Related papers: Variational Integration for Ideal Magnetohydrodyna…
We revisit Parker's conjecture of current singularity formation in 3D line-tied plasmas using a recently developed numerical method, variational integration for ideal magnetohydrodynamics in Lagrangian labeling. With the frozen-in equation…
Newcomb's Lagrangian for ideal magnetohydrodynamics (MHD) in Lagrangian labeling is discretized using discrete exterior calculus. Variational integrators for ideal MHD are derived thereafter. Besides being symplectic and…
We investigate the spatial and temporal evolution of the heating of the corona of a cool star such as our Sun in a three-dimensional magneto-hydrodynamic (3D MHD) model. We solve the 3D MHD problem numerically in a box representing part of…
Many magnetic structures in the solar atmosphere evolve rather slowly so that they can be assumed as (quasi-)static or (quasi-)stationary and represented via magneto-hydrostatic (MHS) or stationary magneto-hydrodynamic (MHD) equilibria,…
Recently a variational integrator for ideal magnetohydrodynamics in Lagrangian labeling has been developed. Its built-in frozen-in equation makes it optimal for studying current sheet formation. We use this scheme to study the…
We investigate the ideal and incompressible magnetohydrodynamic (MHD) equations in three space dimensions for the development of potentially singular structures. The methodology consists in implementing the four-fold symmetries of the…
The nature and detailed properties of the heating of the million-degree solar corona are important issues that are still largely unresolved. Nanoflare heating might be dominant in active regions and quiet Sun, although direct signatures of…
We review and discuss insights on ideal magnetohydrodynamic (MHD) instabilities that can play a role in destabilizing solar coronal flux rope structures. For single flux ropes, failed or actual eruptions may result from internal or external…
Magnetic fields and flows in coronal structures, for example, in gradual phases in flares, can be described by 2D and 3D magnetohydrostatic (MHS) and steady magnetohydrodynamic (MHD) equilibria. Within a physically simplified, but exact…
A variational integrator for ideal magnetohydrodynamics is derived by applying a discrete action principle to a formal Lagrangian. Discrete exterior calculus is used for the discretisation of the field variables in order to preserve their…
The quality of today's research is often tightly limited to the available computing power and scalability of codes to many processors. For example, tackling the problem of heating the solar corona requires a most realistic description of…
Magnetohydrodynamic (MHD) simulations of the solar corona have become more popular with the increased availability of computational power. Modern computational plasma codes, relying upon Computational Fluid Dynamics (CFD) methods, allow for…
We provide a valid magnetohydrostatic equilibrium from the collapse of a 2D X-point in the presence of a finite plasma pressure, in which the current density is not simply concentrated in an infinitesimally thin, one-dimensional current…
This paper reviews some of the many 3D numerical experiments of the emergence of magnetic fields from the solar interior and the subsequent interaction with the pre-existing coronal magnetic field. The models described here are idealized,…
We revisit the Hahm-Kulsrud-Taylor (HKT) problem, a classic prototype problem for studying resonant magnetic perturbations and 3D magnetohydrodynamical equilibria. We employ the boundary-layer techniques developed by Rosenbluth, Dagazian,…
General three-dimensional toroidal ideal magnetohydrodynamic equilibria with a continuum of nested flux surfaces are susceptible to forming singular current sheets when resonant perturbations are applied. The presence of singular current…
We study the magnetic field and current structure associated with a coronal loop. Through this we investigate to what extent the assumptions of a force-free magnetic field break down and where they might be justified. We analyse a 3D MHD…
We present the first results of three-dimensional (3D) numerical magnetohydrodynamic (MHD) simulations of the onset of magnetic reconnection via the tearing instability in dynamically thinning current sheets in the solar corona. In all our…
Context: The majority of studies on stressed 3D magnetic null points consider magnetic reconnection driven by an external perturbation, but the formation of a genuine current sheet equilibrium remains poorly understood. This problem has…
Combined tearing-thermal evolution plays an important role in the disruption of current sheets, and formation of cool condensations within the solar atmosphere. However, this has received limited attention to date. We numerically explore a…