Unit 11 Electromagnetic design Episode IIIAre there other possible lay-outs ? 0 2 4 6 8 10 0 20 40...

USPAS January 2012, Superconducting accelerator magnets

Unit 11 Electromagnetic design

Episode III

Soren Prestemon and Steve Gourlay Lawrence Berkeley National Laboratory (LBNL)

Withsignificantre-useofmaterialfromthesameunitlecturebyEzioTodesco,USPAS2017

USPAS June 2018, Michigan State University Superconducting accelerator magnets 2

QUESTIONS

Where can we operate the magnet ? How far from the critical surface ?

Efficiency: the last Teslas are expensive … are there techniques to save conductor ?

What is the effect of iron ? Does it yield higher short sample fields ?

What happens in coil ends ?

Are there other possible lay-outs ?

0

2

4

6

8

10

0 20 40 60 80equivalent width (mm)

Bc (

T) r=30 mmr=60 mmr=120 mmcos theta

Nb-Ti at 4.2 K


CONTENTS

1. Operational margin

2. Grading techniques

3. Iron yoke

4. Coil ends

5. Other designs

6. A review of dipole and quadrupole lay-outs


Margin and operational risk

Magnets have to work at a given distance from the critical surface, i.e. they are never operated at short sample conditions

At short sample, any small perturbation quenches the magnet One usually operates at a fraction of the loadline which ranges from 60% to 90%

This fraction translates into a temperature margin

Loadline with 20% operational margin Operational margin and temperature margin


Temperature margin is a common figure of merit

How to compute the temperature margin ? One needs an analytic fit of the critical surface jss(B,T) The temperature margin ΔT is defined by the implicit equation

jss(Bop,Top+ΔT)=jop

Nb-Ti at 1.9 K at 80% of the loadline has about 2 K of temperature margin

0.0

0.5

1.0

1.5

2.0

2.5

3.0

3.5

0 2 4 6 8 10 12

Tem

pera

ture

mar

gin

(K)

Bop(T)

Nb-Ti at 1.9 K

90 % margin

80 % margin

70 % margin


Examples of temperate margin and role of superconductor

Some parametric analysis Nb-Ti at 4.2 K loses at least 1/3 of temperature margin w.r.t. 1.9 K

But the specific heat is larger … But helium is not superfluid …

Nb3Sn has a temperature margin 2.5 times larger than Nb-Ti This is due to the shape of the critical surface At 80%, Nb3Sn has about 5 K of temperature margin

Temperature margin of Nb-Ti versus Nb3Sn

0

1

2

3

4

5

6

0 5 10 15 20

Tem

pera

ture

mar

gin

(K)

Bop (T)

Nb3Sn at 1.9 K

Nb-Ti at 1.9 K

Temperature margin of Nb-Ti at 1.9 K and at 4.2 K

0.0

0.5

1.0

1.5

2.0

2.5

0 2 4 6 8 10

Tem

pera

ture

mar

gin

(K)

Bop (T)

Nb-Ti at 4.2 K

Nb-Ti at 1.9 K


Two regimes 1. Fast losses or fast release of energy (J/cm3)

Adiabatic case – all heat stays there Main issue: the conductor must have high enough thermal inertia The deposited energy must not exceed the enthalpy margin Enthalpy margin is the critical parameter

2. Continuous losses (as debris coming from collisions, or losses from the beam) (W/cm3)

All heat is removed – stationary case Main issue: the heat must be extracted efficiently The gradient between the heat sink and the coil must not exceed the temperature margin Temperature margin is the critical parameter

Transient vs steady losses


How to introduce grading

The idea The map of the field inside a coil is strongly non-uniform In a two layer configuration, the peak field is in the inner layer, and outer layer has systematically a lower field A higher current density can be put in the outer layer

How to realize it First option: use two different power supplies, one for the inner and one for the outer layer (not common) Second option: use a different cable for the outer layer, with a smaller cross-section, and put the same current (cheaper)

The inner and outer layer have a splice, and they share the same current Since the outer layer cable has a smaller section, it has a higher current density


Examples of graded dipoles

Examples of graded coils LHC main dipole (~9 T)

grading of 1.23 (i.e. +23% current density in outer layer) 3% more in short sample field, 17% save of conductor

