# Presentation: 296453

## Stability, Training, and Protection in High  Current Density Windings*

- A. D. McInturff
- Lawrence Berkeley National Laboratory and Texas A&M University
- *This work supported by Director, Office of High Energy Physics, Division of Science of the U. S. Dept.of Energy under Contract
- No. DE-AC03-76SF00098

- 5/22/02

## Acknowledgments

- The stability estimate development is given in detail in Dr. M. Wilson’s Book “Superconducting Magnets” Chapters 5 through 7. Some particular equations and relationships were first given in BNL 51412 “Stability of Superconducting ISABELLE Dipole Magnets by Stefan Wipf April 1981

- The data and a majority of the ideas and concepts are the work of or done with,
- or derived from discussions with  colleagues in the research groups of which I am
- a member.  The groups are: Lawrence Berkeley National Lab AFRD Superconducting
- Magnet Group  S. Bartlett, B. Benjegerdes, P. Bish, D. Byford, S. Caspi, L. Chiesa, K.
-  Chow, M. Coccoli, S. Dardin, D. Dell’Orco, D. Dietderich, P. Ferracin, S. Gourlay,
-  M. Goli, R Gupta, R. Hafalia, R. Hannaford, W. Harnden, H. Higley, A. Jackson, T.
-  Jaffrey, A. Lietzke, N. Liggins, S. Mattafirri, G. Millos, L. Morrison, M. Morrison, M.
- Nyman, R. Oort, E. Palmerston, J. Remenarich, G. Sabbi, R. Scanlan, J. Smithwick,
-  J. Swanson, C. Taylor, J. van Oort
- Texas A&M University, Physics Department, Accelerator Physics Magnet Laboratory
- R. Blackburn, T. Elliott, W. Henchel, E. Hill, A. Jaisle, P. McIntyre, P. Noyes, Akhdior
- Sattarov, N. Diaczenko

- 5/22/02

## Windings, Cables, Strands, and Sub-Elements

- Sub-Element Stability Estimate Calculations
- >  Surface Shell (Nb3Sn)
- 	- h = К/w  = 5x10-2 w/mK/16μm
- ~3.1x103w/m2K
- τθ = Cva/h = 206 s
- >  If 10% of sub-element shell were bronze fins:
- 	- “τθ” would decrease ~103
- 	- aids de-coupling magnetically as well
- 	Dθ( Cu7.5w/oSn) = 7x10-2m2/s
- 	Dm = 8x10-2m2/s

- 5/22/02

## Windings, Cables, Strands, and Sub-Elements

- >  If the FJ reduces the composites effective “ρ”
-          Dm would be smaller by 10 (Yasukochi ‘81)
- >  Another more conservative approach would
-     suggest:  if “Bp” were 0.16T then
- 	- μoJcaeff = 0.16T or aeff = 16μm
- 	- ~32μm diameter filaments
- >  This appears to be possible in the near future!
- >  However present operations appear to have     .   Exceeded % short sample predicted by         . .   Stability parameter “βt  “
- βt = μoλ2Jc2a2/Cv(θc- θo)
- Manufacturers  More Jc Please!

- 5/22/02

## Windings, Cables, Strands, and Sub-elements

- Composite & Sub-Element Stability Estimate Calculations
- “Dynamic Stability Calculations”
- a < 81/2d
- d2 = К(θc - θo)( 1 - λ)/λJ2ρ
- d ~41μm
- a = 116μm
- Using HD1 as an example  physically ~70μm
- for the sub-element at 12T
- Bo ~0.08T
- The Flux Jump Field BFJ
- BFJ = (2μoCvJc/(-dJc/dt))1/2
- BFJ ~0.16T

- 5/22/02

## Windings, Cables, Strands, and sub-elements

- Strand Stability Estimate Calculations
- >  Self Field    Bo = μoIt/2Лa   ~0.46T
- >  Diffusivity
- 	-  DΘ = К/Cv
- 	-  Dm = ρ/μo
- >   Time Constants of Composite
- 	- Surface heat transfer ~5.2x10-3s
- 	- Magnetic Flux           ~5.1x10-3s
- 	- Internal heat transfer ~1.7x10-3s

- 5/22/02

## Windings, Cables, strands, and sub-elements

- Boundary Value Currents
- Cross strand Resistance
- non-cored
- cored
- Highest Compaction w/o degradation
- Minimize Epoxy space with glass and surfaces with mica or release agent
- Minimize Insulation film minimum thickness

