Practical magnet design
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Practical magnet design. Iron saturates, when . Fields higher than 2.2 T with super conducting magnets high I. Free currents (coils). magnetization. For a given field we need a certain current (Ampereturns). Can be approximated Final values from computer codes (FEMM, POISSON, TOSCA, etc.

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Practical magnet design

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Practical magnet design

Practical magnet design

  • Iron saturates, when


Practical magnet design

  • Fields higher than 2.2 T with super conducting magnets

    • high I

Free currents (coils)

magnetization

  • For a given field we need a certain current (Ampereturns)

  • Can be approximated

  • Final values from computer codes (FEMM, POISSON, TOSCA, etc.


Current in the coils

Current in the coils

h

e.g. B = 2 T, h = 20 cm, NI = 320000 At


Coil parameters

Coil parameters

  • NI = (NI)needed, but N = ?, I = ?

    • i.e. which conductor?

Dissipated power (heat) P = I2R

  • Must be removed from the system

    • Air cooling

    • Indirect cooling

    • Direct water cooling

      • Hollow conductor

Relatively ineffective


Coil cooling

Coil cooling

  • The dissipated electric power in converted into heat (water temperature).

  • The temperature rise rise between input and output is

where

DT = temperature rise [K]

I = electric current [A]

R = coil resistance [W]

q = water flow [l/min]


Practical magnet design

Usually

Often the requirement is

The resistivity of copper

So: The smaller the DT, the larger q is needed


Practical magnet design

For a large q a large pressure difference (pressure gradient) is needed

Semi empirically

where

DP = pressure difference [bar]

q = water flow [l/min]

a = flow cross section [mm2]

l = flow length [m]


Practical magnet design

Note!

So, the desired pressure increases very rapidly with electric current

Usually

If the desired pressure becomes too high the cooling circuit can be divided into several parallel circuits

(pressure decreases as 1/n2)


Practical magnet design

I2R

T

q

T

q

n parallel cooling circuits (electrically in series)


Practical magnet design

  • Division into parallel cooling circuits is done e.g. with a double pancake structure

    • “wind” starting from the outer radius into the inner radius, come back along the next layer

    • These double pancakes are connected in series electrically and in parallel

Note: The conductivity of the cooling water must be lowion exchanged water, closed cooling circuit, heat exchangers


Hollow conductor

Hollow conductor

R

f

Cu

d


Practical magnet design

Example: K130 cyclotron

380 mm

< 400 mm

parallel

20 layers (axially)

10 turns (double conductor)

per coil


Practical magnet design

  • Desired NI = 400.000 At

    • In one conductor pair 400.000 At/(2x200 t) = 1000 A

      • In one conductor: 500 A

      • Conductor pair is connected in parallel also electrically

  • Length of a double pancake

  • Conductor parameters

    • d = 17 mm

    • = 7 mm

      R = 1 mm

A = 250 mm2


Practical magnet design

Conductor resistance (double pancake/ one conductor)

for one conductor

Dissipated power:

For a hot coil

Pnominal = 130 kW


Cooling

Cooling

We allow DT = 20 oC

Hence the cooling water flow:

for one conductor/dpc

Required pressure drop


Practical magnet design

  • Both coils consist of 10 double pancakes (dpc)

    • Each dpc has two conductors in parallel (both electrically and for cooling)

    • 40 pieces of 180 m long cnductors

      • Total flow = 40 x 2.5 l/min = 100 l/min

  • So: the cooling system must be capable of producing about 6.5 bar pressure difference at a 100 l/min flow rate in order to keep the temperature increase below 20 oC.

    • Note: the cooling system has to cool other devices as well!


Practical magnet design

The conductor was of type

What would happen, if it was replaced with a conductor

where Acu and Awater are the same as well as the conductor outer dimensions?


Practical magnet design

The flow rate in the cooling hole would be doubledand the cross section would be doubled

Change in the pressure drop

Would be beneficial to use one hole with the same total cross section

But: winding would be difficult

r


Practical magnet design

  • Alternatively we could use a square conductor with the same cross section

    • Number of turns would increase and the conductor length as well

    • Higher DP

    • Also the resistance of one dpc would increase

      • More flow

      • Higher pressure


Practical magnet design

Let us calculate this as an example:

Conductor dimensions

=

In one coil 400.000 At/2 = 200.000 At

Keep the current density unaltered

I = 2 x 500 A = 1000 A

N = 200

Full double pancakes

N = (2 x 7 ) x 15 = 210

I = 952 A

i.e. 7 double pancakes (15 turns)


Practical magnet design

The conductor is insulated

diameter 26 mm

Dr= 390 mm

Power dissipation for a double pancake

Total power


Practical magnet design

Water flow rate

Pressure drop

Starts to on the limit!

