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4.3 Comparison between permanent magnet design and electromagnet design

Following table shows a comparison between permanent magnet design versus

electromagnet design. Neo magnet design has smallest overall radius.

Magnet Magnet radius Pole tip radius

Ferrite magnet 16.4" 2 cm

Neo magnet 6.1" 2 cm

Electromagnet 10" 2 cm

Ferrite magnet 15.5" 3 cm

Neo magnet 6.5" 3 cm

Electromagnet 9.8" 3 cm

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Figure 4-3. Electromagnet quadrupole design (3 cm pole tip radius)

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Pole tip field vs. current

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

0 1000 2000 3000 4000 5000 6000 7000 8000 9000

Amp turns

poletipfield

Figure 4-2. Pole tip field versus coil Amp turns (2 cm pole tip radius)

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Figure 4-1. Electromagnet quadrupole design (2 cm pole tip radius)

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4.2 Electromagnet design

A conventional electromagnet design has also been tried for the NLC Damping Ring

Quadrupole. Figure 4-1 shows an electromagnet quadrupole design using a circular outer iron

core so we can make direct comparisons with the pms, we would not necessarily make a

circular iron core for any of these designs. The pole tip radius is 2 cm and the outer radius of

the magnet is 10. In this design, there are total 22 turns of 0.255 square hollow copper

conductor in 2 layers of 11 turns each in each coil. The input current is 347 amps and the

current density is 605.5 Amps/cm2. The approximate coil length is 60 ft. The coil hole

diameter is 0.125 and the calculated coil power is 1.231 kW. Based on these data, the

amount of water flow is obtained from curves generated from the Williams and Hazen

formula. With 4 cooling circuits per quad, the water flow is 0.345 gal/min and the temperature

difference between in the inlet of coil and in the outlet of the coil can be calculated as

345.0

231.18.3 =T =13.6 oC

where 3.8 is a constant. This is well below our operating maximum delta T of 25 oC. Figure

4-2 shows pole tip field versus coil amp turns. It shows pretty much linear for the whole

region.

For 3 cm pole tip radius design, the input amp turns are 6800 Amp turns and the

current density is 659.4 Amps/cm2. The approximate coil length is 54 ft. The calculated coil

power is 1.317 kW. From the curve, the amount of water flow is 0.365 gal/min. Based on

these data, the temperature increase is calculated as 13.7 oC. Next table summarizes the

parameters and temperature rise for electromagnetic DR quads.

pole tip radius(cm)

magnet radius(in) coil turns

Amp turns(Amps)

coil length(ft)

coil hole diameter(in)

coil power(kW)

water flow(gal/min)

temperature rise(oC)

2 10 22 7631.4 60 0.125 1.231 0.345 13.6

3 9.8 18 6800 54 0.125 1.317 0.365 13.7

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IV. Electromagnet design and Comparison for NLC Damping Ring Quadrupole

4.1 Features

1). The magnet radius: 10 for 2 cm pole tip magnet and 9.8 for 3 cm pole tip magnet.

2). For 2 cm pole tip radius magnet:

Total current: 7631.4 Amp turns

Current density: 605.5 Amps/cm2

Number of coil turns: 22

Approximate coil length: 60 ft

Calculated coil power: 1.231 kW

Thickness of two layer coil: 0.596

For 3 cm pole tip radius magnet:

Total current: 6800 Amp turns

Current density: 659.4 Amps/cm2

Number of coil turns: 18

Approximate coil length: 54 ft

Calculated coil power: 1.317 kW

Thickness of two layer coil: 0.596

4). There is 5 cm space between the quadrupole magnet and the other magnet.

3). Temperature rise in the coil: 13.6 oC for 2 cm pole tip and 13.7 oC for 3 cm pole tip

pole tip radius(cm)

magnet radius(in) coil turns

Amp turns(Amps)

coil length(ft)

coil hole diameter(in)

coil power(kW)

water flow(gal/min)

temperature rise(oC)

2 10 22 7631.4 60 0.125 1.231 0.345 13.63 9.8 18 6800 54 0.125 1.317 0.365 13.7

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Figure 3-18. Neo quadrupole magnet in damping ring, demagnetization design II

(3 cm pole tip radius, 0.5 radius tuner, pole tip field=6.13 kG)

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Figure 3-17. Neo quadrupole magnet in damping ring, demagnetization design I


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Integrated field

0

20000

40000

60000

80000

100000

120000

0 2 4 6 8 10 12

gap between magnet and steel plate (in)

integratedfield(G-cm)

Figure 3-14. Integrated field at pole tip ( dlB tippole )

(Without the end plate, the integrated field is 105 kG-cm.)

