Protection heater design for MQXF outer layer *Using long Super- Heating Stations for ensuring quenhces at low currents* Tiina Salmi, Tampere University of Technology (TUT)

Outline Magnet parameters and heater design limitations Heater delay simulations on outer layer – Impact of heater power and Heating Station (HS) length Proposal of a heater layout including long Super-HS for low current protection Simulation of heater delays with the proposed heater (to be used in QP analysis) Appendix including some more details 21 Jan 2016 T. Salmi (TUT) 2

Magnet and cable parameters Parameter (unit)Value Magnet length (m)7.2 Cable width (bare) (mm)18.15 Cable mid-thickness (bare) (mm)1.524 RRR140 Voids fraction of bare cable0.2 (epoxy) Number of strands40 Strand diameter0.85 Strand Cu/SC1.15 Cable insulation (mm)0.145 (G10) Inter-layer insulation (mm)0.5 Insulation btw OL and collar (mm)0.8 Current sharing temperature 21 Jan 2016 T. Salmi (TUT) 3 // // Critical surface parameters (for the Godeke fit) // // Ca1 - Deviatoric strain [T] // Ca2 = 1034*Ca1 [T] // eps_0 - Hydrostatic strain 28.10// Bc2m [T] 16.95// Tcm [K] // C -Preconstant (2^0.5 * C * Hc(0)/A) [A] 0.5// p - Pinning force constant 2.0 // q - Pinning force constant 0.002// e_total - strain for Ic calculation In the Appendix are for plots of T cs and the load line.

Heater design parameters Parameter (unit)Value Voltage (V)450 HFU capacitance (mF)19.2 Max. Current (A)200 Polyimide thickness (mm)0.05 Stainless steel thickness (mm)0.025 OL HF OL LF 16*1.88 mm =30.0 mm : 24 mm wide heater 12*1.88 mm =22.6 mm : 18 mm wide heater (2 turns without coverage) (To get 150 W/cm 2 and not exceed 200 A) 21 Jan 2016 T. Salmi (TUT) 4 (Also 20 mm wide is OK.)

Heater delay simulation 2-D thermal simulation using CoHDA: 2 possible criteria for quench onset A.Cable maximum temperature reaches T cs -> Current redistribution starts, visible in test set-ups B.Cable average temperature reaches T cs -> Current sharing with copper starts, quench propagation starts The criterion B is more conservative, and it is used in this design and analysis. 21 Jan 2016 T. Salmi (TUT) 5 Criterion B gives 5-10 ms longer delays

Simulated heater delays with 150 or 100 W/cm 2 (1D) Higher power improves the delay 1-4 ms at nominal current In this design we consider operation with CLIQ If high power leads to longer period for HS, CLIQ will help in propagation Focus on low current.  so we will use the advantage of higher power and go with 150 W/cm Jan 2016 T. Salmi (TUT) 6 HFU RC time constant = 50 ms B/Bpeak ~ 0.5 – – 0.6 1D simulation means a very long HS

Delays vs. HS length (150 W/cm2) GOAL 1: Make sure it quenches a low current, and quench propagates  HS length should be at least 8 cm GOAL 2: Minimize the delays at high current  Suitable HS length at OL HF 5-6 cm  Suitable HS length at OL LF 6-7 cm 21 Jan 2016 T. Salmi (TUT) 7 DIDN’T COUNT 1 kA B/Bpeak ~ 0.5 – – 0.6

The concept of Super- Heating Stations The idea: Add a few long heating stations to make sure it quenches also at low current (as sure as possible). Only a few HS should be enough at low current The rest of the heater can have shorter HS with shorter period for high current quench protection Super-HS = 2 normal lenght HS combined in every ~ 2 m – According to my preliminary analysis (details in the appendix) this should be enough at low current (1 – 8 kA) but this needs to be confirmed by Vittorio 21 Jan 2016 T. Salmi (TUT) 8

OL HF geometry with 5-cm-long normal HS and 10-cm-long Super-HS Strip width = 18 mm (covers 9 turns) Normal HS length = 5 cm (25 normal HS / strip) Super-HS length = 10 cm (4 super-HS / strip) Period = 25 cm (distance between the centers of heating stations) Period for super-HS = 1.99 m 7.2 m 1.99 m0.62 m 1.99 m Schematic Each distance of HS centers: m = 5 cm long HS = 10 cm long HS … 21 Jan 2016 T. Salmi (TUT) 9 Strip K = 1.8 Ω Tot R with 1 Ω margin = 2.8 Ω I with 450 V = 157 A Peak power = 150 W/cm 2 RC τ with 19.2 mF HFU = 55 ms SS thickness 25.4 µm, ρ = 5e-7 Ωm Cu thickness = 10 µm, ρ = 2e-9 Ωm