In both cases

Power supply: 1000 A/140 V


Practical magnet design

Power supply Current/Voltage

These have also some limitations

  • Current must be taken into account when dimensioning the transport cables from the PS to the magnet

  • The dimensioning (f) depends naturally upon the heat transfer properties of the surroundings

    • Typically power dissipation (heat) can be < 10 W/m

    • e.g. Acu = 400 mm2 and I = 425 AP/L = 7.8 W/m


Practical magnet design

Note:

For I = 1000 A, Acu = 1600 mm2 (7.8 W/m)

4 cm

4 cm

  • In practice the feeding cable is divided into several thinner cables

    • More cooling surface/unit power loss

    • More flexible (mounting)


Practical magnet design

  • For example: K130 cyclotron

    • Inominal = 1000 A, Imax = 1170 A

    • 4 x 150 mm2 cable

      • Maximum current 320 A/cable (depends on the assembly – cooling circumstances)

  • Note also:

    • For high currents the transfer losses (Voltage) may be significant in a long transfer cable

      • The Power Supply sees both the load and the transfer line


Practical magnet design

Important note: choose the hollow conductor dimensions from the manufacturer’s stock list – otherwise you may be surprised by the price!

RECTANGULAR WITH A ROUND HOLE

Dimensions in mm

NO.OD.ID.x/yRKg/m

83294x321/0.50.80.070

83304.3x42.50.9/0.750.80.100

83564.67x4.192.411.13/0.890.760.130

83575.08x4.772.641.22/1.0650.760.163

82905.8x3.72.51.65/0.60.80.143

83276x42.51.75/0.750.80.170

83006x531.5/110.200

83146x5.53.51.25/10.80.200

83706.1x43.21.45/0.40.60.143

83427x532/10.60.250

81157x641.5/110.256

68617x6.33.41.8/1.4510.304

83647x8.541.5/2.2510.412

85217.2x4.22.52.35/0.8510.218

68337.5x532.25/10.50.270

82807.5/7x63.31.98/1.3510.310

68647.5x63.52/1.2510.308

82607.5x75.21.15/0.91/0.250.275

83317.5x841.75/210.420

68797.6x7.23.52.05/1.8510.395

81607.8x6.252.52.65/1.870.50.389

83288x63.22.4/1.40.80.350

81038x63.22.4/1.410.350

82878x642/110.309

83998x6.74.51.75/1.110.329


Practical magnet design

82708x6.93.52.25/1.710.400

82798x73.52.25/1.7510.410

82428x742/1.510.381

85138x7.44.61.7/1.410.370

68638.2x7.23.82.2/1.710.417

68628.2x7.251.6/1.110.343

68578.5x5.52.72.9/1.410.360

82699x7.552/1.2510.420

84489x8.552/1.7510.500

81959.07x84.772.15/1.610.790.484

85189.3x861.65/110.400

81929.4x8.155.052.17/1.550.80.500

61469.5x7.13.53/1.810.512

83639.5/9.1x83.23.15/2.410.593

83489.5/9.1x852.25/1.510.490

83629.5x8/7.452.25/1.510.484

614510x7.13.93.05/1.610.520

616110x7.84.52.75/1.6510.540

839110x943/2.510.685

681210.5x8.24.82.85/1.710.590

825810.6x743.3/1.510.543

837210.7x84.253.225/1.87510.631

813310.7x85.82.45/1.110.520

835510.77x9.955.822.475/2.0651.250.708

823611x734/210.620

816611x753/110.510

839211/10.4x753/110.497

843611x843.5/220.640

841311x8.8/8.653/1.910.677

825911x9.553/2.2510.750


Practical magnet design

614411x9.86.52.25/1.6510.650

844211x1053./2.510.800

844411.3x7.84.823.24/1.491.250.613

826611.5x9.56.72.4/1.410.654

829811.8x10.362.9/2.151.20.820

850711.9x8.583.963.97/2.310.80.798

852712x953.5/20.50.788