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Figure 3-13. Adding an end plate on the magnet

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Figure 3-12. Full model of Neo magnet

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Figure 3-11. One eighth model of Neo magnet

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Figure 3-10. Full model of Ferrite magnet

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Figure 3-9. One eighth model of Ferrite magnet

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Tuner torque for Neo magnet

0

50

100

150

200

250

300

0 50 100 150 200 250 300 350 400

tuner angle (degree)

torque(lb-in)

Figure 3-8. Tuner torque for Neo magnet

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Figure 3-7. Neo quadrupole magnet for tuner torque calculation

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Tuner torque for Ferrite magnet

0

50

100

150

200

250

300

350

400

450

0 50 100 150 200 250 300 350 400

tuner angle

torque(lb-in)

Figure 3-6. Tuner torque for Ferrite magnet

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Figure 3-5. Ferrite quadrupole magnet for tuner torque calculation

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Figure 3-4. Neo quadrupole magnet in damping ring


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Figure 3-3. Neo quadrupole magnet in damping ring


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Figure 3-2. Ferrite quadrupole magnet in damping ring

(3 cm pole tip radius, 1 radius tuner, pole tip field=6.51 kG)

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Figure 3-1. Ferrite quadrupole magnet in damping ring


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% which is thankfully less than that of Ferrite magnet, but nevertheless not a trivial

percentage.

3.6 Adding an End Plate on the Magnet - modeling a design feature of the FNAL Linac

PM Quad

To see if adding a steel end plate would help reduce the end effect, the following

calculations were carried out. An additional steel plate is added onto each end face of magnet

and three dimensional TOSCA calculation is performed to find out the end effects of the

magnet.

Figure 3-13 shows the flux plot for a model with an end plate added on the face of

magnet with a small gap. Several calculations are performed with different space between

magnet and end plate. Figure 3-14 shows integrated field (Bdl ) along z direction, changing

the space between magnet and steel plate. As can be seen, as the steel plate is closer to the

magnet, there is more flux loss. Therefore, adding steel plate to the magnet does not reduce

the end effect. It generates more flux loss from the magnet.

More studies are pending on the end effect with adding an end plate onto the magnet.

3.7 Demagnetization in the permanent magnet bricks

In Figure 3-1, 3-2, 3-3 and 3-4, there are some demagnetization areas in the wedge

shaped permanent magnet bricks adjacent to the pole tip. In the demagnetized area of

permanent magnet brick, the overall field line direction is opposite to the desired field line

direction. New designs were done for Neo magnet quadrupole to avoid the demagnetization in

the permanent magnet bricks. In the new design, the demagnetized parts are removed.

Therefore, the whole dimension had to be increased to generate the same pole tip field

strength. There are two kinds of design for avoiding the demagnetization. Design I is to cut

the permanent magnet brick back to the demagnetization starting point; see Figure 3-15. (B

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symmetrical at 45 degrees and 225 degrees of tuner angle because the Neo magnets on the

bottom and side are symmetric.

3.5.1 Three-dimensional modeling of DR quadrupoles.

Three dimensional models of the DR quads have been made using the TOSCA 3-D

program in order to calculate more precisely the end effect. Before applying the simulation of

3-d, a two dimensional TOSCA calculation is made to see whether the mesh generation and

other computation conditions are good or not. So, from the base plane, the whole magnet

shape is extruded in z-direction to a certain length of z value. A tangential boundary condition

is applied for top and base plane of the simulation. This method simulates an infinitely long

magnet in z-direction similar to the PANDIRA model. It is observed that there is 0.2 % field

strength difference between this TOSCA 2-d result and PANDIRA result for the same

FERRITE magnet at its pole tip location : The value of TOSCA result is 0.2 % higher than

that of PANDIRA. This is remarkably good agreement. Therefore, the mesh generation and

the other conditions in TOSCA are good enough to use it for a 3-d calculation. Three

dimensional computation is done by using this base plane geometry and conditions. The result

shows that the pole tip field strength in the center of the TOSCA 3-D magnet is 18.4 % lower

than that of PANDIRA result. This reduction in B at the pole tip is due to flux leaking out of

the ends which the TOSCA program calculates. Figure 3-9 shows an one eighth model of

the 3-d Ferrite magnet and Figure 3-10 shows a full 3-d magnet. In this case, the one eighth

model is mirrored onto other section.

