1. in our model is described by two equations [4]: the equation for the electric circuit (6) and the energy equation, (7) where i,j - the loop numbers (1 or 2); M ij ; L i - mutual- and self- inductances; n i T i, - temperature and density of plasma in i-th loop; J i = I i /(p r 0 i 2 ) - current density in the loop; Q(T i ) - radiative loss function; H i - background heating. A thin torus approximation is applied for the loops (R loop >>r 0 ). So the inductive coefficients are Fig.4: A pair of rising inductively con- and nected current-carrying loops where d ij is the distance between the centers of the loops tori and j ij, the angle between the normal vectors to the loops planes. A linear increase in time of the major radii of the loops R loop i = R 0 loop i + v i t, i=1,2 is considered, and the initial steady state and thermal equilibrium are assumed. One of the loops is taken to be initially current-free (I 20 = 0). The numerical solution of Eqs. (6), (7) for both loops indicates : Quick build up of the current in the initially current-free loop; ( Significant increase of the current and plasma temperature in the loops when they become to be of the same size (a flare); The most efficient interaction of the parallel loops ( j 12 = 0) Fig.5: Dynamics of currents and plasma temperature in the parallel ( j 12 = 0) loops in dependence on the distance d 12. (R loop 0 1 =2. 10 9 cm, R loop 0 2 =10 8 cm, r 01 =r 02 =5. 10 7 cm v 1 = 5. 10 5 cm/s, v 2 = 10 6 cm/s, n 1 =n 2 = 10 9 cm -3, T 1 (t=0) = T 2 (t=0) = 10 6 K, I 10 =10 11 A, I 20 =0). The inductive electric field produced in the loop can be estimated as When the value of this field exceeds the value, where L e is Coulomb logarithm, the main part of electrons appears to be in a run-away regime and can be ac- celerated by E. According to Fig.6 such a situation takes place in our model for t >2000 s. Finally we obtain that inductive field can accelerate elect- rons in the loop up to energies W = Fig.6: Dynamics of electric fields E and E c q[e]. E[V/m]. l loop [m]=100...1000eV. (for the case j 12 = 0). References [1] Hagyard, M.J., Solar Phys., 115, 107, 1989. [2] Handy, B.N., et al. Solar Phys., 187, 229, 1999. [3] Melrose, D.B., Astrophys. Journal, 451, 391, 1995. [4] Khodachenko, M.L., Zaitsev, V.V., 1998, Astron. Reports, 42, No.2, 265. [5] Spicer, D.S., 1982, Space Sci. Rev., 31, 351. [6] Nishino, M., Yaji, K., Kosugi, T., Nakajima, H., Sakurai, T., 1997, ApJ, 489, 976. [7] Melrose, D.B., 1997, ApJ, 486, 521. [8] Aschwanden, M.J., Kosugi, T., Hanaoka, Y., Nishio, M., Melrose, D.B., ApJ, 526, 1026, 1999. ABSTRACT Effects of electromagnetic inductive interaction in groups of slowly growing current-carrying magnetic loops are studied. Each loop is considered as an equivalent electric circuit with variable parameters (resistance, inductive coefficients) which depend on shape, scale, position of the loop with respect to other loops, as well as on the plasma parameters in the magnetic tube. By means of such a model a process of current generation and temperature change in growing neighbouring magnetic loops was studied. An information about the 3D structure of coronal magnetic loops and their global dynamics (rising, twisting, oscillation) is crucial for this type of models, and we expect that the data from future STEREO mission will appear as a good test for them. 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. Magnetic loops and flux tubes appear to be the main building blocks of the solar atmosphere [1]. In fact, they represent the form in which the magnetic field exists in the Sun. The non-stationary character of solar plasma-magnetic structures appears in various forms of the coronal magnetic loops dynamics (grow motions, oscillations, meandering, twisting) [2]. 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. Complex dynamics of the loops together with action of possible under-photospheric dynamo me- chanisms cause the majority of coronal magnetic loops to be ve- ry likely as the current-carrying ones [3]. 