Hybrid integral-differential simulator of EM force interactions/scenario-assessment tool with pre-computed influence matrix in applications to ITER

Abstract

A necessity to address a wide spectrum of engineering problems in ITER determined the need for efficient tools for modeling of the magnetic environment and force interactions between the main components of the magnet system. The assessment of the operating window for the machine, determined by the electro-magnetic (EM) forces, and the check of feasibility of particular scenarios play an important role for ensuring the safety of exploitation. Such analysis-powered prevention of damages forms an element of the Machine Operations and Investment Protection strategy. The corresponding analysis is a necessary step in preparation of the commissioning, which finalizes the construction phase. It shall be supported by the development of the efficient and robust simulators and multi-physics/multi-system integration of models. The developed numerical model of interactions in the ITER magnetic system, based on the use of pre-computed influence matrices, facilitated immediate and complete assessment and systematic specification of EM loads on magnets in all foreseen operating regimes, their maximum values, envelopes and the most critical scenarios. The common principles of interaction in typical bilateral configurations have been generalized for asymmetry conditions, inspired by the plasma and by the hardware, including asymmetric plasma event and magnetic system fault cases. The specification of loads is supported by the technology of functional approximation of nodal and distributed data by continuous patterns/analytical interpolants. The global model of interactions together with the mesh-independent analytical format of output provides the source of self-consistent and transferable data on the spatial distribution of the system of forces for assessments of structural performance of the components, assemblies and supporting structures. The numerical model used is fully parametrized, which makes it very suitable for multi-variant and sensitivity studies (positioning, off-normal events, asymmetry, etc). The obtained results and matrices form a basis for a relatively simple and robust force processor as a specialized module of a global simulator for diagnostic, operational instrumentation, monitoring and control, as well as a scenario assessment tool. This paper gives an overview of the model, applied technique, assessed problems and obtained qualitative and quantitative results.

Models and scalings for the disruption forces in tokamaks

“…This condition and its consequence F(w−) = 0, where F is the same integral as in (1), but taken on w−, are automatically satisfied when B is found in solving the full equilibrium problem with proper matching of the internal and external solutions. On the contrary, when the plasma is introduced as a rigid ring [3,4,8] or wire [36][37][38] or a set of filaments [21,22,[39][40][41][42][43][44][45][46] with a current J, the tilt and CQ treated as dJ/dt = 0 result in a magnetic field different from B needed for the gaseous (absolutely non-rigid!) plasma equilibrium.…”

Dependence of disruption forces on the plasma position inside the vacuum vessel in tokamaks

“…Calculation of i and/or B w is a separate electromagnetic task [35][36][37][38][39], the main difficulty of which comes from the plasmawall coupling through (3) at S pl because the shape and position of the latter must also react to the plasma changes. Incorporation of this coupling [39,40] is mandatory in the task [19,21,24,34], it leads to an essential difference in the disruption forces from those calculated for the plasma replaced by one [41][42][43] or several [11,[44][45][46][47][48][49] solid current rings. The analysis below is based on the results presented in [39,40] for the large-aspect-ratio model with a circular plasma and almost coaxial wall.…”

“…where 2µ 0 p ψ m ≡ B 2 p wall (45) and the other term represents the contribution from the toroidal field B t :…”