- 5/22/02

## Windings, cables, strands, and sub-elements

- Maximum Compaction w/o degradation
- No Void Space, no epoxy volumes unfilled with fiber glass
- Winding’s Desirable Properties
- Monolithic winding pack
- No bonding to support surfaces with a shear force (or release)
- Pre-exercise to obtain the best modulus (load & unload)

- 5/22/02

## Training Cos  coil - D20

- Jnon cu(12T, 4.2K) ~ 735A/mm2
- Preload<Lorentz load  ~100MPa vrs 140MPa cal. Lorentz
- Pole/1st turn Separation  >pole turns account for 42% of quenches and 23 of 1st 25
- Soft Support for a bottom outer coil lead which is the source of 33% quenches

- 5/22/02

## Training Cos  coil - D20

- Protection Heaters adequate  peak quench spot temperature <235K
- Windings very Rugged  >100 quenches driven and natural no apparent problems
- Low End Loads  less than 5% of calculated load measured at end
- Record Dipole Fields 12.8T , 4.2K and 13.5T , 1.9K

- 5/22/02

##  Training Cos  coil - D20 

- 5/22/02

##  Training Cos  coil - D20 

- Training still at Super Fluid   peak field 13.5T vrs ~13.8T SS
- S.F.T. shortened the 4K training , but did not eliminate it
- Problem with the outer coil lead stability first appears at super fluid temperatures!

- Super Fluid Quenches

- 5/22/02

## Training Cos  coil - D20 

- After fourth cool down,  the magnet ran reliably at 12.5T (12.8T measured short sample)
- The coil had a 20w margin at 12.5T 4.5K
-  Summary:  There were two clear problems:
- Bonding to post &/or low pre-load
- Excess soft insulation leading to conductor motion
- These account for 75% of the 60 training Quenches

- Apparently Stable!

- 5/22/02

## Training  Common Coil - RD2-01

- Magnet          Load at    300K                           300K                           _ _4K                              4K
- configuration
- 	Horizontal	Vertical	Horizontal 	Vertical
- RD-2-01	30 MPa	30 MPa	50 MPa	30 MPa
- RD-2-02	6 MPa	6 MPa	50 MPa	30 MPa
- RD-2-03	6 Mpa	6 Mpa	21 Mpa	12 MPa

-             RD2- Series Assembly

-    First Av. “J” Common Coil
- >  Pre-loads varied over large .   range
- >  Peak Field ~6T
- >  Loads varied over many         .     .   Configurations
- * No Training Observed!

- 5/22/02

## Training  Common Coil RT1

- Coil Module Loading and cycling

- Outer Module’s Configuration

- keys

- RT1

- >  Modules preloaded repeatedly
- >  Weld shrinkage increased load

- 5/22/02

## Training  Common Coil RT1

- RD3 Module Pretesting alias RT1
- High Fields ( 12T)  no gap between
- Large Forces between Modules ~6.9 MN or 775 tons
- Large Module separation ~1.8mm
- 3 Training Quenches  96%, 93%, and 98% of short sample

- RT1 preloaded in Support

- 5/22/02

## Training  Common Coil RD-3

- 14 Tesla Common Coil Design
**Main coil spacing****	****25 mm**
**Quench field at 4.2 K****	****14.4 T**
**Quench Current****	****10.8 kA**
**Number of layers/mod.****	****2**
**Coil modules****	****3**
**Straight section length****	****500 mm**

- 5/22/02

## Training  Common Coil RD-3 

- Large Force  3x106 lbs horizontal
- Conductor Stress  >100 MPa
-                  Performance
- Previously quenched & virgin outer modules displayed similar behavior
- Both outer modules began quenching at a lower Lorentz load than the trained one before (> 13.7 T)
- First time the inner surface of the outer modules were loaded!
- The inner and 2 outer modules had nearly identical short sample limits.

