# Energy Release in the Current-Carrying Magnetic Loops

• V. V. Zaitsev

## Abstract

In the present talk we consider 1) generation of currents inside a magnetic loop due to photospheric convection; 2) some features of a steady-state Joule dissipation of these currents; 3) possibility of explosive Joule dissipation caused by current disruption in a magnetic loop due to a flute instability. Generation of an electric current in a magnetic loop by a photospheric plasma motion is described by a generalized Ohm’s law, and by an equation for a plasma motion.If velocity of convective motion in the photosphere V = {V r , 0, 0}, where V r = V 0 r 0/r 0 (r < r 0), V r = V 0 r 0/r (r > r 0) is directed towards the axis of a vertical magnetic loop, we obtain the following set of equations for the components B z , B ϕ of magnetic field in the loop:

$$\frac{{\partial {B_z}}}{{\partial r}} = \frac{{4\pi \sigma {V_r}}}{{{c^2}}}\frac{{{B_z}}}{{1 + \alpha B_z^2 + \alpha B_\varphi ^2}},\frac{1}{r}\frac{{\partial \left( {rB\varphi } \right)}}{{\partial r}} = \frac{{4\pi \sigma {V_r}}}{{{c^2}}}\frac{{{B_\varphi }}}{{1 + \alpha B_z^2 + \alpha B_\varphi ^2}}$$
(1)

where $$\sigma = \frac{{{e^2}n}}{{{m_e}\left( {{v_{ei}} + {v_{ea}}} \right)}},\alpha = \frac{{\alpha F}}{{{c^2}n{m_i}{v_{ia}}}},{v_{ei}},{v_{ea}},{v_{ia}}$$ are respectively effectivefrequencies of collisions of electrons with ions and neutrals, and ions with neutrals, p k is gas kinetic pressure, ρ, plasma density, F = ρ a /ρ, relative density of neutrals, n, number density of electrons.

## Keywords

Solar Phys Solar Flare Magnetic Loop Magnetic Tube Plasma Motion
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