Power density calculations M Baldini V Marinozzi Quench

Power density calculations M. Baldini, V. Marinozzi

Quench heater test parameters 4 -wires resistance measurements @ 1. 9 K § Pole heater resistance = 0. 643 Ohm (strip 2 -3 in series, 16 stations) § Midplane heater resistance= 0. 725 Ohm (strip 1 -4 in series, 18 stations) External resistance was added to get a time constant t= 32 ms PH 2: pole circuit resistance= 1. 655 Ohm PH 1: Midplane circuit resistance= 1. 641 Ohm HFU voltage have been chosen in order to keep the QH current below 200 A § PH 1 Voltage 324 V, nominal current 197 A § PH 2 voltage 334 V, nominal current 201 A § QH current was measured using an external shunt of 1 m. Ohm 2

Min power density on Mirror magnet • @FNAL Pd peak= I 2 (measured)* R (measured)/ area* #stations Resistance copper was considered negligible • @CERN Pd peak= I 2 (measured)* R (computed)/ area* #stations 3

Energy deposited in mirror Magnet @FNAL the energy deposited was calculated in two different ways: § Pdpeak* t/2 § integration: Pd (t) dt @CERN: Pdpeak * t/2 Energy density calculated with integration is way lower for the HF heaters 4

Integration vs computation HF current is not an exponential function. This is why the energy density is so low 5

Mirror magnet: minimum En. density HF heaters Dep En. Dep. En. Den. integration (CERN) current A J/cm 2 1450 3. 989 4. 328 2000 2. 910 1. 780 3. 157 3300 2. 680 1. 650 2. 908 LF heaters current Dep. En. Den. A J/cm 2 1000 3. 70052064 1450 2. 830213801 2000 2. 424859622 3300 2. 420146717 Dep En. Dep. En. Den. (CERN) integration 4. 017998932 3. 063657643 2. 38 2. 624868733 2. 26 2. 619767094 6

Experimental data so far Max measured* R @ 4. 5 K [Ω] 2. 62 Min measured* R @ 4. 5 K [Ω] 1. 905 Min acceptable* R @ 4. 5 K [Ω] (AUP) 1. 7 Computed QH resistance CERN @ 10 K 4 W measured R @1. 9 K rescaled for long coil trace [Ω] Min measured* resistance @RT (all production traces) [Ω] 4 W measured R @1. 9 K of a QXFA trace [Ω] 2. 26 2. 09 *2 wire measurements on 2 QH strips circuit This is higher of measured resistance that includes Cu Measured for the mirror and rescaled for QXFA coil 3. 4 Ω Around 1. 7 at low T 1. 67 7

Energy density with different method Max 200 A in each heater, time constant= 32 ms Min R @ 4. 5 K [Ω] Total energy on PH [k. J] Energy density on PH [J/cm^2] Peak power density [W/cm^2] 1. 7 (FNAL Criteria) 1. 07865 2. 592908654 163. 4615385 1. 7 (CERN Criteria) 1. 4385384 3. 458025 218 Min quench En. SWAP FNAL 2. 91/2. 42 183/154 Min quench En. SWAP CERN 3. 15/2. 62 198/166 En density estimated from measured Resistance are more conservative. 8

summary § Peak power density calculated using theoretical resistivity data is around 8% higher than the one obtained using measured resistance § Measured resistance does not distinguish between Cu and SS contribution but provides a correct estimation of the total dissipated energy § Theoretical resistivity value results in a QH SS station resistance which is higher than most of the 4 W measured values at cold. § Computation made with SS resistivity theoretical value probably overestimates the Energy dissipated on the heater station § En. Density computation made with measured R are more conservative 9

QH strip resistance data @300 K Data were collected at FNAL, BNL and LBNL Data taken from production traces have been added Not yet installed on coils 10

QH resistance data at 4. 5 K Data taken at BNL Circuits consist of two QH strip in series 11