Integrated codes model for erosion-deposition in long discharges

There is increasing interest in understanding the mechanisms causing the deuterium retention rates which are observed in the longest high power tokamak discharges, and its possible relation to near term choices which must be made for plasma-facing components in next generation devices [1]. Both co-deposition and bulk diffusion models are regarded as potentially relevant. This contribution describes a global model for the co-deposition axis of this dilemma, which includes as many of the relevant processes which may contribute to it as is computationally feasible, following the 'maximal ordering/minimal simplification' strategy described in Kruskal's "Asymptotology" [2]. The global model is interpretative, meaning that some key information describing the bulk plasma is provided by experimental measurement, and the models for the impurity processes relevant to retention, given this measured background, are simulated and compared with other data. In particular, the model describes the carbon balance in near steady-state systems, to be able to understand the relation between retention in present devices and the level which might be expected in fusion reactors, or precursor experiments such as ITER. The key modules of the global system describe impurity generation, their transport in and through the SOL, and core impurity transport. The codes IMPFLU, BBQ, and ITC/MIST, in order of the appearance of the processes they describe, are used to calculate the balance: IMPFLU is an adaptation of the TOKAFLU module of CAST3M [3], developed by CEA, which is a 3-D, time-dependent finite elements code which determines the thermal and mechanical properties of plasma-facing components. BBQ [4, 5] is a Monte Carlo guiding center code which describes trace impurity transport in a 3-D defined-plasma background, to calculate observables (line emission) for comparison with spectroscopy. ITC [6] and MIST [7] are radial core multi-species impurity transport codes. The modules are linked together into a global carbon balance system in order to enable prediction of erosion, re-deposition and co-deposition rates, for comparison with spectroscopic observations. The coupling of these processes is critical since, as will be discussed, owing to the role of self-sputtering the coupled core-SOL-surface model is nonlinear and is not guaranteed to have a finite solution. Idealized examples of possible system behavior are taken from typical conditions of Tore Supra CIEL long discharges. The role of SOL phenomena, such as enhanced self-sputtering due to an LH-induced fast electron component, on resultant core impurity accumulation and co-deposition rate is used as an illustration of the behavior of the coupled system. Experimental validation will require component-by-component spectroscopic validation, additional input from more detailed gryo-orbit codes, especially for intra-gap phenomena, and information from kinetic sheath models. Some outstanding issues in this respect will be discussed.