So, it turns out there is a significant end effect because the overall ferrite magnet

diameter is so large compared to its length. In order to compensate for this end effect (18.4

%), one needs to increase the goal field strength by 18.4 %. That means much larger magnet

is needed and much larger magnet produces much larger end effect. With this trend, the final

design of Ferrite magnet has very large radius. Figure 3-11 shows an one eighth model of Neo

magnet and Figure 3-12 shows a full Neo magnet. For Neo magnet case, the end effect is 10

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3.5 End Effects

There is a field loss through the two end faces of the magnet. It is called the end effect

loss. Since PANDIRA program only calculates for two dimensional design, the following

method is used to compensate the end effect. To compensate for the end effect, the goal field

strength is increased by the same amount of field loss. From 3-D TOSCA result (to be

mentioned later), 18.4 % end effect is applied for a particular Ferrite magnet and 10% for a

Neo magnet.

Figure 3-1 shows a Ferrite magnet having 2 cm pole tip radius. In this magnet a 1.13

radius tuner is used to make 10 % field strength change at the pole tip. The required field

quality is that g

dg

< 1 % at 80 % location of pole tip radius. To obtain this field quality,

shimming is used around the pole tip. It has 18.8 magnet radius and the maximum field is

10.4 kG. Figure 3-2 shows a Ferrite magnet having 3 cm pole tip radius. 1 radius tuner is

used for 10 % field strength change. No shimming is needed to improve the field quality.

Figure 3-3 shows a Neo magnet having 2 cm pole tip radius. Only 0.5 radius tuner is needed

to change the field by 10 % and shimming is needed to improve the field quality. The

magnet is only 6.5 radius magnet. Its a quite small magnet compared to a Ferrite magnet

(Figure 3-1). Figure 3-4 shows a Neo magnet having 3 cm pole tip radius. Shimming is not

needed and 0.5 radius tuner is used. For Neo magnet, a fixture is needed for outer steel yoke

to keep the space for vacuum chamber.

Tuner torques are calculated for a Ferrite magnet (Figure 3-5). Figure 3-6 shows tuner

torques with respect to tuner angle. As can be seen in the figure, the value of maximum tuner

torque is very high. The torque values are not completely symmetric at 45 degrees and 225

degrees of tuner angle. It is because the Ferrite magnets on the bottom and side are not

symmetry. Figure 3-8 shows tuner torques for Neo magnet (Figure 3-7) with respect to tuner

angle. In this case, torque values are smaller than those of Ferrite magnet. Torque values are

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Table 3-1. Damping ring layout from Andy Wolski

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3.2 2-D Poisson for Permanent Magnets

There are two types of pole tip radius in the DR quadrupole magnet layout from Andy

Wolski (Table 3-1). One is 2 cm and the other is 3 cm. In the original layout, the magnets

have the effective lengths of 25 cm or 15 cm. The required pole tip fields are varied as the

required integrated gradient varies. A different approach was taken: a magnet with the highest

pole tip field strength is chosen as a base model, it had effective length of 25 cm and the

lengths of other magnets are changed to arrive at the required integrated strength.

3.3 Temperature Compensation Effects

Either Ferrite or Neodymium Iron Boron (Neo) is used for designing the magnets.

The designs are performed for 2 cm and 3 cm pole tip radius. In the magnet operation, to

offset field variations with temperature, special temperature compensation materials are used.

The detailed explanation of temperature compensation application is in section 1.2 (p.5). The

effect of the temperature compensating material is to make very large Ferrite magnets.

3.4 Tuners

There is another requirement : that the magnet can generate 10 % variation of field

strength at the pole tip. This effect is obtained by rotating a special Neo tuner. This 10 %

requirement makes tuner bigger and eventually the torque needed to rotate the tuner from its

preferred position to the +10% for example, gets ridiculously large.

