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Abstract
Research in fusion energy seeks to develop a green, safe, and sustainable energy source. Nuclear fusion can be achieved by heating a hydrogen gas to temperatures of millions of kelvin. At fusion temperatures, some or all the electrons leave the atomic nucleus of the hydrogen atom. This results in an overall neutral gaseous state of negatively charged free electrons and positively charged ions. This state of matter is called plasma. To achieve and maintain fusion temperatures, the plasma must avoid direct contact with any solid material. Since the plasma consists of charged particles, it can be conﬁned with an appropriate conﬁguration of strong magnetic ﬁelds. Toroidal magnetic conﬁnement devices, such as the tokamak, are the most promising designs for a fusion reactor. A tokamak can operate in two distinct modes of operation. These are the low conﬁnement mode (Lmode) and the high conﬁnement mode (Hmode). Hmode is the preferred operating mode for a fusion reactor. The transition from Lmode to Hmode is called the L–H transition. The conﬁnement properties of a plasma are largely determined by the physics near the edge of the conﬁnement region of the plasma. The edge transport of a magnetically conﬁned plasma is predominantly caused by recurring bursts of coherent plasma structures. These structures are in Lmode called blob ﬁlaments (blobs) and in Hmode categorized into edge localized mode (ELM) ﬁlaments or interELM ﬁlaments. To improve the plasma conﬁnement, it is important to understand the evolution of these structures. We apply a dynamical systems approach to quantitatively describe the time evolution of these structures. Three state variables describe blobs in a plasma convection model. A critical point of a variable deﬁnes a feature point where that variable is signiﬁcant. For a range of Rayleigh and Prandtl numbers, we analyze the bifurcations of the critical points of the three variables with time as the main bifurcation parameter. Plasma simulations can be computationally demanding. We apply a Galerkin method to approximate a plasma convection model with a reduced model. The time evolution of the energies of the pressure proﬁle, the turbulent ﬂow, and the zonal ﬂow capture the dynamic behavior of the convection model. Rayleigh decomposition splits the variables of the model into averaged variables and ﬂuctuation variables. We approximate the ﬂuctuation variables by truncated Fourier series and project the equations onto the Fourier basis functions. This results in a computationally simpler model with the spatial dimension reduced by one. Bifurcation diagrams for the energies show consistency between the bifurcation structures of the full and the reduced model.
Finally, we utilize a datadriven modeling approach called SINDy to identify a reduced model from simulation data of a convection model. The reduced model reveals a predatorprey relationship between the zonal ﬂow energy and the turbulent energy. The analytically derived bifurcation diagram for the reduced model has the same structure as the databased bifurcation diagram for the full model.
Finally, we utilize a datadriven modeling approach called SINDy to identify a reduced model from simulation data of a convection model. The reduced model reveals a predatorprey relationship between the zonal ﬂow energy and the turbulent energy. The analytically derived bifurcation diagram for the reduced model has the same structure as the databased bifurcation diagram for the full model.
Original language  English 

Publisher  DTU Compute 

Number of pages  123 
Publication status  Published  2018 
Series  DTU Compute PHD2017 

Volume  461 
ISSN  09093192 
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Dive into the research topics of 'Topological bifurcations of coherent structures and dimension reduction of plasma convection models'. Together they form a unique fingerprint.Projects
 1 Finished

Dynamical Systems Approach to LH Transition in Magnetically Confined Plasma
Dam, M., Brøns, M., Naulin, V., Sørensen, M. P., Garcia, O. E., Rasmussen, J. J. & Jensen, M. H.
Technical University of Denmark
15/12/2013 → 17/01/2018
Project: PhD