DESIGN ISSUES N U IN A 130 MM APERTURE TRIPLET F. Borgnolutti, E. - - PowerPoint PPT Presentation

Frascati, 7th 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 Nb3Sn 130 mm aperture quadrupoles in Nb3Sn Conclusions

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 2

MOTIVATIONS FOR A 130 MM APERTURE

Proposed LHC triplet lay-out for getting β∗=0.25 (the “symmetric” solution

LHC P j t R t 1000)

solution, LHC Project Report 1000)

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 L(Q1)=L(Q3)=9 2 m

Q1 Q3 l

*

l 2

L(Q1)=L(Q3)=9.2 m L(Q2) =7.8 m Total triplet length 35 m

with gaps 40 m

Q2A Q2B l 1

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 3

with gaps, 40 m

25 50 Distance from IP (m)

MOTIVATIONS FOR A 130 MM APERTURE

The study presented in LHC PR 1000 presents a parametric study of solutions having [E T d

J P K t h k CARE k h V l i 06]

study of solutions having [E. Todesco, J. P. Koutchouk, CARE workshop Valencia06]

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 [

b ]

solutions with MAD [R. De Maria, LIUWG meeting, October 2007] A completely analytical approach on simplified model has been recently developed [R De Maria Phys Rev STAB 10 (2007)]

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 4

recently developed [R. De Maria, Phys. Rev. STAB 10 (2007)]

MOTIVATIONS FOR A 130 MM APERTURE

How to fix the relative lengths of Q1-Q3 and Q2

h l d l l h h b f l h For each total quadrupole length there is a combination of lengths that gives equal beta function in the two planes We compute four cases,

14000

We co pute ou cases, and then we fit

[E. Todesco, J. P. Koutchouk, Valencia06]

4000 6000 8000 10000 12000 14000 β (m)

Betax Betay Q1 Q2 Q3 l *

9 10 th (m) Q1-Q3 Q2 Baseline

2000 4000 50 100 150 200 Distance from IP (m)

Nominal triplet l1=5.50 m l2=6.37 m

7 8 adrupole lengt

10000 12000 14000 )

Betax Q1 Q2 Q3 l *

p

5 6 20 25 30 35 40 l d l l h ( ) Qua

2000 4000 6000 8000 50 100 150 200 β (m)

Betax Betay

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 5

Total quadrupole length (m)

50 100 150 200 Distance from IP (m)

Triplet l1=5.64 m l2=6.22 m

MOTIVATIONS FOR A 130 MM APERTURE

How to fix the gradient

h d d h d This depends on matching conditions 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

250

q q

hl fl G + =

2

1

200 250 T/m)

Baseline

100 150 Gradient (T 50 100 20 25 30 35 40

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 6

Total quadrupole length (m)

MOTIVATIONS FOR A 130 MM APERTURE

What a Nb-Ti quadrupole can give as gradient vs aperture

d h l h l f h bl f We computed three lay-outs with 2 layers of the LHC MB cable, of apertures 100, 120, 140 mm – agreement with the semi-analytical formula [L. Rossi, E. Todesco, Phys. Rev. STAB 9 (2006) 102401]

400

LHC MQ, operational LHC MQX operational

300 400 T/m)

LHC MQX, operational Ostojic,et al PAC05 - MQY Rossi Todesco, Wamdo06 (Bruning, Vale06)

100 200 Gradient (T

LHC cable, 2 layers

100 50 100 150 200 250 80% of Nb-Ti

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 7

50 100 150 200 250 Magnet aperture φ (mm)

MOTIVATIONS FOR A 130 MM APERTURE

We can now have aperture vs quadrupole length

h l b b ld f l f With two layers Nb-Ti we can build focusing triplet of 30 m, 110 mm aperture – or 34 m, 130 mm aperture

200

200 250 (T/m) Baseline

150 (m)

50 100 150 20 25 30 35 40 Total quadrupole length (m) Gradient

40° 53’ 02” N – 72 ° 52’ 32” W

100 Aperture two layers

• ne layer

300 400 )

LHC MQ, operational LHC MQX, operational Ostojic,et al PAC05 - MQY Rossi Todesco, Wamdo06

50 20 25 30 35 40 45 50 Baseline

100 200 300 Gradient (T/m)

, (Bruning, Vale06) LHC cable, 2 layers

80% of Nb-Ti

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 8

20 25 30 35 40 45 50 Total quadrupole length (m)

50 100 150 200 250 Magnet aperture φ (mm)

MOTIVATIONS FOR A 130 MM APERTURE

Longer triplet will give larger beta functions !

b bl l f d f

2 *

Larger, but not terribly larger … we find a fit as

a~77.5 m (where β* is the beta in the IP)

[E. Todesco, J. P. Koutchouk, Valencia06]

