[Paper Review] Characterization of Quasi-Keplerian, Differentially Rotating, Free-Boundary Laboratory Plasmas

V. Valenzuela-Villaseca, L. Suttle+10 more|arXiv (Cornell University)|Jan 25, 2022

Laser-Plasma Interactions and Diagnostics4 citations

TL;DR

This study presents a pulsed-power-driven laboratory experiment that generates quasi-Keplerian, differentially rotating plasma flows with free-boundary conditions, using ablation flows from a Z-pinch wire array to inject angular momentum. The plasma achieves a maximum rotation velocity of $23 \pm 3$ km/s and exhibits a quasi-Keplerian profile with a Rayleigh discriminant $\kappa^2 \propto r^{-2.8 \pm 0.8}$ rad$^2$/s$^2$, confirming hydrodynamic stability and potential for Magneto-Rotational Instability (MRI) in collisional plasmas.

ABSTRACT

We present results from pulsed-power driven differentially rotating plasma experiments designed to simulate physics relevant to astrophysical disks and jets. In these experiments, angular momentum is injected by the ram pressure of the ablation flows from a wire array Z pinch. In contrast to previous liquid metal and plasma experiments, rotation is not driven by boundary forces. Axial pressure gradients launch a rotating plasma jet upwards, which is confined by a combination of ram, thermal, and magnetic pressure of a surrounding plasma halo. The jet has subsonic rotation, with a maximum rotation velocity $23 \pm 3$ km/s. The rotational velocity profile is quasi-Keplerian with a positive Rayleigh discriminant $κ^2 \propto r^{-2.8\pm0.8}$ rad$^2$/s$^2$. The plasma completes $0.5 - 2$ full rotations in the experimental time frame ($\sim 150$ ns).

Motivation & Objective

• To develop a laboratory platform capable of generating free-boundary, differentially rotating plasmas without rigid wall confinement.
• To study the conditions under which Magneto-Rotational Instability (MRI) can be initiated in a collisional plasma, relevant to astrophysical accretion disks.
• To characterize the rotational velocity profile and stability of inertially driven rotating plasma columns using multi-diagnostic techniques.
• To enable future study of MRI, dynamo effects, and jet collimation in a single experimental system with realistic astrophysical scaling.

Proposed method

• A pulsed-power generator drives a Z-pinch wire array (aluminum, 8×40 μm wires) to produce ablation flows via rapid plasma expansion.
• Ablation flows are directed inward and azimuthally by a magnetic field with a radial component from offset return posts, creating ram pressure for radial confinement.
• Axial pressure gradients launch rotating plasma jets from the ends of the rotating column, forming a free-boundary structure.
• Multi-diagnostic measurements include optical and XUV self-emission (5 ns resolution), interferometry, and optical Thomson scattering to determine density, temperature, and velocity profiles.
• Angular velocity profiles are fitted using a power-law $\Omega \propto r^{\gamma}$, and the Rayleigh discriminant $\kappa^2 \propto r^{-3}d(r^4\Omega^2)/dr$ is calculated to assess stability and MRI potential.
• The impact parameter in laser probing is varied ($b = 0.1$ mm, $0.3$ mm) to assess robustness of velocity profile measurements.

Experimental results

Research questions

• RQ1 Can a free-boundary, differentially rotating plasma with a quasi-Keplerian profile be generated in a laboratory setting without rigid wall constraints?
• RQ2 What is the measured rotational velocity profile, and does it satisfy the conditions for Magneto-Rotational Instability (MRI)?
• RQ3 How do the plasma dynamics, including axial jet formation and rotation, evolve over the experimental timescale (~150 ns)?
• RQ4 What is the role of ablation-driven ram pressure in confining and sustaining the rotating plasma column?
• RQ5 Can this platform support the linear growth of seed magnetic fields via differential rotation, leading to MRI onset?

Key findings

• The plasma achieves a maximum rotation velocity of $23 \pm 3$ km/s, with axial jets completing 0.5 to 2 full rotations during the experiment.
• The rotational velocity profile is quasi-Keplerian, with $\Omega \propto r^{\gamma}$ and $\gamma = -1.4 \pm 0.4$, corresponding to a Rayleigh discriminant $\kappa^2 \propto r^{-2.8 \pm 0.8}$ rad$^2$/s$^2 > 0$.
• The positive Rayleigh discriminant confirms hydrodynamic stability against axisymmetric perturbations, while the differential rotation profile satisfies the condition for MRI instability ($-2 < \gamma < 0$).
• Magnetic and viscous diffusion lengths are $\ell_\eta \sim 70$ μm and $\ell_\nu \sim 0.5$ μm, indicating negligible dissipation, so MRI growth timescales ($\sim 150 \pm 100$ ns) are comparable to the orbital period.
• The measured rotation profile is robust across different laser probing impact parameters ($b = 0.1$ mm, $0.3$ mm), confirming consistency of the velocity profile.
• The experiment demonstrates a viable path toward studying MRI, dynamo effects, and jet collimation in a single, free-boundary plasma system with realistic astrophysical relevance.