Specifying a magnet
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Specifying a magnet. Key: A coil Position of upstream edge Inner radius Current in coil Conductor. Upstream. Downstream. This is a generic magnet, it’s not meant to look like the SS or AFC. We can model any magnet we want!. Fitting a field map. Two methods:

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Specifying a magnet

Key: A coil

Position of upstream edge

Inner radius

Current in coil

Conductor

Upstream

Downstream

This is a generic magnet, it’s not meant to look like the SS or AFC. We can model any magnet we want!


Fitting a field map

  • Two methods:

    • Mixing/scaling fit

    • Full 20+ parameter coil fit – takes FOREVER for SS

  • Mixing/Scaling fit procedure:

  • Take data in cylindrical co-ordinates

    • In this case using a pre-calculated map based on SS.

  • Make two detailed field maps with parameters that “bracket” our best guess at the real paramters

  • Minimise for “best fit” parameters:

    • Mixing of the detailed field maps

    • Length scale of the detailed field maps

    • Field scale of the detailed field maps


Fitting a field map

  • Mixing/Scaling fit procedure:

  • Take data in cylindrical co-ordinates

    • In this case using a pre-calculated map based on SS.

Again, a generic magnet

Spectrometer Solenoid parameters


Fitting a field map

Mixing/Scaling fit procedure:

Make two detailed field maps with parameters that “bracket” our best guess at the real parameters

Original magnet

“Long, thin” bracketing magnet

“Short, fat” bracketing magnet


Fitting a field map

  • What do we mean by “detailed”?

    • Measured field on some grid

    • Bracket fields on finer grid, calculated over more points

Mixing/Scaling fit procedure:

Make two detailed field maps with parameters that “bracket” our best guess at the real parameters

Long, thin bracketing magnet ():

Example, all coils 3mm longer and thinner

Short, fat bracketing magnet ():

Example, all coils 3mm shorter and fatter


Fitting a field map

  • Mixing/Scaling fit procedure:

  • Minimise for “best fit” parameters:

    • Mixing of the detailed field maps

    • Length scale of the detailed field maps

    • Field scale of the detailed field maps

, where

, where is a linear scaling of

, where is a linear scaling of

  • Compare to data:

    • is calculated on a finer grid to the data

    • Interpolate to data grid and calculate of each component at each grid point

    • Sum over all grid points and field components

    • Best fit = min

    • Have “best” values of


Aside: Interpolating fields

How well does this work?

(weakest link)

  • Compare to data:

    • is calculated on a finer grid to the data

    • Interpolate to data grid and calculate of each component at each grid point

Test 1:

Calculate field, , on some fine grid spacing,

Calculate field, , an a coarse grid spacing,

Interpolate onto grid 

Subtract “equivalent” fields

Plots show , for all co-ordinates, along (will make more sense after next slide)

1e-15

Test 2:

Calculate field, , on some coarse grid spacing,

Calculate field, , an a fine grid spacing,

Interpolate onto grid 

Subtract “equivalent” fields

Lesson: Make sure the bracketing fields are calculated on a finer grid than the data!


Fitting a field map

  • Fit returns parameters , and we know how we created the “bracket” fields.

  • How well do they compare to the “measured” data?

at

at

Few grid points

Many grid points


Fitting a field map

  • Fit returns parameters , and we know how we created the “bracket” fields.

  • How well do they compare to the “measured” data?

at

at

With no measurement smearing, fit returns

zoomed y-scale


Fitting a field map

  • Fit returns parameters , and we know how we created the “bracket” fields.

  • Add a 20mT field error to the “measurement” and use the same bracket fields?

at

at

With no measurement smearing, fit returns

zoomed y-scale


Improvements to come:

  • Need to account for longitudinal offset + two rotations

    • This is included in the 20+ parameter fit, but is far too slow for the SS map

  • Adding Fourier-Bessel fit to account for residual field (green plots) will improve our map further.

    • Also helps account for Virostek plate

longitudinal offset

rotations

+ in/out of screen


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