Engineering topics
Mok, Y.
Publications and source records attributed to Mok, Y..
Verification of Loop Diagnostics
Many different techniques have been used to characterize the plasma in the solar corona: density-sensitive spectral line ratios are used to infer the density, the evolution of coronal structures in different passbands is used to infer the temperature evolution, and the simultaneous intensities measured in multiple passbands are used to determine the emission measure. All these analysis techniques assume that the intensity of the structures can be isolated through background subtraction. In this paper, we use simulated observations from a 3D hydrodynamic simulation of a coronal active region to verify these diagnostics. The density and temperature from the simulation are used to generate images in several passbands and spectral lines. We identify loop structures in the simulated images and calculate the loop background. We then determine the density, temperature and emission measure distribution as a function of time from the observations and compare with the true temperature and density of the loop. We find that the overall characteristics of the temperature, density, and emission measure are recovered by the analysis methods, but the details of the true temperature and density are not. For instance, the emission measure curves calculated from the simulated observations are much broader than the true emission measure distribution, though the average temperature evolution is similar. These differences are due, in part, to inadequate background subtraction, but also indicate a limitation of the analysis methods.
Thermal Non-equilibrium Consistent with Widespread Cooling
Time correlation analysis has been used to show widespread cooling in the solar corona; this cooling has been interpreted as a result of impulsive (nanoflare) heating. In this work, we investigate wide-spread cooling using a 3D model for a solar active region which has been heated with highly stratified heating. This type of heating drives thermal non-equilibrium solutions, meaning that though the heating is effectively steady, the density and temperature in the solution are not. We simulate the expected observations in narrowband EUV images and apply the time correlation analysis. We find that the results of this analysis are qualitatively similar to the observed data. We discuss additional diagnostics that may be applied to differentiate between these two heating scenarios.
Thermal Non-equilibrium Consistent with Widespread Cooling
Time correlation analysis has been used to show widespread cooling in the solar corona; this cooling has been interpreted as a result of impulsive (nanoflare) heating. In this work, we investigate wide-spread cooling using a 3D model for a solar active region which has been heated with highly stratified heating. This type of heating drives thermal non-equilibrium solutions, meaning that though the heating is effectively steady, the density and temperature in the solution are not. We simulate the expected observations in narrowband EUV images and apply the time correlation analysis. We find that the results of this analysis are qualitatively similar to the observed data. We discuss additional diagnostics that may be applied to differentiate between these two heating scenarios.
Coronal loop formation resulting from photospheric convection
We have demonstrated the dynamic formation of coronal magnetic loops in three dimensions as a result of horizontal vortex-like convection on the photosphere. Localized plasma motions twist bipolar magnetic field lines which are tied to the dense photosphere by high electrical conductivity. The twists propagate into the corona along the field and create a narrow quasi-toroidal region where the field lines interwind. At the same time, this tubeline region rises in altitude, expands in cross section, and distorts into a slight S shape before settling into an equilibrium state. The MHD stability of such line-tied magnetic loop structures is directly exhibited by this dynamic simulation.
The differential emission measure of nested hot and cool magnetic loops
The detailed thermal structure of the magnetized solar transition region, as measured by its differential emission measure (DEM(T)), is poorly known. Building on the fact that the solar surface is strongly magnetized and thereby structured, proposals have been made that envision a significant lower-temperature contribution to the energy balance from (ion) heat flux across an arcade of different temperature loops. In this paper, we describe a self-consistent 2D MHD simulation, which includes the full thermal effects of parallel stability and anisotropic conduction, of a nested-loop model of the thermal and magnetic structure of the transition region. We then demonstrate that the predicted DEM agrees with observations in the conceptually elusive T less than 10 exp 5 K regime.
Formation, levitation, and stability of prominences in the magnetized solar atmosphere
The dynamic formation of prominences in the initial magnetothermal equilibrium and their stability to sideward displacements are investigated focusing on the structure of the 2D solar atmosphere in the presence of coronal arcades or loops. A model based on 2D magnetohydrodynamic equations takes into account gravity, compressible flows, heating, radiation, anisotropic thermal conduction, and coupling to a deep chromosphere. It is found that prominences in simple arcades characterized by magnetic field with significant curvature at the apex are unstable to a lateral displacement.
The thermal structure of the magnetized solar transition region
The detailed thermal structure of the magnetized solar transition region, as measured by its differential emission measure DEM(T), is unknown. Proposals have been made that envision a significant lower-temperature contribution to the energy balance from cross-field (ion) heat flux. In this paper, we describe a self-consistent 2D MHD simulation (including the full effects of anisotropic thermal conduction) of a conceptual model due to Athay (1990). We display the detailed irregular thermal and magnetic structure of the transition region and demonstrate that the predicted DEM agrees with observations, particularly in the T less than 10 exp 5 K regime where previous theories had difficulty.
Dynamic formation and magnetic support of loop or arcade prominences
The results of model dynamic simulations of the formation and support of a narrow prominence at the apex of a coronal magnetic loop or arcade are described. The condensation process proceeds via an initial radiative cooling and pressure drop, and a secondary siphon flow from the dense chromospheric ends. The antibuoyancy effect as the prominence forms causes a bending of a confining magnetic field, which propagates toward the semirigid ends of the magnetic loop. Thus, a wide magnetic 'hammock' or well (of a normal polarity Kippenhahn-Schlueter type) is formed, which supports the prominence at or near the field apex.
