Modular Coil Winding Keystoning Issues

Single Conductor- Results of Bench Top Tests

A

B

C

D

Mod Coil R&D Update

*

Keystone test results so far Four cables/conductor did not work well due to bunchingCables could not slide relative to each other

*

What is actual conductor bend radius? This all depends on what the meaning of radius is

For radius to winding center, we have:From Coil-opt, Rmin = 4.15 inchesFrom Pro-E model = 4.15 inches

Min. radius to edge of four sides of winding pack:

leftrightShell sidePlasma sideM11.5811.6311.3082.443M21.8382.1113.7233.175M31.6881.6063.9593.685Keystoning makes pack tallerKeystoning makes pack wider

*

What is effect of insulation? Keeps 4-cable conductor from sliding relative to each other within insulation wrap

Makes conductor very stiff

Adds to keystoning problem

Options: Teflon tape does epoxy bond to teflon? Do we care?CREPED NOMEX dimensional control, pinholes?Mylar? not any better than kaptonSpiral wrap or butt wrap, not half lapLook at woven glass polyimide stuff

3 layers kapton, .00325 in ea4 layers glass, .007 in ea.Total = .038 inches

*

What are options?

Figure out how much keystoning we have and live with the problemWith and without insulationWith existing and new conductorJim will start this one nowFigure out what reasonable pressure is to squash pack into placePredict winding pack growth and check interferences with VV/adjacent coils ORNL with Jim dataArt checks field errors from predicted keystoning w/o any correction

Pre-keystone conductor ahead of taping head in opposite direction

Go back to 4-cable conductor, wrap onto form w/o insulation, clamp cables in formed position, unwind, insulate, and re-wind

Wind into groove (e.g. on pulley or tube bender) to restrain cable, unwind and rewind

ActionsLook at changing pitch of cable ala Auburn cable JimLook at pretzel coil design/schedule fits in oven, full cross section, prototypical conductor and potting features, clamps, etc.FDR for racetrack coil June 5

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live with the problemPerform keystoning tests to quantify problem, increase size of winding pack, shim between turns to fill all space I.e. live with the problem

Look at both id and od winding forms - ORNL

*

Pre-keystone conductor ahead of taping head in opposite direction

For most regions of the coils, there would be little if any reverse keystoning needed. We can contact NEWC to see what kind of rollers they use on their turkshead, and what it would take to make a turkshead with easily adjustable rollers. Develop an algorithm that would pre-squash the conductor appropriately. We would need to figure out a couple of things, how much overall swelling do we get with the extra squashing?, how much damage do we do to the wires in the process?can the taping machine adapt to different shapes of conductor?

We would still measure every turn and possible shim between them, but we may end up with a tighter pack (i.e. lower current density and more uniform mechanical properties).

*

Go back to 4-cable conductor

Wind bare cables for some distance

Clamp conductor

Carefully unwind and insulate

Put back and clamp

Comments:Tolerance on cable doublesMaybe set up tape machine to tape a curveInvestigate further on roller coaster with close taping - Jim

*

Current density vs insul. thickness and tee width

Chart1

11623.048500195112007.917655830712419.147712537312859.543021492513332.3203384591

12342.296550949812762.102556084113211.472364396913693.64288864514212.3414829119

13130.90344076113590.025938689714082.418182845114611.832400245315182.6071033799

13998.148393187114501.678910927715042.786332977215625.840066813516255.914263056

14954.927912405815508.814131383816105.306982590816749.519261894517447.4158978067

w/o cooling tabs

with cooling tabs

"tee" width (in)

0.50

0.60

0.70

0.80

0.90

turn insulation thickness (in)

current density in copper (A/cm^2)

Current density vs turn insulation thickness and "tee" width 4.1 x 4.67 in envelope, 763 kAmps per coil, 2 winding packs per coil, 28 total turns, chill plates = 2 x .04 in

