Related papers: Dynamical analysis of the nonlinear growth of the …
It is shown that the critical layer analysis, involved in the linear theory of internal modes, can be extended continuously into the early nonlinear regime. For the m=1 resistive mode, the dynamical analysis involves two small parameters:…
The nonlinear evolution of the m=1 internal kink mode is studied numerically in a setting where the tokamak core plasma is surrounded by a turbulent region with low magnetic shear. As a starting point we choose configurations with three…
We have investigated the development of current-driven (CD) kink instability through three-dimensional relativistic MHD simulations. A static force-free equilibrium helical magnetic configuration is considered in order to study the…
The nonlinear evolution of resistive double tearing modes (DTMs) with safety factor values q=1 and q=3 is studied in a reduced cylindrical model of a tokamak plasma. We focus on cases where the resonant surfaces are a small distance apart.…
In magnetic configurations with two or three q=1 (with q being the safety factor) resonant surfaces in a tokamak plasma, resistive magnetohydrodynamic modes with poloidal mode numbers m much larger than 1 are found to be linearly unstable.…
It is well known that the radial displacement of the $m=1$ internal kink mode in a periodic screw pinch has a steep jump at the resonant surface where $\mathbf{k}\cdot\mathbf{B}=0$. In a line-tied system, relevant to solar and astrophysical…
We study the evolution of kink instability in a force-free, non-rotating plasma column of high magnetization. The main dissipation mechanism is identified as reconnection of magnetic field-lines with various intersection angles, driven by…
We present numerical simulation results of the nonlinear evolution of the (1,1) internal kink mode in the presence of various kinds of equilibrium plasma flows. The present studies are carried out in the framework of a two fluid model to…
We aim to study the standing fundamental kink mode of coronal loops in the nonlinear regime, investigating the changes in energy evolution in the cross-section and oscillation amplitude of the loop which are related to nonlinear effects, in…
The growth and saturation of magnetic field in conducting turbulent media with large magnetic Prandtl numbers are investigated. This regime is very common in low-density hot astrophysical plasmas. During the early (kinematic) stage, weak…
In this manuscript using the asymptotic method of multiscale nonlinear theory we construct a nonlinear theory of the appearance of large-scale structures in the stratified conductive medium with the presence of small-scale oscillations of…
Nonlinearity of magneto-dynamics is typically described by a single constant, $\mathcal{N}$, with positive and negative values indicating repulsion and attraction of magnons, respectively. In thin magnetic films with easy-plane magnetic…
Conserved growth models that exhibit a nonlinear instability in which the height (depth) of isolated pillars (grooves) grows in time are studied by numerical integration and stochastic simulation. When this instability is controlled by the…
We have investigated the effect of sheared equilibrium flows on the $m = 1, n = 1$ resistive internal kink mode in the framework of a reduced magnetohydrodynamic model in a periodic cylindrical geometry. Our numerical studies show that…
We consider the generation of magnetic field by a turbulent flow. For the linear induction equation (i.e. the kinematic dynamo problem), we show that the statistical moments of the magnetic field display multiscaling and in particular…
We examine the existence of nonlinear modes and their temporal dynamics, in arrays of split-ring resonators, using a fractional extension of the Laplacian in the evolution equation. We find a closed-form expression for the dispersion…
The linear and nonlinear evolution of magnetic reconnection in collisionless high-temperature plasmas with a strong guide field is analyzed on the basis of a two-dimensional gyrofluid model. The linear growth rate of the reconnecting…
We examine a nonlinear magnetoinductive dimer and compute its linear and nonlinear symmetric, antisymmetric and asymmetric modes in closed-form, in the rotating-wave approximation. A linear stability analysis of these modes reveals that the…
Many nonlinear systems are described by eigenmodes with amplitude-dependent frequencies, interacting strongly whenever the frequencies become commensurate at internal resonances. Fast energy exchange via the resonances holds the key to rich…
We study the growth of a periodic pattern in one dimension for a model of spinodal decomposition, the Cahn-Hilliard equation. We particularly focus on the intermediate region, where the non-linearity cannot be negected anymore, and before…