Prominence condensation and magnetic levitation in a coronal loop
The results of a model dynamic simulation of the formation and support of a narrow prominence at the apex of a coronal magnetic loop or arcade are described. The condensation process proceeds via an initial radiative cooling and pressure drop, and a secondary siphon flow from the dense chromospheric ends. The antibuoyancy effect as the prominence forms causes a bending of the confining magnetic field, which propagates toward the semirigid ends of the magnetic loop. Thus, a wide magnetic 'hammock' or well (of the normal-polarity Kippenhahn-Schlueter-type) is formed, which supports the prominence at or near the field apex. The simplicity of this 1.5-dimensional model, with its accompanying diagnostics, elucidates the various contributions to the nonlinear dynamics of prominence condensation and levitation.
The thermal stability of coronal loops - Numerical simulations
The radiative stability of thermally isolated coronal loops with free-flow boundary conditions by nonlinear numerical simulation are studied. A chromosphere-to-corona loop equilibrium (including the option of a deep chromosphere) is first established by following the nonlinear evolution from an initial isothermal state with rigid boundaries. The end conditions are then changed, to allow free flow and to fix the temperature, and investigate the response to nonisobaric perturbations. Within a family of loops of the same pressure, long hot loops to be stable and short cool loops to be unstable to the thermal chromospheric-expansion mode are found. The stable cases remain so, even when long chromospheric ends and/or gravity are added. In those cases which are unstable, the subsequent nonlinear evolution which exhibits swelling of the chromosphere until the entire loop becomes cool and dense are followed.
Prominence formation in a coronal loop
A model is presented which depends on the preferential deposition of heating in the legs of a coronal loop and which produces a stable prominence-scale condensation at the loop top. Dynamic stability is attained by the subsequent adjustment of local parallel gravity by a magnetic inversion at the loop (or arcade) apex. A nonlinear numerical simulation of this process, which includes a deep chromosphere, a heating rate with a fixed dissipation length, and full solar gravity is described.
Comments on compressible effects on Alfven normal modes in nonuniform plasmas
The paper discusses the regime of validity of the theory of dissipative Alfven normal modes presented by Mok and Einaudi (1985) and Einaudi and Mok (1985), which was based on the incompressible closure of the system of ideal MHD equations. Some simple extensions of the earlier results to the compressible case are described. In addition, certain misunderstandings of this work, which have appeared in other papers, are clarified.
Viscous damping of Alfven normal modes in non-uniform plasmas
The Alfven normal mode in a nonuniform, viscous plasma is investigated. Because the ideal hydromagnetic equation is singular in a nonuniform magnetic field, viscosity is included in order to regularize the equation, analogous to the removal of the singular point by resistivity (Mok and Einaudi, 1985). The eigenvalue equation is then solved numerically for a particular magnetic configuration. The real part of the frequency of this viscous normal mode is found to be similar to the one in the resistive case, while the damping is shown to be comparable, and sometimes to exceed, the resistive effect under certain conditions in which the Lundquist number is sufficiently large. The damping rate is evaluated for various plasma conditions corresponding to different parts of the solar atmosphere. The effects of viscosity are found to dominate resistivity in the quiet sun corona and solar wind.
Resistive Alfven normal modes in a non-uniform plasma
Resistive normal mode solutions of the MHD equations are found numerically in a smooth, nonuniform, magnetic field. The (alpha, S) boundary within which normal mode solutions exist is explicitly computed, where alpha is the normalized wavenumber and S the Lundquist number. As an extension of previous analytic results of Mok and Einaudi (1985), the damping rate of these modes is computed to a higher accuracy, and is found to have an a + bS exp -1/3 dependence, where a and b are independent of S.
Resistive decay of Alfven waves in a non-uniform plasma
The effect of resistive dissipation on the propagation of an MHD disturbance in a nonuniform plasma is examined. The present analysis, based on a boundary-layer technique, shows the existence of resistive normal modes with complex eigenfrequencies. The real part of the eigenfrequency is associated with an oscillatory behavior and defines the location in space of the layer where resistivity is important. The dissipation mechanism is responsible for the damping of the wave, in contrast with previous works in which the ideal MHD theory was used.
Propagation of energetic electron streams in solar flares
The microscopic stability of an electron stream flowing down to the photosphere from the corona is examined. It is found that, while a power-law distribution is stable in the low-density corona, it is unstable against the generation of magnetized electron plasma waves in the high-density photosphere. The scattering of these energetic electrons may alter their radiation signatures.
The thermal instability in a sheared magnetic field - Filament condensation with anisotropic heat conduction
The condensation-mode growth rate of the thermal instability in an empirically motivated sheared field is shown to depend upon the existence of perpendicular thermal conduction. This typically very small effect (perpendicular conductivity/parallel conductivity less than about 10 to the -10th for the solar corona) increases the spatial-derivative order of the compressible temperature-perturbation equation, and thereby eliminates the singularities which appear when perpendicular conductivity = 0. The resulting growth rate is less than 1.5 times the controlling constant-density radiation rate, and has a clear maximum at a cross-field length of order 100 times and a width of about 0.1 the magnetic shear scale for solar conditions. The profiles of the observable temperature and density perturbations are independent of the thermal conductivity, and thus agree with those found previously. An analytic solution to the short-wavelength incompressible case is also given.