coil current

NCSX fields

Initial calculations

Bavg, axis1.7T

Ravg, axis1.4m

I coil =661111.111111111A/coil

Force, max10000lbs/in

Current density14000A/cm^2

I plasma =300000A

dplasma =0.15m

Bplasma =0.4T

Icoil =661111.111111111

dcoil =0.055m

Bcoil =2.404T

radius to field meas1.300

B other coils =2.034T

Btotal, peak =4.456T

Requirements

B0 req.2Tratio =1.1764705882

I req. =777777.777777778A/coil

Force, max =13840.830449827lbs/in

Current density16470.5882352941A/cm^2

I plasma =300000A

dplasma =0.1m

Bplasma =0.6T

Icoil =777777.777777778

dcoil =0.055m

Bcoil =2.828T

radius to field meas1.300

B other coils =2.393T

Btotal, peak =5.256T

modular coil pwer,cryo

NCSX modular coil power

Adiabatic coil heating

Assume

Copper density =8.9g/cc

Cu res at 273K =1.55E-06ohm-cm

Res coeff =6.91E-09ohm-cm/C

Resistivity at 283K1.62E-06ohm-cm

coil 1coil 2coil 3coil 4

max amp-turns/coil5.758E+056.530E+055.281E+050.000E+00A-turns

Length of single turn701.0708.6622.80.0cm

number of coils in circuit6660coils

number of turns/coil36363636turns

Total winding lngth per coil25236.525510.622420.80.0cm

kA-m per coil4.036E+034.627E+033.289E+030.000E+00k-A-m

Current per turn1.599E+041.814E+041.467E+040.000E+00amps

dr (gross sect.)1.200E+011.200E+011.200E+011.600E+01cm

dz (gross sect.)1.000E+011.000E+011.000E+011.200E+01cm

packing fraction3.340E-013.340E-013.340E-013.340E-01

net current dens.1.437E+041.629E+041.318E+040.000E+00A/cm^2

single cond Cu area1.1E+001.1E+001.1E+001.8E+00cm^2

conductor Cu volume28096.628401.824961.80.0cc

approximate cond. Wt.2.50E+022.53E+022.22E+020.00E+00kg / coil

Total k-A-m for coils in set2.42E+042.78E+041.97E+040.00E+00k-A-m

Total wt. Conductor1.50E+031.52E+031.33E+030.00E+00kg/coil set

Total k-A-m for all coils7.17E+04k-A-m

Total wt. , all coils4.35E+03kg

Peak power during pulse3.34E+01MW

Coil power MW

single coil resistance at 283K3.68E-023.72E-023.27E-020.00E+00

Timecoil 1coil 2coil 3coil 4Cryo-cooled, 0.35 kV/coil

00.00E+000.00E+000.00E+000.00E+000.00E+00

0.1756.21E-015.19E-013.69E-010.00E+001.51E+00

0.352.56E+002.13E+001.51E+000.00E+006.19E+00

0.5256.23E+005.11E+003.57E+000.00E+001.49E+01

0.71.27E+011.02E+017.00E+000.00E+002.99E+01

0.7251.30E+011.04E+017.12E+000.00E+003.06E+01

0.751.33E+011.06E+017.25E+000.00E+003.12E+01

0.7751.37E+011.09E+017.37E+000.00E+003.19E+01

0.81.40E+011.11E+017.49E+000.00E+003.25E+01

0.81161.36E+011.07E+017.25E+000.00E+003.15E+01

0.82321.31E+011.04E+017.00E+000.00E+003.05E+01

0.83481.27E+011.00E+016.76E+000.00E+002.95E+01

0.84641.23E+019.67E+006.51E+000.00E+002.85E+01

0.8581.18E+019.32E+006.27E+000.00E+002.74E+01

0.8831.21E+019.50E+006.37E+000.00E+002.80E+01

0.9081.24E+019.67E+006.48E+000.00E+002.85E+01

0.9331.26E+019.86E+006.58E+000.00E+002.91E+01

0.9581.29E+011.00E+016.69E+000.00E+002.96E+01

0.9831.31E+011.02E+016.77E+000.00E+003.01E+01

1.0081.33E+011.03E+016.86E+000.00E+003.05E+01

1.0331.36E+011.05E+016.95E+000.00E+003.10E+01

1.0581.38E+011.07E+017.03E+000.00E+003.15E+01

1.0831.40E+011.08E+017.12E+000.00E+003.19E+01

1.1081.43E+011.10E+017.21E+000.00E+003.24E+01

1.1331.45E+011.11E+017.30E+000.00E+003.29E+01

1.1581.47E+011.13E+017.38E+000.00E+003.34E+01

1.4589.51E+007.16E+004.61E+000.00E+002.13E+01

1.7584.52E+003.38E+002.16E+000.00E+001.01E+01

2.0581.16E+008.64E-015.50E-010.00E+002.57E+00

2.3580.00E+000.00E+000.00E+000.00E+000.00E+00

2.6580.00E+000.00E+000.00E+000.00E+000.00E+00

modular coil pwer,cryo

0000

0.38945124380.50663078250.29092024190

1.5792579082.06240733891.17716163090

3.68522834954.8614615252.73140844410

7.01638855649.4255397875.14683422650

7.10549967449.57698467075.20233017030

7.19516833229.72963278125.25812042270

7.28539532199.88348700345.31420527290

7.376181522410.03855052815.37058504310

7.16322518589.78652423685.20390217110

6.94400652469.52162847195.03403244780

6.71937588739.24523137084.86152144390

6.49016499268.95868127584.68690061270

6.25718518848.66330261644.51068645770

6.5114571639.02956761354.68967790460

6.77365516499.4083671514.87391682610

7.04404474589.80017354535.06356437960

7.322902631110.20548006615.25878829650

7.374933688710.29563321085.29083995830

7.427151917110.38619731175.3229896440

7.479557666710.47717361895.35523748370

7.532151297810.56856341715.38758361150

7.584933180810.6603680265.4200281650

7.637903695810.75258880035.45257128580

7.691063233410.84522712915.48521311920

7.744412193610.93828443655.51795381430

4.77408540786.88234957943.36015269210

2.22185122173.23571618371.55432855560

0.56490639340.8257427150.39431241810

0000

0000

coil 1

coil 2

coil 3

coil 4

elapsed time during pulse

Power dissipated in coil set (MW)

Coil resistive power vs timeli383m_0907 coil set, full current, full beta

Cu resistivity

OFHC Copper resistivity

resistivity =rho273+c1(T)-c2(t^2), T in deg Cc1 =6.91E-09

% IACS at 273K100%c2 =0.00E+00

rho273 =1.55E-06ohm-cm

rho293 =1.70E-06ohm-cm

temp (K)rel. powerdata [1,2]equationtemp(C)rho (1e-6ohm-cm)rho (ohm-cm)equation%iacs

801.09E-012.18E-072.19E-07-1930.2182.18E-072.19E-07779.8%0.24.88E+00

901.42E-012.83E-072.88E-07-1830.2832.83E-072.88E-07600.7%

1001.77E-013.53E-073.58E-07-1730.3533.53E-073.58E-07481.6%0.35

1202.47E-014.93E-074.96E-07-1530.4934.93E-074.96E-07344.8%0.5

1403.19E-016.38E-076.34E-07-1330.6386.38E-076.34E-07266.5%0.7

1603.89E-017.78E-077.72E-07-1130.7787.78E-077.72E-07218.5%

1804.62E-019.23E-079.10E-07-930.9239.23E-079.10E-07184.2%

2005.32E-011.06E-061.05E-06-731.0631.06E-061.05E-06159.9%1.2

2206.02E-011.20E-061.19E-06-531.2031.20E-061.19E-06141.3%

2507.02E-011.40E-061.39E-06-231.4031.40E-061.39E-06121.2%

2737.77E-011.55E-061.55E-0601.5531.55E-061.55E-06109.5%

2958.52E-011.70E-061.71E-06221.7031.70E-061.71E-0699.8%12.4698672114

3139.17E-011.83E-061.83E-06401.83E-061.83E-0692.7%

3239.51E-011.90E-061.90E-06501.90E-061.90E-0689.4%

3381.00E+002.00E-062.00E-06652.00E-062.00E-0685.0%

3531.05E+002.10E-062.11E-06802.10E-062.11E-0680.9%

3581.07E+002.14E-062.14E-06852.14E-062.14E-0679.6%

Cu resistivity

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

00

data [1,2]

equation

Temperature (K)

Electrical Resistivity (ohm-cm)

OFHC copper resistivityrho ~ 1.55e-6 + 6.91e-9*(273-T(K))ref [1] NBS tech note 365, L.A.Hall, Feb 1968 ref [2] Anaconda Copper for Electrical Conductors

PF coil pwer

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

0

LN temp.

Water temp.

rel. power

Temperature (K)

Normalized power

Normalized power vs temperaturenormalized to rho-Cu @ 65 C (= 2 e-6 ohm-cm)

PF coil pwer (2)

PF coil power vs current density


AssumePF 1PF 2PF 3PF 4PF 5

Avg radius of coil16.050.0168.9cm

amp-turns/coil6.700E+047.400E+042.200E+05A-turns

Length of coil100.5314.21061.2cm

number of coils in circuit2.02.02.0coils

number of turns/coil8.08.024.0turns

Current per turn8.375E+039.250E+039.167E+03amps

dr (gross sect.)8.000E+008.000E+001.780E+01cm

dz (gross sect.)8.000E+008.000E+001.990E+01cm

packing fraction5.000E-015.000E-017.000E-01

net current dens.2.094E+032.313E+038.873E+02A/cm^2

Copper resistivity =2.0E-062.0E-062.0E-06ohm-cm

Copper density =8.98.98.9gm/cc

approximate cond. Wt.5.73E-021.79E-014.68E+00tonnes

Current density in CuPower dissipated in coil circuitPower dissipated in coil circuitPower dissipated in coil circuit

(A./ cm^2)(watts)(watts)(watts)

00.00E+000.00E+000.00E+00

2.094E+035.64E+041.95E+051.96E+06

2.313E+036.23E+042.15E+052.16E+06

8.873E+022.39E+048.25E+048.29E+05

2506.74E+032.32E+042.33E+05

5001.35E+044.65E+044.67E+05

7502.02E+046.97E+047.00E+05

10002.69E+049.30E+049.34E+05

12503.37E+041.16E+051.17E+06

15004.04E+041.39E+051.40E+06

17504.71E+041.63E+051.63E+06

20005.39E+041.86E+051.87E+06

22506.06E+042.09E+052.10E+06

Resistive voltage across circuitResistive voltage across circuitResistive voltage across circuit

(volts)(volts)(volts)

00.00.00.0

2.094E+036.721.0213.3

2.313E+037.423.2235.6

8.873E+022.98.990.4

2500.821.0213.3

5001.623.2235.6

7502.48.990.4

10003.22.525.5

12504.05.050.9

15004.87.576.4

17505.610.1101.9

20006.412.6127.3

22507.215.1152.8

PF coil pwer (2)

000

000

000

000

000

000

000

000

000

000

000

000

000

Current density in copper (A/cm^2)

Power dissipated in coil circuit (watts)

Coil circuit power vs current density in copper2 coils per circuit

copper area (3)

PF coil power vs current density


AssumePF 1PF 2PF 3PF 4PF 5

inner ATF coil

Avg radius of coil11.435.7132.9cm

amp-turns/coil6.700E+047.400E+042.200E+05A-turns

Length of coil71.8224.4835.0cm

number of coils in circuit2.02.02.0coils

number of turns/coil8.08.016.0turns

Current per turn8.375E+039.250E+031.375E+04amps

dr (gross sect.)8.000E+008.000E+001.070E+01cm

dz (gross sect.)8.000E+008.000E+001.530E+01cm

packing fraction5.000E-015.000E-017.000E-01

net current dens.2.094E+032.313E+031.920E+03A/cm^2

Copper resistivity =2.0E-062.0E-062.0E-06ohm-cm

Copper density =8.98.98.9gm/cc

approximate cond. Wt.4.09E-021.28E-011.70E+00tonnes

Current density in CuPower dissipated in coil circuitPower dissipated in coil circuitPower dissipated in coil circuit

