LRC-circuit analog of current-carrying magnetic loop: diagnostics of electric parameters

The equation for an equivalent LRC-circuit of current-carrying magnetic loop is obtained. It is suggested that the electric current, driven by the converging flows in the photosphere, flows trough the coronal part of a loop from one footpoint to another, and closes deep in the photosphere where plasma beta β ≈ 1. In a self-consistent approach both the capacitance and the resistance of a LRC-circuit depend on the electric current along the loop. This opens new possibilities for the diagnostics of electric currents in coronal loops, by using data on high-quality modulation of microwave emission during flares. Spectral analysis of the Metsähovi millimeter wave solar data for 16 solar flares have revealed modulation periods 0.7–17 s which give currents I ≈ 6×1010–1.4×1012 A. For two of the events we could compare the total energy of the electric current stored in the magnetic loop with the energy released in the flare. Only 5% of the total energy of the electric circuit was released in both flares, suggesting a very low influence of these flares on the magnetic loop structure. In the studied events there was a tendency to decrease the energy release with the increase of the current. This tendency is interpreted in terms of plasma beta, which is getting smaller as the current grows. Therefore the plasma instabilities responsible for the flare process manifestate themselves weakly with the increase of the current.