Evaluation of Epsilon-Net Calculated Equilibrium Reconstruction Error Bars in the European Integrated Modeling Platform

Abstract

2 AbstractAn important direction of fusion research is the reconstruction of plasma equilibrium from measurements. Most of the plasma modeling codes and plasma control systems use equilibrium data on input. Therefore, the accuracy of reconstructions plays a crucial role in fundamental understanding of processes in present devices and fusion reactors. The results of previous research show that one can get substantially different reconstructions of plasma current densities and safety factors, which fit the measurements even within a relatively small inaccuracy. So, rigorous calculation of the reconstructed functions error bars is required. This paper presents new advances in formulation of the equilibrium reconstruction problem, describes application of the -nets technique for rigorous calculation of the reconstructions error bars and its software implementation, gives examples of error bars evaluation for ASDEX Upgrade.

The Basic Components of Software-Hardware System for Modeling and Control of the Toroidal Plasma by Epsilon-Nets on Heterogeneous Mini-Supercomputers

“…Relatively recently the method of ǫ-nets was developed [1,5] for numerically solving a certain class of ill-posed problems making it possible to find all strongly different solutions or substantiate their absence with given inaccuracy ǫ. In the general case, this method is suitable for numerically analyzing the ill-posedness of a problem with error ǫ, namely, studying the existence and uniqueness of solutions and stability with respect to the input data.…”

“…Sequential algorithms for constructing ǫ-nets were presented in [1,5]. ε-nets of polynomials, splines and their combinations were considered.…”

“…The parallel algorithms of the ǫ-nets method described above were implemented for both CPU/MPI and CPU/GPGPU technologies in the SDSS code (Substantially Different Solution Searcher) [1,5]. The total length of the SDSS code is more than 30000 lines in Fortran 2008.…”

“…Plasma control methods are based on solving the inverse problems of plasma parameters reconstruction according to the measurement data. The problem of a plasma reconstruction can be divided into two subtasks [1,5]: plasma boundary reconstruction and reconstruction of internal plasma parameters. The former one is considered below; the latter one is described in the next section.…”

“…The mathematical statement of the problem of the reconstruction of internal plasma parameters is rather cumbersome, for this reason it is not presented here. The statement of the problem and the methods for its solution are described in full detail in Sections 1.8.1, 2.5, 2.5.7, 4.10 of book [1] and in [5]. Here only a general approach to solving the inverse problem of the reconstruction of internal plasma parameters with the ǫ-net method is presented.…”