Simulation and analysis of eddy current induced in the Globus-M tokamak


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A.F.Ioffe Physical-Technical Institute (St.-Petersburg, Russia) - Globus-M Tokamak

A.F.Ioffe Physical-Technical Institute, (St.-Petersburg, Russia) - Globus-M Tokamak Описание метода: The eddy current analysis was performed with the use of 3D finite-element code, developed at the Efremov Institute. Code allows a transient electromagnetic analysis using a finite-element (FE) representation of thin shell structures in an integral formulation to model arbitrary conducting walls of complex geometry. A numerical simulation of the eddy currents requires a reasonably detailed model of the conducting structures.

Numerical simulation of transient electromagnetic processes in the GLOBUS-M vacuum vessel from the plasma discharge observations gives a prediction for the total toroidal eddy currents.

Fig.8 illustrates a comparison between the modelled and measured variations of the toroidal eddy current. The peak eddy currents of 55-56 kA occur at 112 ms, preceding plasma current ramp-up, and are caused by variations in the central solenoid current.

Oscillations of the evolutions of eddy currents are associated with power supplies. The coils are energized with 110 kV ac transformers connected to mains via six-phase thyristor rectifiers. Output ripple is typically 300 Hz.

The study also included an analysis of an impact of the poloidal angle on the toroidal eddy current density. The toroidal angle was taken as ~270° to fit the external and internal sets of Rogowski coils [6]. The poloidal angle was varied in the plane as given in Fig.9.

Fig.10 shows the eddy current density as a function of the poloidal angle for five typical events of the plasma discharge scenario:

1. 30ms - start of the CS current fast growth;
2. 58ms - plasma current initiation;
3. 114ms - end of practically immovable position of plasma;
4. 115ms - start of plasma current ramp-up and variations of the plasma shape and position;
5. 143ms - peak plasma current of 356.6kA.

Figs.11, 12 illustrate distributions of the eddy currents and current surface density of the eddy for few typical events of the plasma discharge scenario. Simulated variations in the eddy current in main components of the vacuum vessel are shown in Fig.13.

During the period 113 ms to 120 ms, when the eddy current is near maximal, the total eddy current is split so that up to 50%, or 40 kA, pass through the inner cylinder and ~~35%, or 25 kA, through half-spheres. The eddy current in the outer ring is practically zero. The plasma current in this period rises from 5 kA to 105 kA. This situation is typical for spherical tokamaks with a short current path around the inner cylinder and, consequently, low ohmic resistance of this cylinder.

The total resistance for the vacuum vessel is estimated in terms of heat load Q  due to the toroidal eddy current I   using the equation

At p=5.7·10-7 W-m the VV resistance in the toroidal direction is 110 m W.

A full-scale numerical model was developed to study eddy current behavior in the vacuum vessel of the GLOBUS-M tokamak. Analysis of transient electromagnetic processes in the conducting structures was performed using the TYPHOON simulations. Eddy current evolution was modeled on the basis of experimental data for the GLOBUS-M plasma discharge scenario. Simulated and measured curves are in a good agreement. The eddy current simulations were applied to investigate a distribution of the toroidal eddy current surface density and evolution of the total eddy currents for the typical events of the plasma discharge scenario. The results showed that the inner cylinder of the vacuum vessel allocates up to 50% of the total eddy current due to a rather low ohmic resistance in the toroidal direction. The decay time for this cylinder amounts to 0.25-0.3 ms. The vacuum vessel time constant governing a steady-state distribution of eddy currents is evaluated as (2.5-3) ms. The total resistance of the vacuum vessel in the toroidal direction is estimated as 110 m W at p=5.7·10-7 W-m.


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