Comparison of approaches to the electromagnetic analysis of COMPASS-U vacuum vessel during fast transients
Introduction
This paper contributes to R&D activities for the vacuum vessel (‘wall’) of COMPASS-U tokamak [1], which is a medium-size device presently in the conceptual design phase. It will operate at high plasma current (2 MA) and strong magnetic field (5 T), therefore, large electromagnetic (EM) forces on conducting structures near the plasma are expected during disruptions.
The forces appear due to the currents induced or injected into the wall. Traditionally the toroidal current in the wall is considered as the main attribute of disruptions [2,3], for more references see [4]. Recently it was demonstrated that the poloidal currents in the wall can contribute significantly into the disruption forces [[5], [6], [7]]. This study is aimed at evaluation of this effect in COMPASS-U tokamak.
The wall currents are driven by the electric field induced by the magnetic field variations: . The force balance equation requires in the plasma at changes of its pressure (here, at thermal quenches, TQs) and current density (here, at current quenches, CQs). This is accompanied by the changes in the plasma shape and position, which also contributes into in the wall and greatly complicates the description of plasma-wall electromagnetic coupling [4,8,9]. Here both the toroidal and poloidal wall currents are accounted for assuming their purely inductive generation (no halo currents).
Calculation of the poloidal currents in the wall is an additional complication that should be justified. For this purpose, we start from the estimates based on the available theory [4,6,7] and make CarMa0NL [8,10] computations to test the validity of its predictions.
To facilitate the task, we approximate the COMPASS-U tokamak with 3D vacuum vessel (VV) shown in Fig. 1 by a circular tokamak, as illustrated in Fig. 2. Moreover, we do not consider VDEs and related halo currents, but only TQs and CQs, which are assumed to be instantaneous, so that we can treat the wall as ideal.
The motivation of this basic 2D research is to provide a necessary basis for the 3D EM modelling of axisymmetric disruptions on COMPASS-U, which is currently being carried out with ANSYS Maxwell and CarMa0NL. Assuming that mechanical and electromagnetic problems are decoupled, the results of EM modelling are being used for static and transient structural analysis in ANSYS Mechanical. Coupled electromechanical formulation may be considered at later stages of the design process [11].
The mechanical stress on the vessel depends on the time history of the EM loads and their durations. The model described below provides estimates for the EM loads during the worst scenario when all the current is transferred instantaneously to the wall. In this case the duration of the EM force is determined by the resistive decay time of the wall only.
Analytical expressions for local and integral forces on the circular tokamak [7] wall have been derived for the case when the plasma-wall gap on high-field-side (HFS) is smaller than the gap on low-field-side (LFS), see Fig. 2a. Their predictions for a high-aspect-ratio tokamak have been recently verified by CarMa0NL code [12]. In the present study, we investigate the opposite setup when the plasma column is shifted towards HFS (Fig. 2b), which corresponds to several plasma scenarios for COMPASS-U. As will be demonstrated in the following sections, in this case the analytical predictions and numerical results are also in good quantitative agreement.
As was found in [13] for COMPASS-U with pre-disruption poloidal beta and net plasma current , the integral radial force on the wall during TQ is four times smaller than that during CQ. Therefore, in the present study we compare analytical and numerical results primarily for the CQ and adjust poloidal beta for numerical calculations to be as low as . Note for completeness that similar comparisons for TQ forces have been done in [3,14] with greatly contradicting numerical results.
Section snippets
Results for the case with account of the poloidal current in the wall (Aw)
To estimate the EM forces during disruptions, we approximate the COMPASS-U tokamak with 3D VV, shown in Fig. 1, by a circular tokamak with major radius and minor radius , as illustrated in Fig. 2. With plasma minor radius , this choice of wall parameters keeps the same the ratio between plasma and vessel cross-section areas for circular 2D and elongated 3D geometries.
For internal inductance and poloidal beta , the Shafranov shift calculated with
Numerical results obtained with CarMa0NL
In this section we compare analytical predictions (Fig. 3) with CarMa0NL numerical results, presented in Fig. 4, Fig. 5. The CarMa0NL [8,10] solves 2D nonlinear evolutionary equilibrium MHD equations, self-consistently coupled to eddy currents equations, describing 3D volumetric conductors. Despite the 2D nature of the problem under consideration, the choice of CarMa0NL is suggested by the need to include poloidal eddy currents generated in the conducting structures, a rare feature for
Discussion and conclusions
Comparing Figs. 3a and b with 5a and b, respectively, one can see good qualitative agreement between analytical and numerical results for the poloidal distribution of the normal component of EM force. For the case without poloidal eddies, also quantitative agreement for m = 0 harmonic is excellent, within only 6% difference. The difference for other harmonics may be caused by two factors. First, the formulas in [6,7,16] are derived for a circular vessel in the high aspect ratio approximation,
Acknowledgments
This work has been carried out within the framework of the project COMPASS-U: Tokamak for cutting-edge fusion research No. CZ.02.1.01/0.0/0.0/16_019/0000768 and co-funded from European structural and investment funds.
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