1. 1 QXF / SQXF heater design update M. Marchevsky (12/03/13)

2. 2 Design criteria (I) Based on heater tests of HQ01-HQ02, the heater power density is < 100 W/cm 2, as the delay time t d to quench reaches “saturation” at around this value. In fact, power density of 50-70 W/cm 2 appears to be acceptable.  Geometry QXF winding dimensions: Outer layer: Pole MT: 23.74 mm Midplane MT: 31.77 mm Inner layer: Pole MT: 9.19 mm Midplane MT 30.75 mm Length (straight section): SQXF: 1.0 m (IL), 1.07 m (OL) MQXF: 3.9 m QXF: 6.7 m Cable twist pitch: 109 mm  Heater power density:  Quench propagation time We assume conservatively the normal zone propagation velocity to be  10 m/s, which will define time to quench t q a segment between two consecutive heating stations

3. 3 Design criteria (II)  Maximum operating voltage Per P. Fessia “Electrical test guidelines” document (p. 10), 450 V is the standard operational voltage of the LHC Q.H. power supply. The FNAL Q.H. supplies operate at maximum voltage of 350 V. We therefore take this number as the upper limit to determine the heating power. As a design point, we assume that this maximum voltage should be sufficient to provide for 100 W/cm 2 heat power density across the “heating station” elements for the longest (QXF) magnet.  Electrical insulation strength Assuming the maximal quench voltage of 1000 V, the The Coil-to-Heater insulation should sustain up to 1980 V in air (“Electrical test guidelines” document, p. 11). Vq, V2503505001000 VQH-Coil (air), V1366148516631980

4. 4 Design criteria (III) Presently, wiring of the heater is done using gauge 16 (1.32 mm) diameter copper wire, with linear resistance of  12 m  /m at 300 K. Estimated final wire temperature in adiabatic approximation for various combinations of the initial temperature and current and for the two pulse durations are shown in the tables. Simulation of the adiabatic temperature rise of a copper wire (RRR=100) of 1.32 mm diameter, carrying current I=I 0 e -t/ , where I 0 =3100 A and  =50 ms. Initial.wire temperature is 4.5 K. 5100200300 509.7100.1200.1300.2 10013.7100.2200.4300.6 25021.3101.3202.6303.9 50030105.4210.7315.8 100045.1123.5245.9370.1 200093.3231.3475B 3000269BBB 5100200300 5011.5100.1200.2300.3 10016.2100.4200.8301.2 25025.3102.7205.3307.8 50036.2111.1221.8332.7 100059.6152.3301.7471.8 2000215.7BBB 3000BBBB  =50 ms I 0, A T 0, K  =100 ms *B = burnout Maximum current (wiring ) I 0, A

5. 5 SQXF: periodicity with the ½ cable twist pitch Cable twist pitch, p Distance between heating stations, l Heating station width, w If p = 2 n w and l = (2n+1) w, then the supercurrent in all strands of the cable segment of length L= n l can be “interrupted” simultaneously by normal zones created using n heating stations. This can potentially improve heater efficiency, as all cable strands will get resistive and start dissipating heat at the same time. n = 5

6. 6 SQXF: outer layer, mid-plane MT H OMMT = 31.77 mm a = 10.48 mm (=> 12.11 mm along the cable) r1 = 3 mm L = 15 mm  = 60 deg m = 3 mm b = 33 mm 18 segments P/A (straight) = 161 W/cm 2 P/A (curved) = 136 W/cm 2 R heater = 1.60  L seg = 60.7 mm H seg = 31.7 mm 150 V,  =5*10 -7  m, d = 25  m 5 segments (303.5 mm length) will provide simultaneous quenching of all strands. Anticipated heater delay: t d  9 ms (from HQ). Using NZPV of 10 m/s and L seg = 61 mm => t q = 3 ms The entire length will be normal (conservatively) in t d + t q = 12 ms. (Per 1.07 m)

