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We consider the problem of heat diffusion in branched systems and networks on the basis of a model described in terms of heat equation on metric graphs. Using the explicit analytical solutions of the latter, evolution of the temperature…
The transport of heat and particles in the relatively collisional edge regions of magnetically confined plasmas is a scientifically challenging and technologically important problem. Understanding and predicting this transport requires the…
A mathematical model of the heat process in one-dimensional domain governed by a cylindrical heat equation with a heat source on the axis $z=0$ and nonlinear thermal coefficients is considered. The developed model is particularly applicable…
An efficient numerical scheme for solving transport equations for tokamak plasmas within an integrated modelling framework is presented. The plasma transport equations are formulated as diffusion-advection equations in two coordinates (a…
Current density perturbations induced by radiative collapse, which is a possible mechanism governing tokamak plasma disruptions, have been investigated using a reaction-diffusion model. The reaction term of the current diffusion equation,…
The development of a quasi-linear gyrokinetic transport model for tokamak plasmas, ultimately designed to provide physically comprehensive predictions of the time evolution of the thermodynamic relevant quantities, is a task that requires…
The variational heat equation is a nonlinear, parabolic equation not in divergence form that arises as a model for the dynamics of the director field in a nematic liquid crystal. We present a finite difference scheme for a transformed,…
The self-consistent description of Langmuir wave and ion-sound wave turbulence in the presence of an electron beam is presented for inhomogeneous non-isothermal plasmas. Full numerical solutions of the complete set of kinetic equations for…
This paper deals with the numerical study of a nonlinear, strongly anisotropic heat equation. The use of standard schemes in this situation leads to poor results, due to the high anisotropy. An Asymptotic-Preserving method is introduced in…
Boundary plasma physics plays an important role in tokamak confinement, but is difficult to simulate in a gyrokinetic code due to the scale-inseparable nonlocal multi-physics in magnetic separatrix and open magnetic field geometry. Neutral…
The effect of flow shear on turbulent transport in tokamaks is studied numerically in the experimentally relevant limit of zero magnetic shear. It is found that the plasma is linearly stable for all non-zero flow shear values, but that…
Using a perturbative approach, an evolution equation for the space charge density, correct up to the third order, is deduced for arbitrary initial density profiles of the electron and ion fluids in a cold nonrelativistic plasma. The…
For the simulation of disruptions in tokamak fusion plasmas, a fluid model describing the evolution of relativistic runaway electrons and their interaction with the background plasma is presented. The overall aim of the model is to…
The confinement of heat in the core of a magnetic fusion reactor is optimised using a multidimensional optimisation algorithm. For the first time in such a study, the loss of heat due to turbulence is modelled at every stage using…
In tokamak disruptions where the magnetic connection length becomes comparable to or even shorter than the plasma mean-free-path, parallel transport can dominate the energy loss and the thermal quench of the core plasma goes through four…
We propose a quantitative model of ion temperature gradient driven turbulence in toroidal magnetized plasmas. In this model, the turbulence is regulated by zonal flows, i.e. mode saturation occurs by a zonal-flow-mediated energy cascade…
The paper suggests certain regimes of fusion plasma with magnetic confinement, when the Larmor radius $\lambda$ and the angle $\alpha$ (determining the orientation of the local coordinates) form an analytic function $w=\lambda e^{i\alpha}$…
Tokamak turbulence, driven by the ion-temperature gradient and occurring in the presence of flow shear, is investigated by means of local, ion-scale, electrostatic gyrokinetic simulations (with both kinetic ions and electrons) of the…
A machine learning approach has been implemented to measure the electron temperature directly from the emission spectra of a tokamak plasma. This approach utilized a neural network (NN) trained on a dataset of 1865 time slices from…
The aim of this work is to introduce a numerical method to cope with the multiscale nature of confined plasma physics. These investigations are focused on fluid plasma description under large magnetic field. The difficulties in this context…