814412x9.56.52.75/1.51.50.700

689312x1053.5/2.510.890

821212x1172.5/210.830

680112.3x11.87.42.45/2.210.900

817712.6x1053.8/2.510.940

827412.7x6.353.814.445/1.2710.611

851112.7x10.666.63.05/2.031.250.892

675112.7x12.25.63.55/3.30.791.160

828913x1163.5/2.511.018

830713.2x954.1/210.880

811613.5x8.255.14.2/1.5810.810

825313.5x11.56.33.6/2.611.100

849513.5x12.59.83.7/2.710.827

682413.8x13.17.92.95/2.611.160

837814x7.64.54.75/1.5510.801

852814x854.5/1.50.50.824

841214x11.9/11.554.5/3.4511.292

846114x12.55.864.07/3.3211.320

850014x12.664/3.311.317

618014x12.683/2.311.120

823314.3x11.464.15/2.71.51.200

680014.4x12.36.53.95/2.911.270

613214.9x11.96.54.2/2.711.300


Practical magnet design

848215x855/1.510.890

830515/14x84.55.25/1.7510.910

814215x84.55.25/1.7510.920

821915x9.56.54.25/1.510.970

818015x1055/2.511.160

680215x11.86.54.25/2.6511.270

842715/14.2x11.86.54.25/2.65-1.256

614015x12.574/2.751.751.300

832215x136.14.45/3.451.51.460

849715x13.783.5/2.8511.380

689615.2x12.7583.6/2.3821.250

682215.4x1045.7/31.51.250

835116x1055.5/2.521.220

848316x146.54.75/3.751.51.690

817916x1474.5/3.51.51.640

618116x14.5103/2.2511.360

845116/15.2x1593.5/311.543

845516.2x104.775.715/2.61511.260

616016.3x10.86.64.85/2.111.240

818116.5x8.95.25.65/1.851.51.120

827816.5x12.57.354.58/2.5811.460

685516.5x12.58.24.15/2.1511.360

839416.5x12.58.24.15/2.150.51.370

689016.75x8.65.55.63/1.550.51.080

846017x14.5103.5/2.2511.494

819017x156.45.3/4.321.960

842917x1665.5/51.52.160

817017x1694/3.51.51.840

819617.4x10.76.15.65/4.61.51.385

822118x847/21.51.160

683218x1066/20.51.340


Practical magnet design

840018x11.26.65.7/2.31.51.480

688818x1285/211.480

833618x12.659.54.25/1.5811.390

842818/17.2x14104/211.520

843918x14104/211.534

823218x1585/3.521.930

832618x158.54.75/3.2521.880

680618.54x10.464.966.79/2.751.521.540

816918.9x11.475.95/2.21.51.560

850819x12.595/1.751.51.540

812219x1385.5/2.511.750

845319x1676/4.512.400

816719.05x7.924.757.15/1.591.591.170

851719.05x15.8885.525/3.9422.220

849819.05x15.8810.804.13/2.544.751.700

877619.05x15.8812.73.18/1.594.751.400

850619.3/18.3x15.510.54.4/2.521.845

843020x106.56.75/1.7521.460

811920x1286/211.690

682520x1295.5/1.511.560

827120x1467/422.220

847320x1586/3.512.230

846520.1/19.1x19.6114.55/4.32.52.580

814620.2x15105.1/2.51.51.990

818920.4x13.485.7/2.711.860

847820.5x1876.75/5.512.950

685920.5x188.56/4.7512.780

814820.83x15.756.357.24/4.722.620

811720.9x15.6576.95/4.331.52.570

840320.9x20.59.55.7/5.51.53.180

833521x1258/3.512.070

831521x16.57.76.65/4.412.670

835921x1896/4.51.52.790


Practical magnet design

819921x18.27.456.77/5.371.53.000

838821.21x12.679.525.845/1.5751.61.747

841021.5x18.586.75/5.2513.099

852421.5x18.58.56.75/513.04

835222x12.246.357.825/2.9451.522.110

842122x18.9/17.787/5.4523.110

689522.2x18.3115.6/3.650.82.790

838222.22x15.887.927.15/3.981.72.692

681122.5x17.8134.75/2.422.320

847622.7/1987.35/5.523.380

816422.86x16.5111.135.86/2.691.22.490

828423x127.57.75/2.2522.040

846223x14106.5/21.52.159

819823x156.558.22/4.221.52.780

810923x1587.5/3.51.52.600

