1. Two different kinds of the electric current dynamics in the circuit of the loop: 1. LCR-pulsations of the electric current around the equilibrium value I z0 (fact processes) For the typical coronal loop parameters Eq.(1)  2. Slow change of the current I z0, which modulates the LCR-pulsations frequency LCR (I z0 ) (slow processes) As the main driver for the slow change of the current I z0, we consider the inductive electromotive forces appeared in the electric circuits of the coronal magnetic loops due to their rising and relative motions [5]. 3.2. Modelling To model the slow dynamics of electric current we consider a system of two rising inductively connected magnetic current- carrying loops (Fig.2). Each of the loops is described by two equations [5]: The equation for the electric circuit (2) The energy equation (3) where i,j are the loop numbers (1 or 2); M ij and L i are mutual- and self- inductances; n i T i, are temperature and density of plasma in i-th loop; J i =I i /(p r 0 i 2 ) is current den- sity; Q(T i ) and H i are the radiative loss function and background heating. In differ from the Eq.(1), the Eq.(2) contains no capacitance term, which can be neg- lected for the slow variations of current  curr >> 1 / LCR  Approximately balancing each other  effects of the large foopoint resistance and convection dynamo action are Fig.2: A pair of rising inductively con- included into the external potential U 0i term, whereas the term with the coronal resis- nected current-carrying loops tance is considered separately. Significant role in the Eq.(2) play the inductive electromotive forces caused by a changing magnetic flux through the electric circuit of the loop during its rising motion. Varying parameters of the interacting loops ( r 0 ; l (t=0); T(t=0); n; I(t=0); B; rising speed; distance and angle bet- ween the loops) we find those that provide the temporal behaviour of LCR (I z0 ) in both loops similar to the observed in the LF dynamic spectra  Diagnostics of the loop parameters a b c Fig.3: Instantaneous spectra of the LF modulation of the microwave flux and their simulation by the model of 2 interacting loops (a) May 7, 1991 event; (b) May 11, 1991 event; (c) July 13, 1992 event References [1] Handy, B.N., et al. Solar Phys., 187, 229, 1999. [2] Nishino, M., Yaji, K., Kosugi, T., Nakajima, H., Sakurai, T., 1997, ApJ, 489, 976. [3] Aschwanden, M.J., & Alexander, D., 2001, Solar Phys., 204, 91. [4] Melrose, D.B., Astrophys. Journal, 451, 391, 1995. [5] Khodachenko, M.L., et al., A&A, 401, 721, 2003. [6] Zaitsev, V.V., et al., Radiophys.&Quantum Electronics, 44, No.9, 756, 2001. [7] Dulk, G.A., 1985, Ann.Rev.Astron.Astrophys. 23, 169. ABSTRACT Low-frequency (LF) modulations of recorded at the Metsaehovi Radio Observatory 37 GHz microwave radiation during solar flares are considered. A fast Fourier transformation with a sliding window is used to obtain the dynamic spectra of the LF pulsations. We pay attention to the LF dynamic spectra having a specific multi-track structure, which is supposed to be an indication of a complex multi-loop composition of a flaring region. Application of the equivalent electric circuit models of the loops including the effects of electromagnetic inductive interaction in groups of slowly growing current-carrying magnetic loops allows to explain and reproduce the main dynamical features of the observed LF modulation dynamic spectra. Each loop is considered as an equivalent electric circuit with variable parameters (resistance, capacitance, and inductive coefficients) which depend on shape, scale, position of the loop with respect to other loops, as well as on the plasma parameters and value of the total longitudinal current in the magnetic tube. 1. INTRODUCTION The solar corona has a highly dynamic and complex structure. It consists of a large number of constantly evolving, loops and filaments, which interact with each other and are closely associated with the local magnetic field. The non- stationary character of solar plasma-magnetic structures appears in various forms of the coronal magnetic loops dynamics (grow motions, oscillations, meandering, twisting) [1]. Energetic phenomena, related to these types of magnetic activity, range from tiny transient brightenings (micro-flares) and jets to large, active-region-sized flares and CMEs. They are naturally accompanied by different kinds of electromagnetic emission, covering a wide frequency band from radio waves to gamma-rays. Produced within a given plasma environment, the radiation carries signature of physical and dynamic conditions in a radiating source. It follows from a combination of microwave, soft X-ray and magnetogram data that a large number of solar flares occurs in regions where a new magnetic loop emerges and interacts with the existing loops. Multi-frequency observations of flares, including soft X-ray, hard X-ray, and radio wavelengths indicate that quite often multiple loops are involved in a flare process [2],[3]. Thus, it is natural to expect that such structural complexity of a flaring region will manifest itself in a specifics of the emitted radiation. Complex dynamics of the loops together with action of possible under-photospheric dynamo mechanisms cause the majority of coronal magnetic loops to be very likely as the current-carrying ones [4]. In that connection none of the loops can be considered as isolated from the surroundings. The loops should interact with each other via the magnetic field and currents. The simplest way to take into account this interaction consists in application of the equivalent electric circuit model of a loop which