(A./ cm^2)(watts)(watts)(watts)

00.00E+000.00E+000.00E+00

2.094E+034.03E+041.39E+051.54E+06

2.313E+034.45E+041.54E+051.70E+06

1.920E+033.69E+041.28E+051.41E+06

2504.81E+031.66E+041.84E+05

5009.62E+033.32E+043.67E+05

7501.44E+044.98E+045.51E+05

10001.92E+046.64E+047.35E+05

12502.41E+048.30E+049.19E+05

15002.89E+049.96E+041.10E+06

17503.37E+041.16E+051.29E+06

20003.85E+041.33E+051.47E+06

22504.33E+041.49E+051.65E+06

Resistive voltage across circuitResistive voltage across circuitResistive voltage across circuit

(volts)(volts)(volts)

00.00.00.0

2.094E+034.815.0111.9

2.313E+035.316.6123.6

1.920E+034.413.8102.6

2500.615.0111.9

5001.116.6123.6

7501.713.8102.6

10002.31.813.4

12502.93.626.7

15003.45.440.1

17504.07.253.4

20004.69.066.8

22505.210.880.2

copper area (3)

000

40293.1697770417139071.5747901621538552.59059478

44502.903932852153601.4408130151699296.89110468

36945.0315414698127515.5006561921410707.43012434

4811.124749497516605.5611689746183707.772011317

9622.24949899533211.1223379492367415.544022634

14433.374248492549816.6835069239551123.31603395

19244.4989979966422.2446758985734831.088045267

24055.623747487683027.8058448731918538.860056584

28866.748496985199633.36701384771102246.6320679

33677.8732464826116238.9281828221285954.40407922

38488.9979959801132844.4893517971469662.17609053

43300.1227454776149450.0505207721653369.94810185

Current density in copper (A/cm^2)

Power dissipated in coil circuit (watts)

Coil circuit power vs current density in copper2 coils per circuit

copper area (4)

Net copper area vs gross area

Let

No. of turns =36

No. of turns high =9

Total current =6.53E+05Amps

No. turns wide =4

coil struct width (adj)4.10in104.1mm

coil struct height (adj)4.67in118.6mm

flange thickness (adj)0.00in0.0mm

web thickness (adj)0.75in19.1mm

gross coil area15.64in^2

no. of bundles2

ground wrap.0.03in0.8mm

grout0.00in

lateral turn insulation0.054in1.4mm

radial turn insulation0.054in1.4mm

cooling septa width0.04in1.0mm

cooling septa height0.04in

max width avail. for turns1.32in33.5mm

max height avail for turns3.56in90.4mm

radius to clrad to first cond.

conductor width =0.66in16.8mm10566.06765

conductor height =0.40in10.0mm7536.06765

gross area/turn =0.26in^211172.06765

coolant jacket thickness0.00in0.0mm13798.06765

hole dia =0in0.0mm

braid packing fraction0.78

net area / turn =0.20in^2131.2mm^2

net copper / cond area0.468

net copper / total area0.320.3823618906

Gross current density =6469.7A/cm^28.214524393

Current density in copper13825.2A/cm^2236.9316738633m/s

187272.727272727kg

5.256E+09J

no of turnsCurrent density at packing fraction

No. of turns =4436322824160.50.60.70.80.9

No. of turns high =1198764442296119134164011435112756

Total current =653000653000653000653000653000653000362156717973154051348011982

No. turns wide =444444322093217443149511308211629

coil struct width4.104.104.104.104.104.10282033316944145231270811296

coil struct height4.674.674.674.674.674.67241976716473141191235510982

gross coil area19.1519.1519.1519.1519.1519.15161872515604133751170310403

no. of bundles222222

ground wrap.0.030.030.030.030.030.03

lateral turn insulation0.050.050.050.050.050.05

radial turn insulation0.050.050.050.050.050.05

max width avail. for turns1.321.321.321.321.321.32

max height avail for turns3.343.563.673.773.884.10

chill plate0.040.040.040.040.040.04

conductor width =0.660.660.660.660.660.66

conductor height =0.300.400.460.540.651.02

gross area/turn =0.200.260.300.360.430.68

coolant jacket thickness0.000.000.000.000.000.00

hole dia =0.000.000.000.000.000.00

braid packing fraction0.500.500.500.500.500.50

net area / turn =0.100.130.150.180.210.34

net copper / gross area0.230.250.250.260.270.28

Gross current density =5286.225286.225286.225286.225286.225286.22

Current density in copper22961.2021567.2620931.8920332.8919767.2118725.31

No. of turns =443632282416


Total current =653000653000653000653000653000653000

No. turns wide =444444



gross coil area19.1519.1519.1519.1519.1519.15


ground wrap.0.030.030.030.030.030.03





chill plate0.040.040.040.040.040.04

conductor width =0.660.660.660.660.660.66


gross area/turn =0.200.260.300.360.430.68


hole dia =0.000.000.000.000.000.00


net area / turn =0.120.160.180.210.260.41




No. of turns =443632282416


Total current =653000653000653000653000653000653000




gross coil area19.1519.1519.1519.1519.1519.15


ground wrap.0.030.030.030.030.030.03





chill plate0.040.040.040.040.040.04

conductor width =0.660.660.660.660.660.66


gross area/turn =0.200.260.300.360.430.68


hole dia =0.000.000.000.000.000.00


net area / turn =0.140.180.210.250.300.47




No. of turns =443632282416


Total current =653000653000653000653000653000653000




gross coil area19.1519.1519.1519.1519.1519.15


ground wrap.0.030.030.030.030.030.03





chill plate0.040.040.040.040.040.04

conductor width =0.660.660.660.660.660.66


gross area/turn =0.200.260.300.360.430.68


hole dia =0.000.000.000.000.000.00


net area / turn =0.160.210.240.280.340.54




No. of turns =443632282416


Total current =653000653000653000653000653000653000




gross coil area19.1519.1519.1519.1519.1519.15


ground wrap.0.030.030.030.030.030.03





chill plate0.040.040.040.040.040.04

conductor width =0.660.660.660.660.660.66


gross area/turn =0.200.260.300.360.430.68


hole dia =0.000.000.000.000.000.00


net area / turn =0.180.230.270.320.380.61




wc

hc

Wt

Ht

copper area (4)

0000

0000

0000

0000

0000

0000

w/o cooling tabs

with cooling tabs

copperpacking fraction

0.6

0.7

0.8

0.9

no of turns


Current density vs number of turns and Cu packing fraction4.1 in x 4.67 in envelope, 653 kAmps per coil, 2 winding packs per coil, turn insl = .054 in, chill plates = 2 x .04 in

int pulse length

Net copper area vs gross area

Let18.1388888889

No. of turns =2836 trns

No. of turns high =7I/turn (1.7T)2.12E+04

Total current =7.63E+05AmpsI/turn (2T)2.19E+04

No. turns wide =4

coil struct width (adj)4.10in104.1mm

coil struct height (adj)4.67in118.6mm

flange thickness (adj)0.00in0.0mm

web thickness (adj)0.75in19.1mm

gross coil area15.64in^2

no. of bundles2

ground wrap.0.03in0.8mm

grout0.00in

lateral turn insulation0.054in1.4mm

radial turn insulation0.054in1.4mm

cooling septa width0.04in1.0mm

cooling septa height0.04in

max width avail. for turns1.32in33.5mm

max height avail for turns3.77in95.9mm

radius to clrad to first cond.

