Analysis of error field sources in TOKAMAK devices

Due to unavoidable tolerances in components construction and assembly, the actual magnetic fi eld in Tokamak devices differs from the nominal one. The experimental studies nowadays available indicate a strong impact of the error fields on the plasma stability in next generation, large size, devices. Therefore, a careful preliminary analysis aimed at evaluating the impact of possible error field sources, to define tolerance ranges and assess the effect of current feeders, was envisaged before realization of ITER reactor. The paper discusses the tools used to perform ITER tolerance analysis, from the viewpoints of two possible approaches to tolerancing, which are statistical analysis and worst case analysis. The two methods aim to get different characterizations of devices performance, and a critical comparison of drawbacks and advantages of both methods is reported. 1. Error fields in tokamaks In magnetic confinement controlled thermonuclear fusion devices (Tokamaks), the confinement ca- pability of the machine is quite sensitive to discrepancies between the nominal magnetic field and the actual one (called "error fields"), resulting from several causes including non axi-symmetric sources (e.g. current leads for superconducting magnets) and mechanical inaccuracies in the manufacturing and assembly of magnets. The error fields are by their intrinsic nature quite complex to describe; an effective tool for their quantitative analysis is the Fourier toroidal and poloidal decomposition of normal field component on the nominal plasma surface at the start of flat top, when the impact of error fields is the highest. Experimental studies (1) have shown that only some specific Fourier components have the highest impact on plasma confinement. With reference to ITER Tokamak, the Three Modes Error Index (TMEI) hasbeenintroducedasaneffectiveindexto describetheamountoferrorfieldsinthethreemodesrelevant for confinement, namely field harmonic m = 2, n = 1 - with toroidal periodicity index n equal to one and poloidal periodicity index m equal to two - and the two side bands m = 1, n = 1a ndm = 3, n = 1. TMEI is based on the weighted average of normalized mode coefficients, that must remain below the fixed threshold of 5 × 10 −5 to guarantee expected performance (2):