Rarefaction wave in relativistic steady magnetohydrodynamic flows

We construct and analyze a model of the relativistic steady-state magnetohydrodynamic (MHD) rarefaction that is induced when a planar symmetric flow (with one ignorable Cartesian coordinate) propagates under a steep drop of the external pressure profile. Using the method of self-similarity we derive a system of ordinary differential equations that describe the flow dynamics. In the specific limit of an initially homogeneous flow we also provide analytical results and accurate scaling laws. We consider that limit as a generalization of the previous Newtonian and hydrodynamic solutions already present in the literature. The model includes magnetic field and bulk flow speed having all components, whose role is explored with a parametric study.Comment: 12 pages, Accepted in Physics of Plasma

Systematic construction of exact MHD models for astrophysical winds and jets

By a systematic method we construct general classes of exact and selfconsistent axisymmetric MHD solutions describing flows which originate at the near environment of a central gravitating astrophysical object. The unifying scheme contains two large groups of exact MHD outflow models, (I) meridionally self-similar ones with spherical critical surfaces and (II) radially self-similar models with conical critical surfaces. The classification includes known polytropic models, such as the classical Park er model of a stellar wind and the Blandford and Payne (1982) model of a disk-wind; it also contains nonpolytropic models, such as those of winds/jets in Sauty and Tsinganos (1994), Lima et al (1996) and Trussoni et al (1997). Besides the unification of these known cases under a common scheme, several new classes emerge and some are briefly analysed; they could be explored for a further understanding of the physical properties of MHD outflows from various magnetized and rotating astrophysical objects in stellar or galactic systems.Comment: 13 pages, 11 figure

Model-Matching type-methods and Stability of Networks consisting of non-Identical Dynamic Agents

Many recent approaches of distributed control over networks of dynamical agents rely on the assumption of identical agent dynamics. In this paper we propose a systematic method for removing this assumption, leading to a general approach for distributed-control stabilization of networks of non-identical dynamics. Local agents are assumed to share a minimal set of structural properties, such as input dimension, state dimension and controllability indices, which are generically satisfied for parametric families of systems. Our approach relies on the solution of certain model-matching type problems using local state-feedback and input matrix transformations which map the agent dynamics to a target system, selected to minimize the joint control effort of the local feedback-control schemes. By adapting a well-established distributed LQR control design methodology to our framework, the stabilization problem for a network of non-identical dynamical agents is solved. The applicability of our approach is illustrated via a simple UAV formation control problem

A class of exact MHD models for astrophysical jets

This paper examines a new class of exact and self-consistent MHD solutions which describe steady and axisymmetric hydromagnetic outflows from the atmosphere of a magnetized and rotating central object with possibly an orbiting accretion disk. The plasma is driven against gravity by a thermal pressure gradient, as well as by magnetic rotator and radiative forces. At the Alfvenic and fast critical points the appropriate criticality conditions are applied. The outflow starts almost radially but after the Alfven transition and before the fast critical surface is encountered the magnetic pinching force bends the poloidal streamlines into a cylindrical jet-type shape. The terminal speed, Alfven number, cross-sectional area of the jet, as well as its final pressure and density obtain uniform values at large distances from the source. The goal of the study is to give an analytical discussion of the two-dimensional interplay of the thermal pressure gradient, gravitational, Lorentz and inertial forces in accelerating and collimating an MHD flow. A parametric study of the model is also given, as well as a brief sketch of its applicability to a self-consistent modelling of collimated outflows from various astrophysical objects. {The analysed model succeeds to give for the first time an exact and self-consistent MHD solution for jet-type outflows extending from the stellar surface to infinity where it can be superfast, in agreement with the MHD causality principle.Comment: 16 pages, 15 figures. Accepted for publication in MNRA

