The propagation of electron fluxes in the solar corona

The problem of energetic electron flux propagation in the solar coronal plasma is solved with due regard for the influence of the oppositely directed neutralizing cold electron flux and the kinematic escape effect of the electrons with different velocities. It is shown that the flux electrons are accelerated in the process of propagation, thus forming a beam, whose velocity is constant on rather long time scales. Three regimes can be realized in this case. In the first regime, plasma waves do not have time to be excited because they escape rapidly from resonance with the beam. In the second regime, waves are excited, but the beam does not have time to relax. The third regime is quasi-linear relaxation.The generation of solar type III radio bursts in the second regime of electron flux propagation is considered.     

The Energetic Spectrum of Non-Thermal Electrons in an Acceleration Region Calculated From a Solar Microwave Type III Burst with both Positive and Negative Frequency Drifts

A typical event of solar microwave type III burst with both positive and negative frequency drifts was observed by the 1–2 GHz spectrograph at Beijing Observatory on January 5, 1994. The separatrix frequency (1.3 GHz) may correspond to an acceleration region. The energy of the electron beam responsible for the burst is calculated from the drift rate and the height of the source above the photosphere. Moreover, if the solar microwave type III burst is explained by the beam-plasma instability as suggested by Huang (1998), the energy density as well as the particle density of the electron beam may be estimated from the burst flux, the growth rates and the modularity (Huang et al., 1996). So that, a very good power- law distribution is simulated for the energetic spectrum of the electron beam in this event with a spectrum index 4.5. The electron beam may be accelerated by an electric field with a length of 10⁷ m and a strength of <10-4 V m- 1. These results are necessary for understanding the acceleration process in solar flares. This revised version was published online in July 2006 with corrections to the Cover Date.     

A Group of Solar Microwave Type iii Bursts with Reversed Drift Rates on nov. 4, 1997

The most important feature of the microwave type III bursts on Nov. 4, 1997 is the periodically reversed drift rates, which may be contributed to a group of electron beams trapped by a huge magnetic tube (10⁴ km). It is suggested that these electron beams are accelerated by the same mechanism, because there is a power law distribution with index 3.2 in the energetic spectrum of the beam. On the other hand, the energy release in each pulse is quasi-quantized, which is confirmed by the statistical correlation between the rising time and the burst flux. Both of these two results are based on the model of plasma instability responsible for the burst. This revised version was published online in July 2006 with corrections to the Cover Date.     

Modeling of type III bursts dynamic spectra

The one-dimensional process of spatially limited electron stream propagation in the solar corona is simulated. It is shown that the beam instability development results either in strong relaxation in velocity space and inhibition of spatial diffusion (high-stream density) or in velocity space relaxation decrease and simultaneous growth of spatial stream length (low-stream density). Assuming a profile of background plasma density to be exponential, dynamic spectra of type III bursts are modeled, which shows that the emission source velocity is constant, and a duration of the burst emission at a given frequency reduces for high-stream densities.     

On the theory of the type III burst exciter

In situ satellite observations of type III burst exciters at 1 AU show that the beam does not evolve into a plateau in velocity space, contrary to the prediction quasilinear theory. The observations can be explained by a theory that includes mode coupling effects due to excitation of the parametric oscillating two-stream instability and its saturation by anomalous resistivity. The time evolution of the beam velocity distribution is included in the analysis.NAS/NRC Postdoctoral Resident Research Associate.     

Numerical simulation of type III solar radio bursts on meter- and hectometer-waves

Numerical simulation of type III bursts is made by the use of fully numerical scheme showing a general rule for obtaining a numerically stable difference scheme. Although the electron distribution function is one-dimensional in velocity space, the plasma waves is cylindrically symmetric two-dimensional in K-space.It is confirmed that the previous simulation made by the use of semi-analytical method assuming the plateau distribution of electron distribution is qualitatively correct, but the number density of electron beam to have a typical type III burst was overestimated by a factor of about 3.It is demonstrated that a tentative neglection of a term for the induced scattering of plasma waves into nonresonant K-range gives no remarkable effect on the energy loss of the electron beam, though the scattering is strong. The reason is that the scattering reduces the saturation level of plasma waves resulting in a reduction of the energy loss, while a part of the energy of electron beam is indirectly lost by the scattering.     

