Plasma parameters, like the internal inductance, li, and the diamagnetic poloidal beta, βDIA, are of particular relevance for a reliable real-time control system of next step tokamaks. These and other quantities have been obtained at Joint European Torus (JET) with a method that uses the Shafranov integrals S1, S2 and S3. Indeed they allow the direct calculation of the Shafranov parameter Λ = βMHD + li/2 and of βDIA. Moreover, in discharges with a sufficiently high elongation (k > 1.3 typically), the internal inductance can be separated from the MHD poloidal beta, βMHD, and calculated independently, through the Shafranov integrals, with a precision that is more than satisfactory for real-time applications. It is worth mentioning that, since S1, S2 and S3 are integrals defined on the plasma boundary, a specific algorithm, depending on the fast code XLOC, has been expressively developed to determine this quantity.The method to determine the plasma parameters has been verified off-line, benchmarking its outputs with the estimates of the most sophisticated equilibrium codes available. The results of this systematic comparison have been very encouraging both in the limiter and x-point phases of the discharges and on all the investigated plasma configurations. The computational time, necessary to determine the plasma boundary and about 50 signals is only about 1.5 ms on a PC equipped with a 400 MHz Pentium II, well below the 10 ms constraint of JET real-time applications. The code has therefore been implemented on-line, and its outputs have already been exploited to achieve the feedback control of some plasma parameters.
Separation of p and ℓi in tokamaks of non-circular cross-section