- Features

- RD3b awaits Test

- 5/22/02

## Training  Common Coil RD-3

- Quench history slope changes when the quench origin switched from inside to outside.
- Moderate improvement of  “Iq” after a full thermal cycle (a.k.a. D20).
- RD3c (different middle module with larger aperture) had all but 2 quenches in the already tested outer modules.
- RT1 was the only configuration of this series that had a great training history

- 5/22/02

## Training Sub-scale Model Program

- Technology development and increased productivity
- with a parallel test program
- Scaled version of full-size magnet
- Approx. 1/3 scale
- Field range of 9 – 12 Tesla
- Simple two-layer racetrack coils
- 5 kg of material per coil
- Streamlined test facility
- Small dewar (no refrigerator)

- 5/22/02

## Training Sub-Scale Model Series

- First sub-scale magnet (SM01a) was to have the equivalent geometry as RT1
- First version “SM01a” had a nominal load of 13,000 psi
- Second version “SM01b” had a minimum load of 1,500 psi
- The second coil module “SC02” ‘s skins were not welded although pre-stressing cycles were done

- Sub-Scale Model Magnet Series

- 5/22/02

## Training  Block Coil - HD-1 

- HD1 is the present generation LBNL high field
- dipole magnet winding being investigated
- for it’s potential.  HD1’s main objective is field
- not training performance, but it certainly has been
- recorded.  To date the magnet has achieved a
- maximum bore field of 15.97 _+_0.049T at 4.4K

- 5/22/02

## HD1 Conductor

- 5/22/02

## HD1 Conductor

- 5/22/02

## Training

**MAGNET****	****D20****	****RT1****	****RD3b****	****RD3c****	****SM01****	****HD1 **
**Jc (A/mm****2****)**
**(12T, 4.2K)****	**960, 1600 	-	2043	2014	-	   -
**	**1627	2143	2143, 1754	2143, 1754	2260	3000
**Jcu (A/mm****2****)**
**(12T, 4.2K)****	**2240, 1481	-	2270	2319	-	    -
**	**1535	1367	1367, 1329	1367, 1329	2774	1400
**No. strands****	**37	-	40	31	-	  -
**	**47	26	26	26	20	 36
**No. turns ****	**16+26	-	50	16	-	 35
**	**40+56	49	49	49	20	 35
**Cu/SC****	**0.43, 1.08	-	0.90	0.90	-	0.72
**	**1.06	1.64	1.64, 1.35	1.64, 1.35	0.81	0.96
**Strand diam. (mm)****	**0.753 	-	0.800	0.800	  -
**	**0.482	0.800	0.800	0.800	0.710	0.8
**Thickness (mm)****	**1.356 	-	1.386	1.396	  -
**	**0.873	1.408	1.408	1.408	1.270	1.546
**Width (mm)****	**14.45 	-	17.20	13.32	-	   -
**	**11.63	11.34	11.34	11.34	7.80	16.01
**Pitch length (mm)****	**93.50	-	119.80	93.40	   -
**	**81.28	81.28	81.28	81.28	54.88	81.28
- * Cable values are an average of the known strand values.
- ** When two rows exist, the upper row is associated with the inner module.
-       (if it existed) Lower row outer module
- *** The second of two values separated by comma refers to an identical coil
-         with a different conductor

- 5/22/02

## Training -Normalized Quench History

- Summation of all coil’s Performance Normalized

- Poorest Peak Performance RD3c &  SM01a (both candidates for S.F. training)
- RD3b displayed the poorest training history
- Best Performance was RT1 & SM01b
- Both had <50% Lorentz load
- Both had one face loaded the other face not
- Both had experienced large deflections under field

- Note for clarity RD-2-01, RD-2-02, and RD-203 are not  plotted they would be at 1.0 for the 1st quenches.

- 5/22/02

## Training What have we learned?

- Hold Winding package under compression in all dimensions that is greater than the Lorentz Load plus a safety factor.  I.e. do not leave any place for the winding to go.
- Problem This may be very difficult to obtain in multipole magnets
-                              and/or
- Alternate Strategy and/or Scheme
- Remove the bond between the windings and support surfaces that are not supporting the Lorentz Load (particularly separating ones)
- Moderately load the winding enough to remove the fluff. I.e. < MPa and that the windings are in contact with the Lorentz force bearing surface
- Allow the coil to move as much as the desired field quality will permit and it is in contact with the supporting surface from the start of energizing.
- Low RRR is not a problem if fairly uniform and _>_ 10. I.e. both stability and protection are aided by the bronze’s presence.
- Filament sizes in excess of a 100 μm for “MJR” or “RRP” process are on the edge of stability and therefore caution is in order

