Thibaut Lery

Magnetic tower outflows from a radial wire array Z-pinch

We present the first results of high energy density laboratory astrophysics experiments which explore the evolution of collimated outflows and jets driven by a toroidal magnetic field. The experiments are scalable to astrophysical flows in that critical dimensionless numbers such as the Mach number, the plasma β and the magnetic Reynolds number are all in the astrophysically appropriate ranges. Our experiments use the MAGPIE pulsed power machine and allow us to explore the role of magnetic pressure in creating and collimating the outflow as well as showing the creation of a central jet within the broader outflow cavity. We show that currents flow along this jet and we observe its collimation to be enhanced by the additional hoop stresses associated with the generated toroidal field. Although at later times the jet column is observed to go unstable, the jet retains its collimation. We also present simulations of the magnetic jet evolution using our two-dimensional resistive magnetohydrodynamic laboratory code. We conclude with a discussion of the astrophysical relevance of the experiments and of the stability properties of the jet.

The evolution of magnetic tower jets in the laboratory

The evolution of laboratory produced magnetic jets is followed numerically through three-dimensional, nonideal magnetohydrodynamic simulations. The experiments are designed to study the interaction of a purely toroidal field with an extended plasma background medium. The system is observed to evolve into a structure consisting of an approximately cylindrical magnetic cavity with an embedded magnetically confined jet on its axis. The supersonic expansion produces a shell of swept-up shocked plasma that surrounds and partially confines the magnetic tower. Currents initially flow along the walls of the cavity and in the jet but the development of current-driven instabilities leads to the disruption of the jet and a rearrangement of the field and currents. The top of the cavity breaks up, and a well-collimated, radiatively cooled, “clumpy” jet emerges from the system.

Astrophysical radiative shocks: From modeling to laboratory experiments

Radiative shock waves are observed around astronomical objects in a wide variety of environments, for example, they herald the birth of stars and sometimes their death. Such shocks can also be created in the laboratory, for example, by using energetic lasers. In the astronomical case, each observation is unique and almost fixed in time, while shocks produced in the laboratory and by numerical simulations can be reproduced, and investigated in greater detail. The combined study of experimental and computational results, as presented here, becomes a unique and powerful probe to understanding radiative shock physics. Here we show the first experiment on radiative shock performed at the PALS laser facility.The shock is driven by a piston made from plastic and gold in a cell filled with xenon at 0.2 bar. During the first 40 ns of the experiment, we have traced the radiative precursor velocity, that is showing a strong decrease at that stage.Three-dimensional ~3D! numerical simulations, including state-of-art opacities, seem to indicate that the slowing down of the precursor is consistent with a radiative loss, induced by a transmission coefficient of about 60% at the walls of the cell. We infer that such 3D radiative effects are governed by the lateral extension of the shock wave, by the value of the opacity, and by the reflection on the walls. Further investigations will be required to quantify the relative importance of each component on the shock properties.

Structure and Stability of Keplerian Magnetohydrodynamic Jets

MHD jet equilibria that depend on source properties are obtained using a simplified model for stationary, axisymmetric and rotating magnetized outflows (Lery et al.). The present rotation laws are more complex than previously considered and include a Keplerian disc. The ensuing jets have a dense, current-carrying central core surrounded by an outer collar with a return current. The intermediate part of the jet is almost current-free and is magnetically dominated. Most of the momentum is located around the axis in the dense core, and this region is likely to dominate the dynamics of the jet. We address the linear stability and the nonlinear development of instabilities for our models using both analytical and 2.5 dimensional numerical simulations. The instabilities seen in the simulations develop with a wavelength and growth time that are well matched by the stability analysis. The modes explored in this work may provide a natural explanation for knots observed in astrophysical jets.

THE PROPAGATION OF MAGNETOCENTRIFUGALLY LAUNCHED JETS. I.

We present simulations of the propagation of magnetized jets. This work differs from previous studies in that the cross-sectional distributions of the jetss state variables are derived from analytical models for magnetocentrifugal launching. The source is a magnetized rotator whose properties are specified as boundary conditions. The jets in these simulations are considerably more complex than the top-hat constant density, etc. profiles used in previous work. We find that density and magnetic field stratification (with radius) in the jet leads to new behavior including the separation of an inner jet core from a low density collar. We find this jet within a jet structure, along with the magnetic stresses, leads to propagation behaviors not observed in previous simulation studies. Our methodology allows us to compare MHD jets from different types of sources whose properties could ultimately be derived from the behavior of the propagating jets.

