 250 Magnet aperture φ (mm) Design issues in 130mm aperture quadruopoles - 7 F. Borgnolutti, E. Todesco
MOTIVATIONS FOR A 130 MM APERTURE We can now have aperture vs quadrupole length With two layers Nb-Ti we can build focusing triplet of 30 m, 110 mm h l b b ld f l f aperture – or 34 m, 130 mm aperture 250 200 (T/m) Baseline 200 Gradient 150 100 50 (m) 150 20 25 30 35 40 Total quadrupole length (m) Aperture 40 ° 53’ 02” N – 72 ° 52’ 32” W two layers LHC MQ, operational 100 one layer 400 LHC MQX, operational Ostojic,et al PAC05 - MQY Rossi Todesco, Wamdo06 , 300 300 ) Gradient (T/m) (Bruning, Vale06) Baseline LHC cable, 2 layers 200 50 100 80% of Nb-Ti 20 20 25 25 30 30 35 35 40 40 45 45 50 50 0 0 50 100 150 200 250 Total quadrupole length (m) Magnet aperture φ (mm) Design issues in 130mm aperture quadruopoles - 8 F. Borgnolutti, E. Todesco
MOTIVATIONS FOR A 130 MM APERTURE Longer triplet will give larger beta functions ! Larger, but not terribly larger … we find a fit as b bl l f d f 2 2 * * + l al q β = (where β * is the beta in the IP) a ~77.5 m max * β [E. Todesco, J. P. Koutchouk, Valencia06] 15 m 20000 beta*=55 cm beta*=37 cm n (m) beta beta*=25 cm 25 cm beta*=20 cm beta 20 cm ta function 15000 10000 10000 41 ° 49’ 55” N – 88 ° 15’ 07” W 41 49 55 N 88 15 07 W aximum bet 40 ° 53’ 02” N – 72 ° 52’ 32” W 5000 1 9 Km 1.9 Km 1 K 1 Km Ma 0 20 25 30 35 40 Total quadrupole length (m) Total quadrupole length (m) Design issues in 130mm aperture quadruopoles - 9 F. Borgnolutti, E. Todesco
MOTIVATIONS FOR A 130 MM APERTURE β * , β max and the triplet length determine the aperture needs * * 3 / 2 10 σ : the nominal + + ( ( + + ) ) l l l l l l l l t t φ = φ + χφ β + φ + φ N k 0 1 max 2 3 b b * * β β 13 σ : reduces the collimator impedance, and allowing a nominal beam intensity [E. Metral, et al., PAC07, R.W. Assman LIUWG October 2007] bea te s ty [ 15 m , , , ] We chose 130 mm aperture quadrupole, giving a triplet length of 34 m (without gaps) * 0 25 m β β =0.25 m 0.200 m) Aperture (m 0.150 0.150 41 41 ° 49’ 55” N – 88 ° 15’ 07” W 49 55 N 88 15 07 W 40 ° 53’ 02” N – 72 ° 52’ 32” W Nb-Ti, 2 layers 0.100 10 sigma 1.9 Km 1 9 Km 1 K 1 Km 13 sigma 13 sigma 16 sigma 0.050 20 25 30 35 40 45 50 Total quadrupole length (m) Thi i This is our baseline today b li d Design issues in 130mm aperture quadruopoles - 10 F. Borgnolutti, E. Todesco
CONTENTS Motivations for a 130 mm aperture triplet 130 mm aperture quadrupoles in Nb-Ti 130 mm aperture quadrupoles in Nb 3 Sn 130 mm aperture quadrupoles in Nb 3 Sn Conclusions Design issues in 130mm aperture quadruopoles - 11 F. Borgnolutti, E. Todesco
130 MM NB-TI QUADRUPOLE MQXC: operational gradient of 124 T/m 20% operational margin 20% operational margin Operational current 12.5 kA Coil: two layers, with grading (27%), using the LHC MB y g g ( ) g inner and outer layer respectively d l l Peak field 8.4 T (in between MQXA and MQXB) C bl Cable needed to wind d d i d one dipole unit length is enough Inner layer Outer layer length n turns pole length n turns length (m) (per pole) (m) (per pole) (m) MQXC 9.2 18 331 26 478 MQXC 7.8 18 281 26 406 MB 14.3 15 429 25 715 130 mm aperture coil lay-out Design issues in 130mm aperture quadruopoles - 12 F. Borgnolutti, E. Todesco
130 MM NB-TI QUADRUPOLES – field quality Field quality is critical at nominal field – optimization includes iron saturation persistent currents not an issue saturation, persistent currents not an issue Coil design based on: Inner layer: two blocks with [24°,30°,36°] lay-out – this kills b 6 b 10 Outer layer: one block at 60° - this kills b 6 (b 10 not affected by outer layer) Design multipoles at high field lower than 1 unit A first iteration will be needed to fine tune field quality A first iteration will be needed to fine tune field quality Mid-plane shims of 0.375 mm thickness are included in the design, so that it can be varied in both directions for fine tuning 36 ° 60 30 ° 24° 40 mm) y (m I Iron 20 Aperture 0 0 0 20 20 40 40 60 60 80 80 100 100 120 120 x (mm) 130 mm aperture coil lay-out 130 mm aperture coil lay-out, details of one eight Design issues in 130mm aperture quadruopoles - 13 F. Borgnolutti, E. Todesco
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