Dipole circuit & diode functioning Risk analysis of single and double short-to-ground Arjan Verweij, TE-MPE-PE RB circuit and diode functioning Voltage in the circuit Single short Double short

RB circuit L=15.2 H I (6.5 TeV)=11 kA I (7 TeV)=11.85 kA Even point Odd point L=15.2 H I (6.5 TeV)=11 kA I (7 TeV)=11.85 kA Earth current measurement system (H. Thiesen, 2008)

RB circuit & diode functioning Even point Odd point Normal operation (ramp-up/down, plateau): the diodes are not conducting. Quench: - the power converter is switched off, - the quench heaters of the quenching magnet(s) are fired, → voltage over the quenching magnet(s) rapidly increases, → bypass diodes of the quenching magnets open when VQ>6 V, → current in the quenching magnet quickly transfers into its bypass diode, typically with a characteristic time of a few 100 ms. - the EE switches are opened (with 0.34 & 0.6 s delay in odd & even points.

RB circuit & diode functioning The diode voltage reduces quickly (<1 s) from about 6 V to about 1 V due to the warming-up of the silicon wafer. The current in the circuit then decays with a time constant of about 100 s (t=L/REE). The diodes of the quenching magnets, including the busbars towards these diodes, have to support this current. The energy dissipated in the diode, Q=∫VIdt, is mainly absorbed by the heat sink, and finally transferred to the helium.

Some numbers Helium volume in diode box About 5.2 liter Helium enthalpy from 1.9 to 4.3 K 6 kJ Latent heat helium 13 kJ Helium enthalpy from 4.3 K to 100 K 20 kJ Volume heat sink 2x1.6 liter Cross-section diode lead 285 mm2 I [kA] Qstored [MJ] MIIT’s [MA2s] Qdiode [kJ] Tdiode-lead [K] Theat-sink [K] 6 274 1800 600 42 138 11 920 6050 1100 97 191 13 1284 8450 1300 158 211 Assumptions: adiabatic conditions, Vforward=1 V, t=100 s, RRRCu=100, no additional contact resistances

Voltage in the circuit (at 10 kA) After Fast Power Abort (FPA), the voltage distribution in the circuit changes significantly.

Voltage in the circuit after a quench (at 10 kA) The voltage distribution in the circuit does not depend much on the number and location of the quenched magnets.

Single short in the RB circuit A single short with sufficiently low impedance causes the 1 A fuse to blow, hence moving the 0 V of the circuit to the location of the short. The associated strong voltage transients very likely triggers the Quench Detection Systems of one or more magnets. Example for a short at z=2000 m

Probability for a single short LHC statistics: 2 shorts occurred for about 250 quench events, corresponding to about 1000 magnet quenches (with I>1.5 kA) Line A Quench @11 kA Short P1=0.002 Line B 2 secondary quenches @ 9 kA Short P2=2*0.002=0.004 2 secondary quenches @ 3 kA Short P3=2*0.002=0.004 Probability of one short for a high-current quench event is SPi=0.01 A single short should not give collateral damage, but might require warm-up and repair if the fault cannot be removed by the “Earth Fault Burner”.

Possible scenario for a double short-to-ground 1 4 2 10 11 3 89 3 6 5 7 10 11 1. Magnet quench 2. Converter switch-off 3. EE1 and EE2 switched in, giving high V 4. Short 1 6. Trips/quenches in other magnets due to voltage transients 5. Fuse blows 7. Short 2 8. RB circuit divided in 2 sub-circuits 9. Inductance imbalance generates current through the shorts 10. Energy dissipated in the short causes melting of the debris 11. Arcs are generated, probably remaining during most of the discharge

Simulation of a double short-to-ground The RB circuits are modelled in detail using PSpice-STEAM (6500 components per circuit!!) The simulations showed very good agreement with measured transient phenomena: Power converter switch-off, EE switch opening, Appearance of a short-to-ground, Fuse blowing in the earth measurement system. Short 1 Short 2 Unknown parameters in the simulation are: Resistances of the shorts (we assume about 1 W) The heat needed to melt the debris (we assume 3 kJ) Voltage needed to generate an arc (we assume 15 V) Voltage during the arcing process (we assume 15 V)

Simulation of a double short-to-ground I=11 kA (Qstored=920 MJ) Simulations by M. Prioli Edebris 1,2 = 3 kJ Eshort 1,2 = 22 MJ E EE2 = 80 MJ E EE1 = 800 MJ The energy dissipated in the arcs depends mainly on the position of the two arcs, the voltage of the arc, and the current(s) at which the shorts occur.

Remarks The build-up of the current in the shorts is slow, typically 100-1000 A/s. So most likely the debris melts, contrary to the Earth Fault Burner, where the debris might blow away. The heat needed to melt the debris has no impact on the occurrence of arcs and on the energy dissipated in the arcs. For info: =1 mm, length=40 mm 2 𝐾 1500 𝐾 𝐶𝑝𝑉𝑑𝑇 =200 J =10 mm, thickness=2 mm 2 𝐾 1500 𝐾 𝐶𝑝𝑉𝑑𝑇 =1000 J

Probability for a double short Line A 8 quenches @ 11 kA Short 2 P1=8*0.0022 Line B Short 1 8 quenches @ 11 kA Short 2 P2=8*0.0022 2 secondary quenches @ 9 kA Short 2 P3=2*0.0022 2 secondary quenches @ 3 kA Quench @11 kA Short 2 P4=2*0.0022 4 quenches @ 9 kA Short 2 P5=2*4*0.0022 2 secondary quenches @ 9 kA Short 1 4 quenches @ 9 kA Short 2 P6=2*4*0.0022 2 quenches @3 kA 2 secondary quenches @ 3 kA Short 2 P7=2*2*0.0022 Short 1 2 quenches @ 3 kA Short 2 P8=2*2*0.0022

Probability and consequences of a double short Lines I [kA] Qst [MJ] Earcs [MJ] P1 8*(0.002)2=0.0032% A-A 11 908 Small P2 A-B 0 to 46 MJ P3 2*(0.002)2=0.0008% 9 608 0 to 30 MJ P4 3 68 P5 2*4*(0.002)2=0.0032% B-A P6 B-B P7 2*2*(0.002)2=0.0016% P8 0 to 3.4 MJ So about 0.01% (P2+P3+P5+P8) probability of dissipating an amount of energy in the arcs which is >100x the energy needed to melt a hole in the diode tube.

Final remarks Assuming a training campaign with 500 quench events gives: on average 500*0.01=5 shorts-to-ground in the diode tube. → delay of several days (per short) or possibly warm-up a 5% probability of a double short without puncture of the diode tube. → delay of several days or possibly warm-up a 5% probability of a double short with puncture of the diode tube. → severe damage and warm-up (all analysis based on very low statistics) Ongoing or foreseen studies: Further development of the PSpice-STEAM model Study if/how we can reduce the voltage transients in the circuit (change the 100 W bypass resistors, add capacitors) Study if it is beneficial to increase the rating of the earth fuse Study on an improved earth measurement & monitoring system