1. 2. MATHEMATIC MODEL. SELF-SIMILAR APPROACH The dynamics of plasma in the magnetic tube disturbed by a beam is described by standard set of MHD equations, where we take into account the effects of viscosity and thermoconductivity, as well as the Joule heating and radiative energy losses. In order to provide the initial thermodynamical equilibrium of the magnetic tube without a beam a stationary uniform background heating Q was introduced. The Joule heating term j' 2 / s = ( j - j b ) 2 / s in the energy equation includes as well the return current caused by the propagating beam of non-thermal electrons. We study various types of the magnetic tube response onto injection of a beam of energetic electrons using dynamical models of a magnetic tube (Khodachenko, 1996), built on the basis of known self- similar solutions of plasma MHD equations ( Imshennik & Syrovatskii, 1967 ). In the cylindrical coordinate system with z-axis directed along the magnetic tube the self-similar solution have the following form: (1) (2) (3) (4) R, L -- transverse and longitudinal scales of a studied fragment of a flaring magnetic tube R * -- external transverse scale of the whole magnetic structure (r d R << R * ) (see Fig.1) a(t), b(t) -- dimensionless functions of t, characterizing the degree of plasma compression in the magnetic tube (components of the deformation tensor) Assuming small quantities: x 1 = << 1 and x 2 = << 1 any function of type T a (r,z,t) in the energy equation can be presented as T a (r,z,t) > T 0 a (t)[1 - ax 1 -ax 2 ]. This causes an asymptotic character of our non-adiabatic model (Khodachenko, 1996). 3. MHD EVOLUTION OF MAGNETIC TUBE DISTURBED BY A BEAM OF FAST ELECTRONS Modeled by the self-similar solutions the respon- se of the magnetic tube onto a beam is defined by - initial equilibrium plasma parameters (T 0 (t=0)= =T 00, T 1 (t=0)=T 10, T 2 (t=0)=T 20, n 00 = r (t=0)/m i ) - current density of the beam (d = j b / j(t=0) ) - characteristic scales of the model (R, L, R * ) Three general types of dynamics: (1) compressional regime (2) quasi-periodic, pulsating regime (3) decompressional regime The dynamical regimes result from the compe- tition between grad P and [j ´ B] force, whereas the change of temperature is determined by hea- ting and cooling mechanisms acting differently on different dynamical stages of the m.tube evolution Consider 1D case with no variation of quantities along the tube (b(t)=1, T 2 (t)=0) (see Fig.2) Fig.2 Dynamics of r (t) and T 0 (t) in the tube with T 10 /T 00 =10 -2, R = 3. 10 7 cm, during propagation of the beam d = 10 5 for different values of T 00 : (a) 3. 10 5 K; (b) 1.8. 10 5 K; (c) 10 5 K, and n 00 : (1) 10 9 cm -3 ; (2) 10 10 cm -3 ; (3) 10 11 cm -3 Possible observational output: A) B) Pulsating regimes can be analog of flaring events with precursors 4. MHD RELAXATION OF MAGNETIC TUBE AFTER DIS- TURBANCE BY A BEAM OF FAST ELECTRONS The disturbed values of plasma parameters and m.field in the tube appear as the initial conditions for modelling its dynamics with- out the beam. Fig.3 Oscillatory relaxation of magnetic tube with n 00 =1.5. 10 11 cm -3, T 10 /T 00 = T 20 /T 00 =10 -2, R = 3. 10 7 cm, L = 3. R, R * = 3. 10 8 cm in dependence on the T 00 : (1) 10 7 K; (2) 6. 10 6 K and B j 0 (t=0): (a) 55 G; (b) 45 G. Plasma velocities and are normalised here to. Decreasing initial temperature causes smoothing of pulses and decrease of the relaxation time, whereas decrease of B j 0 (t=0) results in the decrease of a number of pulses and transformation of the pulsating regime to a monotonous one (Fig.3). The type of dynamical relaxation of m.tube is not strongly influenced by the initial velocity (Fig.4) 5. OBSERVATIONS AND THE MODEL RESULTS We compare processes predicted by the model dynamics in a m. tube with multichannel observational data from X-ray spectrometers on the Solar Maximum Mission (SMM) satellite. Soft X-ray channels are an indicator of the temporal behaviour of hot plasma temperature Hard X-ray channels indicate an electron beam, interacting with low-chromospheric plasma Fig.5 Examples of events with various types of soft X-ray emission dynamics 6. CONCLUSION Considered here MHD response of plasma in the low coronal / upper chromospheric part of a flaring magnetic loop, caused by propagation of a beam of fast non-thermal electrons, can influence the observational manifestation of the flaring event. Presented ideas can be used for interpretation of various types of temporal behaviour of the flaring electromagnetic emission as well as the for explanation of possible changes of location of the radiating source and specifics of existing material flows. Preliminary self-similar modelling allows to define the main possible dynamic regimes of the disturbed magnetic tube, which depend strongly on the parameters of plasma and scales of event. More detailed quantitative study of the effect requires an extensive numerical MHD simulations. REFERENCES Aschwanden, M.J., Kosugi, T., Hudson, H.S., Wills, M.J., Schwartz, R.A., 1996, ApJ, 470, 1198 Brown, J.C., 1973, Solar Phys., 31, 143 Emslie, A.G., 1996, Eos Trans. AGU, 77(37), 355 Emslie, A.G., 1983, Solar Phys., 86, 133 Imshennik, V.S., Syrovatskii, S.I., 1967, Sov.Phys.JETP, 25, 656 Khodachenko, M.L., 1996, Astronomy reports, 40, No.2, 252 Masuda, S., Kosugi, T., Hara, H., Tsuneta, S., Ogawara, Y., 1994, Nature, 371, 495 Van den Oord, G.H.J., 1990, A & A, 234, 496 Acknowledgements The authors are thankful to E.Rieger for providing the observational data from X1, X2 spectrometers on SMM Substitution of self-similar solution into MHD equations Grouping the terms proportional to 0-th, 1-st, and 2-nd power of r and z Set of ordinary differential equations for a(t), b(t), B j 0 (t), B z0 (t), r (t), T 0 (t), T 1 (t), T 2 (t) Compressional cooling (Figs. 2b(2), 2(a)2, 2(a)3) Conditions of cold and dense photo- sphere-like plasma are formed on the higher (chromospheric / low coronal) levels The source of hard X-ray bursts shifts towards higher than photospheric levels Direct collisional heating of plasma by the beam becomes possible Fig.4 Relaxation of the tube with T 00 = 10 7 K, B j 0 (t=0)=30 G, and all other parameters as in the case on Fig.3 for different V r (r=0,t=0): (a) 0 cm/s; (b) - 5. 10 6 cm/s; (c) 10 7 cm/s Initial flat phase in the emission on Fig.5a is similar to the model regime on Fig.2c(1); Fast increase of emission on Fig.5b is similar to the regimes on Figs. 2b(3), 2c(2), 2c(3). The fact that the second beam on Fig.5b has no influence on the soft X-ray emission can be explained by the decompressional heating regime (Figs.2c(2), 2c(3)) triggered in the tu- be by the first beam. T he second beam here can not disturb the system effectively, and it still does not interact collisionally with the surrounding plasma. Oscillatory decrease of emission on Fig.5c is similar to the regimes on Fig.3. Fast decrease of emission on Fig.5d looks like the regimes on Fig.4 The similarity between the registered radiation of flaring events and the plasma temperature dynamics in our model is just an indication of their possible mutual connection. Further analy- sis supposes a detailed study of complex condi- tions in the radiating region within the frame of the considered flaring scenario.