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III. Damping Ring Quadrupole Magnet Design (NLC)

3.1 Features and recommendations

Magnet Requirements

1). Requirements for quadrupole magnet for NLC damping ring are in Table 3-1.

Two types of pole tip radius: 2 cm and 3 cm

Effective lengths: 25 cm and 15 cm.

Required maximum field strength: 7958 G

Required tuning range: 10 %

Field quality: dg/g < 1 % at 80 % location of pole tip radius

Vacuum chamber space: 9 mm (7.5 mm minimum) => C shaped magnet

Models created in PANDIRA:

2). Ferrite and Neodymium Iron Boron (Neo) are used for the designs.

3). Ferrite magnet with shim (Figure 3-1, Figure 3-2) meets requirements.

Dimension for Figure 3-1: 2 cm pole tip radius, 18.8 radius magnet.


4). Neo magnet with shim (Figure 3-3, Figure 3-4) meets requirements.


Dimension for Figure 3-4: 3 cm pole tip radius, 7 radius magnet.

5). Torque for tuning rod is very high in Ferrite magnet.

6). Field clamp is tried but it doesnt reduce the end effect.

7). Recommendations:

Figures 3-15 3-18 are duplicated here to show the recommended models that avoid

demagnetization in the permanent magnet. Radiation studies will help the choice of allowable

PM operation point along the demagnetization load line (Figure 3-15 vs. Figure 3-16, Figure

3-17 vs. Figure 3-18). The field qualities (dg/g) of models in Figure 3-15 3-18 are about 0.3

%. Again, Ferrite magnet has a too large an overall dimension. So, if radiation damage were

not a problem, or could be mitigated then we would recommend the Neo magnet.

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Figure 2-2. Gradient dipole magnet

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Combining equations (2.5), (2.6) and (2.7) produces

( )

o

o

o

o

pvx

pole

B

V

B

BVhhy =

+=

=4

2

1

01 (2.8)

For ph =2 cm, 1B=660.46 G/cm and oB =12.01 kG, oV can be solved by equation (2.8). By

equation (2.8), oV =24161 G-cm. Using equation (2.5), the pole tip shape can be determined as

xBxB

BVy

o

oo

p055.01

012.2

/1

/

1 =

= (2.9)

Using this pole tip shape, the gradient dipole magnet is designed. Figure 2-2 shows the

gradient dipole magnet and the field lines as predicted by POISSON. Maximum field

variationy

y

B

dBis about 0.08 % at 1.6 cm circle of radius. The requirement of

y

y

B

dBis 0.3 %.

Therefore, this pole tip shape gives a good field quality. Adding shims around the pole tip

edges can make the magnet smaller.

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2.2 Design of the pole tip shape to generate a small gradient.

We model this dipole as a conventional electromagnet. Figure 2-1 shows the pole tip

shape of a gradient dipole magnet.

ph vh

Figure 2-1

Following procedure shows the derivation of the shape of a gradient magnet pole tip. (Ross

Schlueters technical note)

)( zBBiB o = ( oB ,B are real) (2.1)

FiB = (2.2)

Therefore,

2

2z

BzBF o

= (2.3)

Since

== xyByBFIV ooo 1)Im( constant, (2.4)

=xBB

Vy

o

o

pole

1

(2.5)

And

( )== ==

21

2

1

1

0 o

o

o

o

x

pole

BBV

xBBBV

dxdy (2.6)

Also,

v

p

h

h=cos (2.7)

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II. Gradient Dipole Magnet for the main damping ring.

2.1 Requirements and features

1). Requirements for damping ring dipole magnet are

Goal field at the center (x=0, y=0): 12.01 kG with small gradient of 660.46G/cm.

This gradient is created by angling the pole tips slightly. The distance between the 2 pole

tips is to be 4cm at the center of the pole width. This is shown in detail in the next section.

Length: 48 cm

Tolerances on field shape:

Maximum field variationy

y

B

dB= 0.3 % at 1.6 cm circle of radius ( yB is an ideal field.)

Ideal field = pure dipole field + gradient field

2). Electromagnet specs

coil packet size: 5.73 cm 5.73 cm

number of coil turns = 36

coil current = 543.5 Amps

current density = 729 Amps/cm2

two water circuits are required.temperature rise at outlet of water circuit = 12.85 oC

3). Gradient dipole magnet (Figure 2-2) as modeled with POISSON meets the field shape

requirement.

