We investigate, by means of three-dimensional compressible magnetohydrodynamic numerical simulations, the interaction of Kelvin-Helmholtz (KH) and current-driven (CD) instabilities in a magnetized cylindrical jet configuration. The jet has a supersonic axial flow, sheared in the radial direction, and is embedded in a helical magnetic field. The strength of the axial magnetic field component is chosen to be weak, in accord with the '' weak field regime '' previously defined by Ryu, Jones, & Frank for uniformly magnetized configurations. We follow the time evolution of a periodic section where the jet surface is perturbed at m ¼ AE1 azimuthal mode numbers. A m ¼ À1 KH surface mode linearly develops dominating the m ¼ þ1 KH one, in agreement with results obtained using an independent ideal stability code. This lifted degeneracy, because of the presence of the helical field, leads nonlinearly to clear morphological differences in the jet deformation as compared to uniformly magnetized configurations. As predicted by stability results, a m ¼ À1 CD instability also develops linearly inside the jet core for configurations having a small enough magnetic pitch length. As time proceeds, this magnetic mode interacts with the KH vortical structures and significantly affects the further nonlinear evolution. The magnetic field deformation induced by the CD instability provides a stabilizing effect through its azimuthal component B . This helps to saturate the KH vortices in the vicinity of the jet surface. Beyond saturation, the subsequent disruptive effect on the flow is weaker than in cases having similar uniform and helical magnetic field configurations without the CD mode. We discuss the implications of this stabilizing mechanism for the stability of astrophysical jets.

We revisit the ideal MHD stability of the m = 1 kink mode in configurations representative of coronal loops, using a stability code. We adopt different magnetic force-free equilibria defined by the twist function that are embedded into an outer potential field situated at a radial distance r0 from the magnetic axis. In the limit r0 l0, l0 being the axis pitch length, the configurations are driven unstable by the kink mode when the twist exceeds the classical critical value of 2.5π on the axis. However, the critical axis twist strongly depends on the equilibrium in the opposite limit, with sharply increasing values when r0 becomes of the order or smaller than l0. We interpret these results in terms of the stability criterion Φ l = 2.5π, where Φ l is the twist value averaged over a radial length l. It is found that l is of the order of 3−4 times l0, provided r0/l0 > ∼ 5; otherwise it depends on the twist profile via the existence of magnetic resonances.

The Kelvin-Helmholtz ͑KH͒ instability occurring in a single shear flow configuration that is embedded in a uniform flow-aligned magnetic field, is revisited by means of high resolution two-dimensional magnetohydrodynamic simulations. First, the calculations extend previous studies of magnetized shear flows to a higher compressibility regime. The nonlinear evolution of an isolated KH billow emerging from the fastest growing linear mode for a convective sonic Mach number M cs ϭ0.7 layer is in many respects similar to its less compressible counterpart ͑Mach M cs ϭ0.5). In particular, the disruptive regime where locally amplified, initially weak magnetic fields, control the nonlinear saturation process is found for Alfvén Mach numbers 4ՇM A Շ30. The most notable difference between M cs ϭ0.7 vs M cs ϭ0.5 layers is that higher density contrasts and fast magnetosonic shocklet structures are observed. Second, the use of adaptive mesh refinement allows to parametrically explore much larger computational domains, including up to 22 wavelengths of the linearly dominant mode. A strong process of large-scale coalescence is found, whatever the magnetic field regime. It proceeds through continuous pairing/merging events between adjacent vortices up to the point where the final large-scale vortical structure reaches the domain dimensions. This pairing/merging process is attributed to the growth of subharmonic modes and is mainly controlled by relative phase differences between them. These grid-adaptive simulations demonstrate that even in very weak magnetic field regimes (M A Ӎ30), the large-scale KH coalescence process can trigger tearing-type reconnection events previously identified in cospatial current-vortex sheets.

Solving the problem of fast eruptive events in magnetically dominated astrophysical plasmas requires the use of particularly well adapted numerical tools. Indeed, the central mechanism based on magnetic reconnection is determined by a complex behavior with quasi-singular forming current layers enriched by their associated small scale magnetic islands called plasmoids. A new code for the solution of two dimensional dissipative magnetohydrodynamics (MHD) equations in cartesian geometry specifically developed to this end is thus presented. A current-vorticity formulation representative of an incompressible model is chosen in order to follow the formation of the current sheets and the ensuing magnetic reconnection process. A finite element discretization using triangles with quadratic basis functions on an unstructured grid is employed, and implemented via a highly adaptive characteristic-Galerkin scheme. The adaptivity of the code is illustrated on simplified test equations and finally for magnetic reconnection associated to the non linear development of the tilt instability between two repelling current channels. Varying the Lundquist number S, has allowed to study the transition between the steady-state Sweet-Parker reconnection regime (for S < ∼ 10 4 ) and plasmoids dominated reconnection one (for S > ∼ 10 5 ). The implications for the understanding of the mechanism explaining the fast conversion of free magnetic energy in astrophysical environments such as in solar corona are briefly discussed.

Magnetic reconnection associated to the double tearing mode (DTM) is investigated by means of resistive relativistic magnetohydrodynamic (RRMHD) simulations. A linearly unstable double current sheet system in two dimensional cartesian geometry is considered. For initial perturbations of large enough longitudinal wavelengths, a fast reconnection event is triggered by a secondary instability that is structurally driven by the nonlinear evolution of the magnetic islands. The latter reconnection phase and time scale appear to weakly depend on the plasma resistivity and magnetization parameter. We discuss the possible role of such explosive reconnection dynamics to explain the MeV flares observed in the Crab pulsar nebula. Indeed the time scale and the critical minimum wavelength give constraints on the Lorentz factor of the striped wind and on the location of the emission region respectively.