conductor width =0.660in16.8mm10566.06765

conductor height =0.539in13.7mm7536.06765

gross area/turn =0.36in^211172.06765

coolant jacket thickness0.00in0.0mm13798.06765

hole dia =0in0.0mm

braid packing fraction0.78

net area / turn =0.28in^2178.9mm^2

net copper / cond area0.496

net copper / total area0.340.4055744169

Gross current density =7557.6A/cm^28.214524393

Current density in copper15225.6A/cm^2236.9316738633m/s

187272.727272727kg

5.256E+09J

turn insulationtee width

No. of turns =2828282828280.500.600.700.800.90

No. of turns high =7777770.031162312008124191286013332

Total current =7628047628047628047628047628047628040.041234212762132111369414212

No. turns wide =4444440.051313113590140821461215183

coil struct width4.104.104.104.104.104.100.061399814502150431562616256

coil struct height4.674.674.674.674.674.670.071495515509161051675017447

gross coil area19.1519.1519.1519.1519.1519.150.081601416625172851799918775


ground wrap.0.030.030.030.030.030.03



tee width0.5000.5000.5000.5000.5000.500



chill plate0.040.040.040.040.040.04

conductor width =0.780.760.740.720.700.68


gross area/turn =0.470.440.410.390.360.34


hole dia =0.000.000.000.000.000.00


net area / turn =0.360.340.320.300.280.26




No. of turns =282828282828


Total current =762804762804762804762804762804762804




gross coil area19.1519.1519.1519.1519.1519.15


ground wrap.0.030.030.030.030.030.03



tee width0.6000.6000.6000.6000.6000.600



chill plate0.040.040.040.040.040.04

conductor width =0.760.740.720.700.680.66


gross area/turn =0.450.420.400.370.350.33


hole dia =0.000.000.000.000.000.00


net area / turn =0.350.330.310.290.270.25




No. of turns =282828282828


Total current =762804762804762804762804762804762804




gross coil area19.1519.1519.1519.1519.1519.15


ground wrap.0.030.030.030.030.030.03



tee width0.7000.7000.7000.7000.7000.700



chill plate0.040.040.040.040.040.04

conductor width =0.730.710.690.670.650.63


gross area/turn =0.440.410.380.360.340.31


hole dia =0.000.000.000.000.000.00


net area / turn =0.340.320.300.280.260.24




No. of turns =282828282828


Total current =762804762804762804762804762804762804




gross coil area19.1519.1519.1519.1519.1519.15


ground wrap.0.030.030.030.030.030.03



tee width0.8000.8000.8000.8000.8000.800



chill plate0.040.040.040.040.040.04

conductor width =0.710.690.670.650.630.61


gross area/turn =0.420.400.370.350.320.30


hole dia =0.000.000.000.000.000.00


net area / turn =0.330.310.290.270.250.23




No. of turns =282828282828


Total current =762804762804762804762804762804762804




gross coil area19.1519.1519.1519.1519.1519.15


ground wrap.0.030.030.030.030.030.03



tee width0.9000.9000.9000.9000.9000.900



chill plate0.040.040.040.040.040.04

conductor width =0.680.660.640.620.600.58


gross area/turn =0.410.380.360.330.310.29


hole dia =0.000.000.000.000.000.00


net area / turn =0.320.300.280.260.240.22




Glass cloth, co-wound with kapton

Kapton

Compacted cable conductor

Total insulation thickness = 0.030"

Kapton

Glass cloth

Glass cloth, first half-lapped layer

baseline

wc

hc

Wt

Ht

int pulse length

w/o cooling tabs

with cooling tabs

"tee" width (in)

0.50

0.60

0.70

0.80

0.90

turn insulation thickness (in)


Current density vs turn insulation thickness and "tee" width 4.1 x 4.67 in envelope, 763 kAmps per coil, 2 winding packs per coil, 28 total turns, chill plates = 2 x .04 in

temp v time

Pulse Length vs Current Density in Copper

Let:Temperature range

Tmin =758085K

-198-193-188C

Tmax =125130135K

-148-143-138C

Copper spec. heat0.385J/gm-C, RT

Copper density =8.9J/gm-C

% IACS at 273K100%


coolant fraction1.50E-01

coolant spec. heat4.10E+00J/gm-C

coolant density1.00E+00gm/cc


Current density in CuPulse length (equiv square wave)Average temperature rise

(A./ cm^2)(seconds)(deg C/sec)

500024.72.0

600017.12.9255.2222222222

700012.64.0

80009.65.2

90007.66.6

100006.28.1

Tstart (K)85.0283.0300

Tfinish (K)140.0338.0338

avg temp, C-160.537.546.036.111111111165.5555555556

avg specific heat0.2740.3650.365338

avg resistivity4.44E-071.81E-061.87E-06

Temp rise =36.1C

Current density in Cu (A/cm^2)Pulse length (equiv square wave)

Current density

500012.95.53.1

60009.03.82.2

70006.62.81.6

80005.02.11.2

90004.01.71.0

100003.21.40.8

110002.71.10.7

120002.21.00.5

Current density in Cu (A/cm^2)Pulse length (equiv square wave)

Current density

50005.53.1

60003.82.2

70002.81.6

80002.11.2

90001.71.0

100001.40.8

110001.10.7

120001.00.5

Glass cloth, co-wound with kapton

Kapton

Compacted cable conductor

Total insulation thickness = 0.030"

Kapton

Glass cloth

Glass cloth, first half-lapped layer

baseline,0.054 in

temp v time

12.91074442845.47763675073.1467609518

8.96579474193.80391441022.185250661

6.58711450432.79471262791.6054902815

5.04325954232.13970185571.2292034968

3.98479766311.69062862680.971222516

3.22768610711.36940918770.786690238

2.66750917941.13174313030.6501572215

2.24144868550.95097860260.5463126652

LN2, T= 85 to 140 K

Chilled water, T = 275 to 338 K

Water, T = 300 to 338 k

Current density (A/cm^2)

Pulse length , ESW (seconds)

Pulse length vs current density in copper,Cooled by water, chilled water, LN2

ref waveforms

00

00

00

00

00

00

00

00

Chilled water, T = 275 to 338 K

Water, T = 300 to 338 k

Current density (A/cm^2)

Pulse length , ESW (seconds)

waveform,cryo

Temperature (K)

Scenariost(s)M1M2M3PF1PF2PF3PF4PF5PF6TF

350kA Ohmic

-0.70085858580808080808080

0.00094969081828080808080

0.10097999281828080808080

0.2161001019381828080808080

0.3161021039481828080808080

0.5161061069682838080808081

2.69711411210182838080808083

Dissipated Energy (J)1.58E+071.42E+077.14E+062.19E+053.56E+054.57E+041.38E+044.41E+043.29E+044.72E+06

4.26E+07

2T High Beta

-0.80085858580808080808080

0.0001001029381828080808080

0.0501021049481828080808080

0.1181041079581828080808080

0.2131081109781828080808080

0.2181081119781828080808080

2.39912112110781828181808081


5.30E+07

1.7T High Beta

-0.70085858580808080808080

0.00097949280808080808080

0.100100979480808080808080

0.158102999580808181808080

0.2581051019680808181808080

0.45811110610080808181808080

2.63912011410680808181808081


4.78E+07

Initial Ohmic

-1.20085858580808080808080

0.0001051019580808080808080

0.1001081039780818080808080

0.1961111059880818080808080

0.29611310710080818080808080

0.49611811110381818181808080

2.67712511710881828181808081


5.32E+07

1.7T Ohmic

-0.70085858580808080808080

0.00097949280818080808080

0.100100979480818080808080

0.158102999580818080808080

0.2581051019780818080808080

0.45811110610081818080808080

2.63912011410781818181808081


4.75E+07

Max Final Temperature12512110882838181808083

Max Dissipated Energy (J)2.29E+071.95E+071.08E+072.19E+053.56E+053.43E+058.19E+056.49E+043.29E+044.72E+06