- Standard Age olde Wisdom

- 5/22/02

## Training Block coil - TAMU-4”Stress managed”

- Two Surfaces not bonded & possibly a third
- Moderate loads on winding (spring only)

- Training Improvements Attempted

- Cross Section of a coil quadrant

**Green bars in front of turns are springs**

- During heat treatment and before powering

- 5/22/02

## Conditions Assumed in Talk

- •	Protection to be accomplished by a close proximity heater
- •	Highly efficient coil winding package Jeff> 1000 A/mm2
-                                                                      **currently: J****eff ****~ 1500 - 2000 A/mm****2**
- •	Examples given will be limited to Nb3Sn coils.  “Should be applicable to other A-15’s”
- •	Heater constructed composites of Kapton/SS(cu)/ Kapton plus glue

- 5/22/02

## Definitions

- Conductor MIIT’s		               106 Amp2 -sec to reach 450K
- 				                  a)  measured
- 				                  b)  adiabatic calculation
- Critical ramp rate		                Rate of current change at which the 			                  conductor’s temperature rise exceeds           		                                       it’s critical temperature at ~0.9Ic
- Minimum ProtectionWinding  		That length of conductor which will
- volume(conductor length) 	 	result in a L/R time constant period  transitioning 			that will stay within the conductor 				 MIIT’s budget
- RRR                                                                        Resistance Ratio of the conductor
-                                                                                   between room temperature & Tc2+

- 5/22/02

## Typical Design of a Heater for a Nb3Sn Race Track Coil

**Conductor Parameters:**
**	****36 strand cable**
**	****0.8 mm strand diameter**
**	****J****c****(non-cu, 12T, 4.3K) = 3000 amps/mm****2**
**Typical design input:**
**	****Quench output page**
**Typical MIITs Curve:(RD-3 shown)**
**	****Quench’s MIIT’s Curve for HD-1 is 19 Miits instead of 12.4 **
**First order heater considerations HD-1:**
**	****Inductance = 7mh**
- 						 **L/R = ?****	****	****	****	****	****	****at 11.2kA/turn  yields 125 MIIT’s/second**
**	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****MIIT’s limit “Quench” =19.2  - Room Temperature**
**	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	**_**=**_**> 157 milliseconds****	**
**	****	****	****	****   ****	****	****	****	****	****	****	****	****	****	****	****	****	**** ****-**_**    40**_**	****	****	****	****	****“****	****	****	****	****	****	****detection & diffusion **
**	****	****	****	****       ****	****	****	****	****	****	****	****	****	****	****	****	****117****	****	****	****	****	****“**
**	****	****	****	****	****	****	****=>0.235 seconds = ***t***(effective)            **
**	****	****	****	****	****	****	****	****	****	****	****	****R = 0.007/0.235 ~ 0.034 ohms**
**	****	****	****	****	****HD-1 coil’s room temperature resistance = 0.460 ohms**
**	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	**** ****20K R(expected) = 0.02 ohms**
**	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	**** ****20K R(measured)= 0.031  “     note the dramatic  “RRR” effect**
**	****	****	****	****	****	****	****	****	****	****	****	****	****	****=> 1⁄4 of the coil driven normal will work**

- For example HD-1

- 5/22/02

## Typical Design of a Heater for a Nb3Sn Race Track Coil(continued)

**	****	****	****	****	****	****	****=>0.235 seconds = ***t***(effective)            **
**	****	****	****	****	****	****	****	****	****	****	****	****R = 0.007/0.235 ~ 0.031 ohms**
**	****	****	****	****	****HD-1 coil’s room temperature resistance = 0.460 ohms**
**	****	****	****	****	****	****	****	****	****	****	****	****	****	**
**	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	**** ****20K R(measured)= 0.0321 ohms**
**Now a look at the possibility of a quench back!**
**	****	****	****	****	****Assume 1/2 of the magnet is driven normal at ~40 milliseconds**
**	****	****	****	****	****	****	****	****	****	****	****                            ****Then L/R = 0.007/0.016 ~ 0.11 sec**
**	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	****or dI/dt = -25,600 amperes/sec. ->96,000 amperes/sec.**
**The slowest rate is 100 greater than that required to quench HD-1 at 25% of it’s plateau current!**
**   **
**                          ****	****	****	****	****	****	****	****	****	****	****	****	****	****	****	**  **Quench Back     ****will occur <30milliseconds**

