Session NM10: Mini-conference on Understanding Astrophysical Dynamos II

Cyclic dynamo action in numerial simulation of solar convection

I will review recent advances in the production of solar-like cyclic variations of a dynamo-generated large-scale magnetic field arising in global MHD simulations of solar convection. After describing a few representative simulations, I will focus on the turbulent nature of the driving electromotive force. Cyclic variations of the large-scale magnetic component appears to hinge on a fine balance between induction by the large-scale flows, and a turbulent electromotive force, the latter surprisingly akin to simple expectations from mean-field electrodynamics. I will also discuss the nature and mode of operatin of the mechanisms limiting the growth of the large-scale magnetic field in these simulations.   

Convective dynamos in solar-type stars

During their long main-sequence lifetime, stars like our Sun have strong magnetic fields at their surfaces. Indeed, magnetism is a nearly ubiquitous feature of the F- to M-type stars, which all have convective envelopes beneath their photospheres where a plasma dynamo builds and rebuilds the global-scale fields. The surface magnetism depends most strongly on the rotation rate of the star, with young rapidly rotating stars showing significantly more magnetic activity than our Sun, but the source of this correlation remains unclear. Here we explore recent 3-D magnetohydrodynamic simulations of convectively driven dynamos in solar-type stars. These simulations are conducted with the anelastic spherical harmonic (ASH) code on modern supercomputers. These simulations of global-scale convection and dynamo action produce strikingly organized magnetic structures in the bulk of their convection zones. This is a surprise as solar dynamo theory generally holds that a tachocline of shear is required for such global-organization. Here, wreaths of magnetic field fill the convection zone and can undergo regular cycles of polarity reversal, with cyclic behavior a common feature throughout the parameter space we have explored.   

Exploring the Deep Convection and Magnetism of A-type stars

A-type stars have both a near-surface layer of fast convection that can excite acoustic modes and a deep zone of core convection whose properties may be probed with asteroseismology. Many A-type stars also exhibit large magnetic spots that are often attributed to surviving primordial fields of global scale in the intervening radiative zone. We have explored the potential for core convection in rotating A-type stars to build strong magnetic fields through dynamo action. Using the ASH code, we model the inner 30\% by radius of a two solar mass A-type star, rotating at four times the solar rate and capturing the convective core and a portion of the overlying radiative envelope. Convection in these stars drives a strong retrograde differential rotation and yields a core that is prolate in shape. When dynamo action is admitted, the convection generates strong magnetic fields largely in equipartition with the dynamics. Remarkably, introducing a modest but large-scale external field threading the radiative envelope (which may be of primordial origin) can substantially alter the turbulent dynamics of the convective interior. The resulting convection establishes a complex assembly of helical rolls that link distant portions of the core and yield magnetic fields of super-equipartition strength.   

Transition from hydro to magnetohydrodynamics turbulence in a von K\'arm\'an flow

We report on how how an externally applied magnetic field modifies turbulence in a von Karman(VK) swirling flows. Time resolved measurements concern global variables (such as theflow power consumption) and local recordings of the induced magnetic field. From these measurements, we introduce an effective Reynolds number which takes into account changes in the interaction parameter N, as Rm$_{eff}$ = Rm(1 - $\alpha $ N). This definition of the effective magnetic Reynolds number leads to unified scalings for both the global variable and the local induced magnetic field. In addition, when the flow rotation axis is perpendicular to the direction of the applied magnetic field, we observe significant flow and induced magnetic field fluctuations at low interaction parameter values, but corresponding to an Alfven speed V$_A$ of the order of the fluid velocity fluctuations u$_{rms}$. This strong increase in the flow fluctuations is attributed to chaotic changes between hydrodynamics and magnetohydrodynamics velocity profiles.   

Using unmagnetized plasmas to produce dynamos

Constructing a laboratory example of a homogeneous dynamo is a long-standing problem with several examples of qualified successes. Studies using the Madison Dynamo Experiment have demonstrated the robust contribution of large-scale eddies to the mean field induction. By controlling the formation of eddies from unstable shear flow, we demonstrate that the concept of a turbulent resistivity is robust in low magnetic Prandtl number flows. Estimates based on rough mean-field theory $\beta$-effect calculations are in good agreement with experimental measurement. The limitations of liquid metal experiments lead to the desire for a different approach. A new platform for creating, driving, and diagnosing unmagnetized plasmas is being developed to facilitate a dynamo experiment that can explore broad parameter ranges of fluid viscosity and resistivity. Such a device provides both opportunities and challenges in incorporating physics beyond MHD such as ion-neutral drag and collisionless plasma phenomena.   