The participation of nuclei in type-III-related electron streams

We study 27 increases of the flux of 300–800 keV electrons on board HELIOS A or B, associated with intense type III radio bursts close to perihelion passages of the two spacecraft, during the solar minimum. Electrons can be detected inside cones with an angular width between 30° and 60°. Though only intense type III bursts are associated with recognizable electron events in space, such an association does not exist for all of them; this fact and great differences in fluxes of the individual events indicate that, apart from the intensity, also some other charactefistic of the type III burst acceleration or propagation process determines the resulting flux of electrons in space; the energy spectrum of the accelerated electrons is one of the likely candidates. A comparison of the electron flux in these events with the flux of 1.7–3.7 MeV nucl^–1 helium reveals very large variations of the helium/electron flux ratio, by a factor of at least 15 and possibly much higher. We demonstrate that these variations are not caused by propagation effects in interplanetary space. Therefore, they must be due either to propagation effects in the solar corona or, more likely, to intrinsic variations in the relative production of electrons and nuclei in the type III burst process. An extrapolation of the observed fluxes to 1 AU shows that in only 7 of the 27 electron events studied might a marginal > 1.7 MeV helium flux be recognized ar the Earth distance.     

Dynamics of a cloud of fast electrons travelling through the plasma

Numerical analysis of quasi-linear relaxation has been made for four models of electron beam with a finite length travelling through the plasma. In Model 4, a model atmosphere of the corona is adopted and also an increase in the cross-section of the electron beam is taken into account. The electron velocity distribution generally becomes a quasi-plateau form in limited velocity and time ranges. If, however, collisional decay of the fast electrons is too strong and the initial beam density is not high enough, the plateau does not appear. Collisional damping of plasma waves cannot be neglected, since the growth rate of the waves is strongly suppressed by the appearance of the quasi-plateau.An approximate formula for the velocity distribution of the solar electrons passing through the corona has been derived analytically taking into account not only the interaction with plasma waves, but also the collisional damping of the plasma waves and collisions with thermal particles. By the use of this formula, we can easily compute the time profile of the plasma waves caused by these solar electrons at any given place in the interplanetary space. The validity of this semi-analytical approach is checked by the numerical analysis of Model 4, showing a satisfactory fit between the numerical and semi-analytical results.The direct application of this method to the problems of type III radio bursts is left to a later paper.     

Dynamics of electron beams in the inhomogeneous solar corona plasma

Dynamics of a spatially-limited electron beam in the inhomogeneous solar corona plasma is considered in the framework of weak turbulence theory when the temperature of the beam significantly exceeds that of surrounding plasma. The numerical solution of kinetic equations manifests that generally the beam accompanied by Langmuir waves propagates as a beam-plasma structure with a decreasing velocity. Unlike the uniform plasma case the structure propagates with the energy losses in the form of Langmuir waves. The results obtained are compared with the results of observations of type III bursts. It is shown that the deceleration of type III sources can be explained by corona inhomogeneity. The frequency drift rates of the type III sources are found to be in good agreement with the numerical results of beam dynamics.     

Fundamental and Harmonic Emission in Type III Solar Radio Bursts – II. Dominant Modes and Dynamic Spectra

Recent theoretical estimates of the emissivity of fundamental and harmonic radiation in type III solar radio bursts are combined with calculations of electron beam evolution, radiation scattering and propagation delays to estimate dynamic spectra at a remote observer. The burst intensity, brightness temperature, temporal evolution, and dominant mode of emission are then calculated. A simple explanation of the recently observed low-frequency cutoff to type III emission is found and it is noted that some type III beams may propagate without significant radio emission. Criteria for observation of harmonic structure in dynamic spectra are also obtained. The results are shown to be consistent with a wide range of observations.     

