AWB 010801 1

Status of Trim Coil Design

� Helical Post , Sawtooth, Wavy Modular Coils andSaddles� Perceived as truncated helical windings� How large do they need to be?

� Generate series of windings of varying height centered oninboard mid-plane and compare coupling matrices

� Window Pane ( alias Picture Frame ) Coils� Where are they most effective?

� To answer, cover a winding surface with small window panecoils ( effectively dipoles ) and calculate coupling matrix

� Use 1826 surface for now until better surface(s) defined byengineering

AWB 010801 2

[9,6]

[5,3]

[6,3]

[7,3]

Li383 Fixed Boundary

0.30

0.35

0.40

0.45

0.50

0.55

0.60

0.65

0.70

0.00 0.25 0.50 0.75 1.00

S

iota

Li383 ResonancesFor PVR, focus is on [5,3] and [6,3]

AWB 010801 3

Helical Post for m=5

Shown for 3 Periods

360 degHelical PostEquivalent toHelical Winding and Wavy PF at u=0.

AWB 010801 4

Impact of Poloidal Extent on Coupling

Helical Post Coupling for m=5

0.E+00

2.E-07

4.E-07

6.E-07

8.E-07

1.E-06

1.E-06

0 0.1 0.2 0.3 0.4 0.5 0.6

Half Height, du

|ds^

2| =

16*

Cm

n/(

m*i

ota

')

|ds^2| = 1.e-7 corresponds to 1 kA to control a 1% flux island

Wound on 1826 surface

AWB 010801 5

Sawtooth Coils for m=5

360 degSawtoothEquivalent toHelicalWinding andWavy PF atu=0.5

Shown for3 Periods

AWB 010801 6

Impact of Poloidal Extent on Coupling

Wound on 1826 surface

Sawtooth Coupling to m=5

0.E+00

2.E-07

4.E-07

6.E-07

8.E-07

1.E-06

1.E-06

0 0.1 0.2 0.3 0.4 0.5 0.6

Half Height, du

|ds^

2| =

16*

Cm

n/(

m*i

ota

')

AWB 010801 7

Wavy Modular for m=5

360 deg WavyModularEquivalent toHelicalWinding andPlanar Mod atv=0.5

Shown for3 Periods

AWB 010801 8

Impact of Toroidal Extent on Coupling

Wavy Modular Coupling for m=5

0.E+00

2.E-07

4.E-07

6.E-07

8.E-07

1.E-06

1.E-06

0 0.1 0.2 0.3 0.4 0.5 0.6

Half Width, dv

|ds^

2| =

16*

Cm

n/(

m*i

ota

')

Wound on 1826 surface

AWB 010801 9

Saddles for m=5

360 deg SaddlesEquivalent toHelical Windingand Planar Mod atv=0.0 & 0.5

Shown for3 Periods

AWB 010801 10

Impact of Toroidal Extent on Coupling

Saddles for m=5

0.E+00

1.E-07

2.E-07

3.E-07

4.E-07

5.E-07

6.E-07

7.E-07

8.E-07

9.E-07

1.E-06

0 0.1 0.2 0.3 0.4 0.5 0.6

Width, dv

|ds^

2| =

16*

Cm

n/(

m*i

ota

')

Unit currents in each Saddle Wound on 1826 surface

AWB 010801 11

Impact of Extent on Coupling

Coil Coupling to m=5

0.00E+00

2.00E-07

4.00E-07

6.00E-07

8.00E-07

1.00E-06

1.20E-06

0 0.1 0.2 0.3 0.4 0.5 0.6

Half Height(Width), du(dv)

|ds^

2| =

16*

Cm

n/(

m*i

ota

')

Modular

Helical Post

Sawtooth

Saddle

m=5 Helical

Note: Coil extent given in u-v space. Real space comparison may differ

AWB 010801 12

Initial 5 x 7 Window Pane Array

Wound on 1017 ModularCoil winding surface.