5.32E+07

temp vs time,cryo,1.7T

Current waveforms (A)

t(s)M1M2M3PF1PF2PF3PF4PF5PF6TFPlasma

350kA Ohmic Scenario

-0.70000000000000

1.8T low iota0.000200682076315815-18404-18404-2797-2533-5656-198618690

0.100200682076315815-18404-18404-2797-2533-5656-198618690

0.216162011464811590692569254401-1865-2084762616076-350000

0.31616201146481159011008110085332-1009-2013795016076-350000

350kA0.51616201146481159019174191747193702-1870859716076-350000

Maximum2006820763158151917419174719370208597160760

Minimum000-18404-18404-2797-2533-5656-19860-350000

Current direction1110000-101

3.98E+083.78E+082.35E+083.20E+083.15E+082.71E+074.38E+061.62E+072.78E+075.50E+08

0.990.880.940.870.860.520.680.510.382.13

2T High Beta Scenario

-0.80000000000000

Low iota vacuum0.000222282299817518167031670353564967-561474020710

0.050222282299817518167031670353564967-561474020710

2T zero beta0.1182269721265184321765217652158909241166216912420-2050710.9246460658

0.21322685213921800851951916129139904676-2982729-2049890.9301797713

2T high beta0.21822685213921800854054016133139944677-2972729-204989

Maximum226972299818432176521765216133139944677169127290

Minimum0000000-5614-2980-205071

Current direction1111111001

4.79E+084.75E+083.10E+082.24E+082.18E+081.11E+081.71E+082.14E+071.13E+062.02E+08

0.930.900.910.720.700.430.870.680.4027.16

1.7T High Beta Scenario

-0.70000000000000

High iota vacuum0.000221392010217621307230721359015081-5865-1678-47700

0.100221392010217621307230721359015081-5865-1678-47700

0.1581929218075156681605316053137468074143115212057-1743100.8991816974

0.2581928318184153071569156913966121283995-1642320-1742410.9045630069

0.4581928318184153072386238614152122994009-992320-174241

Maximum221392010217621160531605314152150814009152123200

Minimum0000000-5865-1678-4770-174310


4.70E+083.98E+083.07E+082.17E+072.15E+072.04E+082.50E+082.36E+071.38E+061.61E+08

0.960.990.990.080.081.021.100.690.497.09

Initial Ohmic Scenario

-1.20000000000000

0.000195351773715548-7496-7496966511167-5354-2290-42090

0.100195351773715548-7496-7496966511167-5354-2290-42090

0.1961702315949138245788578810219536911166781815-153803

0.29617023159491382498719871111506225118810011815-153803

0.4961702315949138241803618036130117936133116491815-153803

Maximum195351773715548180361803613011111671331164918150

Minimum000-7496-749600-5354-2290-4209-153803


5.23E+084.36E+083.28E+081.52E+081.62E+081.71E+081.53E+082.24E+075.17E+061.47E+08

1.371.391.360.470.501.011.230.780.998.31

1.7T Ohmic Scenario

-0.70000000000000

0.000221392010217621-11218-112181033312086-6116-2811-47700

0.100221392010217621-11218-112181033312086-6116-2811-47700

0.1581929218075156681763176310489508011813882057-174310

0.2581929218075156685846584611419593512527122057-174310

0.4581929218075156681401214012132817647139513592057-174310

Maximum221392010217621140121401213281120861395135920570

Minimum000-11218-1121800-6116-2811-4770-174310


4.70E+083.97E+083.13E+081.24E+081.25E+081.44E+081.24E+081.69E+074.29E+061.57E+08

0.960.981.010.630.640.810.850.450.546.90

Maximum2269722998184321917419174161331508146778597160760

Minimum000-18404-18404-2797-2533-6116-2811-4770-350000

5.23E+084.75E+083.28E+083.20E+083.15E+082.04E+082.50E+082.36E+072.78E+075.50E+08

1.020.900.970.870.860.791.100.630.382.13

Current direction: 1=forward -1=reverse, 0=bidirectional

temp vs time,cryo,1.7T (2)

NCSX inductance estimate

mhu-00.0000012566

For first guess, ratio the ATF inductance and the QOS inductance based on volume and stored energy

ATFLHDli383 estli383 est 2

R02.10003.90001.70001.7000m

acoil0.45750.97501.11411.1141m

Vol, torus8.676273.181941.650041.6500m^3

B01.00004.00001.00001.0000Tesla

total Current,11.050E+077.800E+071.215E+071.215E+07Amps

total current 21.081E+07Amps

Stored energy, Tight torus calc.3.452E+064.659E+081.657E+073.386E+07Joules

Stored energy, from data1.035E+071.600E+093.894E+07Joules.5*L*I^2

single turn inductance1.878E-075.260E-075.276E-070.0000004587Henries

check energy1.035E+071.600E+093.894E+07

ratio, open coil vs tight torus calc.3.003.432.35

Estimated li383 mod coil parameters:

density of copper8.9g/cc

rho @ 0C1.55E-06

temp coeff.6.91E-09

start temp-188C85K

max temp-160C113K

temp end of ramp-18093K

start resistivity2.54E-07ohm-cm

avg start resistivity2.82E-07ohm-cm

avg flat-top resisitivity3.78E-07ohm-cm

total cross section123.53cm^2

copper fraction0.3216905.1443634107temp (K)tempspecific heat (j/g-K)circuit resistance (ohms)energy dissipated in coil (joules)time constant (seconds)time (sec)current in coil (Amps)current in coil (kA)

coil length, avg.6.77mramp up of coil current85-1880.218.47E-020.00E+001.49E+000.0000.000E+000.00

no. of coils1885-1.88E+020.218.49E-029.54E+041.48E+000.1014.874E+034.87

no. of turns/coil3286-1.87E+020.218.55E-024.51E+051.47E+000.2029.396E+039.40

single turn Ind.3.798E-07Henries87-1.86E+020.218.74E-021.11E+061.44E+000.3041.359E+0413.59

multi-turn ind., circuit1.260E-01Henries89-1.84E+020.229.11E-022.03E+061.38E+000.4051.748E+0417.48

res. Per coil during start4.89E-03ohms92-1.81E+020.229.72E-023.26E+061.30E+000.5062.109E+0421.09

res. For coil set8.81E-02ohmsFirst current flat-top95-1.78E+020.231.03E-012.04E+061.22E+000.5562.109E+0421.09

PS internal resistance3.30E-03ohms97-1.76E+020.241.08E-012.18E+061.17E+000.6062.109E+0421.09

Buswork resistance2.03E-03ohmsramp 1 to 299-1.74E+020.241.13E-012.70E+061.12E+000.6681.993E+0419.93

resistance w/o coils5.33E-03ohms102-1.71E+020.251.18E-012.52E+061.06E+000.7311.877E+0418.77

res per circuit9.34E-02ohmssecond current flattop105-1.68E+020.251.24E-012.99E+061.02E+000.8061.877E+0418.77

