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UNIVERSITY OF BUCHAREST
FACULTY OF PHYSICS Guest
2024-11-22 1:44 |
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Conference: Bucharest University Faculty of Physics 2021 Meeting
Section: Theoretical Physics and Applied Mathematics
Title:
A mathematical model for moving the non-linear term from a differential operator to the r.h.s. of the equations
Authors:
Cǎlin V. ATANASIU (1), Leonid E. ZAKHAROV (2, 3), Matthias HOELZL (4)
Affiliation:
1) National Institute for Laser, Plasma and Radiation Physics, Atomiștilor 409, MG-36, 077125 Mǎgurele-Bucharest, Romania
2) LiWFusion, NJ 08543, USA
3) Department of Physics, University of Helsinki, Finland
4) Max Planck Institute for Plasma Physics, Boltzmannstr. 2, 85748 Garching, Germany
E-mail
atanasiu@ipp.mpg.de
Keywords:
boundary integral equations, tokamak, MHD equations
Abstract:
It is known that due to the high non-linear dependence of the MHD solutions on the iron permeability, the MHD calculations are more complicated and more time consuming than in the absence of iron structures. By considering our media as a linear, isotropic and homogeneous one we can replace it by a homogeneous one (vacuum) and a surface-current density distribution on the separation surfaces between subdomains. For example, in the JET (Joint European Torus) tokamak geometry, each segment of a curve is a Liapunov curve, therefore the surface-current density is considered as continuous (Hölder continuity) and of bounded variation, admitting then a uniformly convergent expansion. For simplification, we have used Legendre polynomials, their weight function being equal to one. Thus, we have succeeded to perform MHD computations for an iron-core transformer tokamak in the same way as for air-core transformer tokamaks [1, 2] by developing a boundary integral equations method (Fredholm integral equation of 2nd kind). Our code for simulation of the electromagnetic wall response during Vertical Displacement Events (VDE) received the status of open source license, to be used now by the EUROfusion community in modelling tokamak plasma disruptions. Our mathematical model for calculation of the influence of ferromagnetic components in VDE and stability simulations of tokamak plasmas can be implemented successfully into codes like JOREK-STARWALL [3].
References:
[1] L. E. Zakharov, C.V. Atanasiu, K. Lackner, M. Hoelzl, and E. Strumberger, J. Plasma Phys., 81 (2015) 515810610.
[2] C. V. Atanasiu, L.E. Zakharov, K. Lackner, M. Hoelzl, Journal of Physics: Conf. Series 1141 (2018) 012065.
[3] J. Artola, C. V. Atanasiu, M. Hoelzl, G.T.A. Huijsmans, K. Lackner, S. Mochalskyy, G. Oosterwegel, E. Strumberger and L.E. Zakharov, 2nd report for ITER project IO/16/CT/4300001383 on the Implementation and validation of a model for halo-currents in the nonlinear MHD code JOREK (2018).
Acknowledgement:
This work has been partially carried out within the framework of the EUROfusion Consortium and has received funding from the Euratom research and training programme 2014-2018 and 2019-2020 under grant agreement no. 633053. The views and opinions expressed herein do not necessarily reflect those of the European Commission.
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