Hard X-rays and associated weak decimetric bursts

In previous attempts to show one-to-one correlation between type III bursts and X-ray spikes, there have been ambiguities as to which of several X-ray spikes are correlated with any given type III burst. Here, we present observations that show clear associations of X-ray bursts with RS type III bursts between 16:46 UT and 16:52 UT on July 9, 1985. The hard X-ray observations were made at energies above 25 keV with HXRBS on SMM and the radio observations were made at 1.63 GHz using the 13.7m Itapetinga antenna in R and L polarization with a time resolution of 3 ms. Detailed comparison between the hard X-ray and radio observations shows:

1. In at least 13 cases we can identify the associated hard X-ray and decimetric RS bursts.
2. On average, the X-ray peaks were delayed from the peak of the RS bursts at 1.6 GHz by ～ 400 ms although a delay as long as 1 s was observed in one case.

One possible explanation of the long delays between the RS bursts and the associated X-ray bursts is that the RS burst is produced at the leading edge of the electron beam, whereas the X-ray burst peaks at the time of arrival of the bulk of the electrons at the high density region at the lower corona and upper chromosphere. Thus, the time comparison must be made between the peak of the radio pulse and the start of the X-ray burst. In that case the delays are consistent with an electron travel time with velocity ～ 0.3 c from the 800 MHz plasma level to the lower corona assuming that the radio emission is at the second harmonic.     

Shock-associated kilometric radio emission and solar metric type II bursts

We present statistics relating shock-associated (SA) kilometric bursts (Cane et al., 1981) to solar metric type II bursts. An SA burst is defined here to be any 1980 kHz emission temporally associated with a reported metric type II burst and not temporally associated with a reported metric type III burst. In this way we extend to lower flux densities and shorter durations the original SA concept of Cane et al. About one quarter of 316 metric type II bursts were not accompanied by any 1980 kHz emission, another quarter were accompanied by emission attributable to preceding or simultaneous type III bursts, and nearly half were associated with SA bursts. We have compared the time profiles of 32 SA bursts with Culgoora Observatory dynamic spectral records of metric type II bursts and find that the SA emission is associated with the most intense and structured part of the metric type II burst. On the other hand, the generally poor correlation found between SA burst profiles and Sagamore Hill Observatory 606 and 2695 MHz flux density profiles suggests that most SA emission is not due to energetic electrons escaping from the microwave emission region. These results support the interpretation that SA bursts are the long wavelength extension of type II burst herringbone emission, which is presumed due to the shock acceleration of electrons.Also: Department of Physics and Astronomy, University of Maryland, College Park, MD 20742, U.S.A.     

Solar type III burst profiles at decametre-wave frequencies

Observations of type III burst profiles at 18, 22, 26 and 36 MHz, by Barrow and Achong (1975), are used to calculate the form of the exciter function. The burst profile is treated as the convolution of an exciter function and an exponential decay function. The average form of the exciter profile is obtained directly from calculated profiles and further inferred from the first three statistical moments. Normalised average profiles of the burst and the exciter are presented for each frequency.The analysis shows that over the frequency range 18–36 MHz, (1) the exciter function possesses negative skewness, (2) the shapes of burst profiles and exciter profiles are approximately constant and, (3) burst peak time varies linearly with height in the corona. It is suggested that the passage of the exciting electron stream through field-dominated and flow-dominated coronal regions has different effects on the profiles.     

A comparison of type III solar radio burst theories using satellite radio observations and particle measurements

The required electron density to excite a type III solar burst can be predicted from different theories, using the low frequency radio observations of the RAE-1 satellite. Electron flux measurements by satellite in the vicinity of 1 AU then give an independent means of comparing these predicted exciter electron densities to the measured density. On this basis, one theory predicts the electron density in closest agreement with the measured values.NAS/NRC Postdoctoral Resident Research Associate.     