107-1.66E+020.261.30E-013.14E+069.69E-010.8811.877E+0418.77

110-1.63E+020.271.36E-013.30E+069.25E-010.9561.877E+0418.77

113-1.60E+020.271.43E-013.46E+068.83E-011.0311.877E+0418.77

time constant1.35E+00secondsramp down of current117-1.56E+020.281.50E-014.37E+068.41E-011.1561.252E+0412.52

flattop1 current2.109E+04Amps118-1.55E+020.281.55E-011.77E+068.11E-011.2816.258E+036.26

flattop2 current1.877E+04Amps119-1.54E+020.281.57E-013.68E+058.01E-011.4060.000E+000.00

current density in Cu16905.1A/cm^2

voltage6.300E+03Volts

time to reach current5.059E-01seconds3.37E+01

dump voltage6.300E+03Volts47.63

dump time for const V3.755E-01seconds

flattop1 time0.1second

flattop2 ramp0.125second

flattop2 time0.3secondramp time1.5s

formulasuminductive voltage1771.875V

Energy during ramp8.14E+066.94E+06Joulesresistive volt1.970E+03V

Energy during flattop13.92E+064.22E+06Joules

Energy dur interm. Ramp4.39E+065.22E+06Joules

Energy during flattop29.31E+061.29E+07Joules

Energy during dump4.90E+066.51E+06Joules

total energy3.07E+073.58E+07Joules

mass of conductor4.33E+064.33E+06gramsavg temp-171.1251049498

temp rise in conductor2.81E+013.27E+01deg Ccp @ avg temp0.25

peak temp in conductor-1.60E+02-1.55E+02

ESW7.83E-019.13E-01sec based on first flattop current

no. of intermediate circuits4

Bus length/circuit50m

total bus length400m

bus cross section4.99cm^2(4 x single turn of winding)

bus resistance2.03E-03ohms

structure height160cm

structure width120cm

structure thickness1.6cm

Structure area256cm^2

Copper area39.93cm^2

resistivity Structure7.50E-05ohm-cm

resistance per ibeam1.41E-03ohms1.98E-04

resistance all ibeams7.84E-05ohms

time constant structure4.845E-03seconds

B1.7T

A1m^2

dt1.5s

V1.1333333333V

I8.03E+02Amps

J3.14E+00A/cm^2

q'''7.38E-04W/cc

temp vs time,cryo,1.7T (2)

085

4.695204673985.054003596

9.139085388485.312706722

13.345094961385.9551511575

17.325966110687.1366685234

21.0937588.9993111575

21.0937590.1740593884

21.0937591.370680061

19.9335937592.8063902784

18.773437594.1039148741

18.773437595.5902849664

18.773437597.0994509162

18.773437598.6329346221

18.7734375100.1909272845

12.515625102.0984454542

6.2578125102.8448842038

0102.9961202782

Current

Temperature

Time (seconds)

Current (kA / turn)

Cond. Temp. (K)

NCSX Modular Coil Current vs Time, cryo-cooled, Tstart = 85 K18 coils in series, 32 turns per coil, 350 volts/coil 10 x 12 cm cross section, .39 copper fraction,


Temperature vs time

Let:

Tmin =85K-188C

Tmax =150K-123C

Copper spec. heat0.385J/gm-Cat 300Ktlog Cp =(1.131-9.454*LOG10(B34)+12.99*((LOG10(B34))^2)-5.501*((LOG10(B34))^3)+0.7637*((LOG10(B34))^4))/1000)

Copper density =8.9gm/cc85Cp0.2088286416

% IACS at 273Kreduced 6%94%33.0337078652



no. of turns/coil36363636

ref current6.53E+026.53E+026.53E+026.53E+02kA-turns

ref cd13825.213825.213825.213825.2A/cm^2

ref Cu area47.247.247.247.2cm^2

Current flattop1718.3653.018.1587.70

Current flattop2645.8587.016.3528.30

Current flattop3650.1591.016.4531.90

Current density1=1520813825124430



ramp up time0.7sec

flattop1 time0.1

intermed time 20.058

flattop2 time0.30.458

ramp down time1.2sec

start of ramp down1.15808sec

temperature in conductor

Time (seconds)J1110% baseline, ~15.2kA/cm^2J2100% baseline, ~13.8kA/cm^2J390% baseline, ~12.4kA/cm^2J4Mod coil 4, ~0.0kA/cm^2Baseline current (kA/turn)

0085085085085ramp 10

0.1753801.985.16023456.385.13243110.785.10720.085.00004534.7222222222

0.357603.886.28246912.686.05976221.385.85820.085.00009069.4444444444

0.52511405.889.347910368.988.59009332.087.90540.085.000013604.1666666667

0.715207.795.423013825.293.589012442.791.93880.085.000018138.8888888889

0.72515207.796.588713825.294.542312442.792.70380.085.0000flattop118138.8888888889

0.7515207.797.762413825.295.500912442.793.47210.085.000018138.8888888889

0.77515207.798.944013825.296.464812442.794.24370.085.000018138.8888888889

0.815207.7100.133713825.297.434012442.795.01890.085.000018138.8888888889

0.811614900.5100.678413545.997.877212191.395.37290.085.0000ramp217772.4833333333

0.823214593.3101.202713266.698.303611940.095.71330.085.000017406.0777777778

0.834814286.1101.707012987.498.713411688.696.04030.085.000017039.6722222222

0.846413978.9102.191512708.199.106911437.396.35410.085.000016673.2666666667

0.85813671.7102.656412428.899.484311185.996.65500.085.000016306.8611111111

0.88313694.5103.640612449.6100.282811204.697.29130.085.0000ramp316334.0694444444

0.90813717.3104.633712470.3101.087611223.397.93200.085.000016361.2777777778

0.93313740.1105.636012491.0101.899011241.998.57730.085.000016388.4861111111

0.95813763.0106.647512511.8102.716811260.699.22710.085.000016415.6944444444

0.98313763.0107.666712511.8103.540011260.699.88050.085.0000flattop216415.6944444444

1.00813763.0108.692012511.8104.367111260.6100.53630.085.000016415.6944444444

1.03313763.0109.723612511.8105.198311260.6101.19470.085.000016415.6944444444

1.05813763.0110.761412511.8106.033511260.6101.85550.085.000016415.6944444444

1.08313763.0111.805712511.8106.872811260.6102.51900.085.000016415.6944444444

1.10813763.0112.856412511.8107.716211260.6103.18490.085.000016415.6944444444

1.13313763.0113.913612511.8108.563811260.6103.85350.085.000016415.6944444444

1.15813763.0114.977512511.8109.415711260.6104.52470.085.000016415.6944444444

1.45810322.2124.88119383.8117.33538445.4110.75780.085.0000rampdown12311.7708333333

1.7586881.5130.27596255.9121.59765630.3114.07810.085.00008207.8472222222

2.0583440.7132.32873127.9123.20832815.1115.32570.085.00004103.9236111111

2.3580.0132.62550.0123.44070.0115.50520.085.00000

2.6580.0132.62550.0123.44070.0115.50520.085.000001.4046639232

temp rise47.6338.4430.510.00

Trho elecCp

800.00000031850.1938693395

900.00000038760.22281692960.000000353

1000.00000045670.24785632150.2088286416

1100.00000052580.2691219817

1200.00000059490.2869343621

1300.0000006640.3016926781

1400.00000073310.3138120205

1500.00000080220.3236890336

1600.00000087130.3316851518

1700.00000094040.3381201873

1800.00000100950.3432717371

1900.00000107860.3473776425

2000.00000114770.3506398628

2100.00000121680.3532288182

2200.00000128590.3552876893

2300.0000013550.3569364082

2400.00000142410.3582752291

2500.00000149320.3593878481

2600.00000156230.3603440857

2700.00000163140.3612021703

2800.00000170050.362010666

2900.00000176960.3628100942

3000.00000183870.3636342905


0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0000

0.2 secrampup

0.2 secrampdown

Coils off

ramp up

ramp down

0.46 s

110% baseline, ~15.2kA/cm^2



Baseline current (kA/turn)

time (seconds)

Conductor current (kA)

Conductor temperature (K)

Modular coil current waveform and temperature responsecase 11_02_01-RefScenario_***, (1.7 T), adjusted to 653 kA

Temperature vs time

Let:

Tmin =85K-188C

Tmax =150K-123C

Copper spec. heat0.385J/gm-Cat 300Ktlog Cp =(1.131-9.454*LOG10(B34)+12.99*((LOG10(B34))^2)-5.501*((LOG10(B34))^3)+0.7637*((LOG10(B34))^4))/1000)