MSUT - Nb3Sn model of Univ. of Twente (~11 T) strong grading 1.65 5% more in short sample field, 25% save of conductor

LHC main dipole MSUT dipole


We can study graded magnets using the tools defined earlier

Short sample limit for a graded Nb-Ti dipole Each block has a current density j1 … jn, each one with a dilution factor κ1 … κn

We fix the ratios between the current densities

We define the ratio between central field and current densities

We define the ratio between peak field in each block and central field

11

11 =≡

jj

χ1

22 j

j≡χ

1jjn

n ≡χ

cnnn

cnnnp jjBB γλχ

γλλ1

1, ==≡

cncn jjB γγ 1, ≡=∑


Grading of dipoles - continued…

Short sample limit for a graded Nb-Ti dipole (continued I)

In each layer one has and substituting the peak field expression one has

All these n conditions have to be satisfied – since the current densities ratios are fixed, one has

cncn jjB γγ 1, ≡=∑

)( ,*2, npcnnc BBsj −≤ κ

*2, c

cnnn

nnnc B

ssjγκλχ

κχ

+≤

nnnn

np jB γλχ

1, =

*2

,1, c

cnnn

n

n

ncc B

ssj

jγκλχ

κ

χ +≤= *

21, Min ccnnn

nnc B

ssj

γκλχ

κ

+=


How to calculate the short sample limit

Short sample limit for a graded Nb-Ti dipole (continued II) The short sample current is

and the short sample field is

Comments The grading factor χ in principle should be pushed to maximize the short sample field A limit in high grading is given by quench protection issues, that limit the maximal current density – in general the outer layer has lower filling factor to ease protection Please note that the equations depend on the material – a graded lay-out optimized for Nb-Ti will not be optimized for Nb3Sn

*21, Min c

cnnn

nnc B

ssj

γκλχ

κ

+=

*2Min c

cnnn

cnnss B

ssB

γκλχ

γκ

+=


Comparison of single layer vs graded 2-layer

Results for a two layer with same width sector case, Nb-Ti The gain in short sample field is ~5% But given a short sample field, one saves a lot !

At 8 T one can use 30 mm instead of 40 mm (-25%) At 9 T one can use 50 mm instead of 80 mm (-37%)

4

6

8

10

0 20 40 60 80equivalent width (mm)

Bss

(T)

1 layer 60

2 graded layers w2=w1

Nb-Ti 4.2 K

j 1

j 2j 2j 1


Now apply the technique to quadrupoles

Similar strategy for quadrupoles – gain of 5-10% in Gss

LHC MQXB – quadrupole for IR regions grading of 1.24 (i.e. +24% current density in outer layer) 6% more in short sample field, 41% save of conductor

LHC MQY – quadrupole close to IR regions Special grading (grading inside outer layer, upper pole with lower density) of 1.43 9% more in short sample field, could not be reached without grading

LHC MQXB LHC MQY


Some basic comments concerning the use of iron

An iron yoke usually surrounds the collared coil – it has several functions

Keep the return magnetic flux close to the coils, thus avoiding fringe fields In some cases the iron is partially or totally contributing to the mechanical structure

RHIC magnets: no collars, plastic spacers, iron holds the Lorentz forces LHC dipole: very thick collars, iron give little contribution

Considerably enhance the field for a given current density The increase is relevant (10-30%), getting higher for thin coils This allows using lower currents, easing the protection

Increase the short sample field The increase is small (a few percent) for “large” coils, but can be considerable for small widths This action is effective when we are far from reaching the asymptotic limit of B*

c2


How to size the iron - for shielding

A rough estimate of the iron thickness necessary to avoid fields outside the magnet

The iron cannot withstand more than 2 T (see discussion on saturation, later)

Shielding condition for dipoles:

i.e., the iron thickness times 2 T is equal to the central field times the magnet aperture – One assumes that all the field lines in the aperture go through the iron (and not for instance through the collars) Example: in the LHC main dipole the iron thickness is 150 mm