includes a time-dependent inductance, mutual inductance, and resistance [5],[6]. The equivalent electric circuit model is of course an idealization of the real coronal magnetic loops. It usually involves a very simplified geometry assumptions and is obtained by integrating an appropriate form of Ohm's law for a plasma over a circuit [4],[6]. A simple circuit model ignores the fact that changes of the magnetic field propagate in plasma at the Alfven speed V A. Therefore the circuit equations correctly describe temporal evolution of the currents in a solar coronal magnetic current-carrying structure only on a time scale longer than the Alfven propagation time. We study spectral and temporal evolution of the low-frequency (LF) pulsations modulating the microwave radiation (37 GHz) of solar flares recorded at the Metsaähovi Radio Observatory. For this purpose a "sliding window" Fourier analysis is applied. The dynamical spectra of the LF pulsations are used for the diagnostics of electric currents in the radiating source on the Sun. A physical idea in the background of our approach consists in the following. Microwave radiation of solar flares is usually interpreted as a gyrosynchrotron radiation produced by fast electrons on harmonics of the gyrofrequency   in the magnetic field B of a flaring loop. In the case of a power-low distribution of electrons in energy n( E ) ~ E - , the intensity of gyrosynchrotron radiation I from an optically thin loop is proportional to B (  / B ) 1.22 - 0.9  ~ B -0.22 + 0.9  [7]. For the typical observed values 2 <  < 7 this gives I ~ B 1.58 … 6.08. Thus, any LF variations of the electric current in the radiating source (a flaring magnetic loop), which in their turn produce the LF disturbances of the magnetic field, will modulate the intensity of the gyrosynchrotron radiation [6]. 2. OBSERVATIONS Quite often the dynamic spectra of the LF pulsations contain several spectral tracks demonstrating a similar or slightly different temporal behaviour. We consider the multi-track features as an indication that the detected microwave radiation is produced within a system consisting of a few separate, but closely located magnetic loops having slightly different parameters, and involved in a kind of common global dynamical process. May 7, 1991 event (Fig.1a): Relatively weak microwave burst with the flux of about 18 sfu, which took place at 10.30-11.08 UT in the active region S10W25. The temporal interval of the LF spectrum corresponds to the stage after the burst maximum. May 11, 1991 event (Fig.1b): Microwave burst with the flux of about 600 sfu which took place at 13.19-13.57 UT in the same active region as the burst of May 7, 1991. The center of this active region on May 11, 1991 had coordinates S09W63. The time interval of the LF spectrum corresponds to the decay phase of the burst. July 13, 1992 event (Fig.1c): Microwave burst with the flux of about 10 sfu which has been observed at 07.00-08.20 UT. LF modulation of the microwave radiation here is studied on the time interval before the maximum of the burst. Ref.No. 640 a b c Fig.1: Microwave bursts (at 37 GHz) and dynamical spectra of the LF pulsations modulating the microwave flux (a) May 7, 1991 event; (b) May 11, 1991 event; (c) July 13, 1992 event 3. INTERPRETATION AND MODELLING We interpret the observed multi-track character of the LF modulating signal spectra as a signature of an oscillating electric currents running within the circuits of closely located and interacting with each other coronal magnetic loops. Application of the equivalent electric circuit (or LCR-circuit) models of the loops [5],[6] including the effects of electromagnetic inductive interaction in groups of slowly growing current-carrying magnetic loops allows to explain and reproduce the main dynamical features of the observed LF modulation dynamic spectra. 3.1. LCR-circuit analog of a current-carrying magnetic loop Let’s consider a thin magnetic loop with a cross-section radius being much less than the length of the loop. The following fundamental regions can be distinguished inside the loop: Region 1: The dynamo region located in the photospheric footpoints of the loop, influenced by the supergranulation converging flows of the partially ionized photospheric plasma. r 01 and l 1 are the cross-section radius and length of this part of the loop respectively, and V r B  /c is the plasma convection electromotive force which creates the electric current I = I z along the loop axis (V r << V A, C S ). Region 2: The coronal part of the loop with the cross-section radius r 02 and length l 2. By this, l 2 >> l 1. Inductive interaction of coronal magnetic loops as a modulating factor for the solar microwave radiation M. L. Khodachenko 1, H. O. Rucker 1, V.V. Zaitsev 2, A.G. Kislyakov 2, S. Urpo 3 1 Space Research Institute, Austrian Academy of Sciences, Schmiedlstr.6, A-8042 Graz, Austria 2 Institute of Applied Physics, Russian Academy of Sciences Ulyanov str. 46603950, Nizhny Novgorod Russia 3 Metsaehovi Radio ObservatoryMetsaehovintie 11402540KylmaelaeFinland Integration across and along the loop of the generalized Ohm‘s law where is an average velocity of plasma and is Coulomb conductivity, and parameter F = n a m a / (n (m e +m i ) + n a m a ) defines relative density of neutrals Oscillator equation for the relative variation y = (I z - I z0 )/I z0, |y|<<1 of the longitudinal current about its equilibrium value [6]: (1) Resistance R(I z0 ) of the circuit includes resistance of the footpoints and coronal part ( l 2  r 02 2    with and    0.5 is the effective capacitance is inductance of the LCR-circuit of the loop