OL LF geometry with 5-cm-long normal HS and 10-cm-long Super-HS Strip width = 24 mm (covers 12 turns) Normal HS length = 6 cm (16 normal HS / strip) Super-HS length = 12 cm (4 super-HS / strip) Period = 36 cm (distance between the centers of heating stations) Period for super-HS = 1.8 m 7.2 m 1.8 m0.9 m 1.8 m Schematic Each distance of HS centers: 0.36 m = 6 cm long HS = 12 cm long HS … 21 Jan 2016 T. Salmi (TUT) 10 Strip K = 1.2 Ω Tot R with 1 Ω margin = 2.2 Ω I with 450 V = 202 A Peak power = 140 W/cm 2 RC τ with 19.2 mF HFU = 43 ms SS thickness 25.4 µm, ρ = 5e-7 Ωm Cu thickness = 10 µm, ρ = 2e-9 Ωm Two other options for PH geom. presented in the Appendix.

Updated cable parameters – for simulation of final delays Parameter (unit)Value Magnet length (m)7.2 Cable width (bare) (mm)18.36 Cable mid-thickness (bare) (mm)1.363 RRR150 Voids fraction of bare cable0.2 (epoxy) Number of strands40 Strand diameter0.85 Strand Cu/SC1.15 Cable insulation (mm)0.145 (G10) Inter-layer insulation (mm)0.5 Insulation btw OL and collar (mm)0.8 Current sharing temperature 21 Jan 2016 T. Salmi (TUT) 11 // // Critical surface parameters (for the Godeke fit) // // Ca1 - Deviatoric strain [T] // Ca2 = 1034*Ca1 [T] // eps_0 - Hydrostatic strain 28.10// Bc2m [T] 16.95// Tcm [K] // C -Preconstant (2^0.5 * C * Hc(0)/A) [A] 0.5// p - Pinning force constant 2.0 // q - Pinning force constant // e_total - strain for Ic calculation

Simulated delays at Imag = 16.5 kA B at the conductor edge (T) HS = 5 cm (150 W/cm 2 ) Heater delay (ms) HS = 10 cm (150 W/cm 2 ) Heater delay (ms) HS = 6 cm (140 W/cm 2 ) Heater delay (ms) HS = 12 cm (140 W/cm 2 ) Heater delay (ms) 9.1 (B/Bpeak = 0.8) (B/Bpeak = 0.7) (B/Bpeak = 0.6) (B/Bpeak = 0.5) (B/Bpeak = 0.4) Jan 2016 T. Salmi (TUT) 12 OL HF heater, normal HS OL HF heater, super HS OL LF heater, normal HS OL LF heater, super HS Bpeak in mag. = 11.4 T In the heater delay simulation the conductor field is taken at the edge of the conductor. This is usually the maximum field in the conductor. For quench simulations: Associate the conductor maximum field to these delays.

Simulated delays at Imag = 12 kA B at the conductor edge (T) HS = 5 cm (150 W/cm 2 ) Heater delay (ms) HS = 10 cm (150 W/cm 2 ) Heater delay (ms) HS = 6 cm (140 W/cm 2 ) Heater delay (ms) HS = 12 cm (140 W/cm 2 ) Heater delay (ms) 6.8 (B/Bpeak = 0.8) (B/Bpeak = 0.7) (B/Bpeak = 0.6) (B/Bpeak = 0.5) (B/Bpeak = 0.4) Jan 2016 T. Salmi (TUT) 13 OL HF heater, normal HS OL HF heater, super HS OL LF heater, normal HS OL LF heater, super HS Bpeak in mag. = 8.45 T In the heater delay simulation the conductor field is taken at the edge of the conductor. This is usually the maximum field in the conductor. For quench simulations: Associate the conductor maximum field to these delays.

