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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:
Transcript
Specifying a magnetKey: A coil Position of upstream edgeInner radiusCurrent in coilConductorUpstreamDownstreamThis 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 magnetSpectrometer Solenoid parametersFitting a field mapMixing/Scaling fit procedure:Make two detailed field maps with parameters that “bracket” our best guess at the real parametersOriginal magnet“Long, thin” bracketing magnet“Short, fat” bracketing magnetFitting 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 parametersLong, thin bracketing magnet ():Example, all coils 3mm longer and thinnerShort, fat bracketing magnet ():Example, all coils 3mm shorter and fatterFitting 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 fieldsHow 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-15Test 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 pointsMany grid pointsFitting 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 returnszoomed y-scaleFitting 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 returnszoomed y-scaleImprovements 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 offsetrotations+ in/out of screen
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