Maximum field variationy

y

B

dBis about 0.08 % at 1.6 cm circle of radius. Adding shim

around the pole tip can make the magnet smaller.

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Figure 1-10. Dipole Neo magnet with tuner

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Figure 1-9. Dipole Ferrite magnet with tuner

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Figure 1-8. Dipole Neo magnet with shimming (Nominal oB = 12.987 kG)

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Figure 1-7. Dipole Neo magnet with shimming (Nominal oB = 14.43 kG)

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Figure 1-6. Dipole Neo magnet (Nominal oB = 12.987 kG)

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Figure 1-5. Dipole Neo magnet (Nominal oB = 14.43 kG)

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Figure 1-3. Dipole Ferrite magnet with shimming (Nominal oB = 14.43 kG)

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Figure 1-2. Dipole Ferrite magnet (Nominal oB = 12.987 kG)

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Figure 1-1. Dipole Ferrite magnet (Nominal oB = 14.43 kG)

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and Figure 1-4 are aiming for 12.987 kG of nominal field strength (10 % degradation from

14.43 kG). This 10 % field reduction is made to see how much smaller the magnet gets. So,

comparing Figure 1-1 and Figure 1-2, the height of the magnet is reduced from 46.6 to 34.7.

The 10 % field degradation makes this difference. The shimming is used in Figure 1-4. The

result shows similar pattern compared to Figure 1-1 and Figure 1-3.

Figure 1-5 and Figure 1-7 show Neo magnet designs. Due to the shimming in Figure

1-7, the dimension is smaller than that of Figure 1-5. Similar pattern can be seen between

Figure 1-6 and Figure 1-8. Figure 1-8 uses the shimming. Also, 10 % reduction of goal field

strength reduces height of magnet from 8.9 (Figure 1-5) to 7.9 (Figure 1-6).

Making an adjustable field strength in the gap.

Figure 1-9 shows a Ferrite magnet with a Neo tuner. The Neo cylindrical rod tuner is

used for generating a field variation. By rotating the tuner, the field at the center location can

be changed by 5 %. Figure 1-10 shows a shimmed Neo magnet with Neo tuner. Rotating

tuner makes 5 % field variation. Using Neo magnet and adding shim makes a big height

reduction from 31.4 to 7.9.

Comparing Ferrite magnet and Neo magnet without tuner, there is a significant height

difference. Ferrite magnet has a height of 46.6 (Figure 1-1) and the height of Neo magnet is

8.9 (Figure 1-5).

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So, it looks like the whole magnet has 1.2. This means that is increased by 20 %. To

account this, Hc is degraded by another 20 % to make = 1.2, keeping Br same. The next

diagram shows this procedure.

Hc Br

-12200 12600 Normal values for Neo

20 % 20 %

-9760 10080 Volume effect of temperature compensation

20 %

-7808 Make =1.2

So, in PANDIRA program, Hc = -7808 and Br = 10080 are used for Neo. In a similar fashion,

Hc = -2394.3 and Br = 3373.5 are used for Ferrite.

Reduction of field in the gap due to end effects.

End effect loss is calculated using analytical formulae in a spreadsheet. The end effect

loss is a flux loss from the two end faces of a magnet. It depends on the face and length of

magnet. The calculated delta Bgap from the end effect is added back onto the goal field

strength to give a new goal Bgap. We must put enough pm material in the 2-D magnet to

produce the higher Bgap, but the real magnet will only produce the nominal Bgap.

Description of models made incorporating temperature compensation and end effect

Figure 1-1 shows a Ferrite magnet design and Figure 1-3 shows a design of Ferrite

magnet with shimming in order to improve the field quality of the dipole magnet and to

reduce the pole width. The nominal goal field strength at x=0, y=0 is 14.43 kG for both cases.

The required field quality is 0.1% field variation at x=1.2 cm, y=0 from field at the center. As

can be seen in Figure 1-3, with shimming, the width of the magnet is reduced from 2.2 to

1.7. Consequently, the height of the magnet is also reduced from 46.6 to 43. Figure 1-2

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1.2 Details of the PANDIRA Designs

For any hybrid pm magnet there are two features that need to be accounted for in the

2-D PANDIRA computer models. They are (a) the effect of the temperature compensating

material which must be included in the magnet to maintain its integrated strength while the

magnet temperature varies and (b) the effect of flux that escapes out of the ends of the magnet

which normally PANDIRA ignores.

