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NASA NTRS1979

Thermal instabilities in magnetically confined plasmas - Solar coronal loops

The thermal stability of confined solar coronal structures ('loops') is investigated, following both normal mode and a new, global instability analysis. It is demonstrated that: (1) normal mode analysis shows modes with size scales comparable to that of loops to be unstable, but to be strongly affected by the loop boundary conditions; (2) a global analysis, based upon variation of the total loop energy losses and gains, yields loop stability conditions for global modes dependent upon the coronal loop heating process, with magnetically coupled heating processes giving marginal stability. The connection between the present analysis and the minimum flux corona of Hearn is also discussed.

Habbal, S. R.↗

NASA NTRS1990

Tearing modes in solar coronal loops

It is shown that solar coronal-like magnetic loops, that is loops emerging from and reentering heavy plasma, are unstable to tearing modes. In particular, the previously made assumption of line tying to the heavy plasma, resulting in stabilization, is shown to be inapplicable because the growth rate is sub-Alfvenic in the entire loop, including the submerged part. In fact, it is shown that the tearing mode may grow faster than ordinarily surmised because the growth rate is determined by the average resistivity along an entire flux line rather than by the resistivity in the corona alone.

Hassam, A. B.↗

NASA NTRS1988

Heating of solar coronal loops by resonant absorption of Alfven waves

Numerical calculations governing the efficiency of coronal loop heating by the resonant absorption of shear Alfven waves are reported. The loop structure is modeled by a class of axisymmetric force-free equilibria of a long straight cylinder, approximating a large aspect ratio loop. For a range of parameters characterizing the evolution of solar coronal loops, the absorption bandwidth falls in the frequency range of the photospheric motions due to granulation and p-modes. Resonant Alfven wave absorption is thus a viable mechanism for coronal loop heating.

Grossmann, William↗

NASA NTRS1989

Solar coronal loop heating by cross-field wave transport

Solar coronal arches heated by turbulent ion-cyclotron waves may suffer significant cross-field transport by these waves. Nonlinear processes fix the wave-propagation speed at about a tenth of the ion thermal velocity, which seems sufficient to spread heat from a central core into a large cool surrounding cocoon. Waves heat cocoon ions both through classical ion-electron collisions and by turbulent stochastic ion motions. Plausible cocoon sizes set by wave damping are in roughly kilometers, although the wave-emitting core may be only 100 m wide. Detailed study of nonlinear stabilization and energy-deposition rates predicts that nearby regions can heat to values intermediate between the roughly electron volt foot-point temperatures and the about 100 eV core, which is heated by anomalous Ohmic losses. A volume of 100 times the core volume may be affected. This qualitative result may solve a persistent problem with current-driven coronal heating; that it affects only small volumes and provides no way to produce the extended warm structures perceptible to existing instruments.

Amendt, Peter↗

NASA NTRS1994

The possible role of high-frequency waves in heating solar coronal loops

We investigate the role of high-frequency waves in the heating of solar active region coronal loops. We assume a uniform background magnetic field, and we introduce a density stratification in a direction perpendicular to this field. We focus on ion compressive viscosity as the damping mechanism of the waves. We incorporate viscosity self-consistently into the equations, and we derive a dispersion relation by adopting a slab model, where the density inside the slab is greater than that outside. Such a configuration supports two types of modes: surface waves and trapped body waves. In order to determine under what conditions these waves may contribute to the heating of active regions, we solve our dispersion relation for a range of densities, temperatures, magnetic field strengths, density ratios, wavevector magnitudes, wavevector ratios, and slab widths. We find that surface waves exhibit very small damping, but body waves can potentially damp at rates needed to balance radiative losses. However, the required frequencies of these body waves are very high. For example, the wave frequency must be at least 5.0/s for a slab density of 10(exp 9,5)/cc, a slab temperature of 10(exp 6,5) K, a field strength of 100 G, and a density ratio of 5. For a slab density of 10(exp 10)/cc, this frequency increases to 8.8/s. Although these frequencies are very high, there in no observational evidence to rule out their existence, and they may be generated both below the corona and at magnetic reconnection sites in the corona. However, we do find that, for slab densities of 10(exp 10)/cc or less, the dissipation of high-frequency waves will be insufficient to balance the radiative losses if the magnetic field strength exceeds roughly 200 G. Because the magnetic field is known to exceed 200 G in many active region loops, particularly low-lying loops and loops emanating from sunspots, it is unlikely that high-frequency waves can provide sufficient heating in these regions.