7. 7 SQXF: outer layer, pole block MT H OPMT = 23.74 mm a = 10.48 mm (=> 12.11 mm along the cable) r1 = 3 mm L = 6 mm  = 60 deg m = 3 mm b = 38 mm P/A (straight) = 208 W/cm 2 P/A (curved) = 176 W/cm 2 R heater = 1.40  17 segments L seg = 61.3 mm H seg = 23.9 mm 150 V,  =5*10 -7  m, d = 25  m (Per 1.07 m)

8. 8 SQXF: inner layer, pole MT Proposal: combine mid-plane and pole block heaters in one, spanning the entire width of the inner layer winding of 45.5 mm L IMMT =30.75 mm and L IPMT =9.19 mm Entire inner layer: 45.51 mm a = 10.3 mm (=> 11.87 mm along the cable) r1 = 3 mm L = 30 mm  = 60 deg m = 3 mm b = 26 mm L seg = 61.3 mm H seg = 44.7 mm 16 segments P/A (straight) = 137 W/cm 2 P/A (curved) = 116 W/cm 2 R heater = 1.73  150 V,  =5*10 -7  m, d = 25  m (Per 1.00 m)

9. 9 QXF: periodicity with the cable 2x twist pitch Cable twist pitch, p n = 19 Distance between heating stations, l Heating station width, w p = n w and l = (n+1) w

10. 10 QXF: outer layer, mid-plane MT H OMMT = 31.77 mm a = 10.48 mm (=> 12.11 mm along the cable) r1 = 3 mm L = 15 mm  = 60 deg m = 3 mm b = 203 mm 29 segments P/A (straight) = 69 W/cm 2 P/A (curved) = 58 W/cm 2 R heater = 5.68  L seg = 230 mm H seg = 31.7 mm 350 V,  =5 10 -7  m, d = 25  m Heating station density is 4x less compared to the SQXF. n = 2*109 mm / 12.11 = 18 => hence all strands will be driven normal at once along every 18*L seg = 4140 mm, or  0.6 of the full coil length. Hence each strand will be driven normal at least at one spot per full coil length. Anticipated heater delay: t d  10 ms (from HQ). Using NZPV of 10 m/s and L seg = 230 mm => t q =11.5 ms The entire length will be normal (conservatively) in t d + t q = 21.5 ms (Per 6.70 m)

11. 11 QXF: outer layer, pole block MT H OPMT = 23.74 mm a = 10.48 mm (=> 12.11 mm along the cable) r1 = 3 mm L = 6 mm  = 60 deg m = 3 mm b = 207 mm P/A (straight) = 53 W/cm 2 P/A (curved) = 45 W/cm 2 R heater = 6.49  29 segments L seg = 230.3 mm H seg = 23.9 mm 350 V,  =5*10 -7  m, d = 25  m (Per 6.70 m)

12. 12 QXF: inner layer, pole MT Proposal: combine mid-plane and pole block heaters in one, spanning the entire width of the inner layer winding of 45.5 mm L IMMT =30.75 mm and L IPMT = 9.19 mm Entire inner layer: 45.51 mm a = 10.48 mm (=> 12.11 mm along the cable) r1 = 3 mm L = 30 mm  = 60 deg m = 3 mm b = 195 mm L seg = 230.3 mm H seg = 45.3 mm 29 segments P/A (straight) = 79 W/cm 2 P/A (curved) = 66 W/cm 2 R heater = 5.33  350 V,  =5*10 -7  m, d = 25  m (Per 6.70 m)

13. 13 Adiabatic temperature of the heating station For the highest heating power density, as proposed for the QXF inner layer MT heater (79 W/cm 2, 65.7 A of heater current) we obtain temperature rise up to  340 K! SS304, d = 25  m, a = 10.48 mm, T 0 = 5.0 K Exponential current decay with  = 50 ms is assumed