826223x17.811.85.85/31.52.740

821023x2087.5/61.53.650

836723x21.96.58.25/7.71.54.190

831223.01x18.8712.35.36/3.291.22.810

821823.5x13.98106.75/1.9912.230

680323.5x1697.25/3.52.52.730

812624x117.58.25/1.7511.960

844025x15107.5/2.512.643

819125x176.59.25/5.251.53.470

688225x2011.56.75/4.2513.520

832025x219.17.95/5.9524.080

845725x2114.55.25/3.2533.150

851425x2315.54.75/3.7523.420


Practical magnet design

818425x24126.5/614.340

834325.4x14.356.359.525/41.62.960

839825.4x14.357.928.74/3.2151.62.798

827425.4x19.0512.76.35/3.181.63.170

815225.5x18.398.25/4.651.53.590

842526x18610/61.53.920

810426.5x23.713.56.5/5.114.330

843127x22.513.56.75/4.52.54.103

816227.84x23.428.649.6/7.41.585.280

816127.84x23.4211.38.27/6.061.584.920

833228.1x20.16.111/724.760

832129x19.5/199.89.6/4.7324.290

824330x22138.5/4.514.700

687430x22148/454.330

687630x23811/7.525.680

686830.3x23.7129.15/5.851.55.400

846631.75x27.9419.056.35/4.4454.765.200

683732x22.510.510.75/61.55.650

826332.5x291110.75/917.570

843233x1710.511.25/3.2534.175

683933x246.513.25/8.751.56.770

849933.78x30.6312.710.54/8.9652.388.050

844334x27197.5/445.540

852036x161013/314.440

681637x23814.5/7.51.57.100

843337x24814.5/81.57.470

814537x28227.5/31.55.840

829638x3512.712.65/11.153.510.66


Practical magnet design

840439x31915/11210.21

680439.37x22.868.8915.24/6.992.547.400

687140x127.516.25/2.2513.890

850540.5x22.29.515.5/6.3537.340

820141x23816.5/7.52.57.940

810742x28817/10210.00

826842.2x30.7817.1/11.352.511.08

833343.1x14.66.818.15/3.925.270

826743.2x24.7817.6/8.352.59.040

824043.5x331514.25/9311.20

812045x141017.5/224.190

831647.1x4113.516.8/13.75215.95

829547.7x3812.717.5/12.653.514.97

810848x15820/3.555.810

830848x191118.5/41.57.290

851548x241417/528.890

825048x38820/15215.82

837550x10522.5/2.51.54.280

813750x351219/11.5514.46

829750.8x22.212.719.05/4.763.58.860

843452x21921.5/61.59.190

822652.2x24.511.1120.54/6.692.3810.52

811453.8/53.2x39.51512.25/19.4217.28

836055x229.822.6/6.12.510.10

816860.3x25.415.922.2/4.75211.89

835860.32x25.412.723.81/6.353.1712.49

827365x471027.5/18.5426.50

826575x32833.5/12220.97

810182x351235/11.5224.60

842282x351533.5/10224.00

827585x35838.5/13.5526.00

812395x401540/12.5332.30


Practical magnet design

SQUARE WITH A ROUND HOLE

Dimensions in mm

NO.ODIDx = yRKg/mMARGIN Eur/kg

684442.50.750.50.09811,80

852942.010.50.113

83504.192.40.8950.80.110

83014.32.340.980.760.120

81534.52.5110.136

82064.622.391.110.760.15010,40

81504.763.180.7910.124

6867521.510.179

821552.51.2510.172

68315310.70.157

84165.63.051.27510.21010,00

68815.63.6110.183

83395.793.181.30510.220

82356x6/5.631.510.250

8283631.510.250

686063.51.250.80.230

683564110.200

84086x6/5.64110.197

820464.50.7510.173

84056.152.541.8050.6350.290

84176.353.151.610.280

81496.354.750.81.270.190

84246.4031.710.300

68736.44.4110.230

83856.483.181.6510.297

68586.531.7510.300

83256.53.11.70.80.310

68696.53.51.510.280

81566.541.250.50.260

81256.54.5110.220

81326.741.3510.280


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