Shielding condition for quadrupoles:

satiron BtrB ~

mm 100~2

3.8*28~ =sat

iron BrB

t

satiron BtGr ~2

2


We can analyze the influence of iron using image currents

The iron yoke contribution can be estimated analytically for simple geometries

Circular, non-saturated iron: image currents method Iron effect is equivalent to add to each current line a second one

at a distance

with current

Limit of the approximation: iron is not saturated (less than 2 T)

ρρ

2

' IR=

II11'

+

−=µ

µ

ρ

ρ 'R I


Some comments concerning image currents and iron

Remarks on the equations

When iron is not saturated, one has µ>>1 and then Since the image is far from the aperture,

its impact on high order multipoles is small The impact of the iron is negligible for

Large coil widths Large collar widths High order multipoles

The iron can be relevant for Small coil widths, small collar widths, low order multipoles, main component

At most, iron can double the main component for a given current density (i.e. can give a Δγ=100%)

This happens for infinitesimally small coil and collar widths

ρρ

2

' IR= II11'

+

−=µ

µ

II ='

ρ

ρ 'R I

USPAS June 2018, Michigan State University Superconducting accelerator magnets

R 2R 1

R I

19

Iron influence on main field

Estimate of the gain in main field Δγ for a sector coil

the current density has to satisfy the integral condition

and one obtains

For higher order multipoles The relative contribution becomes very small

kjwB =1 )(' 121 RRkjB iron −=Δ

jwRRj

BBiron )(' 12

1

1 −=

Δ

rR

R I2

2 =

wrR

R I

+=

2

1

21

1 )(11

I

iron

Rrwr

BB +

+

−=

Δ

µ

µ

n

In

ironn

Rrwr

BB

⎥⎦

⎤⎢⎣

⎡ +

+

−=

Δ2

)(11

µ

µ

k is just a temporary transfer function term…

j⇥(r + w)2 � r2

⇤=

µ� 1

µ+ 1j0⇥R2

2 �R21

⇤

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Examples of iron enhancement to main field

Estimate of the gain in main field for fixed current in a sector coil

Examples of several built dipoles Smallest: LHC ∼ 16% (18% actual value) Largest: RHIC ∼ 55% (56% actual value)

R 2R 1

R I

21

1 )(11

I

iron

Rrwr

BB +

+

−=

Δ

µ

µ

1

2

3

4

0.0 0.5 1.0 1.5 2.0equivalent width w/r

R I/r

(adi

m)

TEV MB HERA MBSSC MB RHIC MBLHC MB FrescaMSUT D20HFDA NED

+15% +20%+25% +30%

+40%

+50%Forbidden zone


Influence of iron on short sample field

Impact of the iron yoke on dipole short sample field, Nb-Ti

The change of γc is the change of B for a fixed current, previously computed

Two regimes: for λκsγc<<1 the increase in γ corresponds to the same increase in the short sample field (“thin coils”) for λκsγ c >>1 no increase in the short sample field (“thick coils”)

Please note that the “thin” and “thick” regimes depend on filling ratio κ and on the slope s of the critical surface

For the Nb3Sn one has to use the corresponding equations Phenomenology is similar, but quantitatively different

*21 c

c

css B

ssB

γλκ

γκ

+=


Examples of iron influence

Impact of the iron yoke on short sample field Large effect (25%) on RHIC dipoles (thin coil and collars) Between 4% and 10% for most of the others

(both Nb-Ti and Nb3Sn)

RHIC main dipole and yoke

D20 and yoke

0

5

10

15

20

25

30

0 10 20 30 40 50 60equivalent width w (mm)

Gai

n in

Bss

[%]



Influence of iron on quadrupole field strength

Similar approach can be used in quadrupoles Large effect on RHIC quadrupoles (thin coil and collars) Between 2% and 5% for most of the others The effect is smaller than in dipoles since the

contribution to B2 is smaller than to B1

LHC MQXA and yoke

0

20

40

0 20 40 60 80x (mm)

y (m

m)

RHIC MQ and yoke

0

5

10

15

20

25

0.0 0.2 0.4 0.6 0.8 1.0 1.2weq/r (adim)

