Electron-cyclotron maser emission in solar microwave spike bursts

A new model is developed for electron-cyclotron maser emission from flaring loops, which incorporates competition between driving of the instability and maser-induced relaxation, together with interactions between small neighboring regions of unstable plasma. This results in a picture in which radiation is emitted in bursts from regions whose length scale is determined self-consistently by previous bursts, while the unstable plasma fluctuates about the point, close to marginal stability, at which driving of the instability is balanced by relaxation due to maser-induced electron diffusion. Under the conditions applicable to flaring loops, time scales of fundamental x-mode (x1) driving and saturation are approximately equal at 1 ms, resolving a (10⁴–10⁶)-fold discrepancy in previous models and agreeing with the observed time scales of microwave spike bursts. Saturation effects are found to be especially effective in suppressing amplification of the most strongly growing modes. This suppression enables fundamental o-mode (o1) and second-harmonic x-mode (x2) emission to compete more effectively against x1 emission for the available free energy than has previously been estimated. Consideration of mode competition, burst time scales, suppression of growth due to overlap between amplification and absorption bands, and escape of radiation through absorption layers to the observer, implies that the observed radiation probably escapes from the corona principally in the o-mode, either emitted directly as o1 radiation or mode converted from x1 emission.     

Propagation and absorption of electron-cyclotron maser radiation during solar flares

The electron-cyclotron maser is believed to be the source of microwave spike bursts often observed during solar and stellar flares. Partial absorption of this radiation as it propagates through the corona can produce plasma heating and soft X-ray emission over an extended region. In this paper, the propagation and absorption of the maser radiation during solar flares are examined through linear theory and electro-magnetic particle simulations. It is shown using linear theory that strong absorption of the radiation should occur as it propagates towards the second harmonic layer where the magnetic field is half as strong as in the emission region. Only radiation propagating nearly parallel to the magnetic field in a low-temperature plasma may be able to escape under certain, limited conditions. Finite temperature effects can cause radiation propagating nearly perpendicular to the magnetic field to refract, causing enhanced absorption. Particle simulations are then used to evaluate the nonlinear response of the plasma as the maser radiation propagates through the absorption layer. It is shown that some of the maser radiation is able to escape through a process of absorption below the second harmonic of the local gyrofrequency and re-emission above it. The fraction able to escape is much higher than that predicted by linear theory, although the amount of escaping energy is only a small fraction of the incident energy. The bulk of incident energy goes into the perpendicular heating of the ambient electrons, with the rate of energy absorption showing no signs of leveling off during the simulations. This indicates that the absorption layer does not become optically thin after continuous heating by the maser radiation. A few electrons are accelerated to several tens of keVs as a result of the heating.     

Evolvement of microwave spike bursts in a solar flare on 2006 December 13

Solar radio spikes are one of the most intriguing spectral types of radio bursts. Their very short lifetimes, small source size and super-high brightness temperature indicate that they should be involved in some strong energy release, particle acceleration and coherent emission processes closely related to solar flares. In particular, for the microwave spike bursts, their source regions are much close to the related flaring source region which may provide the fundamental information of the flaring process. In this work,we identify more than 600 millisecond microwave spikes which recorded by the Solar Broadband Radio Spectrometer in Huairou(SBRS/Huairou) during an X3.4 solar flare on 2006 December 13 and present a statistical analysis about their parametric evolution characteristic. We find that the spikes have nearly the same probability of positive and negative frequency drifting rates not only in the flare rising phase, but also in the peak and decay phases. So we suppose that the microwave spike bursts should be generated by shockaccelerated energetic electrons, just like the terminational shock(TS) wave produced by the reconnection outflows near the loop top. The spike bursts occurred around the peak phase have the highest central frequency and obviously weak emission intensity, which imply that their source region should have the lowest position with higher plasma density due to the weakened magnetic reconnection and the relaxation of TS during the peak phase. The right-handed polarization of the most spike bursts may be due to the TS lying on the top region of some very asymmetrical flare loops.     

Electron cyclotron maser emission from solar flares

Energetic electrons, with energies 10–100 keV, accelerated during the impulsive phase of solar flares, sometimes encounter increasing magnetic fields as they stream towards the chromosphere. A consequence of the conservation of their magnetic moment is that the electrons with large initial pitch angle will be reflected at different heights from the atmosphere. Energetic electrons reflected below the transition zone will lose most of their energy to collisions and will never return to the corona. Thus, electrons reflected above the transition zone form a loss-cone velocity distribution which can be unstable to Electron Cyclotron Maser (ECM). The interaction of quasi-perpendicular shocks with the ambient coronal plasma will form a ‘ring’ or ‘hollow beam’ velocity distribution upstream of the shock. ‘Ring’ velocity distributions are also unstable to the ECM instability. A review of the recent results on the theory of ECM will be presented. We will focus our discussion on the questions: (a) What are the characteristics of the linear growth rate of the ECM during solar flares? (b) How does the ECM saturate and what is its efficiency? (c) How does the ECM generated radiation modify the flare environment? Finally we will review the outstanding questions in the theory of ECM and we will relate the theoretical predictions to current observations.     

