Scaling law for the heating of solar coronal loops

We report preliminary results from a series of numerical simulations of the reduced magnetohydrodynamic equations, used to describe the dynamics of magnetic loops in active regions of the solar corona. A stationary velocity field is applied at the photospheric boundaries to imitate the driving action of granule motions. A turbulent stationary regime is reached, characterized by a broadband power spectrum $E_k\simeq k^{-3/2}$ and heating rate levels compatible with the heating requirements of active region loops. A dimensional analysis of the equations indicates that their solutions are determined by two dimensionless parameters: the Reynolds number and the ratio between the Alfven time and the photospheric turnover time. From a series of simulations for different values of this ratio, we determine how the heating rate scales with the physical parameters of the problem, which might be useful for an observational test of this model.Comment: 12 pages, 4 figures. Astrophysical Journal Letters (in press

Consequences of spontaneous reconnection at a two-dimensional non-force-free current layer

Magnetic neutral points, where the magnitude of the magnetic field vanishes locally, are potential locations for energy conversion in the solar corona. The fact that the magnetic field is identically zero at these points suggests that for the study of current sheet formation and of any subsequent resistive dissipation phase, a finite beta plasma should be considered, rather than neglecting the plasma pressure as has often been the case in the past. The rapid dissipation of a finite current layer in non-force-free equilibrium is investigated numerically, after the sudden onset of an anomalous resistivity. The aim of this study is to determine how the energy is redistributed during the initial diffusion phase, and what is the nature of the outward transmission of information and energy. The resistivity rapidly diffuses the current at the null point. The presence of a plasma pressure allows the vast majority of the free energy to be transferred into internal energy. Most of the converted energy is used in direct heating of the surrounding plasma, and only about 3% is converted into kinetic energy, causing a perturbation in the magnetic field and the plasma which propagates away from the null at the local fast magnetoacoustic speed. The propagating pulses show a complex structure due to the highly non-uniform initial state. It is shown that this perturbation carries no net current as it propagates away from the null. The fact that, under the assumptions taken in this paper, most of the magnetic energy released in the reconnection converts internal energy of the plasma, may be highly important for the chromospheric and coronal heating problem

Hall magnetohydrodynamics of partially ionized plasmas

The Hall effect arises in a plasma when electrons are able to drift with the magnetic field but ions cannot. In a fully-ionized plasma this occurs for frequencies between the ion and electron cyclotron frequencies because of the larger ion inertia. Typically this frequency range lies well above the frequencies of interest (such as the dynamical frequency of the system under consideration) and can be ignored. In a weakly-ionized medium, however, the Hall effect arises through a different mechanism -- neutral collisions preferentially decouple ions from the magnetic field. This typically occurs at much lower frequencies and the Hall effect may play an important role in the dynamics of weakly-ionised systems such as the Earth's ionosphere and protoplanetary discs. To clarify the relationship between these mechanisms we develop an approximate single-fluid description of a partially ionized plasma that becomes exact in the fully-ionized and weakly-ionized limits. Our treatment includes the effects of ohmic, ambipolar, and Hall diffusion. We show that the Hall effect is relevant to the dynamics of a partially ionized medium when the dynamical frequency exceeds the ratio of ion to bulk mass density times the ion-cyclotron frequency, i.e. the Hall frequency. The corresponding length scale is inversely proportional to the ion to bulk mass density ratio as well as to the ion-Hall beta parameter.Comment: 11 page, 1 figure, typos removed, numbers in tables revised; accepted for publication in MNRA

Shock formation and the ideal shape of ramp compression waves

We derive expressions for shock formation based on the local curvature of the flow characteristics during dynamic compression. Given a specific ramp adiabat, calculated for instance from the equation of state for a substance, the ideal nonlinear shape for an applied ramp loading history can be determined. We discuss the region affected by lateral release, which can be presented in compact form for the ideal loading history. Example calculations are given for representative metals and plastic ablators. Continuum dynamics (hydrocode) simulations were in good agreement with the algebraic forms. Example applications are presented for several classes of laser-loading experiment, identifying conditions where shocks are desired but not formed, and where long duration ramps are desired

Analysis of a global Moreton wave observed on October 28, 2003

We study the well pronounced Moreton wave that occurred in as- sociation with the X17.2 are/CME event of October 28, 2003. This Moreton wave is striking for its global propagation and two separate wave centers, which implies that two waves were launched simultane- ously. The mean velocity of the Moreton wave, tracked within different sectors of propagation direction, lies in the range of v ~ 900-1100 km/s with two sectors showing wave deceleration. The perturbation profile analysis of the wave indicates amplitude growth followed by amplitude weakening and broadening of the perturbation profile, which is con- sistent with a disturbance first driven and then evolving into a freely propagating wave. The EIT wavefront is found to lie on the same kinematical curve as the Moreton wavefronts indicating that both are different signatures of the same physical process. Bipolar coronal dim- mings are observed on the same opposite East-West edges of the active region as the Moreton wave ignition centers. The radio type II source, which is co-spatially located with the first wave front, indicates that the wave was launched from an extended source region (& 60 Mm). These findings suggest that the Moreton wave is initiated by the CME expanding flanks.Comment: accepted to Ap