Gss

incr

ease

due

to ir

on [%

] ISR MQ TEV MQHERA MQ SSC MQRHIC MQ RHIC MQYLHC MQY LHC MQLHC MQM LHC MQXALHC MQXB


Influence of iron is strongly field-dependent

Iron saturation: B-H curve

for B<2 T, one has µ>>1 (µ∼103-104), and the iron can give a relevant contribution to the field according to what discussed before

for B>2 T, µ→1, and the iron becomes “transparent” (no effect on field)

HB 0µµ=

1E+00

1E+01

1E+02

1E+03

1E+04

1E+05

1E+06

1E+07

0 2 4 6 8B (T)

H (A

mpe

re tu

rns/

m2)

1

10

100

1000

10000

µ


Iron saturation complicates modeling and analysis

Impact on calculation When iron saturates → image current method cannot be applied, finite element method is needed (Poisson, Opera, Ansys, Roxie, …) Accuracy of model is good (error less than 10% if B-H well known)

Impact on main component and multipoles The main field is not ∝ current → transfer function B/i drops Since the field in the iron has an

azimuthal dependence, some parts of the iron can be saturated and others not → variation of b3

It was considered critical Led to warm iron design in Tevatron Today, even few % of saturation

seem manageable in operationImpact of yoke saturation in HERA dipole and quadrupoles,

From Schmuser, pg 58, fig. 4.12

40 units


Optimization of iron yoke to compensate for saturation effects

Corrective actions: shaping the iron In a dipole, the field is larger at the pole – iron will saturate there first

The dependence on the azimuth of the field in the coil provokes different saturations, and a strong impact on multipole

One can optimize the shape of the iron to reduce these effects Optimization of the position of holes (holes anyway needed for cryogenics) to minimize multipole change RHIC is the most challenging case, since the iron gives a large contribution (50% to γ, i.e. to central field for a given current)

1

2

3

4

0.0 0.5 1.0 1.5 2.0equivalent width w/r

R I/r

(adi

m)


+15% +20%+25% +30%

+40%

+50%Forbidden zone


Examples of iron shaping - RHIC

Corrective actions: shaping the iron – the RHIC dipole The field in the yoke is larger on the pole Drilling holes in the right places, one can reduce saturation impact on b3 from 40 units to less than 5 units (one order of magnitude), and to correct also b5

A similar approach has been used for the LHC dipole Less contribution from the iron (20% only), but left-right asymmetries due to two-in-one design [S. Russenschuck, C. Vollinger, ….]

Another possibility is to shape the contour of the iron (elliptical and not circular)

Field map in the iron for the RHIC dipole, with and without holes From R. Gupta, USPAS Houston 2006, Lecture V, slide 12

Correction of b3 variation due to saturation for the RHIC dipoles, R. Gupta, ibidem


Magnet end design is a critical issue

Main features of the coil end design ++Mechanical: find the shape that minimizes the strain in the cable due

to the bending (constant perimeter) In a cos(θ) magnet this strain can be large if the aperture is small In a racetrack design the cable is bent in the ‘right’ direction and therefore the strain is much less It is important to have codes to design the end spacers that best fit the ends, giving the best mechanical support – iteration with results of production is usually needed

End of a cosθ coil [S. Russenschuck, World

Scientific, Fig. 32.13]

End spacers supporting the ends of a cosθ coil [S. Russenschuck,World Scientific, Fig. 32.13]

CASPI AND FERRACIN: TOWARD INTEGRATED DESIGN 1299

Fig. 2. Typical turns generated by BEND loaded into the CAD ProE program.

Fig. 3. Typical nesting coils and spacers in CAD ProE.

their needs. At LBNL we have placed a Tcl/Tk interface infront of BEND and added several conversion programs thatupload the coil geometry into the CAD program ProE [16].Other conversion programs can create DXF files as well asconductor files suitable for the magnetic program TOSCA [13].

B. Creating the CAD Model

The ProE CAD coil model is a set of subassemblies of manyparts. In our model each turn is broken into four parts—twostraight sections and two end sections (return and lead sides).This is necessary to prevent the CAD system from attemptingto smooth out the transition between the end and the straightsections.

