Multiple domain scheme for heat transport analysis in plasmas with magnetic islands: a first study.

In magnetically confined experiments the presence of rational surfaces allows perturbations (either self generated by the plasma or externally induced) to grow and break the magnetic topology of flux surfaces nested around a single axis. The bifurcated magnetic configuration takes the form of one or more islands embedded in the main plasma, each with their own magnetic axis. Stochastic layers develop around the flux surface containing the island X-point (the separatrix) and divide the nested flux surfaces of the islands from the nested flux surfaces of the bulk plasma. The presence of islands strongly modifies particle and heat fluxes. Transport studies in fusion community benefit of the availability of several well developed 1.5D transport codes (ASTRA, CRONOS, JETTO, RITM ...) that solve the flux surface averaged transport equations across shaped flux surfaces, on the grounds that the variation of physical quantities along the flux surfaces is small. They constitute a powerful and relatively user-friendly tool since they are able to capture the main features of transport phenomena without the complexity of 2D transport codes. However 1.5D codes are applicable nowadays only for flux surfaces nested around a single axis. Our goal is to develop a user friendly modelling tool applicable to 1.5D transport codes to be exploited in plasmas in the presence of single harmonic magnetic islands. To this aim a multiple domains scheme is adopted and three regions inside the plasma are identified: the first around the main magnetic axis (core), the second around the island axis (island) and the third that includes the separatrix stochastic area and the outer plasma (edge). In each domain the magnetic flux can be chosen as an effective radial coordinate. This scheme is independent from the equilibrium magnetic configuration hence it can be applied to tokamak, stellarator and Reversed Field Pinch. In this work we present the first study in this direction. We mimic the ASTRA transport module solving, in each domain, the 1.5D equation for the heat diffusion by means of a dedicated numerical code. A predictive simulation is performed providing the code with the diffusivity profile for the core, island and edge region, studying the mathematical issues arising in the context of the equation solution, in particular the matching at the common boundaries, in steady-state as well as time-dependent cases. Our study is carried out in synthetic but realistic scenarios from the RFX-mod Experiment. We show that qualitative agreement with experiments is quite easily recovered.