NG21A-0200 INVITED
Relaxation of Line-tied Coronal Plasmas to MHD Equilibria with Current Singularities
The spontaneous formation of current singularities in line-tied magnetic configurations is a problem of fundamental interest, with important applications to the problem of coronal heating. In this talk, we will discuss some rigorous results which demonstrate that such singular states are formed as an ideally unstable system relaxes to a state of minimum energy subject to the constraints of line-tying. We simulate such systems using the 3D reduced MHD equations and identify criteria that enable us to describe the location and structure of these singularities. It is shown that these sites are qualitatively similar to so-called "quasi-separatrix layers" in the 3D coronal MHD literature. These results provide a rigorous foundation for the nanoflare model proposed by E. N. Parker, widely regarded as a model which identifies a promising mechanism for coronal heating.
NG21A-0201 INVITED
Relaxation in the Heliosphere
The solar wind is a driven, non-linear, open, non-equilibrium system. Streams, slow flows, ejecta, shocks, and turbulence produced near the Sun interact to create an evolving complex multiscale structure. During the declining phase of the solar cycle, large structures (seen as Corotating Merged Interaction Regions, CMIRs and Large-Scale Fluctuations) grow from 1 AU to ~15 AU. During solar maximum, Global Merged Interaction Regions (GMIRs) grow out to ~40 AU by the merging of systems of transient flows and other flows. After the formation of CMIRs, GMIRs, and Large-Scale Fluctuations, the solar wind tries to relax toward an equilibrium state. The relaxation as a function of distance out to the termination shock can be described by the evolution of the multi- scale probability distributions of increments of B (q-Gaussian functions), multifractal spectra, and correlation functions, using observations made by Voyager. Tsallis suggested that the evolution toward equilibrium could be described by a "q-triplet" derived from these properties, and the Voyager observations support this hypothesis. Voyager 1 observations show that the solar wind remains complex and non-linear in the heliosheath, after passing through the TS, but in some respects the heliosheath is closer to equilibrium than the supersonic solar wind.
NG21A-0202 INVITED
Magnetohydrodynamic Relaxation Processes in the Solar Corona
The magnetohydrodynamic (MHD) relaxation model, which was originally developed by J.B.Taylor, provided us a basic framework to understand the spontaneous formation and the transition of characteristic structures in MHD plasmas of low-beta and high-magnetic Reynolds number. The observation and numerical simulations have suggested that the Taylor-type relaxation could be operated not only in laboratory plasma but also in the solar corona, and may play a crucial role to form the typical large-scale helical structure, so-called sigmoid, in solar coronal active regions. However, the recent sophisticated data analysis indicated that magnetic shear parameter alpha, which is defined by the ratio between magnetic field and the curl of that, is highly distributed within an active region. It implies that the solar corona is far complicated than the theoretical model, and we cannot straightforwardly apply the simple relaxation model, which predict that the linear force-free field must be self-organized, to the solar coronal plasma. In this paper, first, we review the previous studies of the relaxation processes in the solar corona, and, second, represent the results of our recent works based on the reconstruction analysis of the three-dimensional magnetic field of active region using the high-accurate vector magnetogram observed by the Solar Optical Telescope (SOT) boarded on Hinode satellite. The results indicate that the relaxation scenario may be applicable, even though the magnetic field in flaring region is more complicated than previous thought. Finally, let us explain our recent effort to reproduce the flaring dynamics using the high-resolution numerical simulation driven by the real data. The comparative study between the simulation and the relaxation theory will be also represented.
NG21A-0203 INVITED
Study of Physics of Magnetic Reconnection and Magnetic Self-organization in Laboratory and Space Plasmas*
Magnetized plasma systems are often driven such that excess free energy excites instabilities that cause the system to relax to a lower energy state by self-organizing its large-scale structure. In this magnetic self- organization process, the magnetic field fluctuates in space or time and thus the instabilities are magnetic. Laboratory plasmas which can be driven to a state of high magnetic energy by an applied electric field (such as seen in toroidal pinch devices) often self-organized to a relaxed state. Magnetospheric substorms are driven by the solar wind; solar dynamo and coronal activity may be driven by convection and rotation; magnetic activity in accretion disks may be driven by rotation. The specification of the drive differs between situation, and in some of the phenomena rearrangement of quantities other than the magnetic field may dominate. But, the phenomena share the underlying physics of magnetic self-organization. It has been recognized that "physics-issue-dedicated" laboratory experiments can contribute significantly to the understanding of the fundamental physics for the magnetic self-organization phenomena since they can create fundamental physics processes in a controlled manner and provide well-correlated measurements at multiple locations simultaneously. This paper reviews the findings of recent laboratory experiments which address magnetic reconnection and related physics issues, including two-fluid physics which have been intensively studied in recent decades. This paper also describes the goals and major results from the Center for Magnetic Self-organization to study magnetic self-organization phenomena, a common frontier for both laboratory and space astrophysics research. *In collaboration with the members of the Center for Magnetic Self-Organization. http://mrx.pppl.gov/
NG21A-0204
Minimum Dissipative Relaxed States in Astrophysical Plasmas
We review briefly the problem of relaxation of a magnetized plasma based on the principle of minimum dissipation rate (MDR) of energy. Two situations are considered; one is under the constraint of constant global helicity for a closed system and the other is constant helicity injection rate for an open system. The principle of minimum dissipation rate is closely related to the well-known theorem of irreversible thermodynamics, principle of minimum entropy production rate. Magnetic fields obtained from both the MDR models are essentially non- force free and can support a finite pressure gradient. A self-consistent, time-dependent numerical simulations of dissipative plasmas at a higher Landquist number, typically ~ O(106-107), using full three dimensional compressible MHD code with a numerical resolution of 1283 shows that the global helicity remains approximately constant while magnetic energy is decaying faster and dissipation rate is decaying even faster than the magnetic energy. This justifies the use of of the principle of MDR as an effective minimizer during the process of plasma relaxation. Using a two fluid description, we show that Solar arcade structures can be modeled as a minimum dissipative relaxed state, and different types of arcade structures can be generated. We also present an approach to obtain the flux rope solution and discuss the properties of such flux ropes.