Generating the end spacers, shoes, poles and wedges can bedone manually by the CAD designer or automatically by a com-puter program that recognizes turns and assigns their corre-sponding identical surfaces to the spacer. Applying the samesurface to adjacent turns and spacers ensures a perfect matchbetween the turns and the spacers. That program also generatesa ProE trail file capable of creating a solid part from its externalenclosing surfaces. Typical end spacers in a cos–theta magnetare composed of two cylindrical surfaces (inner and outer ra-dius of each layer) and inside and outside surfaces of the adja-cent turns. Whereas inner and outer surfaces of each spacer maybe planes as in a racetrack coil or cylindrical as in a coil,the other two surfaces adjacent to the turns are described by aset of straight geodesic lines created as rulings by the programBEND. Full advantage is taken of the rulings during manufac-turing since they correspond to the position of a straight cutter

Fig. 4. A 3D TOSCA magnetic model of a quadrupole magnet.

Fig. 5. Magnetic model details of optimized iron features above the coil ends.

and can be used in a 5 axis EDM or water-jet machines. De-scribing each turn within CAD is of great help during the leadsdesign and the layer to layer transition. When such details arenot needed the turns can be lumped together into a block thatis similar to that of a solid end spacer. The CAD model asidefrom being the main design tool is also a convenient way totransfer entire magnet assemblies into analysis programs suchas TOSCA and ANSYS [17]. That connection aside from beinga time saver in model creation reduces human errors and pro-vides an unexpected check of the CAD model quality.

C. Creating the Magnetic Model (TOSCA)

The CAD ProE magnet assembly can be loaded directly intoTOSCA with the help of the MODELLER program. A simpleway to do it is through a SAT file. Prior to the transfer we elim-inate from the CAD model all nonmagnetic components, unim-portant details and the coils as well. The coils (8 node bricks)can be added later and read directly into the MODELLER froma modified BEND output file. Setting up the magnetic modelis quick and repeating the process can become fairly seamless(Fig. 4).

Reducing the complexity of the magnetic model setup im-proves the iron optimization process. Revisions can easily bedone in CAD and uploaded into TOSCA. Fig. 5 shows severaldetails in the inner iron pads that went through an optimization

Caspi, Ferracin TAS Vol 16, 2006


Figure of merit for end design

Main features of the coil end design + Magnetic: find the shape that allows to avoid a higher field in the ends

Due to the coil return, the main field in the ends is enhanced (typically several %) On the other hand, the ends are often the most difficult parts to manufacture It is common to reduce the main field in the ends by adding spacers - this makes the design a bit more complicated

Simple coil end with increased field in P [Schmuser,pg. 58]

Coil end with spacers to decrease the main field in the end

[Schmuser,pg. 58]


Magnet end design influences field quality

Main features of the coil end design +/- Magnetic: take care of field quality (especially if the magnet is short)

In general a coil end will give a non-negligible contribution to multipoles Two possibilities

Leave it as it is and compensate the coil end with the straight part so that the multipoles integral over the magnet is optimal (cheap, simple) Optimize the end spacer positions to set to zero the integral multipoles in each the head (more elegant, complicated)

In the plot pseudo-multipoles are shown, extracted as Fourier coefficients

The scaling with the reference radius is not valid They are not unique – if you start from

radial or tangential expression, Bx or By you get different things

They give an idea of the behavior of the field harmonics, and way to get a compensation

The real 3d expansion can be written (see A. Jain, USPAS 2006 in Phoenix: “Harmonic description of 2D fields”, slide 4)

Main field and pseudo-multipoles in coil end optimized to have null integrated b3

[Schmuser,pg. 58]


Lets look at other design concepts again…

Block coil Cable is not keystoned Cables are perpendicular to the midplane Ends are wound in the easy side, and slightly opened Internal structure to support the coil is needed Example: HD2 coil design

HD2 design: 3D sketch of the coil (left) and magnet cross section (right) [from P. Ferracin et al, MT19, IEEE Trans. Appl. Supercond. 16 378 (2006)]


Flared-racetrack example

Block coil – HD2 Two layers, two blocks Enough parameters to have a good field quality Ratio peak field/central field not so bad:

1.05 instead of 1.02 as for a cosθ with the same quantity of cable

Ratio central field/current density is 12% less than a cos(θ) with the same quantity of cable

