SIMION®
The field and particle trajectory simulator
Industry standard charged particle optics software
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SIMION v8.1.3.0-TEST posted.
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Current Density

Current density \v{j} is a vector field in the same direction as current \v{I} but with magnitude of current per area. It may also be represented as \v{j} = \rho \v{v_d}, where \rho is charge density (i.e. charge per volume) and \v{v_d} is the drift velocity of charged particles. Current density is related to electric field via \v{j} = \sigma \v{E} via the conductivity constant \sigma of the material. See Wikipedia:Current_density for background.

SIMION specific

SIMION in its poisson solver (in Early Access Mode) can solve for current density throughout space when given a conductivity (\sigma) throughout space and boundary conditions on electric potential. The governing Poisson Equation is

\div (\sigma \grad \phi) = 0

which is the same as equation used in dielectrics problems \div (\epsilon \grad \phi) = 0 but with the dielectric constant \epsilon replaced with \sigma.

SIMION Early Access Mode can also utilize a known distribution of current density for calculating (vector) Magnetic Potential and hence magnetic fields. (See Magnetic Potential for details.)

Note

This page is abridged from the full SIMION 8.1.1 “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:
  • SIMION Modeling Details - Calculating current density from conductivity
  • Plotting current density vector fields
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