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Perturbation of vacuum magnetic fields in W7X due to construction errors

Outline:

• Introduction concerning the generation of magnetic islands

• Sensitivity of the magnetic configuration with iota=1

• Asymmetric target loads due to error fields

• Impact of the perturbation fields on high and low iota case

• Effect of coil shift

• Effect of coil declination• Conclusion

T. Andeeva Y. Igitkhanov J. Kisslinger

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Johann Kißlinger

• inexact coil shape

• positioning errors during assembly (shift and declination)

Four assembly steps

• coil imbedding • half module assembly• module assembly• device integration

Construction error possibilities

The construction errors produce symmetry breaking perturbations.

• introduce new island at any periodicity

• modify existing islands• generate and enhance stochastic regions

Perturbations due to inexact coil shape and positioning errors of single coils: Dr. Andreeva’s talk.

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Johann Kißlinger

target

Island geometry

x-point

reso

nant

radi

al fi

eld

ri ~ √ (bmn/('*m))

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Johann Kißlinger

cross-section #cross-section #

Difference of deviation aab14-aab17

Simulation of deviation with different wave length

nlen = 3

nlen = 5nlen = 1

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Johann Kißlinger

Sensitivity of the system

Perturbation by declination of modular coils of 0.02° along a helical axis with m=1

resonant fourier component B11/Bo 1.7*10- 4 , average displacement 0.28mm, max. displacement 0.55mm

= 0°

= 36°

= 72°

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Johann Kißlinger

Perturbation with mainly B22 field component

lateral and radial deviation of up to 7 mm

data set: dl07 ds07 l5 s07

B11/Bo 0.3*10- 4 , B22/Bo 1.9*10- 4

deviation: average 3.6mm

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Johann Kißlinger

Statistical declination of whole modules up to 0.1°

= 0°

= 180°

This specific distribution: B11/Bo 2.3*10- 4 , deviation: average max. 2.3 7.4mm

30 different distributions: fourier coef. B11 B22 B33 B44

average 1.9 0.5 0.3 0.1 max. value 4.4 1.0 0.6 0.2 average dev. 3.4 mm

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Johann Kißlinger

Statistical declination of whole modules up to 0.1°

= 0°

B11/Bo 2.3*10- 4

B11/Bo 1.7*10- 4

declination of modular coils of 0.02° along a helical axis

= 180°

first contact with target

9Johann Kißlinger magnetic field perturbation

period 1

period 2

period 3

period 4

period 5

top target bottom targets

each field period is statistically rotated by 0.1° (3 axis).

Footprints on targets with perturbed field, standard case

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Johann Kißlinger

Statistical shift of whole modules up to 3mm

10 different distributions: fourier coef. B11 B22 B33 B44

average 0.5 0.6 0.2 0.1 max. value 1.1 1.2 0.35 0.15 average dev. 1.75 mm

This specific distribution: B11/Bo 1.1*10- 4 , deviation: average 2.5 max. 3mm

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Johann Kißlinger

high iota standard case low iota

Equal perturbation have different influences at different iota values

FP 2 FP3

x ≈ R* Bmn /(( - r)*m)

with - r >>' x

12Johann Kißlinger magnetic field perturbation

period 1

period 2

period 3

period 4

period 5

each field period is statistically rotated by 0.1° (3 axis).

Footprints on targets with perturbed field, high iota

bottom targetstop targets

13Johann Kißlinger magnetic field perturbation

period 1

period 2

period 3

period 4

period 5

each field period is statistically rotated by 0.1° (3 axis).

Footprints on targets with perturbed field, low iota

bottom targetstop targets

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Johann Kißlinger

Partly compensation of the field component B11

by use of the control coils with individual currents

FP1 2 3 4 5Currents in control coils top 10 -15 -18 0.0 25 kA bottom 0.0 25 10 -15 -18 kA

Field perturbation by statistical declination of 0.1° around 3 axis of whole periods, no compensation

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Compensation by a constant horizontal magnetic field

Field perturbation by statistical declination of 0.1° around 3 axis of whole periods.Compensation of B11 component with Bx = 12G.

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Coordinate system for the coils

M´

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Coordinate system for the coils

M´

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T. Andreeva

Assumptions and scheme of modeling

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7 real and 43 simulated coils

AN11 = 1.3G; AN22 = 1.12G

T. Andreeva

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Effect of coil shifts on B

T. Andreeva

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Effect of rotation on B (-varies)

T. Andreeva

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Effect of rotation on B (-varies)

T. Andreeva

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Effect of rotation on B (-varies)

T. Andreeva

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Effect of rotation on B (=)

T. Andreeva

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Effect of shift and rotation on B (degree

T. Andreeva

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Effect of shift and rotation on B (=0.1 degree)

T Andreeva

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Effect of shift and rotation on B (=0.2 degree)

T. Andreeva

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Tamara Andreeva

Effect of shift and rotation on B (=0.3 degree)

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x10-4

B for an average deviation of 1mm caused by different types of coil errors

x10-4

Average perturbation Maximum perturbation

T. Andreeva

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Conclusions:

• Deviations with an average value of 1.5 to 2mm with a statistical distribution may generate effective field perturbations in the range of 2*10-4 given by the proposal.

• Mainly the m=1, n=1 island appears.

• The field perturbation go almost linearly with the amplitude of the deviation.

• Due to the low-order islands the load on the targets is asymmetric.

• In the high iota configuration the centre region is displaced while the edge region is not

so strong influenced.

• The more systematic deviations due to rotation of coils and whole modules is more

effective in producing low order B perturbations then the deviations of coil shape

and shift errors.

• The small scale deviations of the manufacturing errors enhances the stochastic structures at the edge.• The control coils are not very effective for compensating low-order error fields.

Outlook: Continue the calculation in collaboration with the engineering team. Compensation of the low order error fields with the planar coils should be more effective but needs extra current feeders. Consider the possibility of evaluation of scaling law for the magnetic field perturbations.