Magnetohydrodynamics of Gamma-Ray Burst Outflows

Using relativistic, axisymmetric, ideal MHD, we examine the outflow from a disk around a compact object, taking into account the baryonic matter, the electron-positron/photon fluid, and the large-scale electromagnetic field. Focussing on the parameter regime appropriate to gamma-ray burst outflows, we demonstrate, through exact self-similar solutions, that the thermal force (which dominates the initial acceleration) and the Lorentz force (which dominates further out and contributes most of the acceleration) can convert up to ~50% of the initial total energy into asymptotic baryon kinetic energy. We examine how baryon loading and magnetic collimation affect the structure of the flow, including the regime where emission due to internal shocks could take place.Comment: To be published in ApJ Letters. 4 pages, 1 figur

Rarefaction acceleration in magnetized gamma-ray burst jets

Relativistic jets associated with long/soft gamma-ray bursts are formed and initially propagate in the interior of the progenitor star. Because of the subsequent loss of their external pressure support after they cross the stellar surface, these flows can be modeled as moving around a corner. A strong steady-state rarefaction wave is formed, and the sideways expansion is accompanied by a rarefaction acceleration. We investigate the efficiency and the general characteristics of this mechanism by integrating the steady-state, special relativistic, magnetohydrodynamic equations, using a special set of partial exact solutions in planar geometry (r self-similar with respect to the "corner"). We also derive analytical approximate scalings in the ultrarelativistic cold/magnetized, and hydrodynamic limits. The mechanism is more effective in magnetized than in purely hydrodynamic flows. It substantially increases the Lorentz factor without much affecting the opening of the jet; the resulting values of their product can be much grater than unity, allowing for possible breaks in the afterglow light curves. These findings are similar to the ones from numerical simulations of axisymmetric jets by Komissarov et al and Tchekhovskoy et al, although in our approach we describe the rarefaction as a steady-state simple wave and self-consistently calculate the opening of the jet that corresponds to zero external pressure.Comment: 11 page

Distributed LQR Methods for Networks of Non-Identical Plants

Two well-established complementary distributed linear quadratic regulator (LQR) methods applied to networks of identical agents are extended to the non-identical dynamics case. The first uses a top-down approach where the centralized optimal LQR controller is approximated by a distributed control scheme whose stability is guaranteed by the stability margins of LQR control. The second consists of a bottom-up approach in which optimal interactions between self-stabilizing agents are defined so as to minimize an upper bound of the global LQR criterion. In this paper, local state-feedback controllers are designed by solving model-matching type problems and mapping all the agents in the network to a target system specified a priori. Existence conditions for such schemes are established for various families of systems. The single-input and then the multi-input case relying on the controllability indices of the plants are first considered followed by an LMI approach combined with LMI regions for pole clustering. Then, the two original top-down and bottom-up methods are adapted to our framework and the stability problem for networks of non-identical dynamical agents is solved. The applicability of our approach for distributed network control is illustrated via a simple example

Jet simulations extending radially self-similar MHD models

We perform a numerical simulation of magnetohydrodynamic radially self-similar jets, whose prototype is the Blandford & Payne analytical example. The reached final steady state is valid close to the rotation axis and also at large distances above the disk where the classical analytical model fails to provide physically acceptable solutions. The outflow starts with a sub-slow magnetosonic speed which subsequently crosses all relevant MHD critical points and corresponding magnetosonic separatrix surfaces. The characteristics are plotted together with the Mach cones and the super-fast magnetosonic outflow satisfies MHD causality. The final solution remains close enough to the analytical one which is thus shown to be topologically stable and robust for various boundary conditions.Comment: 11 pages, 8 figures, minor changes to match the version accepted by MNRA

A disk-wind model with correct crossing of all MHD critical surfaces

The classical Blandford & Payne (1982) model for the magnetocentrifugal acceleration and collimation of a disk-wind is revisited and refined. In the original model, the gas is cold and the solution is everywhere subfast magnetosonic. In the present model the plasma has a finite temperature and the self-consistent solution of the MHD equations starts with a subslow magnetosonic speed which subsequently crosses all critical points, at the slow magnetosonic, Alfven and fast magnetosonic separatrix surfaces. The superfast magnetosonic solution thus satisfies MHD causality. Downstream of the fast magnetosonic critical point the poloidal streamlines overfocus towards the axis and the solution is terminated. The validity of the model to disk winds associated with young stellar objects is briefly discussed. ~Comment: 13 pages, MNRAS accepted for publicatio