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. Below we present a mechanism which could cause and influence the currents flow- ing in the coronal magnetic loops It is based on the effects of the inductive electromagnetic inter- action of relatively moving (ris- ing and growing) neighbouring magnetic loops. We pay our attention to the fact that in any realistic geometry of a current- Fig.1: Loop-loop flaring interaction carrying loop in which the cur- rent is confined to a current chan-nel, it generates a magnetic field outside the channel. This implies that magnetic loops should interact with each other through their magnetic fields 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 [4]. 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 [3],[5]. 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. This should always be taken into account when one applies the equivalent electric circuit approach for the interpretation of real processes in solar plasmas. Inductive currents in coronal magnetic loops The equation for the electric current I in the coronal circuit of a sepa-rate (but not isolated from surroundings) magnetic loop can be written in the following form (1) - inductance of the thin loop ( R loop >> r 0 ) - resistance, where s (T) is conductivity of plasma; U 0 - drop of potential between the loop’s foot-points; - external magnetic flux through the circuit of the loop; - inductive electromotive force; EAE03-A-01160 R loop and S loop are, respectively, the main radius of the loop and the area covered by the loop. For the multiple loop systems E ind appears as EMF of mutual inductan-ce, where i,j are the loop numbers, and M ij, mutual inductances. Characteristic time of the current change t c =L /R c 2 in the coronal elect- ric circuit is very large (~ 10 4 years), so the dynamics of the current is defined by the loops motion (emergence, submergence, etc.) resulting in the evolution of the inductive coefficients with the time scales and. To show how the inductive electromotive force E ind, caused by the tem-poral change of an external magnetic flux Y ext through the circuit of a loop, can result in the appearance of a significant longitudinal current in the loop, we consider a loop, rising in a constant homogeneous background magnetic field. It is not very important which particular process is responsible for the temporal change of Y ext. In principle, it could be, that the magnetic loop doesn't move and only a new magnetic flux emerges below it. Equally, one can consider a situation when the magnetic loop grows up and the space below it is filled with a magnetic field newly emerging from below the photosphere. In our particular case the Eq.(1) can be written as (2) where Taking account of slow variation of the term the Eq.(2) can be reduced to (3) where Fig.2: Loop rising in constant magnetic field. For the initial condition I(t=0) = 0 and R loop (t) = R 0 loop + a t the Eq.(3) can be solved analytically (4) For b 1 t = t/t c << 1 from (4) follows the approximate formula: (5) The model explains typical relatively fast build up of the current in the beginning of the loop rising and its following more slow change: Fig.3: Dynamics of the current generated in the initially current-free loop (r 0 = 5. 10 7 cm, R 0 loop = 2. 10 8 cm, T = 10 6 K) growing up in the background magnetic field B 0 = 100 G. Different values of the loop rising speed are con- sidered (a = 2.5. 10 5, 10 5, 10 4 cm/s ). Interaction of two current-carrying loops. „Loop-loop interaction“ It follows from observations that a large number of flares occurs in the regions where a new magnetic loop emerges and interacts with the existing loops [6] (See Fig.1). Such events are known as the “interac- ting flare loops”. Here we present a further development of the idea of the loop-loop inductive interaction, which was first suggested by Mel- rose [7] and later applied by Aschwanden et al. [8] for interpretation of observations. In addition to [7] and [8], we note that the relative motion of the loops creates significant inductive electromotive forces in their electric circu- its which appear as a powerful source for changing the currents in the loops. Change of the currents disturbs the initial thermal equilibri- um of the loops and results in a change of the plasma temperature, which in its turn influences the resistivity of the circuit and the radiati- ve energy losses. Therefore, each of the rising magnetic loops (Fig.1, 4) Electromagnetic inductive models for the loop-loop flaring interaction M. L. Khodachenko, and H. O. Rucker Space Research Institute, Austrian Academy of Sciences, Schmiedlstr.6, A-8042 Graz, Austria