Type III burst pair

We present a special solar radio burst detected on 5 January 1994 using the multi-channel (50) spectrometer (1.0–2.0 GHz) of the Beijing Astronomical Observatory (BAO). Sadly, the whole event could not be recorded since it had a broader bandwidth than the limit range of the instrument. The important part was obtained, however. The event is composed of a normal drift type III burst on the lower frequency side and a reverse drift type III burst appearing almost simultaneously on the high side. We call the burst type III a burst pair. It is a typical characteristic of two type III bursts that they are morphologically symmetric about some frequency from 1.64 GHz to 1.78 GHz on the dynamic spectra records, which indicates that there are two different electron beams from the same acceleration region travelling simultaneously in opposite directions (upward and downward). A magnetic reconnection mode is a nice interpretation of type III burst pair since the plasma beta 0.01 is much less than 1 and the beams have velocity of about 1.07×10⁸ cm s^–1 after leaving the reconnection region if we assume that the ambient magnetic field strength is about 100 G.     

On the theory of type III radio bursts in the nonhomogeneous interplanetary space (quasi-linear approximation)

Within the limits of geometrical optics frequency characteristics of perturbations of one-dimensionally non-uniform system “electron beam-solar wind plasma” are investigated in linear approximation on the basis of Maxwell equations closed by the derived constitutive equation. The beam is generated by the active region during solar flares and it appears as a source of type III radio emission in the interplanetary space. The appropriate dispersion equation is solved. Resonance interaction of wave with electron beam appears to happen only in two space points. Such transient (pointwise) mechanism of resonance throws light on one of the basic problems of physics of electron beams generated by solar flares: incomparably more long-term time of their existence compared to the time of existence resulting from the former theoretical estimates of velocity of beam energy loss on radiation within the limits of homogeneous medium. The degree and time of electron beam dissipation were determined in quasi-linear approximation.     

Low frequency spectra of type III solar radio bursts

Flux density spectra have been determined for ninety-one simple type III solar bursts observed by the Goddard Space Flight Center radio astronomy experiment on the IMP-6 spacecraft during 1971 and 1972. Spectral peaks were found to occur at frequencies ranging from 44 kHz up to 2500 kHz. Half of the bursts peaked between 250 kHz and 900 kHz, corresponding to emission at solar distances of about 0.3 to 0.1 AU. Maximum burst flux density sometimes exceeds 10^–14 W m^–2 Hz^–1. The primary factor controlling the spectral peak frequency of these bursts appears to be variation in intrinsic power radiated by the source as the exciter moves outward from the Sun, rather than radio propagation effects between the source and IMP-6. Thus, a burst spectrum strongly reflects the evolution of the properties of the exciting electron beam, and according to current theory, beam deceleration could help account for the observations.     

Type III solar radioburst profiles and the associated electron energy spectra

An attempt is made to explain the observed frequency-time profiles of type III solar radiobursts in terms of a rapid plasma wave decay rate combined with the exciter model recently proposed by the author. The decay rate is assumed to be sufficiently rapid for the plasma wave energy density profile to be similar to the excitor power density time profile; this is consistent with the exciter model, the rapid decay being caused by Landau damping on the electrons of the modified high energy tail of the ambient plasma electron velocity distribution. The model is compared with radio observations by making simple assumptions about the dependence of the radio intensity upon the plasma wave energy. A comparison is made with simultaneous radio and electron observations by further assuming a simple power-law velocity distribution for the electrons at their point of ejection from the Sun.     

Numerical simulation of type III solar radio bursts caused by high-density electron beam

Numerical simulation for the type III solar radio bursts in meter wavelengths was made with the electron beam of a high number density enough to emit fundamental radio waves comparable in intensity with the second harmonic.This requirement is fulfilled if the optical thickness ₁ for the negative absorption (amplification) becomes -23 to -25. Since ₁ is roughly proportional to the time-integral of the electron flux of the beam, the intensity of the fundamental waves depends strongly on the parameters which determine the electron flux. Therefore, it is most unlikely that the harmonic pairs of type III bursts of the first and the second harmonics occur frequently with comparable intensities in a wide frequency range, say 200 MHz to 20 MHz, if we take the working hypothesis that the fundamental waves are caused by the scattering of electron plasma waves by thermal ions and amplified during the propagation along the beam.However, we cannot rule out the possibility that single type III bursts with short durations or group of such bursts are the fundamental waves emitted by the above mechanism, but only if the observed large size of the radio source can be attributed to the radio scattering alone.