An inversion technique has been developed to generate high resolution 2-D images of the plasma density and current profiles from interferometer and polarimeter data collected at arbitrarily positions and viewing angles through a tokamak plasma. This technique satisfies Maxwell's Equations for a toroidal geometry, and may be utilized in the presence of significant levels of refraction.

Maxwell's Equations in a Toroidal Geometry

The toroidal coordinate system is shown below, and may be represented by the following equations:

Coordinates Coordinate Equations
Maxwell's Equations in a toroidal geometry read as:

Coordinate Equations
From these equations, the magnetic profile may be exapanded as:

Coordinate Equations
These surfaces are shown below.
Zero order magnetic surfaces Zero order surfaces with an m=1 shift
Zero order surfaces with an m=2 shift Zero order surfaces with an m=3 shift

For more information, contact Ross Geck at geck@ece.ucdavis.edu.