Session UM10: Mini-Conference on Momentum Transport in Magnetic Fusion and Astrophysical Systems II

Planet Formation in Magnetized Accretion Disks

Stars form by the flow of matter through an accretion disk. An efficient mechanism of angular momentum transport is required to drive this flow. The magneto rotational instability (MRI) is the leading candidate (along with self-gravity in the early stages of growth) to drive turbulent momentum transport in disks. I will briefly summarize the current status of MRI turbulence in weakly magnetized circumstellar disks. Then I will describe how MRI turbulence affects the formation of planets. By vigorously mixing small solids, turbulence generally tends to oppose the accumulation into planets. Yet somehow planets form. MRI turbulence has the tendency to launch long-lived, axisymmetric zonal flows. These super- and sub-Keplerian flows surround a pressure maximum which efficiently accumulates cm to m scale solids. These solids are subject to a strong aerodynamic clumping mechanism driven by the streaming instability (Youdin \& Goodman, 2005). When sufficiently dense, clumps of small solids collapse gravitationally into 100 km-scale solid planetesimals. This theory of early planet formation is recorded in the asteroid and Kuiper belts of our Solar System, in the debris disks surrounding other stars and in magnetized meteorite fragments that fall to Earth.   

Study of Angular Momentum Transport in Hydrodynamic and Magnetohydrodynamic Experiments

Rapid angular momentum transport has been observed to occur in both laboratory fusion plasmas and astrophysical plasmas, but its physical mechanisms still remain illusive. In this paper, we describe a series of laboratory fluid experiments in order to investigate a variety of the proposed mechanisms either in hydrodynamics or magnetohydrodynamics (MHD). They include (1) hydrodynamic turbulence for Keplerian flows\footnote{H. Ji, M. Burin, E. Schartman, and J. Goodman, Nature {\bf 444}, 343 (2006)}, (2) Magnetocoriolis (MC) waves\footnote{M. Nornberg, H. Ji, E. Schartman, A. Roach, and J. Goodman, Phys. Rev. Lett. {\bf 104}, 074501 (2010)}, (3) Magnetorotational Instability (MRI), (4) Rossby waves, and (5) Magneto-Rossby waves. The first three mechanisms have been or are being investigated on the ongoing Princeton MRI experiment (http://mri.pppl.gov) while the last two mechanisms will be investigated on a newly built experiment\footnote{E. Edlund et al., this mini-conference} and on a further modified Princeton MRI experiments. Implications of these experimental results for the astrophysical problems will be discussed.   

A new experiment for the study of hydrodynamic waves and turbulence

As a complement to the existing Princeton MRI Experiment, which is used for studies of MHD waves in a rotating liquid metal, a new device is being constructed by modifying the existing Couette water experiment for the study of purely hydrodynamic waves and turbulence. A primary objective of this new device is the study of Rossby waves, which will be excited by forcing a potential vorticity gradient through surfaces which are inclined relative to the azimuthal plane. A modular design allows for change of these fluid interfaces to study of Rossby waves under different forcing conditions. The experiment will be equipped with a two dimensional laser Doppler velocimetry (LDV) system, which can measure correlated fluctuations of radial and azimuthal velocities to form a measure of the Reynolds stress. The additional use of an ultrasonic Doppler velocimetry (UDV) system will allow for instantaneous measurement of the azimuthal and radial velocity profile at multiple locations to identify bulk flow characteristics and low-order wave structures. These measurement techniques allow for detailed study of the interplay between large scale waves, turbulence and angular momentum transport.   

Convective Instability in the Plasma Couette Experiment

The emergence of flux from the tachocline and through the sun's surface is thought to occur by the magnetic buoyancy instability (Parker instability). The Plasma Couette Experiment (PCX) at U. Wisconsin-Madison presents a unique opportunity to explore this instability, as well as an instability due to compositional buoyancy, in the laboratory. In PCX, a cylindrical, axisymmetric plasma is confined in a ring cusp magnetic field, and rotated using ring electrodes, positioned between the magnets, which provide an ExB drift at the plasma boundary. Initial plasmas are characterized by densities of $10^{10}$ cm$^{-3}$, temperatures of 10 eV, and rotation velocities of 3 km/s. The rotation, as recorded by Mach probes, appears to be modulated by diamagnetic flows at the boundary. To achieve buoyant instability, we plan to inject either a light ion species (helium into a spinning argon plasma) or a small spheromak at the rotating boundary. Progress towards these goals will be discussed. Work supported by NSF and DOE (CMTFO).   