Short sample field is around 5% less than what could be obtained by a cosθ with the same quantity of cable

Reached 87% of short sample

0

20

40

60

80

100

0 20 40 60 80 100x (mm)

y (m

m)

0

5

10

15

20

25

0 20 40 60 80w (mm)

B (T

)

sector [0-48,60-72]No ironWith iron

B * c2


Common coil example

Common coil A two-aperture magnet Cable is not keystoned Cables are parallel to the mid-plane Ends are wound in the easy side

Common coil lay-out and cross-section R. Gupta, et al., “React and wind common coil

dipole”, talk at Applied Superconductivity Conference 2006, Seattle, WA, Aug. 27 - Sept. 1, 2006.


Example dipole layouts - RHIC

RHIC MB Main dipole of the RHIC 296 magnets built in 04/94 – 01/96 Nb-Ti, 4.2 K

weq~9 mm κ~0.23

1 layer, 4 blocks no grading

0

2

4

6

8

10

12

0 20 40 60 80w (mm)

B (T

)


B *c2


Example dipole layouts - Tevatron

Tevatron MB Main dipole of the Tevatron 774 magnets built in ∼1980

0

2

4

6

8

10

12

0 20 40 60 80w (mm)

B (T

)


B *c2

Nb-Ti, 4.2 K weq~14 mm κ~0.23



Example of dipole layouts - HERA

HERA MB Main dipole of the HERA 416 magnets built in ∼1985/87 Nb-Ti, 4.2 K

weq~19 mm κ~0.26


0

2

4

6

8

10

12

0 20 40 60 80w (mm)

B (T

)


B *c2


Example dipole layouts - SSC

SSC MB Main dipole of the ill-fated SSC 18 prototypes built in ∼1990-5 Nb-Ti, 4.2 K

weq~22 mm κ~0.30

4 layer, 6 blocks 30% grading

0

2

4

6

8

10

12

0 20 40 60 80w (mm)

B (T

)


B *c2


Example dipole layouts - HFDA

HFDA dipole Nb3Sn model built at FNAL

6 models built in 2000-2005

Nb3Sn, 4.2 K

jc~2000 to 2500 A/mm2 at 12 T, 4.2 K (different strands)

weq~23 mm κ~0.29

2 layers, 6 blocks no grading

0

20

40

60

80

100

0 20 40 60 80 100x (mm)

y (m

m)

0

5

10

15

20

25

0 20 40 60 80w (mm)

B (T

)


B * c2


Example dipole layouts - LHC MB

LHC MB Main dipole of the LHC 1276 magnets built in 2001-06 Nb-Ti, 1.9 K

weq~27 mm κ~0.29

2 layers, 6 blocks 23% grading

02468

101214

0 20 40 60 80w (mm)

B (T

)


B *c2


Example dipole layouts - LHC MB - FRESCA

FRESCA Dipole for cable test station at CERN 1 magnet built in 2001 Nb-Ti, 1.9 K

weq~30 mm κ~0.29


02468

101214

0 20 40 60 80w (mm)

B (T

)


B *c2


Example dipole layouts - MSUT

MSUT dipole Nb3Sn model built at Twente U.

1 model built in 1995Nb3Sn, 4.2 K

jc~1100 A/mm2 at 12 T, 4.2 K

weq~35 mm κ~0.33


0

5

10

15

20

25

0 20 40 60 80w (mm)

B (T

)


B * c2


Example dipole layouts - D20

D20 dipole Nb3Sn model built at LBNL (USA)

1 model built in ~1998Nb3Sn, 4.2 K

jc~1100 A/mm2 at 12 T, 4.2 K

weq~45 mm κ~0.48


0

5

10

15

20

25

0 20 40 60 80w (mm)

B (T

)


B * c2


Example dipole layouts - HD2

HD2 Nb3Sn model being built in LBNL

1 model to be built in 2008 Nb3Sn, 4.2 K

jc~2500 A/mm2 at 12 T, 4.2 K

weq~46 mm κ~0.35

2 layers, racetrack, no grading

0

20

40

60

80

100

0 20 40 60 80 100x (mm)

y (m

m)

0

5

10

15

20

25

0 20 40 60 80w (mm)

B (T

)


