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Astron. Astrophys. 357, 1105-1114 (2000)

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1. Introduction

Radio and hard X-ray observations of solar flares provide evidence of pulsations in the flare emission. Some events show several quasi-periodic pulses during the flare (Kane et al. 1983; Nakajima et al. 1983). Other events start with several pulses with enhanced amplitude in the pre-flash phase which exhibit then an explosive energy release (flash phase) (Benz et al. 1983; Urpo et al. 1992; Lee & Wang 1998). Both pre-flash and flash phases make up the impulsive phase (Benz et al. 1983). After the flux maximum, the long-term modulation has lower amplitude (a few percent) and persists often throughout the entire gradual decay phase of the flare (Urpo et al. 1992). Long-term modulation was interpreted in the frame of equivalent LRC-circuit oscillations (Zaitsev et al. 1998).

[FIGURE] Fig. 1a and b. Two examples of simple loop flares in 14-53 keV emission observed by Yohkoh (Sato et al. 1998). a  1992 September 6, 0903 UT, b  1993 March 15, 0959 UT

A number of papers are devoted to the origin of pulse structures in solar flare emission. Sakai & de Jager (1996) reviewed the flare pulsations and their fine structure and explained them in terms of collisions between current-carrying loops (see also Tajima et al. 1987; Chargeishvili et al. 1993; Nishikawa et al. 1994; Sakai & de Jager 1997). Two-current-loop coalescence can explain quasi-periodic amplitude oscillations and double sub-peak structure. Sakai & de Jager (1996) mentioned that "flares are different". A two-loop interaction model cannot explain various time histories of the flare energy release. In particular single-loop flares are also possible. Indeed, X-ray and microwave image data from Skylab, SMM, Yohkoh, VLA, Nobeyama, and TRACE suggest that in many cases the flare occurs in a single loop (Marsh & Hurford 1980; Masuda 1994; Doshek et al. 1995; Sakao & Kosugi 1996; Enome 1996; Kucera et al. 1996; Sato et al. 1998; Ciuderi Drago et al. 1998; Schrijver et al. 1999). Also the emission from simple flare loop shows pulsations. Fig. 1 presents two examples of such events in the hard ([FORMULA] keV) X-ray emission (Sato et al. 1998). Alfvén & Carlqvist (1967), Heyvaerts et al. (1977), Spicer (1977), Colgate (1978), Uchida & Shibata (1988), Zaitsev & Stepanov (1992), Tsuneta (1996), Zaitsev & Khodachenko (1997) considered the flare energy release in the frame of a simple loop approach. To interpret the pulses, MHD-oscillations of a magnetic loop have been used (Rosenberg 1970; Roberts et al. 1984; Aschwanden 1987; Stepanov et al. 1992). Gas pressure in the coronal part of the loop can rise fast due to prompt energy release. As a consequence, the radial fast magneto-sonic oscillations of a magnetic arch appear. Alfvén-type oscillations of a magnetic loop can arise during the evaporation of chromosphere plasma (Stepanov et al. 1992) or in response of a loop to the injection of magnetic flux (Cargill et al. 1994). Recently we proposed a model of long-term pulsations of mm-wave emission arising due to electric current oscillations in a magnetic loop as an equivalent LRC-circuit (Zaitsev et al. 1998). Using this model the electric currents in flare loops were estimated to as high as [FORMULA] - [FORMULA] A.

In pulsation models, the non-self-consistent approach has been applied because only the influence of the variation of the loop magnetic field on the modulation of radio and X-ray emission was considered. Moreover, most of the above mentioned models do not explain the explosive energy release.

In this paper we consider the temporal dynamics of Joule heating of plasma and DC-electric field acceleration of electrons in a single current-carrying loop and interpret both the pulsating and the explosive energy releases in the impulsive phase of a flare. As an example we consider an advanced circuit model (Zaitsev & Stepanov 1992; Zaitsev et al. 1998) based on the idea of Alfvén & Carlqvist (1967) where the solar flare is described as an equivalent electric circuit. According to this model the flare energy release occurs in a current-carrying coronal magnetic loop due to the injection of partially ionized plasma into the current channel from the prominence (near the loop top) or from the chromosphere (at the loop foot-points). This process is driven by the flute instability. The loop conductivity drops by many orders of magnitude due to ion-atom collisions (Cowling conductivity). As a result the effective current dissipation leads to a flare. We propose a self-consistent model in which the feedback of the magnetic field variations is taken into account on the penetrating "tongue". This allows us to consider both the pulsating and explosive regimes of the energy release in the temporal dynamics of solar flares. We avoid the difficulties of the energy release mechanism in a current-carrying loop with plasma beta [FORMULA], which was mentioned by Wheatland & Melrose (1995). Both plasma heating and particle acceleration are driven by one parameter, the penetration depth of a plasma "tongue" into the current-carrying loop.

In Sect. 2 we describe Metsähovi mm-wave observations of flares. A self-consistent approach for Joule heating and DC-particle acceleration in single current loops is considered in Sect. 3. Solutions for pulsating and explosive energy release are given in Sect. 4. The results are discussed in Sect. 5.

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© European Southern Observatory (ESO) 2000

Online publication: June 5, 2000