Anisotropically Scaled Grid Cells in SIMION



Fig. 23 Figure: PA with non-square grid cells.

As of SIMION 8.1, potentials array grid cells can be anisotropically scaled (rather than isotropically scaled), which means that the grid density in the X, Y, and Z directions can be scaled by different amounts. This allows grid cells to be narrow rectangles (2D) or rectangular boxes (3D), rather than just squares and cubes as permitted in previous versions of SIMION.

The anisotropic scaling support utilizes a new feature in SIMION 8.1.0, also described here, where you can store the X, Y, Z cell lengths in mm inside the PA file (rather than or in addition to using the PA instance scale factor in the workbench IOB). This feature can be useful even for isotropically scaled PAs. It is required, for example, in the Poisson Solver in SIMION, and it can provide convenience in Laplace conditions as well.

Purpose of Anisotropic Scaling

The anisotropic scaling feature allows certain geometries, particularly some geometries that are long in one direction, to be more efficiently and/or accurately modeled. As an example, you may have long multipole rods or a narrow lens system where the grid density in the radial direction is much more critical that the grid density in the axial direction, particularly if there are surface errors due to curved electrodes that don’t align to grid lines. With anisotropic scaling, you can set the axial grid density to be finer than the radial grid density. (2D planar arrays, such as used in the “quad” example, may be effective too though.) Anisotropic scaling may also in some cases permit better alignment of surfaces to grid units for higher accuracy.

Purpose of Storing Cell Lengths in PA Files

Prior to SIMION 8.1.0, potential array files didn’t contain an explicit physical size. Their sizes were measured instead in unitless/dimensionless “grid units”. It wasn’t until you projected an “instance” of a potential array on a workbench (IOB) and assigned a mm/gu scaling factor on that instance that the physical size became known.

This changed some in SIMION 8.1.0, where the X, Y, Z cell lengths in mm can optionally be stored in the PA file itself. This feature is somewhat necessary for the Poisson Solver in SIMION, where the absolute physical size of the array (and its space-charge) is not arbitrary as is true in the Laplace solver. This feature is also helpful when grid cells are anisotropically scaled (i.e. X, Y, Z cell lengths are different), so the Laplace solver needs to know these cell lengths (actually only their relatively lengths, although having absolute lengths doesn’t hurt). This feature is also convenient in visualizing PAs not yet added to IOB’s–e.g. seeing real mm units in the Modify 3D preview screen.

SIMION 8.1.0 still allows you to interpret these PA cell lengths as relative values, if you wish, and you are still allowed to rescale instances of the arrays on the workbench using a scaling factor. In particular, SIMION 8.1.0 always assumes SIMION 8.0 formatted PA files have cell lengths of 1 mm/gu (i.e. mm = gu), so any PA instance scaling factor that multiplies these lengths can still be understood as a mm/gu scaling factor if you wish, so full backward compatiblity with SIMION 8.0 is maintained.


This page is abridged from the full SIMION "Supplemental Documentation" (Help file). The following additional sections can be found in the full version of this page accessible via the "Help > Supplemental Documentation" menu in SIMION 8.1.1 or above:
  • PA Changes
  • Effect on Refine
  • Effect on the Workbench and View Screen
  • Effect on Magnetic Arrays (ng Scaling Constant)
  • Effect on the Fly’m
  • PA File Format
  • IOB Format Changes
  • Refine
  • Geometry Files
  • STL Import
  • User Programs
  • Lua Potential Array Interface
  • SL Libraries
  • Double and Halve Functions
  • 3D Visualization

Gradient Contour Plots

The potential contours, gradient contours, and PE views should work with anisotropically scaled arrays.


This page is abridged from the full SIMION "Supplemental Documentation" (Help file). The following additional sections can be found in the full version of this page accessible via the "Help > Supplemental Documentation" menu in SIMION 8.1.1 or above:
  • Other Assorted Changes
  • Other [FIX-TODO] Items

See Also

See Electrode Surface Enhancement / Fractional Grid Units for more accurately handling surfaces that do not align to PA grid units (e.g. curved surfaces).


  • - SLTools(STL->PA): Fixed non-“square cells” with “region rotate” defined. mm/gu sizes were being applied to wrong axes, causing obvious distortions to geometric aspect ratio.
  • - Fixed GEM file handling of 0.5 grid unit (gu) surface adjustment in within/notin commands when using anisotropically scaled grid cells. See above and SIMION Software Change Log for more details.