An approach to rapid plasma shape diagnostics in tokamaks

A study is made of a diagnostic procedure which allows one to estimate the plasma boundary shape and location in a tokamak by using numerical values of the poloidal magnetic flux function ψ in the vicinity of the plasma. In the case of the Impurity Study Experiment (ISX-B) tokamak, the magnetic sensor coils located around the periphery of the vacuum chamber provide information on ∂ B R /∂ t and ∂ B z /∂ t , which can be processed to obtain data on ψ (and ∂ψ/∂ n ) through the relation B R = - R -1 ∂ψ/∂ Z and B z = R -1 ∂ψ/∂ R . This leads to a Cauchy boundary condition for the Grad-Shafranov equation Δ*ψ = 0 in the region between the contour of the sensor coil locations and the plasma boundary flux surface. Numerical equilibria calculated for the ISX-B with different shapes are used to simulate ψ data along the coil locations. Random errors are added to the data to test the efficacy of two different approaches: global fitting and local fitting. Reasonably accurate results are obtained by the method of global fitting of the boundary values, which is based on the expansion of ψ in terms of eigenfunctions of Δ*ψ = 0 in a toroidal ring co-ordinate system. This approach is found to permit a relatively large random error in poloidal B field values at the sensor coils and appears to have the potential of rapidly displaying the plasma shape and location.