Effects of turbulence on the electron cyclotron-maser mechanism for solar microwave spike bursts

It is shown that small magnetic perturbations can significantly alter the rates of cyclotron growth, absorption, mode conversion, and refraction because of the sensitive dependence of these processes on the field strength in narrow layers. In particular, growth lengths are increased, absorption depths decreased, mode conversion becomes more effective, and turbulent refraction leads to isotropization of the emission. The criteria for significant effects to occur are derived and it is shown that they can be met by the few-percent field perturbations observed in coronal loops. Relative to the theory of cyclotron-maser emission in smoothly varying plasmas, perturbations enable fundamental o-mode (o1) and second-harmonic x-mode (x2) radiation to saturate more effectively, increase the chance of x1, o1, and x2 radiation escaping to infinity through absorption and mode-coupling windows, and partially isotropize radiation emitted near the x-mode cutoff. It is concluded that o1 and x1 emission are both likely to be present, and that x2 emission is possible under some circumstances. However, x1 radiation can escape only at near-parallel propagation ( 0) or via mode conversion to the o-mode at 90°, whereas o1 and x2 emission can escape for a wide range of angles around = 0 and, under many circumstances, near = 90°.     

Quasi-periodic structure in solar microwave bursts

High sensitivity, high time resolution recordings of microwave radio bursts show a number of periodic and quasi-periodic bursts which exhibit intervals of the order of 10–20 s. Some of the bursts are accompanied by simultaneous pulsations of the same interval detected in X-rays, type III-m, and extreme ultraviolet emissions. Mechanisms to explain solar radio pulsations are reviewed to see which can explain or be extended to explain these observations.Supported by a company-financed research program of The Aerospace Corporation.     

Fine structure in solar microwave bursts

We have designed and constructed a new multi-channel radio spectrograph for the study of short-lived structures in solar microwave bursts. It measured the integrated flux over the whole solar disc in two circular polarizations at 36 frequencies between 4 and 8 GHz, with a time constant of 0.5 ms. We have analyzed all 119 recorded bursts observed in 1981 and 1983. We focused our attention on events with a lifetime of less than 1 s. Fine structure occurs in about 30% of the observed bursts, and can be as rich in detail as in bursts observed at lower frequencies. We found at least four different classes of events. In one event neither bandwidth nor time resolution of the receiver appear to be sufficient to resolve the fine structure. The bulk of the drifts is found to be towards higher frequencies. Periodic flux variations were found in two cases.     

High-resolution microwave spectra of solar bursts

Microwave observations with exceptionally high spectral resolution are described for a set of 49 solar flares observed between May and October 1981. Total power data were obtained at 40 frequencies between 1 and 18 GHz by the Owens Valley frequency-agile interferometer with 10 s time resolution. Statistical analysis of this sample of microwave bursts established the following significant characteristics of their microwave spectra: (i) Most ( 80%) of the microwave events displayed complex spectra consisting of more than one component during some or all of their lifetime. Single spectral component bursts are rare. It is shown that the presence of more than one component can lead to significant errors when data with low spectral resolution are used to determine the low-side spectral index. (ii) The high-resolution data show that many bursts have a low-side spectral index that is larger than the maximum value of about 3 that might be expected from theory. Possible explanations include the effect of the underlying active region on the perceived burst spectrum and/or the necessity for more accurate calculations for bursts with low effective temperatures, (iii) the peak frequencies of the bursts are remarkably constant during their lifetimes. This is contrary to expectations based on simple models in which the source size and ambient field remain constant during the evolution of a burst.Swiss National Science Foundation Fellow from the University of Bern.     

Homologous microwave bursts and associated solar flares

Homologous characteristics of radio bursts at 3000 MHz and associated optical flares are studied. It is found that flares associated with homologous radio bursts are also homologous optically.Published with the permission of the Director-General of Observatories, New Delhi.     

Direct generation of solar and stellar radio bursts by energetic electron maser

A fully relativistic electron maser is proposed for the explanation of certain non-thermal solar and stellar radio bursts. This mechanism (maser synchrotron) is based on a gyroresonant interaction between waves and electrons of high energies and uses the free energy contained in an electronic distribution function that peaks for energies around 1 MeV.By a calculation of the growth rates of the three electromagnetic modes, we show that the X-mode prevails for values of _p/ _cup to 2 or 3. This result is very different from the standard cyclotron maser case where such values of _p/ _clead to quench the X-mode growth. Hence, the synchrotron maser instability appears to be a direct and efficient amplification process for considerably larger physical conditions than the cyclotron maser. In addition, the radiation, emitted over the second gyroharmonic, freely propagates without a strong reabsorbtion at the 2 _clayer. All these points can constitute major advantages of this mechanism in an astrophysical context.Proceedings of the Second CESRA Workshop on Particle Acceleration and Trapping in Solar Flares, held at Aubigny-sur-Nère (France), 23–26 June, 1986.     

