Numerical Simulations of Z-Pinch Experiments to Create Supersonic Differentially Rotating Plasma Flows

Abstract

The physics of accretion disks is of fundamental importance for understanding of a wide variety of astrophysical sources that includes protostars, X-ray binaries, and active galactic nuclei. The interplay between hydrodynamic flows and magnetic fields and the potential for turbulence-producing instabilities is a topic of active research that would benefit from the support of dedicated experimental studies. Such efforts are in their infancy, but in an effort to push the enterprise forward we propose an experimental configuration which employs a modified cylindrical wire array Z-pinch to produce a rotating plasma flow relevant to accretion disks. We present three-dimensional resistive magnetohydrodynamic simulations which show how this approach can be implemented. In the simulations, a rotating plasma cylinder or ring is formed, with typical rotation velocity ∼30 km s −1 , Mach number ∼4, and Reynolds number in excess of 10 7 . The plasma is also differentially rotating. Implementation of different external magnetic field configurations is discussed. It is found that a modest uniform vertical field of 1 T can affect the dynamics of the system and could be used to study magnetic field entrainment and amplification through differential rotation. A dipolar field potentially relevant to the study of accretion columns is also considered.

Rotating plasma disks in dense Z-pinch experiments

“…By considering the expected time for ablation start, 80 ns, and the time of flight of plasma from the wires to the disk, 40 ns (at 1.4x10 7 cms -1 , see [7] and below), we can calculate the expected formation time as 120 ns. This agrees reasonably well with the observed time and very well with GORGON simulations of this experiment [2] (also 120 ns); therefore this is the formation time that will be used in further analysis. From the full images, similar to figure 2 but for 16 wires, we estimate the flow width as 0.5 mm; this is roughly the same as the initial disk thickness.…”

“…Angular momentum can be introduced to the flow by the addition of a radial field B r at the wires [2,4] which gives a Lorentz force F θ = J z ×B r . The combination of F r and F θ produces "off axis" flows at an angle θ to r with the convergence of these flows producing a rotating disk structure ( fig.1c).…”

“…Computational studies have already shown that scalable accretion disk plasmas should be achievable on Z-pinch experiments [2,3]. Building on the experience of z-pinch rotating jets demonstrated by Ampleford et al [4] a rotating plasma experiment was designed which would be complimentary to laser driven work first proposed by Ryutov [5]; work on this laser driven focus is currently being undertaken by Drake et al [R. P. Drake, private correspondence].…”

Formation of radiatively cooled, supersonically rotating, plasma flows in Z-pinch experiments: Towards the development of an experimental platform to study accretion disk physics in the laboratory

“…The converging flows are maintained in a quasi-steady state for the duration of the current pulse or until a significant fraction of the wire mass has been ablated; this results in the accumulation of mass on the axis. Angular momentum, with respect to the symmetry axis, can be introduced to the flow by the addition of a radial field B r at the wires [4,2] which gives a Lorentz force F θ = J z × B r . The combination of F r and F θ produces "off axis" flows at an angle θ with respect to the radial direction .…”

“…Computational studies have already shown that scalable accretion disk plasmas should be achievable on Z-pinch experiments [2,3]. The ability to controllably introduce rotation to a z-pinch system was first shown by Ampleford et al [4] for rotating jets.…”