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Accueil > Plus d’actualités > Anna Krupka a soutenu sa thèse "Plasma speed optimization for improved tokamak plasma confinement"
Anna Krupka a soutenu sa thèse "Plasma speed optimization for improved tokamak plasma confinement"
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Le 22 novembre 2024, Anna Krupka a soutenu sa thèse "Plasma speed optimization for improved tokamak plasma confinement".
Abstract : Maximizing plasma confinement is essential to the performance of future magnetic fusion reactors. Playing with plasma speed can be a way to stabilize possible instabilities and control turbulence with a very beneficial impact on fusion yield. It is, therefore, essential to understand how a tokamak plasma can be rotated. Ideally, the tokamak should work in a stationary state as a fusion reactor. It is, therefore, reasonable to determine the steady states of a tokamak plasma in full generality without imposing the nullity of the plasma velocity field. In the visco-resistive magnetohydrodynamics (MHD) framework, this amounts in particular to retaining the non-linear term (v.grad)v in the stationary Navier-Stokes equation.
Using the FreeFem++ open-source software for solving partial differential equations using the finite element method, we numerically determined the axisymmetric stationary states of a tokamak plasma in realistic JET. This thesis shows that the plasma velocity root-mean-square behaves as f(H) as long as the inertial term remains negligible, where H stands for the Hartmann number, which describes how viscous and resistive plasma is. We show that f(H) follows a power-law behavior in the limits of both small (H << 1) and large (H >> 1) Hartmann numbers. In the latter limit, we establish that f(H) scales as H^1/4, which is consistent with numerical results. Additionally, this work establishes Poisson’s equation governing the pressure profile. It is shown that the simplifying assumption of a toroidal current density component arising solely from Ohm’s law in response to a time-independent, curl-free toroidal electric field fails to produce realistic pressure levels. To overcome this, we introduce additional non-inductive current drives, comparable to those from neutral beam injection, modeled as modifications to the toroidal current. The new model is validated using numerical simulations, showing significant pressure profile improvements. For the examples considered, the effect of these current drives on the velocity profiles is moderate except in the case where the drives induce some reversals in the total toroidal current density, producing non-nested flux surfaces with internal separatrices. Finally, the effect of fixed current density profiles is examined, revealing a new second regime, where toroidal and poloidal velocities scale with Hartmann number as H^2.
Supervisor : Dr. Marie-Christine Firpo
Jury :
Prof. Alain Ghizzo, University of Lorraine – Rapporteur
Prof. Alessandro Biancalani, Ecole Supérieure d’Ingénieurs Léonard de Vinci – Rapporteur
Dr. Wouter Bos, École Centrale de Lyon
Prof. Jean-Marcel Rax, Université de Paris-Saclay
Prof. Xavier Leoncini, Aix-Marseille Université
Prof. Luca Guazzotto, Auburn University