15 m

* 2 * max

β β

q

al l + =

20000 n (m)

beta*=55 cm beta*=37 cm beta*=25 cm beta*=20 cm

41° 49’ 55” N – 88 ° 15’ 07” W

10000 15000 ta function

beta 25 cm beta 20 cm

1 9 Km

41 49 55 N 88 15 07 W

1 K

40° 53’ 02” N – 72 ° 52’ 32” W

5000 10000 aximum bet

1.9 Km 1 Km

20 25 30 35 40 Total quadrupole length (m) Ma

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 9

Total quadrupole length (m)

MOTIVATIONS FOR A 130 MM APERTURE

β*, βmax and the triplet length determine the aperture needs

l l l l

2 / 3 * *

) ( + +

10 σ: the nominal 13 σ : reduces the collimator impedance, and allowing a nominal beam intensity [E. Metral, et al., PAC07, R.W. Assman LIUWG October 2007]

15 m

b b t t

k N l l l l

* 3 * 2 max 1

) ( β φ β φ β χφ φ φ + + + + + =

bea te s ty [

, , , ]

We chose 130 mm aperture quadrupole, giving a triplet length of 34 m (without gaps)

β

* 0 25 m 41° 49’ 55” N – 88 ° 15’ 07” W

β =0.25 m 0.150 0.200 m)

1 9 Km

41 49 55 N 88 15 07 W

1 K

40° 53’ 02” N – 72 ° 52’ 32” W

0.100 0.150 Aperture (m Nb-Ti, 2 layers 10 sigma 13 sigma

Thi i b li d

1.9 Km 1 Km

0.050 20 25 30 35 40 45 50 Total quadrupole length (m) 13 sigma 16 sigma

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 10

This is our baseline today

CONTENTS

Motivations for a 130 mm aperture triplet 130 mm aperture quadrupoles in Nb-Ti 130 mm aperture quadrupoles in Nb3Sn 130 mm aperture quadrupoles in Nb3Sn Conclusions

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 11

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 d l l y g g ( ) g inner and outer layer respectively Peak field 8.4 T (in between MQXA and MQXB)

C bl d d i d Cable needed to wind

• ne dipole unit length is enough

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 Inner layer Outer layer

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 12

130 mm aperture coil lay-out

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 b6 b10 Outer layer: one block at 60° - this kills b6 (b10 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

40 60 mm)

36° 30° 24°

I 20 20 40 60 80 100 120 y (m Iron Aperture

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 13

130 mm aperture coil lay-out 130 mm aperture coil lay-out, details of one eight 20 40 60 80 100 120 x (mm)

130 MM NB-TI QUADRUPOLES – FORCES

According to analytical model [P. Fessia, F. Regis, E. Todesco, ASC06]

f d h l f Lorentz forces induce a stress in the coil of 70 MPa, i.e. 40% more than for the MQXA-B (50 MPa) Does not look so critical, but mechanical structure should be

• es
• t ook so c t ca , but

ec a ca st uctu e s ou d be carefully designed

150 2 70 Nb-Ti 1.9 K φ 100 MPa] 2r=70 mm 2r=130 mm φ φ

MQXC

50 Stress [M

MQXA-B

100 200 300 C iti l di t [T/ ]

Larger coil width

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 14

Critical gradient [T/m]

Stress versus gradient for quads with 70 mm and 130 mm aperture, scan over the coil width 20% operational margin on Nb-Ti short sample limit

130 MM NB-TI QUADRUPOLES – FORCES

Cross-check with computations using FEM model

MQXC: ∼80 MPa MQXA: ∼ 70 MPa, MQXB: ∼ 50 MPA

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 15

Stress in the coil due to e.m. forces in infinitely rigid structure evaluated with FEM

130 MM NB-TI QUADRUPOLES – PROTECTION

This MQXC is longer and larger than the previous ones

d l Inductance similar to MQY, MB, MQXA Operating current similar to MB, MQ, MQXB Stored energy is ∼5 MJ: twice than MQXA and 50% larger than one Stored energy is ∼5 MJ: twice than MQXA, and 50% larger than one aperture of an MB Preliminary hot spot temperature evaluations show that the order of Preliminary hot spot temperature evaluations show that the order of magnitudes are similar to the MB

Time for firing quench heaters to avoid hot spot larger than 300 K must be not larger than 0.1 s [M. Sorbi, Qlasa code] challenging, but feasible

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 16

CONTENTS

Motivations for a 130 mm aperture triplet 130 mm aperture quadrupoles in Nb-Ti 130 mm aperture quadrupoles in Nb3Sn 130 mm aperture quadrupoles in Nb3Sn Conclusions

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 17

130 MM NB3SN QUADRUPOLES - general

Main hypothesis

d h b l f b h b

15 m

We consider the possibility of substituting the Nb-Ti 130 mm aperture magnets with 130 mm aperture Nb3Sn quadrupoles [proposal by