Copper density =8.9gm/cc85Cp0.2088286416

% IACS at 273Kreduced 6%94%33.0337078652





ref cd13825.213825.213825.213825.2A/cm^2

ref Cu area47.247.247.247.2cm^2

Current flattop1587.7653.018.1718.30

Current flattop2523.1581.216.1639.30

Current flattop3558.3620.417.2682.40

Current density1=1100012000130001400015000

Current density2=988910788116871258613485

Current density3=995510860117651267013575

ramp up time0.70.70.70.70.7

flattop1 time0.10.10.10.10.1

intermed time 20.058124.99030.058125.00510.058125.02090.058125.02560.058124.9991

flattop2 time1.041.1980.7360.8940.50.6580.3130.4710.1620.32

ramp down time1.21.21.21.21.2

start of ramp down1.8981.5941.3581.1711.02


Time (seconds)J111.0kA/cm^2Time (seconds)J212.0kA/cm^2Time (seconds)J313.0kA/cm^2Time (seconds)J414.0kA/cm^2Time (seconds)J415.0kA/cm^2Coil 2 current (kA/turn)

00850085008500850085ramp 10

0.1752750.085.08380.1753000.085.09970.1753250.085.11700.1753500.085.13570.1753750.085.15583936.058321416

0.355500.085.67070.356000.085.79820.356500.085.93690.357000.086.08670.357500.086.24767872.116642832

0.5258250.087.26890.5259000.087.70170.5259750.088.17260.52510500.088.68170.52511250.089.229311808.174964248

0.711000.090.40990.712000.091.44890.713000.092.58210.714000.093.81070.715000.095.135615744.233285664

0.72511000.091.00250.72512000.092.15840.72513000.093.42020.72514000.094.78950.72515000.096.2679flattop115744.233285664

0.7511000.091.59710.7512000.092.87070.7513000.094.26230.7514000.095.77390.7515000.097.407615744.233285664

0.77511000.092.19380.77512000.093.58600.77513000.095.10850.77514000.096.76390.77515000.098.554815744.233285664

0.811000.092.79250.812000.094.30420.813000.095.95890.814000.097.75950.815000.099.709615744.233285664

0.811610777.893.06570.811611757.694.63220.811612737.496.34740.811613717.298.21480.811614697.0100.2382ramp215426.1997732936

0.823210555.693.32820.823211515.294.94740.823212474.896.72110.823213434.498.65290.823214394.0100.747015108.1662609232

0.834810333.493.58030.834811272.895.25030.834812212.297.08010.834813151.699.07400.834814091.0101.236314790.1327485528

0.846410111.293.82220.846411030.495.54080.846411949.697.42480.846412868.899.47830.846413788.0101.706414472.0992361823

0.8589889.094.05390.85810788.095.81940.85811687.097.75530.85812586.099.86620.85813485.0102.157414154.0657238119

0.94466666679905.595.75220.919333333310806.097.26430.899666666711706.598.92020.884083333312607.0100.72240.871513507.5102.6730ramp314177.6820737404

1.03133333339922.097.47290.980666666710824.098.72620.941333333311726.0100.09700.910166666712628.0101.58570.88513530.0103.191814201.2984236689

1.1189938.599.21651.04210842.0100.20530.98311745.5101.28570.9362512649.0102.45620.898513552.5103.713914224.9147735974

1.20466666679955.0100.98371.103333333310860.0101.70221.024666666711765.0102.48670.962333333312670.0103.33410.91213575.0104.239314248.5311235259

1.29133333339955.0102.77201.164666666710860.0103.21471.066333333311765.0103.69810.988416666712670.0104.21800.925513575.0104.7673flattop214248.5311235259

1.3789955.0104.57911.22610860.0104.74061.10811765.0104.91821.014512670.0105.10650.93913575.0105.296814248.5311235259

1.46466666679955.0106.40541.287333333310860.0106.28021.149666666711765.0106.14691.040583333312670.0105.99950.952513575.0105.828114248.5311235259

1.55133333339955.0108.25141.348666666710860.0107.83381.191333333311765.0107.38461.066666666712670.0106.89730.96613575.0106.360914248.5311235259

1.6389955.0110.11751.4110860.0109.40161.23311765.0108.63131.0927512670.0107.79980.979513575.0106.895514248.5311235259

1.72466666679955.0112.00421.471333333310860.0110.98391.274666666711765.0109.88711.118833333312670.0108.70720.99313575.0107.431714248.5311235259

1.81133333339955.0113.91211.532666666710860.0112.58111.316333333311765.0111.15231.144916666712670.0109.61941.006513575.0107.969614248.5311235259

1.8989955.0115.84181.59410860.0114.19351.35811765.0112.42701.17112670.0110.53651.0213575.0108.509314248.5311235259

2.1987466.3121.04991.8948145.0120.33121.6588823.8119.55521.4719502.5118.71151.3210181.3117.7823rampdown10686.3983426444

2.4984977.5123.80862.1945430.0123.60021.9585882.5123.37411.7716335.0123.11831.626787.5122.81327124.265561763

2.7982488.8124.84182.4942715.0124.82832.2582941.3124.81352.0713167.5124.78511.923393.8124.72313562.1327808815

3.0980.0124.99032.7940.0125.00512.5580.0125.02092.3710.0125.02562.220.0124.99910

3.3980.0124.99033.0940.0125.00512.8580.0125.02092.6710.0125.02562.520.0124.999101.4046639232

temp rise39.9940.0140.0240.0340.00

Trho elecCp

800.00000031850.1938693395

900.00000038760.22281692960.000000353

1000.00000045670.24785632150.2088286416CD"flattop"

1100.00000052580.2691219817110001.04

1200.00000059490.2869343621120000.736

1300.0000006640.3016926781130000.5

1400.00000073310.3138120205140000.313

1500.00000080220.3236890336150000.162

1600.00000087130.3316851518

1700.00000094040.3381201873

1800.00000100950.3432717371

1900.00000107860.3473776425138250.3

2000.00000114770.3506398628

2100.00000121680.3532288182

2200.00000128590.3552876893

2300.0000013550.3569364082

2400.00000142410.3582752291

2500.00000149320.3593878481

2600.00000156230.3603440857

2700.00000163140.3612021703

2800.00000170050.362010666

2900.00000176960.3628100942

3000.00000183870.3636342905

8585858585

85.083798346385.099726957685.117040665585.1357394785.1558233712

85.670667340485.798213046785.936872692486.08665203386.2475572861

87.268939907687.701673839788.172562936488.681739555289.2293469868

90.409866385391.448873135392.582146713693.81069257695.1356078227

91.002498884392.158357930993.420227447194.789542238296.2678780642

91.597142763792.870730401694.262345934695.773913627497.4075576936

92.193813152593.586017019995.108546597196.763878651498.5547595422

92.792525486994.304244847695.958874924797.7595110799.7095995247

93.065689792294.632165987196.347408942898.2148267503100.238221131

93.328230710294.947434671896.721084449398.6529025162100.7470486969

93.580327262495.250254383197.080127643899.0739843461101.236343643

93.822161550595.540832955797.424770704799.4783262302101.7063778988

94.053918656795.81938244597.755251620699.866189966102.1574336665

95.752193041297.264291172798.9202073079100.7223685707102.6729591608

97.472862873298.7261571096100.0969588252101.585687777103.1917625445

99.216490585100.2053491084101.2857179313102.4562454212103.7138732293

100.9836636081101.7022494805102.4867024933103.3341414354104.2393210372

102.772028583103.2147457948103.6981275603104.2180120895104.7672606843

104.5791259748104.7406445467104.9181527818105.1064621148105.2968345091

106.4054138409106.2802221573106.1469197849105.9995463392105.8280541518

108.2513650288107.8337624918107.3845732063106.8973204276106.3609313569

110.1174669231109.4015567559108.6312606606107.7998408757106.8954779731

112.0042212665110.9839034175109.8871327138108.7071650047107.4317059527

113.9121440436112.5811081524111.1523428644109.6193509566107.9696273512

115.8417654225114.1934838108112.4270475292110.5364576911108.5092543269

121.0498649386120.3311601593119.5552372325118.7115127504117.7822904926

123.8085741133123.6002043454123.3741112827123.1182842309122.8131588774

124.8418207964124.8283236827124.8135005759124.7850863205124.7230960517

124.9903414813125.0050613181125.0209034579125.0255837393124.9990750314

124.9903414813125.0050613181125.0209034579125.0255837393124.9990750314

0.2 secrampup

0.2 secrampdown

Coils off

mod coilramp up

1.04s flattop@ 11 kA/cm^2

Ipramp

0.16s flattop@ 15 kA/cm^2

11.0kA/cm^2

12.0kA/cm^2

13.0kA/cm^2

14.0kA/cm^2

15.0kA/cm^2

time (seconds)

