# Practical magnet design 1.Iron saturates, when. Fields higher than 2.2 T with super conducting magnets high I Free currents (coils) magnetization 2.For.

## Presentation on theme: "Practical magnet design 1.Iron saturates, when. Fields higher than 2.2 T with super conducting magnets high I Free currents (coils) magnetization 2.For."— Presentation transcript:

Practical magnet design 1.Iron saturates, when

Fields higher than 2.2 T with super conducting magnets high I Free currents (coils) magnetization 2.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 h e.g. B = 2 T, h = 20 cm, NI = 320000 At

Coil parameters NI = (NI) needed, but N = ?, I = ? i.e. which conductor? Dissipated power (heat) P = I 2 R Must be removed from the system Air cooling Indirect cooling Direct water cooling Hollow conductor Relatively ineffective

Coil cooling The dissipated electric power in converted into heat (water temperature). The temperature rise rise between input and output is where  T = temperature rise [K] I = electric current [A] R = coil resistance [  ] q = water flow [l/min]

Usually Often the requirement is The resistivity of copper So: The smaller the  T, the larger q is needed

For a large q a large pressure difference (pressure gradient) is needed Semi empirically where  P = pressure difference [bar] q = water flow [l/min] a = flow cross section [mm 2 ] 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/n 2 )

T q T q I2RI2R n parallel cooling circuits (electrically in series)

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  R d Cu

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

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 mm 2

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

Cooling We allow  T = 20 o C Hence the cooling water flow: for one conductor/dpc Required pressure drop

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 o C. Note: the cooling system has to cool other devices as well!

The conductor was of type What would happen, if it was replaced with a conductor where A cu and A water are the same as well as the conductor outer dimensions?

The flow rate in the cooling hole would be doubled and 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

Alternatively we could use a square conductor with the same cross section Number of turns would increase and the conductor length as well Higher  P Also the resistance of one dpc would increase More flow Higher pressure

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)

The conductor is insulated diameter 26 mm  r= 390 mm Power dissipation for a double pancake Total power

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

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 (  ) depends naturally upon the heat transfer properties of the surroundings Typically power dissipation (heat) can be < 10 W/m e.g. A cu = 400 mm 2 and I = 425 AP/L = 7.8 W/m

Note: For I = 1000 A, A cu = 1600 mm 2 (7.8 W/m) 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 I nominal = 1000 A, I max = 1170 A 4 x 150 mm 2 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

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

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

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

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

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

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

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

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

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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