A practical method for performing a tokamak equilibrium reconstruction
in real time for arbitrary time varying discharge shapes and current
profiles is described. An approximate solution to the Grad-Shafranov e
quilibrium relation is found which best fits the diagnostic measuremen
ts. Thus, a solution for the spatial distribution of poloidal flux and
toroidal current density is available in real time that is consistent
with plasma force balance, allowing accurate evaluation of parameters
such as discharge shape and safety factor profile. The equilibrium so
lutions are produced at a rate sufficient for discharge control. This
equilibrium reconstruction algorithm has been implemented on the digit
al plasma control system for the DIII-D tokamak. The first application
of real time equilibrium reconstruction to discharge shape control is
described.