Simulated delays at Imag = 8 kA B at the conductor edge (T) HS = 5 cm (150 W/cm 2 ) Heater delay (ms) HS = 10 cm (150 W/cm 2 ) Heater delay (ms) HS = 6 cm (140 W/cm 2 ) Heater delay (ms) HS = 12 cm (140 W/cm 2 ) Heater delay (ms) 4.6 (B/Bpeak = 0.8) (B/Bpeak = 0.7) (B/Bpeak = 0.6) (B/Bpeak = 0.5) (B/Bpeak = 0.4) Jan 2016 T. Salmi (TUT) 14 OL HF heater, normal HS OL HF heater, super HS OL LF heater, normal HS OL LF heater, super HS Bpeak in mag. = 5.76 T In the heater delay simulation the conductor field is taken at the edge of the conductor. This is usually the maximum field in the conductor. For quench simulations: Associate the conductor maximum field to these delays.

Simulated delays at Imag = 4 kA B at the conductor edge (T) HS = 5 cm (150 W/cm 2 ) Heater delay (ms) HS = 10 cm (150 W/cm 2 ) Heater delay (ms) HS = 6 cm (140 W/cm 2 ) Heater delay (ms) HS = 12 cm (140 W/cm 2 ) Heater delay (ms) 2.4 (B/Bpeak = 0.8) (B/Bpeak = 0.7) (B/Bpeak = 0.6) (B/Bpeak = 0.5) (B/Bpeak = 0.4) Jan 2016 T. Salmi (TUT) 15 OL HF heater, normal HS OL HF heater, super HS OL LF heater, normal HS OL LF heater, super HS Bpeak in mag. = 2.99 T In the heater delay simulation the conductor field is taken at the edge of the conductor. This is usually the maximum field in the conductor. For quench simulations: Associate the conductor maximum field to these delays.

Simulated delays at Imag = 1 kA B at the conductor edge (T) HS = 5 cm (150 W/cm 2 ) Heater delay (ms) HS = 10 cm (150 W/cm 2 ) Heater delay (ms) HS = 6 cm (140 W/cm 2 ) Heater delay (ms) HS = 12 cm (140 W/cm 2 ) Heater delay (ms) 0.6 (B/Bpeak = 0.8) (B/Bpeak = 0.7) (B/Bpeak = 0.6) (B/Bpeak = 0.5) (B/Bpeak = 0.4) Jan 2016 T. Salmi (TUT) 16 OL HF heater, normal HS OL HF heater, super HS OL LF heater, normal HS OL LF heater, super HS Bpeak in mag. = 0.81 T In the heater delay simulation the conductor field is taken at the edge of the conductor. This is usually the maximum field in the conductor. For quench simulations: Associate the conductor maximum field to these delays.

Conclusions Seems that the heaters manage to quench at low current, if power is 150 W/cm 2 and HS are longer than 6-7 cm – Large uncertainty at low current simulations: Better to opt for long HS, and high power to make sure it quenches Heater design proposed for outer layer – Includes longer ”super-HS” to ensure quenches at low current – large period (2 m) – Includes shorter ”normal-HS” for protection at high current – period 25 or 36 cm Also these ”normal-HS” are longer than in the latest heater designs for R&D magnets Based on my prelimnary analysis the amount of super-HS is sufficient to protect the magnet at 1-8 kA. BUT, need proper analysis by Vittorio and QLASA – Include impact of CLIQ in the analysis? – The delays from this presentation can be used as an input to QLASA – At low current the simulations have large uncertainty. I recommend QLASA simulations also with much longer delays (e.g. test with 100 – 300 ms at 1 – 8 kA) At low current also cooling has more effect. Need experiments at low current. – If these Super-HS don’t initiate a quench, could explore advantage of increasing capacitance 21 Jan 2016 T. Salmi (TUT) 17

Appendix.

Load line and Tcs in heater delay simulations 21 Jan 2016 T. Salmi (TUT) 19

Heater delay simulation 1D HFU RC time constant = 50 ms 100 W/cm2150 W/cm2 21 Jan 2016 T. Salmi (TUT) 20

Simulation vs. HS length, zoom at high current, 150 W/cm 2 21 Jan 2016 T. Salmi (TUT) 21

Impact of quench onset criteria Difference is ~5-10 ms. We use the more conservative criterion B. 21 Jan 2016 T. Salmi (TUT) 22 A.Cable maximum temperature reaches T cs B.Cable average temperature reaches T cs 150 W/cm2, tau = 50 ms, 1D sim.