Copper temperature (K)

Modular coil current waveform and temperature response(1.7T High Beta Scenario from CDR, adjusted to 653 kA max current)

1.040.3

0.736

0.5

0.313

0.162

Current density in copper (kA/cm^2)

Flattop time (s)

Flattop time vs current density

Temperature vs time

Let:

Tmin =85K-188C

Tmax =150K-123C

Copper spec. heat0.385J/gm-Cat 300Klog Cp =(1.131-9.454*LOG10(B34)+12.99*((LOG10(B34))^2)-5.501*((LOG10(B34))^3)+0.7637*((LOG10(B34))^4))/1000)

Copper density =8.9gm/cc

% IACS at 273K100%





ref cd13825.213825.213825.213825.2A/cm^2

ref Cu area47.247.247.247.2cm^2

Current flattop1507.0460.9414.80






ramp up time1.5sec

flattop1 time0.1

intermed time 20.141

flattop2 time1

ramp down time1.2sec

start of ramp down1.95808sec


Time (seconds)J1Mod coil 1, ~10.7kA/cm^2J2Mod coil 2, ~9.8kA/cm^2J3Mod coil 3, ~8.8kA/cm^2J4Mod coil 4, ~0.0kA/cm^2Coil 2 current (kA/turn)

0085085085085ramp 10

0.3752683.785.18452439.785.15252195.885.12350.085.00003200.9803921569

0.755367.486.10924879.585.91644391.585.74210.085.00006401.9607843137

1.1258051.188.54307319.287.92276587.387.36350.085.00009602.9411764706

1.510734.893.36879758.991.88068783.090.54700.085.000012803.9215686275

1.52510734.893.80429758.992.23468783.090.82940.085.0000flattop112803.9215686275

1.5510734.894.24199758.992.59008783.091.11270.085.000012803.9215686275

1.57510734.894.68179758.992.94688783.091.39690.085.000012803.9215686275

1.610734.895.12359758.993.30518783.091.68200.085.000012803.9215686275

1.628210518.095.61439561.893.70278605.691.99830.085.0000ramp212545.2823529412

1.656410301.196.08789364.794.08608428.292.30290.085.000012286.6431372549

1.684610084.396.54409167.694.45508250.892.59590.085.000012028.0039215686

1.71289867.596.98318970.494.80998073.492.87750.085.000011769.3647058824

1.7419650.697.40538773.395.15097896.093.14790.085.000011510.7254901961

1.82433333339666.798.63268787.996.14137909.193.93270.085.0000ramp311529.931372549

1.90766666679682.899.87968802.697.14567922.394.72710.085.000011549.137254902

1.9919698.9101.14678817.298.16397935.595.53100.085.000011568.3431372549

2.07433333339715.0102.43408831.899.19647948.796.34460.085.000011587.5490196078

2.15766666679715.0103.73998831.8100.24167948.797.16670.085.0000flattop211587.5490196078

2.2419715.0105.06228831.8101.29787948.797.99580.085.000011587.5490196078

2.32433333339715.0106.40128831.8102.36517948.798.83210.085.000011587.5490196078

2.40766666679715.0107.75718831.8103.44357948.799.67550.085.000011587.5490196078

2.4919715.0109.13008831.8104.53337948.7100.52620.085.000011587.5490196078

2.57433333339715.0110.52018831.8105.63447948.7101.38410.085.000011587.5490196078

2.65766666679715.0111.92778831.8106.74707948.7102.24940.085.000011587.5490196078

2.7419715.0113.35308831.8107.87117948.7103.12200.085.000011587.5490196078

3.0417286.3117.41196623.9111.06565961.5105.59690.085.0000rampdown8690.6617647059

3.3414857.5119.59724415.9112.77523974.3106.91440.085.00005793.7745098039

3.6412428.8120.45322208.0113.44271987.2107.42740.085.00002896.887254902

3.9410.0120.62570.0113.57700.0107.53050.085.00000

4.2410.0120.62570.0113.57700.0107.53050.085.000001.4046639232

temp rise35.6328.5822.530.00

Trho elecCp

800.00000021940.1938693395

900.00000028850.2228169296

1000.00000035760.2478563215

1100.00000042670.2691219817

1200.00000049580.2869343621

1300.00000056490.3016926781

1400.0000006340.3138120205

1500.00000070310.3236890336

1600.00000077220.3316851518

1700.00000084130.3381201873

1800.00000091040.3432717371

1900.00000097950.3473776425

2000.00000104860.3506398628

2100.00000111770.3532288182

2200.00000118680.3552876893

2300.00000125590.3569364082

2400.0000013250.3582752291

2500.00000139410.3593878481

2600.00000146320.3603440857

2700.00000153230.3612021703

2800.00000160140.362010666

2900.00000167050.3628100942

3000.00000173960.3636342905

baseline

8585850

85.115898783885.149067006685.09747954343200.9803921569

85.696288445485.895883500585.5855109956401.9607843137

87.216909597487.8567881286.86260942099602.9411764706

90.198888902591.722991448689.359448554512803.9215686275

90.462767217692.068445096689.57918479112803.9215686275

90.72746548792.415261204389.799499966912803.9215686275

90.992984315492.763441465390.02039437812803.9215686275

91.259324339493.112987659790.241868336312803.9215686275

91.554125988493.500206154390.486895187612522.2352941176

91.836916975393.871985517190.721818861712240.5490196078

92.107863577894.228501005690.946793151211958.862745098

92.367141256494.569942947491.161978368611677.1764705882

92.614934250394.896516089491.367541057411395.4901960784

93.343478590995.857398747591.971668747611587.5490196078

94.102727847296.860940850892.600490120611779.6078431373

94.893730515497.908772776193.254790348611971.6666666667

95.717575723299.002599305693.935381964612163.7254901961

96.5619578941100.126321533894.63201984812163.7254901961

97.4139165943101.2628194195.333971922612163.7254901961

98.2734872564102.41218993296.041255836112163.7254901961

99.140707812103.574536781796.753890503612163.7254901961

100.0156186809104.749970293197.471896102312163.7254901961

100.8982627603105.938607421698.195294067612163.7254901961

101.7886854142107.14057171798.924107087912163.7254901961

102.6869344638108.355993299299.658359100412163.7254901961

105.2354130332111.8125995012101.73881087259122.7941176471

106.5931874118113.6665302222102.84318314156081.862745098

107.1220613358114.3912393608103.27252275213040.931372549

107.2283538789114.5370933398103.35874623210

107.2283538789114.5370933398103.35874623210

0.2 secrampup

0.2 secrampdown

Coils off

ramp up

ramp down

1.24 s

Mod coil 1, ~8.5kA/cm^2



Coil 2 current (kA/turn)

time (seconds)

Conductor current (kA)

Conductor temperature (K)

Modular coil current waveform and temperature responsecase 11_02_01-RefScenario_***, (1.2 T)

The design is being done as a collaborationThe concept meets all the physics requirementsThe concepts have margin to accommodate some changes and upgradesThe components will be described staring from the modular coils inward, then from the modular coils outwardPoint out all the components

The concept meets all the physics requirementsThe concepts have margin to accommodate some changes and upgradesThe components will be described staring from the modular coils inward, then from the modular coils outwardPoint out all the components












Documents

Modular Coil Winding Keystoning Issues