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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
Practical magnet design

  • Iron saturates, when


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]


Usually

Often the requirement is

The resistivity of copper

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


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]


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)


I2R

T

q

T

q

n parallel cooling circuits (electrically in series)


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


Hollow conductor
Hollow conductor double pancake structure

R

f

Cu

d


Example: K130 cyclotron double pancake structure

380 mm

< 400 mm

parallel

20 layers (axially)

10 turns (double conductor)

per coil


  • Desired NI = 400.000 At double pancake structure

    • 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


Conductor resistance (double pancake/ one conductor) double pancake structure

for one conductor

Dissipated power:

For a hot coil

Pnominal = 130 kW


Cooling
Cooling double pancake structure

We allow DT = 20 oC

Hence the cooling water flow:

for one conductor/dpc

Required pressure drop


  • 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!


The conductor was of type double pancake structure

What would happen, if it was replaced with a conductor

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


The flow rate in the cooling hole would be doubled double pancake structureand 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



Let us calculate this as an example: cross section

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)


The conductor is insulated cross section

diameter 26 mm

Dr= 390 mm

Power dissipation for a double pancake

Total power


Water flow rate cross section

Pressure drop

Starts to on the limit!

In both cases

Power supply: 1000 A/140 V


Power supply cross sectionCurrent/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 A P/L = 7.8 W/m


Note: cross section

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)


  • For example: K130 cyclotron cross section

    • 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


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/y R Kg/m

8329 4x3 2 1/0.5 0.8 0.070

8330 4.3x4 2.5 0.9/0.75 0.8 0.100

8356 4.67x4.19 2.41 1.13/0.89 0.76 0.130

8357 5.08x4.77 2.64 1.22/1.065 0.76 0.163

8290 5.8x3.7 2.5 1.65/0.6 0.8 0.143

8327 6x4 2.5 1.75/0.75 0.8 0.170

8300 6x5 3 1.5/1 1 0.200

8314 6x5.5 3.5 1.25/1 0.8 0.200

8370 6.1x4 3.2 1.45/0.4 0.6 0.143

8342 7x5 3 2/1 0.6 0.250

8115 7x6 4 1.5/1 1 0.256

6861 7x6.3 3.4 1.8/1.45 1 0.304

8364 7x8.5 4 1.5/2.25 1 0.412

8521 7.2x4.2 2.5 2.35/0.85 1 0.218

6833 7.5x5 3 2.25/1 0.5 0.270

8280 7.5/7x6 3.3 1.98/1.35 1 0.310

6864 7.5x6 3.5 2/1.25 1 0.308

8260 7.5x7 5.2 1.15/0.9 1/0.25 0.275

8331 7.5x8 4 1.75/2 1 0.420

6879 7.6x7.2 3.5 2.05/1.85 1 0.395

8160 7.8x6.25 2.5 2.65/1.87 0.5 0.389

8328 8x6 3.2 2.4/1.4 0.8 0.350

8103 8x6 3.2 2.4/1.4 1 0.350

8287 8x6 4 2/1 1 0.309

8399 8x6.7 4.5 1.75/1.1 1 0.329


8270 8x6.9 3.5 2.25/1.7 1 0.400 the manufacturer’s stock list – otherwise you may be surprised by the price!

8279 8x7 3.5 2.25/1.75 1 0.410

8242 8x7 4 2/1.5 1 0.381

8513 8x7.4 4.6 1.7/1.4 1 0.370

6863 8.2x7.2 3.8 2.2/1.7 1 0.417

6862 8.2x7.2 5 1.6/1.1 1 0.343

6857 8.5x5.5 2.7 2.9/1.4 1 0.360

8269 9x7.5 5 2/1.25 1 0.420

8448 9x8.5 5 2/1.75 1 0.500

8195 9.07x8 4.77 2.15/1.61 0.79 0.484

8518 9.3x8 6 1.65/1 1 0.400

8192 9.4x8.15 5.05 2.17/1.55 0.8 0.500

6146 9.5x7.1 3.5 3/1.8 1 0.512

8363 9.5/9.1x8 3.2 3.15/2.4 1 0.593

8348 9.5/9.1x8 5 2.25/1.5 1 0.490

8362 9.5x8/7.4 5 2.25/1.5 1 0.484

6145 10x7.1 3.9 3.05/1.6 1 0.520

6161 10x7.8 4.5 2.75/1.65 1 0.540

8391 10x9 4 3/2.5 1 0.685

6812 10.5x8.2 4.8 2.85/1.7 1 0.590

8258 10.6x7 4 3.3/1.5 1 0.543

8372 10.7x8 4.25 3.225/1.875 1 0.631

8133 10.7x8 5.8 2.45/1.1 1 0.520

8355 10.77x9.95 5.82 2.475/2.065 1.25 0.708

8236 11x7 3 4/2 1 0.620

8166 11x7 5 3/1 1 0.510

8392 11/10.4x7 5 3/1 1 0.497

8436 11x8 4 3.5/2 2 0.640

8413 11x8.8/8.6 5 3/1.9 1 0.677

8259 11x9.5 5 3/2.25 1 0.750


6144 11x9.8 6.5 2.25/1.65 1 0.650 the manufacturer’s stock list – otherwise you may be surprised by the price!