B * c2


Example dipole layouts - FRESCA-2

Fresca2 dipole Nb3Sn test station founded by UE

cable built in 2004-2006 Operational field 13 T To be tested in 2014

Nb3Sn, 4.2 K

jc~2500 A/mm2 at 12 T, 4.2 K

weq~80 mm κ~0.31

Block coil 4 layers


Review of quadrupole layouts - RHIC

RHIC MQX Quadrupole in the IR regions of the RHIC 79 magnets built in July 1993/ December 1997 Nb-Ti, 4.2 K w/r~0.18 κ~0.27 1 layer, 3 blocks, no grading

0

50

100

150

200

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)


B *c2/r


Review of quadrupole layouts - RHIC (2)

RHIC MQ Main quadrupole of the RHIC 380 magnets built in June 1994 – October 1995 Nb-Ti, 4.2 K w/r~0.25 κ~0.23 1 layer, 2 blocks, no grading

0

20

40

60

0 20 40 60 80 100 120x (mm)

y (m

m)

0

50

100

150

200

250

300

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)


B *c2/r


Review of quadrupole layouts - LEP II

LEP II MQC Interaction region quadrupole of the LEP II 8 magnets built in ∼1991-3

Nb-Ti, 4.2 K, no iron w/r~0.27 κ~0.31 1 layers, 2 blocks, no grading

0

20

40

60

0 20 40 60 80 100 120x (mm)

y (m

m)

0

20

40

60

80

100

120

140

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)

sector [0-24,30-36]

No iron

B *c2/r


0

50

0 50 100 150x (mm)

y (m

m)

Review of quadrupole layouts - ISR

ISR MQX IR region quadrupole of the ISR 8 magnets built in ~1977-79 Nb-Ti, 4.2 K w/r~0.28 κ~0.35 1 layer, 3 blocks, no grading

0

20

40

60

80

100

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)


B *c2/r


Review of quadrupole layouts - LEP I

LEP I MQC Interaction region quadrupole of the LEP I 8 magnets built in ~1987-89

Nb-Ti, 4.2 K, no iron w/r~0.29 κ~0.33 1 layers, 2 blocks, no grading

0

20

40

60

0 20 40 60 80 100 120x (mm)

y (m

m)

0

20

40

60

80

100

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)

sector [0-24,30-36]

No iron

B *c2/r


Review of quadrupole layouts - Tevatron

Tevatron MQ Main quadrupole of the Tevatron 216 magnets built in ~1980 Nb-Ti, 4.2 K w/r~0.35 κ~0.250 2 layers, 3 blocks, no grading

0

20

40

60

0 20 40 60 80 100 120x (mm)

y (m

m)

0

50

100

150

200

250

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)


B *c2/r


Review of quadrupole layouts - HERA

HERA MQ Main quadrupole of the HERA

Nb-Ti, 1.9 K w/r~0.52 κ~0.27 2 layers, 3 blocks, grading 10%

0

100

200

300

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)


B *c2/r

0

20

40

60

0 20 40 60 80 100 120x (mm)

y (m

m)


Review of quadrupole layouts - LHC

LHC MQM Low- gradient quadrupole in the IR regions of the LHC 98 magnets built in 2001-2006 Nb-Ti, 1.9 K (and 4.2 K) w/r~0.61 κ~0.26 2 layers, 4 blocks, no grading

0

100

200

300

400

500

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)


B *c2/r



LHC MQY Large aperture quadrupole in the IR regions of the LHC 30 magnets built in 2001-2006 Nb-Ti, 4.2 K w/r~0.79 κ~0.34 4 layers, 5 blocks, special grading 43%

0

100

200

300

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)


B *c2/r



LHC MQXB Large aperture quadrupole in the LHC IR 8 magnets built in 2001-2006 Nb-Ti, 1.9 K w/r~0.89 κ~0.33 2 layers, 4 blocks, grading 24%

0

100

200

300

400

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)


B *c2/r


Review of quadrupole layouts - SSC

SSC MQ Main quadrupole of the ill-fated SSC

Nb-Ti, 1.9 K w/r~0.92 κ~0.27 2 layers, 4 blocks, no grading

0

100

200

300

400

500

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)


