PermanentMagnetDesign

Matlab software for designing magnets with permanent magnet cubes. Used in the course on that topic (1FA362) at Uppsala University.

The theory behind the code is described in two publications. Check them out for the details

• V. Ziemann, Closed-form expressions for the magnetic field of permanent magnets in three dimensions, arXiv:2106.04153, June 2021.

• V. Ziemann, Strap-on magnets: a framework for rapid prototyping of magnets and beam lines, Instruments 2021 5(4) 36, December 2021 and arXiv:2106.14676, June 2021.

Here is an image of a prmanent-magnet quadrupole with eight cubes

The description of the MATLAB files to handle cubes:

• README.md

  • this file

• PM_multipoles.m

  • main program to design multipole magnets, all plots are copied into a subdirectory named tmp/

• PM_solenoid_axial.m

  • main program to design axial solenoids all plots are copied into a subdirectory named tmp/

• PM_solenoid_radial.m

  • main program to design radial solenoids all plots are copied into a subdirectory named tmp/

• Bsheets.m

  • Bout=Bsheets(sheets,r2)
  • returns the field 'Bout(r2)' from the 'sheets'

• draw_sheets.m

  • draw_sheets(sheets)
  • draws the geometry of the 'sheets'

• field_along_line2.m

  • Bline=field_along_line2(sheets,line)
  • returns the field 'Bline' along the 'line' generated by the 'sheets'

• field_from_sheets2D.m

  • field_from_sheets2D(gx,gz,sheets,limit)
  • generates an arrow plot on a plane specified by the gridpoints 'gx' and 'gy' 'limit' prevents drawing very large arrows

• field_from_sheets3.m

  • field_from_sheets3(gx,gy,gz,sheets,limit)
  • generates an arrow plot on the grid specified by 'gx', 'gy', and 'gz'

• make_cubez.m

  • sheets=make_cubez(a,alpha,Br)
  • returns the sheets of a cube with size 'a', aspect ratio 'alpha', and remanent field 'Br'

• make_brick.m

  • sheets=make_brick(a,b,c,Br)
  • returns the sheets of a brick with the specified sides.

• make_polygon_hollow.m

  • sheets=make_polygon_hollow(n,ri,ro,h,Br)
  • returns the sheets of a hollow polygon with 'n' sides, inner radius 'ri', outer radius 'ro', and height 'h'.

• make_polygon.m

  • sheets=make_polygon(n,r,h,Br)
  • returns the sheets of a polygon with 'n' sides, radius 'r', and height 'h'.

• sheets_rotate.m

  • out=sheets_rotate(sheets,R)
  • returns the 'sheets' after transfroming them with a 3x3 rotation matrix 'R'.

• sheets_rotate_x.m

  • out=sheets_rotate_x(sheets,phi)
  • rotates the sheets by angle 'phi' (in degree) around the x-axis there are corresponding functions to implement rotations around the other two axes.

• sheets_translate.m

  • out=sheets_translate(sheets,dx)
  • returns the 'sheets' after translating them by 'dx'.

Matlab files in subdirectory filament/ to handle current filaments

• field_of_current_filament.m

  • generates a plot with field around a single wire.

• Bline.m

  • B=Bline(I,ra,rb,r2)
  • returns the field 'B(r2)' at 'r2' created by a line segment from 'ra' to 'rb' that carries the current 'I'.

OpenSCAD files in the subdirectory openscad/

• Frame.scad
  • generates a very simple frame for multipoles

Disclaimer

I do not claim that this software serves any purpose. You use it at your own risk.