8442 11x10 5 3./2.5 1 0.800

8444 11.3x7.8 4.82 3.24/1.49 1.25 0.613

8266 11.5x9.5 6.7 2.4/1.4 1 0.654

8298 11.8x10.3 6 2.9/2.15 1.2 0.820

8507 11.9x8.58 3.96 3.97/2.31 0.8 0.798

8527 12x9 5 3.5/2 0.5 0.788

8144 12x9.5 6.5 2.75/1.5 1.5 0.700

6893 12x10 5 3.5/2.5 1 0.890

8212 12x11 7 2.5/2 1 0.830

6801 12.3x11.8 7.4 2.45/2.2 1 0.900

8177 12.6x10 5 3.8/2.5 1 0.940

8274 12.7x6.35 3.81 4.445/1.27 1 0.611

8511 12.7x10.66 6.6 3.05/2.03 1.25 0.892

6751 12.7x12.2 5.6 3.55/3.3 0.79 1.160

8289 13x11 6 3.5/2.5 1 1.018

8307 13.2x9 5 4.1/2 1 0.880

8116 13.5x8.25 5.1 4.2/1.58 1 0.810

8253 13.5x11.5 6.3 3.6/2.6 1 1.100

8495 13.5x12.5 9.8 3.7/2.7 1 0.827

6824 13.8x13.1 7.9 2.95/2.6 1 1.160

8378 14x7.6 4.5 4.75/1.55 1 0.801

8528 14x8 5 4.5/1.5 0.5 0.824

8412 14x11.9/11.5 5 4.5/3.45 1 1.292

8461 14x12.5 5.86 4.07/3.32 1 1.320

8500 14x12.6 6 4/3.3 1 1.317

6180 14x12.6 8 3/2.3 1 1.120

8233 14.3x11.4 6 4.15/2.7 1.5 1.200

6800 14.4x12.3 6.5 3.95/2.9 1 1.270

6132 14.9x11.9 6.5 4.2/2.7 1 1.300


8482 15x8 5 5/1.5 1 0.890 the manufacturer’s stock list – otherwise you may be surprised by the price!

8305 15/14x8 4.5 5.25/1.75 1 0.910

8142 15x8 4.5 5.25/1.75 1 0.920

8219 15x9.5 6.5 4.25/1.5 1 0.970

8180 15x10 5 5/2.5 1 1.160

6802 15x11.8 6.5 4.25/2.65 1 1.270

8427 15/14.2x11.8 6.5 4.25/2.65 - 1.256

6140 15x12.5 7 4/2.75 1.75 1.300

8322 15x13 6.1 4.45/3.45 1.5 1.460

8497 15x13.7 8 3.5/2.85 1 1.380

6896 15.2x12.75 8 3.6/2.38 2 1.250

6822 15.4x10 4 5.7/3 1.5 1.250

8351 16x10 5 5.5/2.5 2 1.220

8483 16x14 6.5 4.75/3.75 1.5 1.690

8179 16x14 7 4.5/3.5 1.5 1.640

6181 16x14.5 10 3/2.25 1 1.360

8451 16/15.2x15 9 3.5/3 1 1.543

8455 16.2x10 4.77 5.715/2.615 1 1.260

6160 16.3x10.8 6.6 4.85/2.1 1 1.240

8181 16.5x8.9 5.2 5.65/1.85 1.5 1.120

8278 16.5x12.5 7.35 4.58/2.58 1 1.460

6855 16.5x12.5 8.2 4.15/2.15 1 1.360

8394 16.5x12.5 8.2 4.15/2.15 0.5 1.370

6890 16.75x8.6 5.5 5.63/1.55 0.5 1.080

8460 17x14.5 10 3.5/2.25 1 1.494

8190 17x15 6.4 5.3/4.3 2 1.960

8429 17x16 6 5.5/5 1.5 2.160

8170 17x16 9 4/3.5 1.5 1.840

8196 17.4x10.7 6.1 5.65/4.6 1.5 1.385

8221 18x8 4 7/2 1.5 1.160

6832 18x10 6 6/2 0.5 1.340


8400 18x11.2 6.6 5.7/2.3 1.5 1.480 the manufacturer’s stock list – otherwise you may be surprised by the price!

