Astron. Astrophys. 364, 793-798 (2000)

4. Discussion

4.1. Evolution of the fine structure

Simple U bursts are generally interpreted as being produced by electron streams travelling once along the closed magnetic lines from the first foot to the second foot; in the event the tube is pinched at the second foot, the electrons with not too small a pitch angle are mirrored near the second foot. The electrons might then generate a second U emission on their way from the second foot back to the first; the combination of the first and second U burst creates a M burst. We interpret this fine structure as a microwave M burst.

As shown in Fig. 4, an asymmetrical magnetic arch (the two mirrors are not located at a same plasma level) is expected in this flare; a plasmoid trapped near the top of magnetic arch moves together with this expanding arch. It is the radio source of type IV-DCIM: the plasmoid sets up Langmuir oscillations on its passage, which then are converted into electromagnetic waves at the local plasma frequency. Meanwhile, the electrons in the plasmoid are also propagating along the field lines in both directions. A electron beam could be formed from the plasmoid during the burst and then move along magnetic lines and mirrored by the second pinched tube (the higher mirror) near the top of arch. At the same time, the plasmoid is just propagating through the same plasma layer, emitting the type IV-DCIM bursts, while the beam emission is the microwave M burst which in Fig. 2 overlaps on the continuum (DCIM).

Fig. 4. A possible arch model for the flare on May 3 1999; the shaded zone represents the radio source (a plasmoid) of the type IV-DCIM, from which an electron beam is formed during the burst; the dashed areas are the two magnetic mirrors near the feet of the arch.

Therefore, the M burst is another radio evidence for a magnetic mirror effect on beam of electrons in the solar corona after the N-burst (Caroubalos et al. 1987; Hillaris et al. 1988). As in case of simple U emission, the M burst is a new sub-class of type III bursts because it is produced by a same electron beam; however, it is a fine structure detected in type IV-DCIM bursts.

4.2. Mirror evidence

We interpreted the four consecutive branches, which are numbered 1 (first branch, descreasing frequency along time), 2 (second branch, increasing ), 3 (third branch, descreasing ) and 4 (fourth branch, increasing ), as an emission produced by a same electron beam, so we have to prove it and rule out any possible coincidence whereby a U-burst could have been followed by another, unrelated U-burst. If the four branches of fine structure are emitted by a same electron beam, we expect that the duration of the time profile at fixed frequency to increase regularly along each of the four branches and continuously from one to next. This is because of the dispersion of the beam velocity. As a matter of fact, it is difficult to measure the duration because a continuum, which results from the velocity dispersion of electron beam 1 and 2, is encountered between the branches 2 and 3. However, we measured the durations at fixed frequency of branches 1 and 4, as given in Fig. 5. The duration of time profiles increases regularly along branches 1 and 4 and also increases from branch 1 and 4 (dD(t)/dt 0); despite the absence of 2 and 3 branches, this fact is enough to support the conclusion that these branches all are produced by a same electron beam.

Fig. 5. Measurements of the duration (D) along the branches 1 () and 4 (); the slopes of the regression line are all positive, dD/dt0.

The intensity at given frequency of branch 4 decreases with increasing frequencies, and finally fades away into the DCIM. This is because the Coulomb collisions with the ambient plasma are stronger at the lower altitudes than at higher altitudes; and it is also because, due to these collisions, the electrons of the beam decelerate and change their distribution, finally part of them is lost, so they cannot gradually propagate their emissions out at the beginning of the branch 4 (the intensities decrease). The branch 4 has a longer average duration than branch 1, which is due to the velocity dispersion. The extent of the electron beam increases with the elapsed time, because

where : speed dispersion of beam, : elapsed time after beam left the acceleration region, (when , , is the original length of electron beam). In addition, if the magnetic mirror is not located high enough, the reflection process cannot occur because the injected beam (branch 2) would be absorbed due to the collisions along its way before it approaches the mirror; if the second mirror were located at a lower altitude, the electron beam 4 would have been damped by collisions before being reflected.

4.3. Magnetic arch

We have interpreted that this M burst is emitted by a same electron beam, which has to propagate through a relatively dense medium (corresponding to the plasma frequency of 3 GHz). As noted earlier, the beam can be quickly isotropized by Coulomb collisions in this high density medium unless certain conditions are met. The collision time is given by

where is the electron density and (cm/s) is the beam speed (Benz et al. 1992). The plasma frequency corresponds closely to the observed frequency for plasma mechanism, from which we deduce the electron density around the radio sources, at the plasma frequency of 3 GHz. To achieve an average lifetime =170 ms (which is average duration of the branch 1 from Fig. 5) as required by the present observation, we require a speed of beam roughly 0.28c (c is the light speed in vacuum) corresponding to 1 branch. The beam decelerates its speed from branch 1 to 4 due to the collisions, ultimately the second U-emission has a longer duration of about 0.8s than the first one (about 0.5s). So we can also roughly deduce the length of this arch

where we have used the duration of the first U-burst and the speed of the beam in branch 1.

In order for the coronal plasma to be magnetically confined, the plasma parameter , which expresses the ratio of thermal to magnetic pressures, has to be less than 1,

we find that in order to confine the plasma contained in the coronal arch the magnetic field has to exceed 20 Gauss if we assume the temperature K.

© European Southern Observatory (ESO) 2000

Online publication: January 29, 2001
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