Accuracy assessment of numerical tracing of 3-D magnetic field lines in Tokamaks with analytical invariants.

We consider the problem of the accurate tracing of long magnetic field lines in tokamaks, which is in general crucial for the determination of the plasma-boundary as well as for the magnetic properties of the scrape off layer. The accurate field line tracing is strictly related to basic properties of Ordinary Differential Equation (ODE) integrators, in terms of invariant properties preservation and local accuracy for the long term analysis. We introduce and discuss some assessment criteria and procedure for the specific problem, using them to compare standard ODE solvers with a Volume Preserving (VP) algorithm for given accuracy requirements. In particular, after the validation for an axisymmetric plasma, a 3-D configuration is described by means of Clebsch potentials, which provide analytical invariants for the accuracy assessment of the numerical integration. A standard 4th order Runge-Kutta routine at fixed step reveals to be well suited to the problem in terms of reduced computational burden, with extremely good results as for accuracy and volume preservation. Then we tackle the problem of field line tracing for the determination of plasma-wall gaps for a 3-D configuration, demonstrating the effective feasibility of the plasma boundary evaluation in tokamaks by means of field lines tracing with standard tools.