A Global Jet/Circulation Model for Young Stars

Powerful, highly collimated jets, surrounded by bipolar molecular outflows, are commonly observed near Young Stellar Objects (YSOs). In the usual theoretical picture of star formation, a jet is ejected from a magnetized accretion disk, with a molecular outflow being driven either by the jet or by a wider wind coming from the disk. Here, we propose an alternative global model for the flows surrounding YSOs. In addition to a central accretion-ejection engine driving the jet, the molecular outflow is powered by the infalling matter and follows a circulation pattern around the central object without necessarily being entrained by a jet. It is shown that the model produces a heated pressure-driven outflow with magneto-centrifugal acceleration and collimation. We report solutions for the three dierent parts of this self-similar model, i.e. the jet, the infalling envelope and the circulating matter that eventually forms the molecular outflow. This new picture of the accretion/outflow phase provides a possible explanation for several observed properties of YSO outflows. The most relevant ones are the presence of high mass molecular outflows around massive protostars, and a realistic fraction (typically 0.1) of the accretion flow that goes into the jet.

Ambipolar Diffusion in Young Stellar Object Jets

We address the issue of ambipolar diffusion in Herbig-Haro (HH) jets. The current consensus holds that these jets are launched and collimated via MHD forces. Observations have, however, shown that the jets can be mildly to weakly ionized. Beginning with a simple model for cylindrical equilibrium between neutral, plasma, and magnetic pressures, we calculate the characteristic timescale for ambipolar diffusion. Our results show that a significant fraction of HH jets will have ambipolar diffusion timescales equivalent to, or less than, the dynamical timescales. This implies that MHD equilibria established at the base of an HH jet may not be maintained as the jet propagates far from its source. For typical jet parameters one finds that the length scale at which ambipolar diffusion should become significant corresponds to the typical size of large (parsec) scale jets. We discuss the significance of these results for the issue of magnetic fields in parsec-scale jets.

Interacting Jets From Binary Protostars

Aims. We investigate potential models that could explain why multiple proto-stellar systems predominantly show single jets. During their formation, stars most frequently produce energetic outflows and jets. However, binary jets have only been observed in a very small number of systems. Methods. We model numerically 3D binary jets for various outflow parameters. We also model the propagation of jets from a specific source, namely L1551 IRS 5, known to have two jets, using recent observations as constraints for simulations with a new MHD code. We examine their morphology and dynamics, and produce synthetic emission maps. Results. We find that the two jets interfere up to the stage where one of them is almost destroyed or engulfed into the second one. We are able to reproduce some of the observational features of L1551 such as the bending of the secondary jet. Conclusions. While the effects of orbital motion are negligible over the jets dynamical timeline, their interaction has significant impact on their morphology. If the jets are not strictly parallel, as in most observed cases, we show that the magnetic field can help the collimation and refocusing of both of the two jets.

Protostellar evolution during time-dependent anisotropic collapse

The formation and collapse of a protostar involves the simultaneous infall and outflow of material in the presence of magnetic fields, self-gravity and rotation. We use self-similar techniques to self-consistently model the anisotropic collapse and outflow by using a set of angle-separated self-similar equations. The outflow is quite strong in our model, with the velocity increasing in proportion to radius, and material formally escaping to infinity in the finite time is required for the central singularity to develop. Analytically tractable collapse models have been limited mainly to spherically symmetric collapse, with neither magnetic field nor rotation. Other analyses usually employ extensive numerical simulations, or either perturbative or quasistatic techniques. Our model is unique as an exact solution to the non-stationary equations of self-gravitating magnetohydrodynamics (MHD), which features co-existing regions of infall and outflow. The velocity and magnetic topology of our model is quadrupolar, although dipolar solutions may also exist. We provide a qualitative model for the origin and subsequent evolution of such a state. However, a central singularity forms at late times, and we expect the late-time behaviour to be dominated by the singularity, rather than depend on the details of its initial state. Our solution may, therefore, have the character of an attractor among a much more general class of self-similarity.

European success stories in industrial mathematics

Foreword.- Preface.- Introduction.- Health Biology.- Energy & Environment.- Finance & Modelling.- Automotive Industry & Manufacturing.- Aerospace & Electronics.- Services, Transport & Logistics.- Annex. Summary Report of the E.S.F. Forward Look.