6888 18x12 8 5/2 1 1.480

8336 18x12.65 9.5 4.25/1.58 1 1.390

8428 18/17.2x14 10 4/2 1 1.520

8439 18x14 10 4/2 1 1.534

8232 18x15 8 5/3.5 2 1.930

8326 18x15 8.5 4.75/3.25 2 1.880

6806 18.54x10.46 4.96 6.79/2.75 1.52 1.540

8169 18.9x11.4 7 5.95/2.2 1.5 1.560

8508 19x12.5 9 5/1.75 1.5 1.540

8122 19x13 8 5.5/2.5 1 1.750

8453 19x16 7 6/4.5 1 2.400

8167 19.05x7.92 4.75 7.15/1.59 1.59 1.170

8517 19.05x15.88 8 5.525/3.94 2 2.220

8498 19.05x15.88 10.80 4.13/2.54 4.75 1.700

8776 19.05x15.88 12.7 3.18/1.59 4.75 1.400

8506 19.3/18.3x15.5 10.5 4.4/2.5 2 1.845

8430 20x10 6.5 6.75/1.75 2 1.460

8119 20x12 8 6/2 1 1.690

6825 20x12 9 5.5/1.5 1 1.560

8271 20x14 6 7/4 2 2.220

8473 20x15 8 6/3.5 1 2.230

8465 20.1/19.1x19.6 11 4.55/4.3 2.5 2.580

8146 20.2x15 10 5.1/2.5 1.5 1.990

8189 20.4x13.4 8 5.7/2.7 1 1.860

8478 20.5x18 7 6.75/5.5 1 2.950

6859 20.5x18 8.5 6/4.75 1 2.780

8148 20.83x15.75 6.35 7.24/4.7 2 2.620

8117 20.9x15.65 7 6.95/4.33 1.5 2.570

8403 20.9x20.5 9.5 5.7/5.5 1.5 3.180

8335 21x12 5 8/3.5 1 2.070

8315 21x16.5 7.7 6.65/4.4 1 2.670

8359 21x18 9 6/4.5 1.5 2.790


8199 21x18.2 7.45 6.77/5.37 1.5 3.000 the manufacturer’s stock list – otherwise you may be surprised by the price!

8388 21.21x12.67 9.52 5.845/1.575 1.6 1.747

8410 21.5x18.5 8 6.75/5.25 1 3.099

8524 21.5x18.5 8.5 6.75/5 1 3.04

8352 22x12.24 6.35 7.825/2.945 1.52 2.110

8421 22x18.9/17.7 8 7/5.45 2 3.110

6895 22.2x18.3 11 5.6/3.65 0.8 2.790

8382 22.22x15.88 7.92 7.15/3.98 1.7 2.692

6811 22.5x17.8 13 4.75/2.4 2 2.320

8476 22.7/19 8 7.35/5.5 2 3.380

8164 22.86x16.51 11.13 5.86/2.69 1.2 2.490

8284 23x12 7.5 7.75/2.25 2 2.040

8462 23x14 10 6.5/2 1.5 2.159

8198 23x15 6.55 8.22/4.22 1.5 2.780

8109 23x15 8 7.5/3.5 1.5 2.600

8262 23x17.8 11.8 5.85/3 1.5 2.740

8210 23x20 8 7.5/6 1.5 3.650

8367 23x21.9 6.5 8.25/7.7 1.5 4.190

8312 23.01x18.87 12.3 5.36/3.29 1.2 2.810

8218 23.5x13.98 10 6.75/1.99 1 2.230

6803 23.5x16 9 7.25/3.5 2.5 2.730

8126 24x11 7.5 8.25/1.75 1 1.960

8440 25x15 10 7.5/2.5 1 2.643

8191 25x17 6.5 9.25/5.25 1.5 3.470

6882 25x20 11.5 6.75/4.25 1 3.520

8320 25x21 9.1 7.95/5.95 2 4.080

8457 25x21 14.5 5.25/3.25 3 3.150

8514 25x23 15.5 4.75/3.75 2 3.420


8184 25x24 12 6.5/6 1 4.340 the manufacturer’s stock list – otherwise you may be surprised by the price!