Patchy Reconnection in a Y-Type Current Sheet

We study the evolution of the magnetic field in a Y-type current sheet subject to a brief, localized magnetic reconnection event. The reconnection produces up- and down-flowing reconnected flux tubes which rapidly decelerate when they hit the Y-lines and underlying magnetic arcade loops at the ends of the current sheet. This localized reconnection outflow followed by a rapid deceleration reproduces the observed behavior of post-CME downflowing coronal voids. These simulations support the hypothesis that these observed coronal downflows are the retraction of magnetic fields reconnected in localized patches in the high corona.Comment: 4 pages, 3 figure

Elastic constants of nematic liquid crystals of uniaxial symmetry

We study in detail the influence of molecular interactions on the Frank elastic constants of uniaxial nematic liquid crystals composed of molecules of cylindrical symmetry. A brief summary of the status of theoretical development for the elastic constants of nematics is presented. Considering a pair potential having both repulsive and attractive parts numerical calculations are reported for three systems MBBA, PAA and 8OCB. For these systems the length-to-width ratio ${x_0}$ is estimated from the experimentally proposed structure of the molecules. The repulsive interaction is represented by a repulsion between hard ellipsoids of revolution (HER) and the attractive potential is represented by the quadrupole and dispersion interactions. From the numerical results we observe that in the density range of nematics the contribution of the quadrupole and dispersion interactions are small as compared to the repulsive HER interaction. The inclusion of attractive interaction reduces the values of elastic constants ratios. The temperature variation of elastic constants ratios are reported and compared with the experimental values. A reasonably good agreement between theory and experiment is observed

Paraphrases and summaries: A means of clarification or a vehicle for articulating a preferred version of student accounts?

The use of group discussions as a means to facilitate learning from experiences is well documented in adventure education literature. Priest and Naismith (1993) assert that the use of the circular discussion method, where the leader poses questions to the participants, is the most common form of facilitation in adventure education. This paper draws on transcripts of facilitation sessions to argue that the widely advocated practice of leader summaries or paraphrases of student responses in these sessions functions as a potential mechanism to control and sponsor particular knowledge(s). Using transcripts from recorded facilitation sessions the analysis focuses on how the leader paraphrases the students’ responses and how these paraphrases or ‘formulations’ function to modify or exclude particular aspects of the students’ responses. I assert that paraphrasing is not simply a neutral activity that merely functions to clarify a student response, it is a subtle means by which the leader of the session can, often inadvertently or unknowingly, alter the student’s reply with the consequence of favouring particular knowledge(s). Revealing the subtle work that leader paraphrases perform is of importance for educators who claim to provide genuine opportunities for students to learn from their experience

Evidence for a singularity in ideal magnetohydrodynamics: implications for fast reconnection

Numerical evidence for a finite-time singularity in ideal 3D magnetohydrodynamics (MHD) is presented. The simulations start from two interlocking magnetic flux rings with no initial velocity. The magnetic curvature force causes the flux rings to shrink until they come into contact. This produces a current sheet between them. In the ideal compressible calculations, the evidence for a singularity in a finite time $t_c$ is that the peak current density behaves like $|J|_\infty \sim 1/(t_c-t)$ for a range of sound speeds (or plasma betas). For the incompressible calculations consistency with the compressible calculations is noted and evidence is presented that there is convergence to a self-similar state. In the resistive reconnection calculations the magnetic helicity is nearly conserved and energy is dissipated.Comment: 4 pages, 4 figure

Formation of collisionless shocks in magnetized plasma interaction with kinetic-scale obstacles

We investigate the formation of collisionless magnetized shocks triggered by the interaction between magnetized plasma flows and miniature-sized (order of plasma kinetic-scales) magnetic obstacles resorting to massively parallel, full particle-in-cell simulations, including the electron kinetics. The critical obstacle size to generate a compressed plasma region ahead of these objects is determined by independently varying the magnitude of the dipolar magnetic moment and the plasma magnetization. We find that the effective size of the obstacle depends on the relative orientation between the dipolar and plasma internal magnetic fields, and we show that this may be critical to form a shock in small-scale structures. We study the microphysics of the magnetopause in different magnetic field configurations in 2D and compare the results with full 3D simulations. Finally, we evaluate the parameter range where such miniature magnetized shocks can be explored in laboratory experiments