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Practical magnet design

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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  1. Practical magnet design • Iron saturates, when

  2. 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.

  3. Current in the coils h e.g. B = 2 T, h = 20 cm, NI = 320000 At

  4. 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

  5. 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]

  6. Usually Often the requirement is The resistivity of copper So: The smaller the DT, the larger q is needed

  7. 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]

  8. 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)

  9. I2R T q T q n parallel cooling circuits (electrically in series)

  10. 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 low ion exchanged water, closed cooling circuit, heat exchangers

  11. Hollow conductor R f Cu d

  12. Example: K130 cyclotron 380 mm < 400 mm parallel 20 layers (axially) 10 turns (double conductor) per coil

  13. 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

  14. Conductor resistance (double pancake/ one conductor) for one conductor Dissipated power: For a hot coil Pnominal = 130 kW

  15. Cooling We allow DT = 20 oC Hence the cooling water flow: for one conductor/dpc Required pressure drop

  16. 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!

  17. 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?

  18. 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

  19. 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

  20. 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)

  21. The conductor is insulated diameter 26 mm Dr= 390 mm Power dissipation for a double pancake Total power

  22. Water flow rate Pressure drop Starts to on the limit! In both cases Power supply: 1000 A/140 V

  23. 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 A P/L = 7.8 W/m

  24. 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)

  25. 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

  26. 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

  27. 8270 8x6.9 3.5 2.25/1.7 1 0.400 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

  28. 6144 11x9.8 6.5 2.25/1.65 1 0.650 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

  29. 8482 15x8 5 5/1.5 1 0.890 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

  30. 8400 18x11.2 6.6 5.7/2.3 1.5 1.480 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

  31. 8199 21x18.2 7.45 6.77/5.37 1.5 3.000 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

  32. 8184 25x24 12 6.5/6 1 4.340 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

  33. 8404 39x31 9 15/11 2 10.21 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

  34. SQUARE WITH A ROUND HOLE 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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