Temperature Compensation.

For all the NLC DR magnets we have tried designs with either Ferrite or Neodymium

Iron Boron (Neo) bricks. How much temperature compensation material is needed has to be

worked out empirically for each design on a prototype magnet, in the absence of prototype

magnets we have used percentages of temperature compensation established in real FNAL

permanent magnets built for the Recycler. From these magnets the field strength in the gap

degradations caused by the temperature compensation material are 13.5 % for Ferrite and 20

% for Neo.

One has to be careful in accounting for these substantial percentages in a PANDIRA

model. The following assumptions are made in case of a Neo magnet, Hc and Br are each

decreased by 20 %, this is because adding temperature compensation material makes the

volume of permanent magnet smaller by 20 % for a fixed set of dimensions. Since most

temperature compensating materials have 2, the next process is used for taking account of

2.

PM temperature compensation material

( =1) ( =2)

80 % 20 %

From this figure, the relation is

1 x 0.8 + 2 x 0.2 = 1.2.

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I. DR Transport Line Dipole Design

1.1 Features and recommendation

Requirements for transport line dipole magnet are

Nominal goal field at the center (x=0, y=0): 14.43kG

Field quality: 0.1% field variation at elliptic region of x=1.2 cm, y=0 from center field

Half gap of the magnet: 0.395 (full gap = 2cm)

Effective length = 0.6m

Tuning requirement: 5 %

Several different models were tried using PANDIRA, the details of these models are

given in succeeding pages. We can make a recommendation based on the predictions:

1). Two styles of pm magnets with iron poles were modeled : (a) Ferrite and (b) Neodymium

Iron Boron (Neo)

2). Ferrite magnet with shim (Figure 1-3) meets requirements, but is much too tall:

Dimensions: 86 tall, 19.4 width, 6563.94 in3 volume of PM in 22.6 length.

3). Neo magnet with shim (Figure 1-7) meets requirements.

Dimensions: 16.26 tall, 13.2 width, 482.28 in3 volume of PM in 22.6 length.

4). If we relaxed field strength by 10% and increased length by 10%, to maintain the

integrated strength, the magnet dimensions would become smaller.

Ferrite magnet: 62 tall, 19.4 width, 4833.78 in3 volume of PM in 24.86 length (28 %

height reduction, 26 % reduction of PM volume) (fig. 1-4) STILL TOO TALL!

Neo magnet: 14.7 tall, 13.2 width, 462.89 in3 volume of PM in 24.86 length

(10 % height reduction, 4 % reduction of PM volume) (Figure 1-8)

5). By Neo tuner, there is 5 % field variation at the center of magnet.6). Recommendation: Figure 1-10 is duplicated here to show the recommended model

having reasonable compact dimensions. If radiation damage effects could be minimized or

mitigated theNeo magnet is much preferred.

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Contents

I. DR Transport Line Dipole Design 3

1.1 Features and recommendation 3

1.2 Details of the PANDIRA Designs 5

II. Gradient Dipole Magnet for the main damping ring 18

2.1 Requirements and features 18

2.2 Design of the pole tip shape to generate a small gradient 19

III. Damping Ring Quadrupole Magnet Design (NLC) 22

3.1 Features and recommendations 22

3.2 2-D Poisson for Permanent Magnets 27

3.3 Temperature Compensation Effects 27

3.4 Tuners 27

3.5 End Effects 29

3.5.1 Three-dimensional modeling of DR quadrupoles 30

3.6 Adding an End Plate on the Magnet - modeling a design feature of the FNAL

Linac PM Quad 31

3.7 Demagnetization in the permanent magnet 31

IV. Electromagnet design and Comparison for NLC Damping Ring Quadrupole 51

4.1 Features 51

4.2 Electromagnet design 52

4.3 Comparison between permanent magnet design and electromagnet design 56

8/6/2019 LCC-0077 rev. 1

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LCC-0077

SUMMARY OF LBL/SLAC DESIGN WORK

ON NLC MAGNETS

11/00 10/01

Jin-Young Jung

LCC-0077 rev. 1

Documents

Transcript of LCC-0077 rev. 1