This award funds research to carry out numerical simulations in support of Plasma Dynamo and Couette Flow experiments. A Plasma Couette experiment, the first of its kind, has been constructed to study Magnetorotational Instability (MRI) in a hot, unmagnetized and fast flowing plasma. Plasma is confined by a strong multipole magnetic field at the plasma surface. The goals of the experiment are to study the MRI and possible self-generation of magnetic field by MRI-driven turbulence at high magnetic Reynolds numbers (the regime applicable to astrophysical plasmas). If successful, the concept could be readily extended to a larger, plasma-based dynamo experiment, studying the self-generation of magnetic field (MHD dynamo) but through hydrodynamic-driven turbulence in a confined plasma. Numerical modeling and theoretical studies are crucial for advancing the understanding of these two experiments and assuring their ultimate success. Numerical simulations using the extended MHD code, NIMROD, will be done and the numerical results will be directly compared with the experimental measurements. Numerical simulations are also expected to provide a guidance for the experimental design.
The proposed simulations with NIMROD code would strongly benefit the validation of a code, NIMROD, extensively used by the Magnetic Fusion community. In addition, the Magneto-rotational Instability (MRI) is thought to play a vital role in many astrophysical settings. Thus it is essential to have a line of physical experiments and computational models carried out that can test, guide and perhaps challenge many of the precepts now being applied in theoretical models with regard to MRI.
This proposal was submitted to the NSF-DoE Partnership in Plasma Science and Engineering joint solicitation 08-589. This award is being funded jointly by the Divisions of Physics and Astronomical Sciences of the Mathematical and Physical Sciences Directorate.
Large-scale magnetic fields have been observed in widely different types of astrophysical objects, such as planets and stars, as well as accretion disks and galaxies. The source of this magnetic field is the well-known dynamo effect, which has stimulated an extensive search for models in which large-scale magnetic fields are self-generated from turbulence and sustained despite the presence of dissipation. In addition to understanding the dynamo mechanism in astrophysical accretion disks, anomalous angular momentum transport has also been a longstanding problem in accretion disks and laboratory plasmas. In astrophysical disks, as matter accretes onto a central object (such as protostars, neutron stars and black holes), angular momentum is rapidly transported outward. Some ways to attack this problem are by numerical modeling of laboratory experiments that are intended to simulate nature or by considering configurations with direct relevance to astrophysical disks. In this project, we have performed numerical modeling of the Madison Plasma Dynamo and Plasma Couette Flow eXperiments (MPDX and PCX, respectively). Our simulations use fluid approximations (Magnetohydrodynamics - MHD model), where plasma is treated as a single fluid, or two fluids, in the presence of electromagnetic forces. In some astrophysical disks, where plasma is weakly ionized, the ions can be demagnetized by collisions with neutrals and drift relative to the electrons. In this regime, the two-fluid Hall term, which arises from the difference between the electron and ion velocities, can become important. In plasma experiments in Madison, the two-fluid Hall term is also expected to be important. We have therefore performed both single fluid and two-fluid Hall simulations in the global domain of the experiment. These simulations have provided guidance, and have been necessary to obtain quantitatively reliable predictions for PCX. We believe this to be generally true for a plasma magneto-rotational instability (MRI) / dynamo experiment. Project outcomes/intellectual merit: Our three major findings throughout this project are as follows. (1) We found that the two-fluid physics alters the onset of MRI, also it significantly changes the nonlinear evolution, saturation and momentum transport of the axisymmetric MRI. (2) Nonlinear simulations of cylindrical von Karman dynamos were also performed in the Hall and MHD regimes. Using nonlinear 3-D NIMROD simulations, critical magnetic Reynolds numbers relevant to PCX were obtained. (3) Turbulent dynamo effect, which is essential for the amplification of large-scale magnetic fields have also been numerically examined. It was demonstrated that much can be learned by viewing the dynamo problem in both laboratory and astrophysical plasmas from a common perspective. The constraint imposed by magnetic helicity conservation on the alpha effect is considered for two important and very different examples of tearing instability in laboratory plasmas (magnetically dominated self-organized plasmas) and MRI in flow driven astrophysical disks (flow dominated self-organized plasmas). By analysis and direct numerical simulations (DNS), it was demonstrated that in both cases a dominant contribution to the alpha effect can be cast in the functional form of a total divergence of an averaged helicity flux, called the helicity-flux-driven alpha effect. Project outcomes/broader impact: Our simulations have provided validation exercises for a widely used code in the magnetic fusion community (the NIMROD code), in a new flow-driven plasma and in a simpler configuration than the fusion experiments. Our work has been closely coordinated with activities in the NSF Frontier Center CMSO (Center for Magnetic-Self Organization), and have been mutually beneficial for both the center and our project.