AWB 010801 13

Initial 5 x 7 Window Pane ArrayCurrents for Assumed Island Sizes

Target ( ds 2 ) I_max, KA I_m in, KA Sum(I**2)m5 = .0025 only 34.4 -45.3 4.44E+09m5=.0025, m6=0. 35.0 -42.7 4.95E+09m6=.0025 only 266.7 -593.3 6.22E+11

ds^2 = .0025 is a 5% flux island Bn on boundary not targeted( or evaluated - TBD)

AWB 010801 14

5 x 7 Window Pane ArrayCoupling Matrix

Window Pane Coils on Modular Coil Winding SurfaceWP1 WP2 WP3 WP4 WP5 WP6 WP7 WP8 WP9

B.n/Ic s iota'Boundary 1 1.9E-08 6.4E-09 2.3E-08 4.7E-09 1.8E-08 2.6E-08 1.5E-08 3.0E-08 1.0E-08

ds 2/Ic9,2 0.92 0.019 1.5E-09 -4.6E-09 2.6E-08 2.6E-10 -4.3E-08 -1.2E-07 -5.6E-09 1.8E-08 -4.5E-115,1 0.63 0.318 -7.2E-09 4.2E-10 2.1E-09 -4.7E-10 -2.2E-09 -2.5E-08 -2.6E-09 8.4E-09 2.4E-116,1 0.29 0.286 -2.4E-09 1.3E-10 -8.7E-10 -1.1E-10 1.1E-09 -1.0E-09 2.1E-10 -9.5E-10 -2.6E-107,1 0.08 0.399 2.9E-11 -2.8E-12 1.4E-11 1.3E-12 -2.2E-11 4.7E-11 -8.7E-12 1.1E-11 -1.6E-12

B.n(gauss) for ds=.059,2 0.92 0.019 315.2 -34.5 21.8 452.1 -10.5 -5.4 -67.2 40.8 -5625.45,1 0.63 0.318 -66.5 379.3 276.2 -253.6 -208.6 -25.3 -145.7 89.2 10741.66,1 0.29 0.286 -202.1 1245.9 -654.9 -1072.4 421.8 -628.0 1810.4 -787.5 -981.77,1 0.08 0.399 16395.4 -57684.7 39694.0 91465.6 -20204.8 13654.0 -43617.1 68717.2 -154230.4

Ic(KA) for ds=.059,2 0.92 0.019 1634.6 -540.3 95.3 9584.4 -58.0 -21.0 -443.1 136.7 -55543.25,1 0.63 0.318 -345.1 5937.7 1208.2 -5375.8 -1153.0 -98.2 -960.4 299.0 106058.06,1 0.29 0.286 -1047.9 19502.3 -2864.9 -22735.5 2331.4 -2438.1 11931.5 -2639.5 -9692.9

AWB 010801 15

5 x 7 Window Pane ArrayCoupling Matrix

WP10 WP11 WP12 WP13 WP14 WP15 WP16 WP17 WP18B.n/Ic s iota'Boundary 1 2.3E-08 3.2E-08 1.6E-08 1.5E-08 1.0E-08 1.1E-08 1.7E-08 1.6E-08 6.6E-09

ds 2/Ic9,2 0.92 0.019 -1.7E-08 7.3E-08 8.9E-09 2.0E-09 -3.2E-08 7.5E-09 3.3E-08 2.1E-08 -6.7E-105,1 0.63 0.318 -8.6E-09 1.9E-08 -5.3E-10 1.4E-09 -6.7E-09 1.1E-09 8.9E-09 6.5E-09 -6.1E-126,1 0.29 0.286 8.9E-11 4.5E-10 -5.3E-11 -5.3E-11 -1.7E-10 6.8E-12 3.7E-11 -3.4E-10 2.0E-117,1 0.08 0.399 -1.4E-11 6.2E-11 -8.6E-12 4.5E-12 -2.0E-12 -6.1E-12 7.3E-12 -1.0E-11 -2.3E-12

B.n(gauss) for ds=.059,2 0.92 0.019 -33.2 10.8 44.6 188.1 -7.9 35.7 12.4 19.9 -244.75,1 0.63 0.318 -66.4 40.9 -742.7 278.8 -38.0 239.3 46.4 63.3 -27068.16,1 0.29 0.286 6438.6 1763.3 -7486.1 -7328.3 -1464.8 39289.2 11053.4 -1218.1 8356.67,1 0.08 0.399 -41660.6 12781.1 -45761.0 84969.3 -130142.6 -43570.2 56562.1 -40478.9 -71070.9

Ic(KA) for ds=.059,2 0.92 0.019 -144.6 34.2 282.2 1220.7 -77.5 335.0 74.9 120.8 -3715.35,1 0.63 0.318 -289.4 129.1 -4700.2 1809.6 -371.4 2242.8 281.3 384.1 -410994.96,1 0.29 0.286 28073.2 5563.8 -47374.5 -47562.0 -14326.6 368221.1 66957.7 -7390.3 126884.2