Alternative heater geometries (with 150 W/cm2) Option A: – OL HF: 6 cm HS, OL LF: 7 cm HS Option B: – OL HF: 5 cm HS, OL LF: 6 cm HS (will have shorter period than option A) Option C: In case can re-design only the OL LF – OL LF: 7 cm long HS – (OL HF: 4 cm HS, 16 cm period, width 20 mm – design exist) OL HF does not have super-HS, so more super-HS located in the LF heater 21 Jan 2016 T. Salmi (TUT) 23

A: OL HF geometry (150 W/cm2, 6 cm long HS) OL HF: Had 27 HS, with 4 super-HS now has 23 HS. – Period = 7.2 m / 23 = m – Period for super-HS: 6*0.313 m = m 7.2 m 1.88 m m m Schematic Each distance of HS centers: m = 6 cm long = 12 cm long … 21 Jan 2016 T. Salmi (TUT) 24

A: OL LF geometry (150 W/cm2, 7 cm long HS) OL LF: Had 21 HS, with 4 super-HS now has 17 HS. – Period = 7.2 m / 17 = m – Period for super HS: 4*0.424 m = 1.69 m 7.2 m 1.69 m 1.06 m 1.69 m Schematic Each distance of HS centers: m = 7 cm long = 14 cm long … 21 Jan 2016 T. Salmi (TUT) 25

B: OL HF geometry (150 W/cm2, 5 cm long HS) OL HF: 5 cm long HS, period 21.5 cm, had 33 HS, with 4-super HS now has 29 HS. – Period = 7.2 m / 29 = m – Period for super-HS: 8*0.248 m = m 7.2 m 1.99 m0.62 m 1.99 m Schematic Each distance of HS centers: m = 5 cm long = 10 cm long … 21 Jan 2016 T. Salmi (TUT) 26

B: OL LF geometry (150 W/cm2, 6 cm long HS) OL LF: 6cm long HS, period 30 cm, had 24 HS, with 4 super-HS now has 20 HS. – Period = 7.2 m / 20 = 0.36 m – Period for super HS: 5*0.36 m = 1.8 m 7.2 m 1.8 m 0.9 m 1.8 m Schematic Each distance of HS centers: 0.36 m = 6 cm long = 12 cm long … 21 Jan 2016 T. Salmi (TUT) 27

C: If can re-design only the LF heater (150 W/cm2, 7 cm long HS) OL LF: Make 7 super-HS, In total 14 HS -> Period = 0.51 m, super-HS period = 1.02 m OL HF is the one already designed (4 cm HS, 16 cm period) *No super-HS* 7.2 m 1 m 0.5 m Schematic Each distance of HS centers: 0.51 m = 7 cm long = 14 cm long … 1 m 0.7 m 21 Jan 2016 T. Salmi (TUT) 28

Impact of period on hotspot temperature Simulation usign Coodi (T. Salmi, et al., MT-24) A HS length = 6 cm, delay = 20 ms Heater covers 22 turns on OL. NZPV = 10 m/s: (remember, current is decaying, AC-loss may contribute (esp. With CLIQ) IL and non-covered OL turns have the same ”heater geometry”, and delay of 35 ms Detection time = 15 ms Period 20 cm -> K Period 30 cm -> K Period 40 cm –> K … 17 K per 10 cm additional period… HS length = 6 cm, delay = 18 ms for 22 OL turns (other turns have 33 ms) – Period 20 cm -> K – Period 30 cm -> K – Period 40 cm –> K … 16 K per 2 ms additional delay… 21 Jan 2016 T. Salmi (TUT) 29

Analysis of hotspot temperature at low current Heaters quench 21 turns on OL No quench propagation to other turns Consider only the super heating stations The heater delays are taken longer than CoHDA simulations to estimate the available margin No initial quech propagation No AC-losses, no dump, no diode, no any additional resistance Detection + validation + switches etc. = 30 ms NZPV = 2 m/s 1-4 kA), NZPV = 5 m/s 8 kA), (longit., btw Super-HS) Simulation using Coodi – adiabatic temperature calculation, accounting for metal, epoxy and cable insulation in the heat capacity, material properties from NIST (epoxy simulated as G10) – This was just for my preliminary analysis if amount to super HS is sufficient, simulation with other software needed to confirm Coodi assumes a linear temperature profile for quench propagation between HS – the error may become large for long distances. 21 Jan 2016 T. Salmi (TUT) 30

Simulated hotspot temperatures (only super-HS) Imag (kA)Heater delays at Super-HS (ms) Hotspot temperature (K) Jan 2016 T. Salmi (TUT) 31 Note that heater delays simulated with CoHDA were ms. The uncertainty of the simulation is large at low current, that’s why exploring worse cases.