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3.5 Alternative mechanisms

The idea that a coronal loop is twisted and then carries an electric current gave rise to several alternative mechanisms for the loop oscillations. An LCR-circuit model developed by Zaitsev et al. (1998) explains the loop oscillations in terms of eigen oscillations of an equivalent electric circuit, where the current is associated with the loop twist. Approximating the magnetic loop by a thin torus and estimating the effective circuit capacitance C and inductance L as
c4r S2 C = ---0--, (39) 2pLI2
( ) 8L 7 L = 4L log -----1/2-- -- , (40) (pS) 4
where c is the speed of light, r0 is the density inside the loop, L and S are the length and cross-sectional area of the coronal part of the loop, respectively, and I is the electric current along the loop axis. The period of the oscillations is then given by the expression
2p- 1/2 P = c (LC) . (41)
As one of the physical quantities perturbed by this effect is the current (or the twist), its periodic pulsations would be observed through the direct modulation of the gyrosynchrotron emission by the period change of the angle between the LOS and the magnetic field in the emitting region. Also, as the periodic twist is accompanied by perturbations of density - see Equation (26View Equation) -, the oscillations would modulate thermal emission as well. Also, twist perturbations could modulate the loop minor radius, resembling the sausage mode. The decay of the oscillations is normally estimated by this model to be very small.

Khodachenko et al. (2003) applied the idea of inductive interaction of electric currents in a group of neighbouring loops to an alternative interpretation of kink oscillations, suggesting that they are caused by the ponderomotoric interaction of currents in groups of inductively coupled current-carrying loops. More specifically, the ponderomotoric interaction of current-carrying magnetic loops can lead to the oscillatory change of the loops inclination. The efficiency of coupling, the period of oscillations and the decay time are connected with mutual inductance of different loops in the active region analysed. Also, it was pointed out that the interaction of the oscillating loop with neighbouring loops can lead to strong damping of the oscillations.

We would like to stress that the periods of loop oscillations described by LCR-contour models should be longer than the Alfvén travel time along the loop, which determines the response time of the current system, so P > L/CA0.

Dynamic models of magnetic reconnection predict that the processes of tearing instability and coalescence of magnetic islands occur iteratively, leading to an intermittent or impulsive bursty energy release and particle acceleration. Tajima et al. (1987) demonstrated the possibility of oscillatory regimes in coalescence of current carrying loops, combining a simplified 1D analytical approach and numerical modelling. The minimal period of oscillations was found to be

C3s0e P = 2p --4-, (42) C A0
where e is the characteristic length of the interaction process, connected in this case with the width of a current sheet formed at the boundary between two interacting twisted loops. These oscillations are essentially nonlinear, and it is likely that their period is somehow connected with amplitude.


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