# Presentation: 177355

## Mechanical Realignment of Modular Coilsto Mitigate Field Errors from As-Built Coils

- Art Brooks
- 26 April 2007

- AWB042607

## Overview

- Objective
- To adjust alignment of each Modular Coil to balance field errors induced from deviation in current center of as-built coils.
- Explore various alignment schemes for effectiveness and required alignment
- Method
- Generate as-built coils file from metrology data
- at present 12 coils are wound, A1-A4, B1-B3, C1-C5
- Calculate Target Field Errors (b) from VACISLD code
- Used 3/5, 3/6 (symmetric) and 1/2 sine and cosine modes on M50 ref plasma
- Generate family of coils files with unit displacements (1 mm) and rotations  (1 millirad) from as-built coils files
- dr, dth, dz, rx, rth, rz
- Calculate Coupling Matrix (A) of each displacement with each mode for each coil
- Solve SVD problem Ax=b for  coil displacements (x)
- Construct final coil transform from displacements and verify coil performance

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## As Built Coil Data

- There are presently 12 of 18 Coils wound and current centers measured
- A1 thru A4
- B1 thru B3
- C1 thru C5
- Design Goal of +/- .020” achieved over most of coils but not everywhere.
- Coils  wound to match current center achieved on prior wound coils to minimize symmetry breaking field errors.

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## Modular Coil CastingsClamp Numbering

- A

**B**

**C**

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## Modular Coil Winding Cross Section

- Current Center determined
- by averaging
-  Casting Measurements
- (prior to winding)
- and Bundle Measurements
- (after winding) at each turn.

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## As-Built Coil GeometryA1 thru A4 Lateral Current Center Shifts

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## As-Built Coil GeometryA1 thru A4 Radial Current Center Shifts

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## As-Built Coil GeometryB1 thru B3 Lateral Current Center Shifts

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## As-Built Coil GeometryB1 thru B3 Radial Current Center Shifts

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## As-Built Coil GeometryC1 thru C5 Lateral Current Center Shifts

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## As-Built Coil GeometryC1 thru C5 Radial Current Center Shifts

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## Field Errors from As-built Coils

- Differential coil files constructed by adding current center deviations to original coil files and subtracting original coils file (ie reversing current)
-  Differential field added to VMEC field for reference plasma configuration (full current, full beta) within VACISLD code and normal (radial) field on resonant surfaces computed. Island size estimated from Bmn.
- VACISLD code originally written as a module for Stellopt, the suite of codes used to design Modular Coils and Plasma

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## Li383 Targeted Resonances

- 3/7 near axis and 6/9 near edge not targeted

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## Island Width Evaluation used in VACISLD using VMEC data

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## Field Error from All Coils not much different than worse coil taken separately 

- Winding Error Only – Assumes Coil Perfectly Positioned

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## Some Possible Alignment Schemes

- Align each coil to target it’s own field errors
- Pro: No Impact on assemble schedule
- Con: Requires larger displacements and can target fewer resonances (at most 6, more practically only 4)
- Align all coils of each type to target collective field errors
- Pro: More dofs can target more resonances with smaller displacements
- Pro: All coils of same type carry same current
- Con: Requires all coils wound before first coil can be assembled (schedule impact)
- Align all coils of a given period to target collective field errors
- Pro: More dofs (than single coil) can target more resonances with smaller displacements
- Pro: No Schedule Impact (coils are assembled by period)
- Con: Coil types carry different currents. Effectiveness may drop as currents change

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## Coil Displacements and Rotations madeRelative to Local Coordinate Systems

- 3rd Period

- y

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## Effect of Displacements and Rotations on Sine Phase of 3/5 Resonance for C1 as-built Coil

- Coupling fairly linear, but not independent
- Some displacements ineffective

- Similar
- Behavior
- Found with
- Other Coils
- And Modes

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## Field Error Reduction for Each Coil Independently Correcting their Own Errors*

**A1-A4**

- *Note: Only 4 modes targeted due to ill-conditioning

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## Field Error Reduction for Each Coil Independently Correcting their Own Errors*

- *Note: Only 4 modes targeted due to ill-conditioning

- C1-C4

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## Field Error Reduction for All Type C Coils Collectively Correcting the Net Errors

- Note: Targeting 6 modes with 24 dof
- More modes may be feasible. Not yet explored

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## Required Realignment MovementsWith Each Coils Targeting It’s Own Field Error 

- Movements are large relative to coil winding tolerance of +/- 0.5 mm
- Makes Coil Assembly (flange, shim mate up) more difficult
- Also induces fear of the unknown (what else is it doing)

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## Required Realignment MovementsEach Coil Type Targeting Their Own Field Error

- Movements are significantly smaller than when aligning coils independently.
- Comparable to coil winding tolerance of +/- 0.5 mm

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## Required Realignment MovementsAll Coils in Period Target Collective Field Error

- Movements are much smaller than when aligning coils independently.
- Much less than coil winding tolerance of +/- 0.5 mm
- Minimizes impact on coil assembly.
- Results for Period 1. Need B4 before Period 2 can be evaluated.

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## Points for Discussion

- What is the preferred Mechanical Alignment scheme?
- Can we tolerate aligning full period together?
- If the required motions are very small, should we just not bother?
- Are the right modes being targeted?
- Are the near resonance a concern (2/3)?
- Other plasma scenarios with different iota profiles?
- How to assess damage caused by non resident fields (ie at boundary)? Or do we care?
- Max field ~20 Gauss or higher if individual coils targeted
- Is Mechanical Alignment a reasonable starting point for the Magnetic Alignment (if Project Approves) or is it better to do nothing?
- Not clear that they target the same thing.

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