• L. Rossi, LARP collaboration meeting, October 2007]

Constraints

Same powering current of Nb-Ti (12 5 kA)

41° 49’ 55” N – 88 ° 15’ 07” W

Same powering current of Nb Ti (12.5 kA) Having a safe operational margin Having a reasonable level of forces P idi l h l l f di

41 49 55 N 88 15 07 W

Providing at least the same level of gradient Satisfy the optics requirements

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 18

130 MM NB3SN QUADRUPOLES - DESIGN

We considered 3 designs, based on LARP strand

2-4 layers with the present 10 mm width LARP cable (∼TQ) 2 layers with a 15 mm width cable, same strand of 0.7 mm diameter Assuming 3000 A/mm2 at 12 T 4 2 K 20% operational margin Assuming 3000 A/mm at 12 T, 4.2 K, 20% operational margin

41° 49’ 55” N – 88 ° 15’ 07” W 41 49 55 N 88 15 07 W

l bl Two layers 10 mm cable: Gss=183 T/m Gop=147 T/m and Iop=11.0 kA Four layers 10 mm cable: Gss=216 T/m Gop=173 T/m and Iop=7.6 kA Two layers 15 mm cable: Gss=200 T/m Gop=160 T/m and Iop=13.1 kA

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 19

The 15 mm cable is the only one that can bear the 12.5 kA current

Sketch of A MIXED TRIPLET FOR THE UPGRADE FOR THE UPGRADE

Same lay-out as for the Nb-Ti triplet, but Q1-Q3 replaced by Nb S d l 7 2 l

15 m

Nb3Sn quadrupoles 7.2 m long

Operating at 160 T/m, at 20% margin, in series with Q2a-Q2b, Q2 in the same position and with the same lengths in the “Nb-Ti Q2 in the same position and with the same lengths in the Nb-Ti

• nly” lay-out

Small trim on the current (4% larger) than in the Nb-Ti only option

41° 49’ 55” N – 88 ° 15’ 07” W

a small gain in the maximal beta function (∼5%)

We will try also to replace Q2 …

16000 18000 Q2 l * 16000 18000 Q2 l *

41 49 55 N 88 15 07 W

6000 8000 10000 12000 14000 16000 β (m) Betax Betay Q1 Q Q3 6000 8000 10000 12000 14000 16000 β (m) Betax Betay Q1 Q2 Q3 l 2000 4000 50 100 150 200 Distance from IP (m) 2000 4000 6000 50 100 150 200 Distance from IP (m)

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 20

Optical functions in the sketch of a lay-out with Nb3Sn (Q1,Q3) and Nb-Ti (Q2) quadrupoles Optical functions in the sketch of a lay-out with Nb-Ti

• nly quadrupoles

130 MM NB3SN QUADRUPOLES - FORCES

At operational values (20% margin from short sample) peak t d t f i l (120 MP ) b t ithi 150

15 m

stress due to e.m. forces is large (120 MPa), but within 150 MPa

with a model in an infinitely rigid structure – more analysis should with a model in an infinitely rigid structure – more analysis should be done with the real structure

2 layers 15 mm has ∼10% less stress than the 10 mm cable designs

41° 49’ 55” N – 88 ° 15’ 07” W 41 49 55 N 88 15 07 W

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 21

Stress due to e.m. forces evaluated with ANSYS, infinitely rigid structure

130 MM NB3SN QUADRUPOLES

Please note that at short sample the stress is (25%)2=56% l

15 m

larger

The magnet can go up to ∼200 MPa It cannot be powered at the short sample !! It cannot be powered at the short sample !!

It could be a nice destructive test to find out the stress (strain) limits in Nb3Sn in a short model

41° 49’ 55” N – 88 ° 15’ 07” W

Temperature margin

With the mixed la

• ut Nb Sn has 4 7 K temperature margin with

41 49 55 N 88 15 07 W

With the mixed lay-out, Nb3Sn has 4.7 K temperature margin with respect to 2.1 of Nb-Ti

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 22

CONCLUSIONS

We outlined the motivations to go for a 130 mm aperture in a Nb-Ti LHC triplet LHC triplet

β*=0.25 m with 3 σ clearance for collimation

We discussed a conceptual design of the Nb-Ti magnet

Field quality, stresses, protection

We considered the possibility of replacing Q1-Q3 with Nb3Sn magnets

Not possible with the present 10 mm cable p p With 15 mm cable could be viable, with margin and stresses within limits Optics seems viable, should be validated by exact matching It would give a more than a factor 2 in temperature margin (and would be It would give a more than a factor 2 in temperature margin (and would be the first test of Nb3Sn in operational conditions)

• F. Borgnolutti, E. Todesco

Design issues in 130mm aperture quadruopoles - 23