Porter, Lisa J.↗

NASA NTRS1985

Spatial and temporal variations of solar coronal loops

Skylab EUV observations of an active region near the solar limb with both hot and cool loops present were analyzed. The observed intensity variations for hot loops were small, typically a few percent over a period of 30 min. The cool loops exhibited stronger variations, sometimes appearing and disappearing in 5 to 10 min. Most of the cool material observed in the loops appeared to be caused by the downward flow of coronal rain and by the upward ejection of chromospheric material in surges. The frequent EUV brightenings observed near the loop footpoints appear to have been produced by both in situ transient energy releases and the infall/impact of coronal rain. The mean energy input required to balance the radiative and conductive cooling of the hot loops is approximately 0.003 erg/cu cm/s.

Habbal, S. R.↗

NASA NTRS1982

The thermal structure of solar coronal loops and implications for physical models of coronae

EUV spectra of three active region loops observed above the solar limb with the SO55 spectrometer on Skylab are analyzed. It is noted that the lengths, peak temperatures, and pressures of the loops are typical of the X-ray coronal loops to which static models have been applied. It is found that the physical parameters of the coronal loop plasma derived from EUV spectra and raster pictures are not well represented by the static models. Although the loops also contain a significant quantity of cool plasma, no physical reason is found to differentiate them from other active region loops of similar length, pressure, and temperature. Several line ratios in the loop spectrum suggest departures from ionization equilibrium caused by rapid cooling. The source of this cooling material is discussed with reference to several models of loop dynamics.

Raymond, J. C.↗

NASA NTRS1988

Magnetic fine structure of solar coronal loops

A numerical simulation of the effect of a random photospheric flow on the magnetic structure of a coronal loop is presented. An initially uniform field embedded in a perfectly conducting plasma is assumed, extending between two flat parallel plates representing the solar photosphere at both ends of the loop. The field is perturbed by a sequence of randomly phased, sinusoidal flow patterns applied at one of the boundary plates, and the corresponding sequence of force-free fields is determined. It is found that the electric currents generated by these flows develop a fine structure on a scale significantly smaller than the wavelength of the velocity patterns. This suggests that magnetic energy is transferred to smaller scale via a cascade process.

Van Ballegooijen, A. A.↗

NASA NTRS2007

Shell Models of RMHD Turbulence and the Heating of Solar Coronal Loops

A simplified nonlinear numerical model for the development of incompressible magnetohydrodynamics in the presence of a strong magnetic field B|| and stratification, nicknamed 'Shell-Atm,' is presented. In planes orthogonal to the mean field, the nonlinear incompressible dynamics is replaced by two-dimensional shell models for the complex variables u and b, allowing one to reach large Reynolds numbers while at the same time carrying out sufficiently long integrations to obtain good statistics at moderate computational cost. The shell models of different planes are coupled by Alfve'n waves propagating along B||. The model may be applied to open or closed magnetic field configurations where the axial field dominates and the plasma pressure is low; here we apply it to the specific case of a magnetic loop of the solar corona heated by means of turbulence driven by photospheric motions, and we use statistics for its analysis. The Alfven waves interact nonlinearly and form turbulent spectra in the directions perpendicular and, through propagation, also parallel to the mean field. A heating function is obtained and shown to be intermittent; the average heating is consistent with values required for sustaining a hot corona and is proportional to the aspect ratio of the loop to the -1.5 power, and haracteristic properties of heating events are distributed as power laws. Crosscorrelations show a delay of dissipation compared with energy content.

corona↗

NASA NTRS1978

Resonant absorption of Alfvenic surface waves and the heating of solar coronal loops

A first-order mass- and energy-balance model is developed for steady-state EUV 'coronal rain' loops that are not associated with postflare events and are often seen over sunspot umbrae. The model disregards variations in a loop's thermodynamic and magnetic properties along magnetic-field lines and yields average properties of the resonant absorption sheath, the boundary layer, and the loop's interior. Both irreversible heating by Alfvenic surface waves and energy transport via induced boundary-layer convection are taken into account in the analysis. Results that include predictions of the temperatures of the sheath and the boundary-layer plasma, the temperature of the interior plasma, the radiative output of the loop, and the filling factor associated with this radiation are given in terms of the period and velocity amplitude of the relevant surface wave as well as various parameters that characterize a typical 'coronal rain' loop. These results are shown to be consistent with the observed minimum and maximum temperatures as well as the radiative output of typical 'coronal rain' loops.

Ionson, J. A.↗

NASA NTRS1979

The stability of solar coronal loops

The stability of the 'quasi-static' models of coronal loops was examined. It was found that all models in which the heat flux at the base of the loop is assumed to vanish are unstable to the growth of thermal perturbations. The growth rates and the profiles of the unstable modes indicate that the instability involves primarily the low-temperature, transition-region plasma. The models can be made stable only by assuming that the heat flux at the base of the loop is large, of the order of 13% of the maximum flux in the loop. The results imply that the transition region must be intrinsically dynamic.