NG21A-0205
The sequence of self-organization of MHD plasmas
Traditional models of plasma magnetic self-organization assume zero β on the grounds that the actual β is very small. However, a model [1] inspired by laboratory experiments suggest that the behavior of plasma with small β is not the same as a zero β \ plasma because the behavior involves a competition between β and another small parameter, namely α2a2 where α=μ0I/ψ. Here, ψ is the axial flux in the flux tube, I is the axial current flowing in the flux tube, and a is the flux tube radius. The plasma can be considered as an assembly of small aspect ratio individually pressurized flux tubes, somewhat like strands of spaghetti wrapped around each other. Each flux tube (spaghetti strand) is not force-free, but rather has its axial current I balance a small radial pressure gradient such that the pressure is peaked on the flux tube axis. To an outsider the flux tube appears as an element of force-free current because the outsider is aware that the current I in the flux tube flows parallel to the flux tube axis. The external observer makes this deduction by measuring the azimuthal magnetic field associated with the axial current. Flux tubes interact with each other by the current in one flux tube `feeling' the azimuthal magnetic field due to an adjacent flux tube. The flux tubes collectively try to assume a force-free state whereby the current in each flux tube flows parallel to the magnetic field produced by all the other flux tubes and by any external source for the magnetic field. \qquad The sequence of evolution is (i) formation of the individual plasma-filled flux tubes via axial pumping of plasma from the ends of the flux tubes to fill up the flux tubes with plasma (this process also collimates [1] the individual flux tubes so that they look like spaghetti strands), (ii) kink instability of the individual collimated flux tubes, and (iii) interaction of adjacent collimated flux tubes with each other resulting in the flux tubes wrapping around each other to be maximally force-free. Stages (ii) and (iii) involve the system relaxing to a lower-energy nearly force-free state. Experiments which demonstrate all three of the above steps will be described. \newline [1] P. M. Bellan, Why current-carrying magnetic flux tubes gobble up plasma and become thin as a result, Phys. Plasmas 10 Pt 2, 1999 (2003)
NG21A-0206
3D Simulations of Principle of Minimum Dissipation Rate
We present preliminary results of a self-consistent, time-dependent numerical simulations of dissipative turbulent plasmas at a higher Landquist number, typically upto {\cal O}(106), using full three dimensional compressible MHD code with a numerical resolution of 1283. Our simulations follow the time variation of global helicity, magnetic energy, and the dissipation rate and show that the global helicity remains approximately constant while magnetic energy is decaying faster and dissipation rate is decaying even faster than the magnetic energy. This establishes that the principle of minimum dissipation rate under the constraint of (approximate) conservation of global helicity is a viable approach for plasma relaxation
NG21A-0207
Intrinsic Structure of the Homogeneous Turbulent Dynamo
Ideal, homogeneous, magnetohydrodynamic turbulence is represented by finite Fourier series whose coefficients form a statistical ensemble. Eigenvalues (all positive) and eigenvectors of the covariance matrix for each modal probability density are determined. The smallest eigenvalues occur at the lowest wave number and are associated with three dominant eigenvectors. When phase space is aligned with these three principal axes, the associated variables, in statistical equilibrium, are seen to be quasi-static and to contain significant energy, and thus define the homogeneous turbulent dynamo. Adding dissipation is expected to have minimal effect, since this intrinsic structure exists at the lowest wave number.
NG21A-0208
Applications of the Principle of Minimum Dissipation Rate to Solar Corona
In analogy to the Principle of Minimum Energy, the Principle of Minimum Dissipation Rate (MDR), originating from irreversible thermodynamics, follows a variational approach, but is more suitable for a complex and externally driven system like the solar corona. And in contrast, while the former yields a linear (constant α) force-free magnetic field, the MDR gives a more general non-force free magnetic field with flow. The solution to the equation describing non-force free magnetic field resulted from MDR can be expressed as a linear superposition of two linear force-free fields with distinct α parameters, and one potential field (α\equiv0). We present recent progress on applying the MDR theory to solar corona, in particular, an MDR-based approach to deriving three-dimensional non-force free coronal magnetic field from vector magnetograms at multiple photospheric and/or chromospheric levels. We present several test case studies to illustrate the feasibility of the method. We discuss further improvement to the method and its application to real magnetograph measurements of solar active regions.