Abstract
Joule heating in a slender magnetic flux tube is investigated. The distribution of the magnetic field and electric sheet current encircling a vertical cylindrical magnetic tube is determined by equating the converging magnetic flux, which results from the converging and downward flow of the granulation, and the dissipative expanding magnetic flux due to Ohmic decay. Here, to ensure the mass flux conservation, an overshooting convective flow pattern resembling recent simulations was assumed. Even with the electrical resistivity from neutral hydrogen, the width of the current sheet was found to be ≈2 km, being much smaller than the tube diameter of ≈ 150 km, either from an exact or approximate (Gaussian) field distribution.
The resultant energy flux density due to Joule heating averaged over the cylindrical cross sectional area, is ≈1 × 109 erg cm-2 s-1 for an assumed photospheric magnetic field of 1500 G. This amount may supply enough energy to heat the temperature minimum region of the flux tube by ΔT = 300 K in accord with observations, though our estimation of the excess radiation loss which should be supplied by the Joule heating to keep ΔT = 300 K is rather uncertain.
A possible role of the Joule heating on spicule formation is briefly discussed together with discussions on the slab geometry, general flow patterns, and non-constant field distributions inside the flux tube.
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Hirayama, T. The current sheet and Joule heating of a slender magnetic tube in the upper photosphere. Sol Phys 137, 33–50 (1992). https://doi.org/10.1007/BF00146574
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DOI: https://doi.org/10.1007/BF00146574