Antiochos, S. K.↗

NASA NTRS1981

The stability of solar coronal loops with realistic photospheric boundary conditions

Finite-length effects are the primary influence for the MHD stability of coronal loops. This paper gives a new physical description of the photospheric boundary conditions, and the first complete and uniformly convergent initial-perturbation set. A general energy-principle (or variational) stability analysis is then developed. The results of this calculation show that large classes of cylindrical-symmetry perturbations, those with separable contributions to the energy integral, are completely stable. Comparisons are also made with other more restrictive formulations of this problem.

Van Hoven, G.↗

NASA NTRS1982

The structure, stability and flaring of solar coronal loops

A review is given of recent progress in the theory of the magnetohydrodynamic behavior of coronal loops, beginning with a brief characterization of thy observations. The equilibrium magnetic field is described, along with the consequences of the empirical requirement for short-term, or infinite-conductivity, stability which is shown to be dominated by the end-effect influence of thy quasi-rigid photosphere. A new loop-flare model is then developed, which takes account of the finite loop length. The primary resistive-sausage-mode instability exhibits the necessary threshold behavior, and produces a number of spatially and energetically distinct flare-release manifestations.

Van Hoven, G.↗

NASA NTRS1987

Pressure structure of solar coronal loops

The steady state pressure structure of a coronal loop is discussed in terms of the MHD global invariants of an incompressible plasma. The steady state is represented by the superposition of two Chandrasekhar-Kendall functions corresponding to (n=m=0) and (n=m=1) modes. The relative contribution of the two modes (epsilon) is found to depend on the surface pressure of the coronal loop which is also the pressure of the external medium. The mixed mode state does not exist for high values of the external pressure because epsilon becomes complex.

Krishan, V.↗

NASA NTRS1991

Kelvin-Helmholtz instability in an Alfven resonant layer of a solar coronal loop

A Kelvin-Helmholtz instability has been identified numerically on an azimuthally symmetric Alfven resonant layer in an axially bounded, straight cylindrical coronal loop. The set of equations is solved numerically as an initial value problem. The linear growth rate of this instability is shown to be approximately proportional to the Alfven driving amplitude and inversely proportional to the width of the Alfven resonant layer. It is also shown that the linear growth rate increases linearly with m - 1 up to a certain m, reaches its maximum value for the mode whose half wavelength is comparable to the Alfven resonant layer width, and decreases at higher azimuthal mode number.

Uchimoto, E.↗

NASA NTRS1982

A magnetohydrodynamic theory of coronal loop transients

The physical and geometrical characteristics of solar coronal loop transients are described in an MHD model based on Archimedes' MHD buoyancy force. The theory was developed from interpretation of coronagraphic data, particularly from Skylab. The brightness of a loop is taken to indicate the electron density, and successive pictures reveal the electron enhancement in different columns. The forces which lift the loop off the sun surface are analyzed as an MHD buoyancy force affecting every mass element by imparting an inertial force necessary for heliocentrifugal motion. Thermal forces are responsible for transferring the ambient stress to the interior of the loop to begin the process. The kinematic and hydrostatic buoyancy overcome the gravitational force, and a flux rope can then curve upward, spiralling like a corkscrew with varying cross section around the unwinding solar magnetic field lines.

Yeh, T.↗

NASA NTRS1985

The propagation of solar flare particles in a turbulent coronal loop

Energetic solar flare particles, both electrons and protons, must survive the turbulent environment of a flaring loop and propogate to the lower corona or chromosphere in order to produce hard X-ray and gamma ray bursts. This plasma turbulence, often observed in soft X-ray line widths to be in excess of 100 km/s, is presumably capable of efficiently scattering the fast flare particles. This prevents to some degree the free streaming of accelerated particles and depending on the amplitude of the turbulence, restricts the particles to diffusive propagation along the length of the loop to the target chromosphere. In addition this turbulence is capable of performing additional acceleration of the fast particles by the second order Fermi mechanism. For compact flares with rise times 10s, the acceleration effect is small and the propagation of the particles is governed by spatial diffusion and energy loss in the ambient medium. The solution of the time dependent diffusion equation with velocity dependent diffusion and energy loss coefficients yields for the case of nonrelativistic protons particle precipitation rates which are necessary for calculating thick target gamma ray emission and also yields the total thin target emissivity.

Ryan, J. M.↗

NASA NTRS1983

MHD stability of incompressible coronal loops with radiative energy loss

Previous studies of the magnetohydrodynamic (MHD) stability of solar coronal loops have not taken into account the effects of radiative energy loss in the energy equation. However, since coronal loops continuously lose energy by radiation and heat conduction, it is important to understand how these energy loss mechanisms affect MHD stability. We investigate the problem assuming that a magnetic loop has cylindrical geometry. As a first step, stability is studied for a localized mode, and the result is applied to a specific equilibrium. We find that the radiative energy loss effect not only changes the growth rate of ideally unstable modes, but also alters the stability boundary predicted by ideal MHD theory.

An, C.-H.↗