Periodic thermomagnetic structures in solar plasma
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E PLASMA
Periodic Thermomagnetic Structures in Solar Plasma V. A. Kovalev and A. I. Laptukhov Pushkov Institute of Terrestrial Magnetism, Ionosphere, and Radio Wave Propagation, Russian Academy of Sciences, Troitsk, Moscow oblast, 142190 Russia Received June 17, 2008
Abstract—Stationary solutions in the form of smallscale periodic cells in a plane perpendicular to the mag netic field are obtained in the framework of twofluid magnetohydrodynamics. The solutions are established as a result of the development of thermal instability and represent a superposition of standing temperature waves. In solving the problem, an expression is used for a generalized heat source (including heating and radi ative cooling) that forms a temperature transition region between the chromosphere and corona. PACS numbers: 44.05.+e, 44.40.+a, 44.90.+c DOI: 10.1134/S1063780X09040059
to the magnetic field and represent a superposition of standing temperature waves.
1. INTRODUCTION Highresolution spacecraft observations of the Sun in the UV and Xray ranges have revealed various smallscale structures: loops, contrast sources, etc. The presence of such structures reflects the specific character of dissipation of the energy of the corona heating source, the mechanism of which is still unclear. On the other hand, smallscale structures affect the corona energy balance, the intensity of dis sipative processes, and the wave propagation condi tions; hence, they should be taken into account in constructing corona models [1]. The key role in the formation of temperature structures is played by ther mal instability [2]. The possibility of formation of periodic tempera ture structures in the solar atmosphere due to the onset of thermal instability was shown in [3] by analytically and numerically solving a timeindependent one dimensional nonlinear heatconduction equation with a generalized alternatingsign source. For one dimensional thermal structures, the effects of the magnetic field and thermocurrents were taken into account in [4]. Analytical solutions with a powerlaw thermal conductivity and a model source [5] showed that different types of onedimensional structures can be established, depending on the nonlinearity of the generalized source. In [6], we discussed the formulation of a two dimensional problem in a plane perpendicular to the magnetic field. In the present paper, we consider the temperature distribution across the magnetic field. In solving the problem, we use a generalized heat source (including heating and radiative cooling) in the form of an alternatingsign polynomial. Stationary two dimensional solutions to twofluid MHD equations have the form of periodic cells in a plane perpendicular
2. GENERALIZED SOURCE AND CHROMOSPHERE−CORONA TRANSITION REGION The energy balance of an immobile plasma in the chromosphere−corona transition region (TR) is described by the equation [7, 8] ∇ ⋅ (λ ( T )∇ T ) + q h − q r = 0,
(1)
where λ ( T ) is the thermal conductivity tensor of a weakly collisional plasma in a magnetic fiel
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