A mechanism for pulsation in solar microwave bursts

I suggest that the pulsation in solar microwave bursts is a modulation of gyro-synchrotron radiation. Whistler waves at the foot of a coronal loop (radio source) interact with nonthermal electrons with loss-cone distribution at the top. As a consequence, electrons outside the loss-cone diffuse into the loss-cone, pass through the loop foot, sink in the atmosphere, and emit gyro-synchrotron radiation as additional pulses. Electrons remaining outside the loss-cone give the background radiation of the burst.Assuming the configuration of a magnetic dipole lying below the photosphere, I calculated the period of pulsation to be 1 s- 1 min. The ratio of the pulse peak to background intensity is calculated to be 0 – 100%; the calculated pulse width is about 0.3 – 50 s. These values are consistent with the observed values. A brief discussion of the probable interpretation of fast, millisecond structures is also given.     

Observations and interpretation of solar decametric absorption bursts

The observations of intensity reductions or absorption bursts in the solar decametric radio-continuum are reported. The reductions are interpreted as the absorption of continuum radiation by a shock-generated ion-sound turbulence present in the layer above the continuum level. The duration of the absorption is attributed to the lifetime of the ion-sound turbulence while the depth of absorption is determined by the level of Langmuir waves generated as a result of absorption.     

MHD oscillations in the solar spike radiation

In this paper the observed 1.4–1.6 s quasi-periodic oscillations in the spike radiation of the microwave outburst of 1981 May 16 are analysed in teras of MHD waves. We point out that the fast magnetoacoustic waves (“sausage” mode) propagating inside and outside a loop can modulate the magnetic field and the pitch angle distribution of the electron beams in the source region. The growth rate of electron-cyclotron-maser instability is then affected to give rise to the quasi-periodic oscillations. Quantitative estimates of relevant physical parameters are given.     

The secondary spectral component of solar microwave bursts

Microwave observations in the range 1 to 18 GHz with high spectral resolution (40 frequencies) have shown that many events display a complex microwave spectrum. From a set of 14 events with two or more spectral components, we find that two different classes of complex events can be distinguished. The first group (4 events) is characterized by a different temporal evolution of the spectral components, resulting in a change of the spectral shape. These events probably can be explained by gyrosynchrotron emission from two or more individual sources. The second class (10 events) has a constant spectral shape, so that the two spectral components vary together in intensity. For all ten events in this second class, the ratio of primary to secondary peak frequencies is remarkably similar, exhibiting an average value of 3.4, and both components show a common circular polarization. These properties suggest either a common source for the different spectral components or several sources which are closely coupled. An additional example of this class of burst was observed interferometrically to provide spatial resolution. This event suggests that the primary and secondary components have a similar location, but that the surface area of the secondary component is larger.Swiss National Science Foundation Fellow from the University of Bern.     

Simultaneous multi-frequency imaging observations of solar microwave bursts

We review the results of simultaneous two-frequency imaging observations of solar microwave bursts with the Very Large Array. Simultaneous 2 and 6 cm observations have been made of bursts which are optically thin at both frequencies, or optically thick at the lower frequency. In the latter case the source structure may differ at the two frequencies, but the two sources usually seem to be related. However, this is not always true of simultaneous 6 and 20 cm observations. The results have implications for the analysis of non-imaging radio data of solar and stellar flares.     

On the superfine structure of solar microwave bursts

Solar microwave bursts with a zebra pattern commonly exhibit a superfine time structure: the zebra stripes consist of separate spike-like pulses. We investigate the superfine structure in the April 21, 2002 event. The emission pulses are shown to exhibit a high periodicity (with a period of about 30 ms); there is a clear correlation between the individual zebra stripes. This structure of the dynamic spectra most likely reflects a periodic injection of electron beams, which generate emission at the double plasma resonance levels.     

Emission and absorption of cyclotron radiation in non-equilibrium plasma

From the kinetic Klimontovich theory we derive the equation of radiative transfer for the case of homogeneous and stationary nonequilibrium plasma in a magnetic fiel. For the sake of simplicity we shall consider only the propagation of cyclotron-radiation in the direction of the magnetic field. Explicit expressions for the coefficients of absorption and spontaneous emission, valid also at the cyclotron frequency, will be obtained. In the final results the plasma is allowed to be weakly inhomogeneous in the z-direction. Application is made of the theory to the simple equilibrium case as a test yields the Rayleigh-Jeans formula of the black-body-radiation.     

Correlation between solar microwave bursts and hard X-ray flares

We compared the microwave bursts with short timescale fine structure observed at 2.84 GHZ at Beijing Astronomical Observatory with the hard X-ry bursts (HXB) observed by the YOHKOH satellite during the period 1991 Oct–1992 Dec, and found that of the 20 microwave events, 12 had HXB counterparts. For the typical event of 1992-06-07, we analyzed the common quasi-period oscillations on the order of 10² s and calculated the parameters of the source region, together with a brief discussion.