Numerical simulations of plasma dynamo in cylindrical and spherical von Karman flows

We present the results of dynamo simulations in cylindrical and spherical von Karman plasma flows with parameters relevant to the Madison Plasma Couette Experiment (MPCX) and Madison Plasma Dynamo Experiment (MPDX). Simulations are done using the extended magnetohydrodynamic (MHD) code NIMROD for an isothermal compressible plasma model including two-fluid effects (Hall term in Ohm's law), which is beyond the standard incompressible MHD picture. It is found that the counter-rotating von Karman flows result in sustained dynamo action and self-generation of magnetic field when the magnetic Reynolds number exceeds a critical value. Depending on geometry and plasma parameters the dynamo field can either saturate at certain amplitude corresponding to a new stable equilibrium (laminar dynamo) or lead to turbulent dynamo. It is shown that plasma compressibility results in increase of the critical magnetic Reynolds number while inclusion of the Hall term in Ohm's law changes the level of saturated dynamo field but not the critical value for the onset of dynamo action. The work is supported by NSF.   

First Steps Towards Magnetorotational Instabilities and Dynamos in Plasma Experiments

A sufficiently hot, unmagnetized flowing plasma experiment is ideal for studying basic mechanisms of astrophysical plasma phenomena. The Plasma Couette Experiment (PCX) will generate a differentially rotating plasma at parameters necessary to study the magnetorotational instability (MRI) or possibly a dynamo, and will explore effects specific to plasma, such as the Hall effect, plasma-neutral interactions, and compressibility. In PCX, plasma is confined by a cylindrical, axisymmetric, highly localized ring cusp magnetic field at the boundary. Emissive filaments are biased in the magnetized region to create JxB torque, and velocity couples inward to the unmagnetized region through viscosity. Torque can be applied at the inner, outer, or endcap boundaries, resulting in a controlled, differentially rotating plasma. Proof of principle studies in Helium plasmas (Te=5 eV, n=1.5x10$^{11}$, 5 km/s flow speeds) are approaching MRI unstable regimes predicted by local linear analysis and global Hall-MHD numerical simulations. Progress towards establishing controlled differential rotation profiles will be presented.   

Dynamics of torsional oscillations in the solar convective zone

In this presentation I will discuss the dynamics of torsional oscillations arising in a magnetohydrodynamical simulation of solar convection producing solar-like polarity reversals of its large-scale axisymmetric magnetic component. I will show that the driving of these oscillations arises not only through periodic variations of the Lorentz force associated with the cycling large-scale magnetic component, but also through magnetically-mediated changes in the other forces controlling the azimuthal dynamics, namely Reynolds stresses, Coriolis force, and Maxwell stresses associated with the small-scale turbulent magnetic component. To this end, various characterizations of the components will be displayed : angular momentum fluxes, force densities and power densities. I will also compare and contrast the properties of these oscillations with their solar counterparts, as measured by helioseismology.   

MHD Simulation-driven kinematic mean-field models of the solar cycle

Using numerical data from global magnetohydrodynamical simulations of solar convection, I extract all nine components of the full alpha-tensor relating the mean electromotive force to the mean cycling magnetic field arising in the simulation. I then use this alpha-tensor as input to a conventional kinematic $\alpha^2\Omega$ mean-field model, and compare the behavior of the resulting cyclic solutions to those observed in the fully dynamical numerical simulations. This comparison helps to disentangle contributions to cyclic variations in the numerical simulations tied to the dynamical variations of the large-scale flows, from those driven by the turbulent electromotive force.   

Role of Hyperresistivity in Laboratory and Astrophysical Dynamos

It has been known for about 25 years that within the context of mean-field dynamo theories, the turbulent electromotive force (emf) can be represented as the total divergence of a physical quantity that, in some cases of great interest, can be shown to be proportional the gradient of the parallel current density. This form of the turbulent emf is often referred to as hyperresistivity (or electron viscosity). When hyperresistivity is included in theories of alpha quenching for astrophysical dynamos, it can be shown that in the presence of non-trivial magnetic field topologies or differential flows, hyperresistivity remains as the only remnant due to a cancellation in the alpha and beta effects of kinematic dynamo theory. In this talk, we will discuss the relevance of this concept to the dynamo effect produced by the magnetorotational instability, as well as its role in producing fast reconnection in weakly collisional plasmas.