8343 25.4x14.35 6.35 9.525/4 1.6 2.960

8398 25.4x14.35 7.92 8.74/3.215 1.6 2.798

8274 25.4x19.05 12.7 6.35/3.18 1.6 3.170

8152 25.5x18.3 9 8.25/4.65 1.5 3.590

8425 26x18 6 10/6 1.5 3.920

8104 26.5x23.7 13.5 6.5/5.1 1 4.330

8431 27x22.5 13.5 6.75/4.5 2.5 4.103

8162 27.84x23.42 8.64 9.6/7.4 1.58 5.280

8161 27.84x23.42 11.3 8.27/6.06 1.58 4.920

8332 28.1x20.1 6.1 11/7 2 4.760

8321 29x19.5/19 9.8 9.6/4.73 2 4.290

8243 30x22 13 8.5/4.5 1 4.700

6874 30x22 14 8/4 5 4.330

6876 30x23 8 11/7.5 2 5.680

6868 30.3x23.7 12 9.15/5.85 1.5 5.400

8466 31.75x27.94 19.05 6.35/4.445 4.76 5.200

6837 32x22.5 10.5 10.75/6 1.5 5.650

8263 32.5x29 11 10.75/9 1 7.570

8432 33x17 10.5 11.25/3.25 3 4.175

6839 33x24 6.5 13.25/8.75 1.5 6.770

8499 33.78x30.63 12.7 10.54/8.965 2.38 8.050

8443 34x27 19 7.5/4 4 5.540

8520 36x16 10 13/3 1 4.440

6816 37x23 8 14.5/7.5 1.5 7.100

8433 37x24 8 14.5/8 1.5 7.470

8145 37x28 22 7.5/3 1.5 5.840

8296 38x35 12.7 12.65/11.15 3.5 10.66


8404 39x31 9 15/11 2 10.21 the manufacturer’s stock list – otherwise you may be surprised by the price!

6804 39.37x22.86 8.89 15.24/6.99 2.54 7.400

6871 40x12 7.5 16.25/2.25 1 3.890

8505 40.5x22.2 9.5 15.5/6.35 3 7.340

8201 41x23 8 16.5/7.5 2.5 7.940

8107 42x28 8 17/10 2 10.00

8268 42.2x30.7 8 17.1/11.35 2.5 11.08

8333 43.1x14.6 6.8 18.15/3.9 2 5.270

8267 43.2x24.7 8 17.6/8.35 2.5 9.040

8240 43.5x33 15 14.25/9 3 11.20

8120 45x14 10 17.5/2 2 4.190

8316 47.1x41 13.5 16.8/13.75 2 15.95

8295 47.7x38 12.7 17.5/12.65 3.5 14.97

8108 48x15 8 20/3.5 5 5.810

8308 48x19 11 18.5/4 1.5 7.290

8515 48x24 14 17/5 2 8.890

8250 48x38 8 20/15 2 15.82

8375 50x10 5 22.5/2.5 1.5 4.280

8137 50x35 12 19/11.5 5 14.46

8297 50.8x22.2 12.7 19.05/4.76 3.5 8.860

8434 52x21 9 21.5/6 1.5 9.190

8226 52.2x24.5 11.11 20.54/6.69 2.38 10.52

8114 53.8/53.2x39.5 15 12.25/19.4 2 17.28

8360 55x22 9.8 22.6/6.1 2.5 10.10

8168 60.3x25.4 15.9 22.2/4.75 2 11.89

8358 60.32x25.4 12.7 23.81/6.35 3.17 12.49

8273 65x47 10 27.5/18.5 4 26.50

8265 75x32 8 33.5/12 2 20.97

8101 82x35 12 35/11.5 2 24.60

8422 82x35 15 33.5/10 2 24.00

8275 85x35 8 38.5/13.5 5 26.00

8123 95x40 15 40/12.5 3 32.30


SQUARE WITH A ROUND HOLE the manufacturer’s stock list – otherwise you may be surprised by the price!

Dimensions in mm

NO. OD ID x = y R Kg/m MARGIN Eur/kg

6844 4 2.5 0.75 0.5 0.098 11,80

8529 4 2.0 1 0.5 0.113

8350 4.19 2.4 0.895 0.8 0.110

8301 4.3 2.34 0.98 0.76 0.120

8153 4.5 2.5 1 1 0.136

8206 4.62 2.39 1.11 0.76 0.150 10,40

8150 4.76 3.18 0.79 1 0.124

6867 5 2 1.5 1 0.179

8215 5 2.5 1.25 1 0.172

6831 5 3 1 0.7 0.157

8416 5.6 3.05 1.275 1 0.210 10,00

6881 5.6 3.6 1 1 0.183

8339 5.79 3.18 1.305 1 0.220

8235 6x6/5.6 3 1.5 1 0.250

8283 6 3 1.5 1 0.250

6860 6 3.5 1.25 0.8 0.230

6835 6 4 1 1 0.200

8408 6x6/5.6 4 1 1 0.197

8204 6 4.5 0.75 1 0.173

8405 6.15 2.54 1.805 0.635 0.290

8417 6.35 3.15 1.6 1 0.280

8149 6.35 4.75 0.8 1.27 0.190

8424 6.40 3 1.7 1 0.300

6873 6.4 4.4 1 1 0.230

8385 6.48 3.18 1.65 1 0.297

6858 6.5 3 1.75 1 0.300

8325 6.5 3.1 1.7 0.8 0.310

6869 6.5 3.5 1.5 1 0.280

8156 6.5 4 1.25 0.5 0.260

8125 6.5 4.5 1 1 0.220

8132 6.7 4 1.35 1 0.280


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