AWB 010801 16

24 x 24 �Dipole� Array with Unit Currents

Finer Mesh with fullcoverage on 1826 surface

Still finer mesh requires codemodifications not yet complete

AWB 010801 17

24 x24 Dipole ArrayCoupling Matrix

ds^2=2.81e-6 ds^2=3.59e-7

AWB 010801 18

Grouping Of Like Sign Dipoles RevealsHelical Winding with some Modulation

M = 5 Helical Winding M = 6 Helical Winding

Contours of dipole currents shows same pattern

AWB 010801 19

Dipoles Uniform in u-v, Not Real Space

Real Space Area Distributionfor uniform du*dv

AWB 010801 20

Adjusting for Area, Dipoles want to beinboard at bean section

AWB 010801 21

Coupling Strength Appears Driven byLocal Distance to Resonance Surface

Plots of 1/d**m

AWB 010801 22

Should be able to Realize ~50% ofCoupling for only ~20% of coverage

m5

0.0E+00

5.0E-07

1.0E-06

1.5E-06

2.0E-06

2.5E-06

3.0E-06

0 50 100 150 200 250 300

Number of Dipoles

To

tal

|ds

^2

|

m6

0.0E+00

5.0E-08

1.0E-07

1.5E-07

2.0E-07

2.5E-07

3.0E-07

3.5E-07

4.0E-07

0 50 100 150 200 250 300

Number of Dipoles

To

tal

|ds

^2

|

AWB 010801 23

24x24 Dipole ArrayCurrents for Assumed Island Sizes

ds^2 = .0025 is a 5% flux island Bn on boundary not targeted( or evaluated - TBD)

All Dipoles Retained

Targe t ( ds^2 ) I_max, KA I_m in, KA Sum(I**2)m5 = .0025 only 1.9 -1.9 9.71E+07m5=.0025, m6=0. 1.9 -1.9 9.87E+07m6=.0025 only 18.6 -14.4 2.74E+09

AWB 010801 24

24x24 Dipole ArrayCurrents for Assumed Island Sizes

ds^2 = .0025 is a 5% flux island Bn on boundary not targeted( or evaluated - TBD)

Dipoles eliminated at [-.125 < u < +.125], [-.250 < v < +.250]For NB access

Target ( ds 2 ) I_max, KA I_m in, KA Sum(I**2)m5 = .0025 on ly 3.0 -2.8 1.86E+08m5=.0025, m6=0. 3.8 -4.5 2.11E+08m6=.0025 only 37.7 -33.2 6.98E+09

AWB 010801 25

24x24 Dipole ArrayCurrents for Assumed Island Sizes

ds^2 = .0025 is a 5% flux island Bn on boundary not targeted( or evaluated - TBD)

Dipoles eliminated at [-.125 < u < +.125], [-.250 < v < +.250] for NB access plus all inboard dipoles [.25 < u < .75]

Target ( ds 2 ) I_max, KA I_m in, KA Sum(I**2)m5 = .0025 on ly 4.8 -5.3 3.75E+08m5=.0025, m6=0. 5.3 -4.8 3.92E+08m6=.0025 only 72.2 -92.7 4.84E+10

AWB 010801 26

Further Plans

� Resolve difficulties representing winding surface receivedfrom engineering

� Pursue alternate locations proposed ( ie inside VV )� Identify additional block-out regions on winding surface

dictated by machine access needs� Discretize dipoles into larger Window Panes ( or other

topology ) based on results� Verify ability to target multiple resonances is retained with (

hopefully ) a single layer of coils� Complete code modifications required to refine dipole mesh (

needed to provide smoother solution )

� Demonstrate effectiveness of resultant coil set by runningthru PIES

AWB 010801 27

Summary

� Topology scan did not reveal any strongpreference when targeting individual m=5 mode

� Dipole investigation has so far shown:� Most effective regions are those closest to resonance

which for li383 occurs at v=0 section inboard andoutboard ( neither of which is very accessible )

� By excluding those regions, current demands increasesignificantly ( ~ 3 � 5 x )

� Whether this is acceptable depends on targetrequirements ( ds^2 TBD ) and final surface location