- For example HD-1 continued

- 5/22/02

## Protection of D20

**A very conservative approach was taken:**
**	****	****70% of the magnet volume was under heaters**
**	****	****The power level was set for Super Fluid operation**
**	****	****	****	****Layer 1 = 53 watts/cm****2**
**	****	****	****	****Layer 2 = 23  “**
**	****	****	****	****Layer 3 = 29   “**
**	****	****	****	****Layer 4 = 27    “**
**The highest average  temperature Quench was: **outer turn = 165K - 185K
-                                                                                    inner turn = 80K - 120K
**The MIIT’s curve predicted**: outer turn = 234K ; inner turn = 152K

- 5/22/02

## “Quench” Code Input/Output for MIITs

- 5/22/02

## Design Input necessary for Protection Stainless Steel Heater Analysis

**Table**
**Integrated Stainless Steel Specific Heat Versus Peak Temperature**
**	****	****Temperature****	****	****	****Energy/unit volume**
**	****	****Adiabatic(K)****	**** ****	****	****joules/cubic ****	****	****	****	****	****	****centimeter**
**	****	****100****	****	****	****80**
** ****	****	****200****	****	****	****316**
**	****	****300****	****	****	**** 642**
**	****	****400****	****	****	****1034**
**	****	****500****	****	****	****1494**
**Kapton Failure****	****770K                      ****	****	****2700**
**Typical Resistivity (Stainless Steel) ****	****	****50 micro-ohm-cm****	****	****              RRR****	****	****	****1.5**
**Typical Time constants (1/e) **
** ****Heater pulse****	****	****	****	****30 – 100 milliseconds**
**Typical detection plus thermal**
**Diffusion time at 70% short Sample****	****                           ~40 milliseconds**
**(typically the peak MIIT’s value)**
**Typical Heater Power supply****	****	****	****450v**
**Parameters (x2 if stacked)****	****	****	****2 to 20 millifarad**

- 5/22/02

## Summary of Typical Process

- Obtain MIITs curve for magnet		Calculate from “Quench” code or Measure
- Calculate minimum coil volume( conductor length)      I (operate), L (millihenries)
- Design heater area greater than necessary	Heater area calculated
- to switch minimum coil volume( conductor length)
- Residual Resistance Ratio (conductor)                          Most effective 10 - 20*
- Heater design resistances calculated		ohms to few 10’s of ohms
- Temperature (heater) targets		150K to 200K
- Wattage (heater) at the surface		20w/cm2 for LHe &  40w/cm2 for Super-fluid He
- Time (heater) constants		30 millisec. to 100 millisec.
-                                                                       *New Knob discovered by serendipity
**An efficient heater should:                                           especially pertinent to longer magnets**
- Include an active length (non-cu plated)	1 cable transposition length
- Minimum heater thickness (ss)		13 micron preferred, but 25 micron is normal
- Min. thickness Kapton under layer and/or	25 microns (3 kV checked)
- Alumna filled Kapton (x2 thermal conduct.)	 25          “             “             thermal diffusion time ~20-25ms

- Protection Heater Design

- 5/22/02

## Training Summary

- >  Provided Structure is able to preload the windings in all directions, such that the coil 	 can not move under any Lorentz load permutation.

- Olde Method
- ---Works---

-           Newer Strategy
- --Works under careful control--

- >  Do not bond winding to any surface that is possible to be in shear or non contact with
- 	I.e. not surfaces that become unloaded like Cosθ winding poles, solenoid spool

- >  Control integration of the Lorentz forces to limit winding deflections ( a field quality
- 	issue)  I.e. load enough to remove fluff  and insure support contact (springs?)

- >   Higher the metal packing fraction the lower the deflection per given load.  (higher
- 	ampere-turn)  This results in a higher modulus and lower voltages

- >   Avoid magnet designs with parallel surfaces under load in contact with winding

- 5/22/02

## State of Present High Field Magnet Coil’s Protection

- The Heater design is per unit length
- 		**provided the heater is segmented properly **
- Therefore heaters can be effective on “Long or Short” magnets
- The length limit using this protection mode is thermal mechanical
- 		**limited by stresses caused by differences in coil’s temperature  and the support structure**
**	****	****Later designs attempted <100K**
- Overall “J’s” in the range of 2000 amperes/mm2 appear possible at this time although results for windings in the 1000 amperes/mm2 range are available.

- Protection Heater Mode

- 5/22/02