B *c2/r

0

20

40

60

0 20 40 60 80 100 120x (mm)

y (m

m)



LHC MQ Main quadrupole of the LHC 400 magnets built in 2001-2006 Nb-Ti, 1.9 K w/r~1.0 κ~0.250 2 layers, 4 blocks, no grading

0

20

40

60

0 20 40 60 80 100 120x (mm)

y (m

m)

0

100

200

300

400

500

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)


B *c2/r



LHC MQXA Large aperture quadrupole in the LHC IR 18 magnets built in 2001-2006 Nb-Ti, 1.9 K w/r~1.08 κ~0.34 4 layers, 6 blocks, special grading 10%

0

100

200

300

400

0.0 0.5 1.0 1.5 2.0weq/r (adim)

Gss

(T/m

)


B *c2/r



LHC MQXC Nb-Ti option for the LHC upgrade LHC dipole cable, graded coil 1-m-long model built in 2011-2 to be

tested in 2012 w/r~0.5 κ~0.33 2 layers, 4 blocks


Review of quadrupole layouts - LARP

LARP HQ 120 mm aperture Nb3Sn option for the

LHC upgrade (IR triplet) 1-m-long model tested in 2011, more

to come plus a 3.4-m-long w/r~0.5 κ~0.33 2 layers, 4 blocks


CONCLUSIONS

Grading the current density in the layers can give a larger performance for the same amount of conductor

3-5% more in dipoles, 5-10% more in quadrupoles

The iron has several impacts Useful for shielding, can considerably increase the field for a given current – the impact on the performance is small but not negligible Drawbacks: saturation, inducing field harmonics at high field – can be cured by shaping or drilling holes in the right place

Coil ends – the design must aim at reducing the peak field

Other lay-outs: pro and cons

We shown a gallery of dipole and quadrupole magnetic designs used in the past 30 years


REFERENCES

Iron M. N. Wilson, P. Schmuser, Ch. 4 Classes given by R. Gupta at USPAS 2006, Unit 5 R. Gupta, Ph. D. Thesis, available on his web site C. Vollinger, CERN 99-01 (1999) 93-109

Grading S. Caspi, P. Ferracin, S. Gourlay, “Graded high field Nb3Sn dipole magnets“, 19th Magnet Technology Conference, IEEE Trans. Appl. Supercond., (2006) in press.. L. Rossi, E. Todesco, Electromagnetic design of superconducting quadrupoles Phys. Rev. ST Accel. Beams 9 (2006) 102401.

Coil ends S. Russenschuck, CERN 99-01 (1999) 192-199 G. Sabbi, CERN 99-01 (1999) 110-120

Other designs Classes given by R. Gupta at USPAS 2006, Unit 10 R. Gupta, et al., “React and wind common coil dipole”, talk at Applied Superconductivity Conference 2006, Seattle, WA, Aug. 27 - Sept. 1, 2006 P. Ferracin et al, MT19, IEEE Trans. Appl. Supercond. 16 378 (2006) Work by G. Ambrosio, S. Zlobin on common coil magnets at FNAL

http://prst-ab.aps.org/abstract/PRSTAB/v9/i10/e102401?qid=ed70c20985705bb5&qseq=1&show=10

http://prst-ab.aps.org/abstract/PRSTAB/v9/i10/e102401?qid=ed70c20985705bb5&qseq=1&show=10


REFERENCES

Plus… A whole series of papers about each magnet that has been presented


ACKNOWLEDGEMENTS

L. Rossi for discussions on magnet design F. Borgnolutti B. Auchmann, L. Bottura, A. Devred, V. Kashikin, T. Nakamoto, S. Russenschuck, T. Taylor, A. Den Ouden, A. McInturff, P. Ferracin, S. Zlobin, for kindly providing magnet designs P. Ferracin, S. Caspi for discussing magnet design and grading A. Jain for discussing the validity of field expansion in the ends

Unit 11 Electromagnetic design Episode IIIAre there other possible lay-outs ? 0 2 4 6 8 10 0 20 40...

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Transcript of Unit 11 Electromagnetic design Episode IIIAre there other possible lay-outs ? 0 2 4 6 8 10 0 20 40...