Nonlocal Studies of the Magnetorotational Instability

Viewed from the perspective of nonlocal studies of plasmas with sheared flows, the magnetorotational instability (MRI) is an important member of a larger family of shear- driven instabilities in a magnetized disk. A comprehensive analytical and numerical approach to these instabilities was first developed by Hameiri (1976) and Bondeson and coworkers (1987) with applications to fusion plasmas, and more recently applied by Keppens and cooworkers (2002) to Keplerian disks. The general framework uncovers a number of new features that must be included in our understanding of the linear as well as well as nonlinear evolution of the MRI. These include (1) overstability due the presence of compressibility for non-axisymmetric modes, and (2) the presence of an infinite sequence of discrete unstable modes accumulating toward the edge of the slow wave continuum at the Doppler-shifted frequency, regardless of the pressure gradient. For linear studies of these nonlocal instabilities, we present numerical results from a linear eignemode solver, and compare the predictions with NIMROD. We then use NIMROD to examine the consequences of these nonlocal instabilities for the nonlinear evolution of the MRI, where coupling to non-axisymmetric modes has already been shown to play an important role in the saturation of the instability.   

Global Hall-MHD simulations of magnetorotational instability

Hall-MHD numerical simulations of the Madison Plasma Couette Flow Experiment (MPCX) have been performed using the extended MHD code NIMROD. The MPCX has been constructed to study the Magnetorotational Instability (MRI) in an unmagnetized and fast flowing plasma. The two-fluid Hall effect, which is relevant to some astrophysical situations such as protostellar disks, is also expected to be important in the MPCX. We first derive the local Hall dispersion relation including resistivity and viscosity, extending earlier work by S. Balbus and C. Terquem. The predictions of the local analysis are compared with global linear stability analysis of the MRI for a range of magnetic Prandtl and magnetic Reynolds numbers. It is found that in all cases the MHD stability limit and mode structure are altered by the Hall term. Two-fluid physics also affects significantly the nonlinear evolution and the saturation of the axisymmetric MRI. To further study momentum transport and self-generation of magnetic field in an MRI-driven turbulent state, we have carried out fully nonlinear MHD computations. Non-axisymmetric modes play an increasingly important role as the magnetic Reynolds number increases, and grow to large amplitudes. Supported by NSF grant 0962244.   

Kinetic Dissipation of Magnetized Relativistic Astrophysical Momentum Outflow

Many high energy astrophysical phenomena involve relativistic outflows, from pulsar winds, blazar jets to gamma ray bursts. How these objects efficiently convert their outflow momentum and energy into energetic particles and radiation remains one of the outstanding unsolved problems in astrophysics. Since relativistic plasmas are highly collisionless, such dissipation must be studied at the kinetic level. Here we present Particle-in-Cell (PIC) simulations of two specific examples: dissipation of Poynting flux in the context of pulsar equatorial stripe winds, and relativistic shear layers in the context of differentially moving jets. In the former case we show how comoving ponderomotive acceleration can efficiently convert electromagnetic energy and momentum into accelerated particles in an overdense but high a0 (= dimensionless vector potential) plasma. In the latter case we show how relativistic boundary layers develop and energize particles at the expense of outflow momentum shear. We study the dissipation rate as a function of relative Lorentz factor, magnetic field strength and orientation.   

Turbulence Suppression in a coherent structure of localized current and vorticity

As a prelude to studying momentum transport in the RFP we examine the quasi-single helicity state of RFX as a transport barrier. Using analytic and numerical approaches we investigate turbulence suppression by a coherent structure of localized current and vorticity with a reduced MHD model. Previously, suppression was investigated inside a localized vortex structure in 2D Navier-Stokes turbulence\footnote{P.~W. Terry, D.~E. Newman, and N.~Mattor. \emph{Phys. Fluids A}, 4\penalty0 (5):927--937, 1992.} and a localized current structure in kinetic Alfv\'en wave turbulence.\footnote{P.~W. Terry and K.~W. Smith. \emph{Astrophys. J.}, 665\penalty0 (1):402--415, 2007.} Following the previous works, the time scales of coherent structures with a flow shear and magnetic field shear and ambient turbulence are assumed to be separated and a variant of eddy-damped quasinormal Markovian (EDQNM) closure is applied to the turbulence. Qualitative criteria will be estimated for flow shear dominated, and magnetic field shear dominated suppression of turbulence. Numerical calculations will be given for comparison with the analytical estimates.   

Exact momentum conservation laws for gyrofluid and gyrokinetic models

Exact momentum conservation laws for gyrofluid and gyrokinetic models are derived by Noether method applied to the gyrofluid [1] and gyrokinetic [2,3] action functionals, respectively. As a result of the separation of a nonuniform (and time-independent) background magnetic field from the time-dependent dynamical fields, the gyrofluid and gyrokinetic momentum-stress tensors are asymmetric, which implies transport of angular momentum. The nature of the momentum-stress asymmetry for the gyrofluid model [1] is discussed in terms of reduced polarization and magnetization effects. The conservation of momentum for the gyrokinetic model [4], on the other hand, involves the Hamiltonian dynamics of the gyrocenter canonical momentum. \\[4pt] [1] A. J. Brizard, R. E. Denton, B. Rogers, and W. Lotko, Phys. Plasmas {\bf 15}, 082302 (2008). \newline \noindent [2] A. J. Brizard, Phys. Plasmas {\bf 7}, 4816 (2000). \newline \noindent [3] A. J. Brizard, Phys. Plasmas {\bf 17}, 042303 (2010). \newline \noindent [4] A. J. Brizard and N. Tronko, in preparation (2010).