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.     

Fundamental emission for type III bursts in the interplanetary medium: The role of ion-sound turbulence

It is argued (a) that the onset times of type III radio emission and of the streaming electrons implies that type III bursts in the interplanetary medium are generated predominantly at the fundamental, (b) that in view of recent observations of ion-sound waves in the interplanetary medium the theory of the generation of the bursts should be revised to take account of these waves, and (c) the revised theory favours fundamental emission. A detailed discussion of the effect of ion-sound waves on type III bursts is given. The most important results are: (1) Ion-sound waves cause enhanced (over scattering off thermal ions) fundamental emission. (2) Second harmonic emission is also enhanced for T _e> 5 × 10⁵ K, e.g., low in the corona, but is suppressed for T _e< 5 × 10⁵ K, e.g., in the interplanetary medium. (3) The bump-in-the-tail instability for Langmuir waves can be suppressed by the presence of ion-sound waves; it may be replaced by an analogous instability in which fundamental transverse waves are generated directly, with no associated second harmonic, but there are unresolved problems with theory for this process. (4) Very low frequency ion-sound waves can scatter type III radiation. (5) Although the ion-sound waves which have been observed are at too high a frequency to be relevant for these processes, it seems likely that ion-sound waves of the required frequencies are present and do play important roles in the generation of type III bursts.     

用粒子模拟方法研究离子声波

<正>向传播朗缪尔波被离子声波散射是太阳射电Ⅲ型暴基波和谐波激发的重要过程.使用粒子模拟方法对电子束流激发朗缪尔波的过程进行了模拟,同时对产生的反向朗缪尔波、朗缪尔波2次谐波和朗缪尔波通过非线性过程产生的离子声波的性质进行了分析研究.为了更好地研究离子声波,模拟时单独计算了由离子扰动引起的电场.模拟计算了不同初始参数下产生的离子声波强度,发现离子的温度和质量对离子声波的产生有重要作用,验证了反向朗缪尔波与离子声波的相关性.同时在模拟中验证了朗缪尔波的衰变过程,确认了离子声波对反向朗缪尔波的放大作用.     

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.     

THE POLARISATION OF SECOND HARMONIC CORONAL TYPE III BURSTS

The process of second harmonic plasma emission is considered, where two simplifying approximations made in previous treatments are relaxed. The revised theory can account for strong polarisation observed in some harmonic coronal type III bursts, and predicts that a correlation between these bursts and the fastest electron beam speeds associated with type III emission should be apparent. These high observed degrees of polarisation could not be explained in the earlier theory. In most cases, polarisation in the sense of the magnetoionic o-mode is predicted. The predicted degree of polarisation is shown to be strongly dependent on the form of the Langmuir wave number spectrum, and in particular on the magnitude of the wave number offset between beam-driven and backscattered Langmuir waves.     

Wave localization in solar type III events

A suggested application of the theory of wave localization to type III solar radio events in the solar wind is discussed critically. A classical wave theory that enables one to relate wave localization to the observed spectrum of density fluctuations is summarized. Localization (in one dimension) is due to backscattering and depends on the density spectrum at a wavenumber equal to twice that of the scattered wave. The localization length is estimated for the Langmuir waves, for which the appropriate density fluctuations require ion sound waves, and for transverse waves, for which (at least for the fundamental) the spectrum of the appropriate density fluctuations has been measured in situ. In all cases the localization length is much shorter than the size of a type III event. For fundamental radiation the localization length can be even shorter than the observed sizes of clumps of Langmuir waves.It is concluded that although wave localization may be significant in type III events, most of its consequences have already been recognized in models that invoke multiple scattering. A notable exception is localization of fundamental transverse waves to the clumps of Langmuir waves, which provides a natural explanation for the observed brightness temperatures and for the initial predominance of fundamental over harmonic emission.     

Emission of Type II Radio Bursts – Single-Beam Versus Two-Beam Scenario

The foreshock region of a CME shock front, where shock accelerated electrons form a beam population in the otherwise quiescent plasma is generally assumed to be the source region of type II radio bursts. Nonlinear wave interaction of electrostatic waves excited by the beamed electrons are the prime candidates for the radio waves’ emission. To address the question whether a single, or two counterpropagating beam populations are a requirement for this process, we have conducted 2.5D particle-in-cell simulations using the fully relativistic ACRONYM code. Results show indications of three-wave interaction leading to electromagnetic emission at the fundamental and harmonic frequency for the two-beam case. For the single-beam case, no such signatures were detectable.     

Fundamental and Harmonic Emission in Type III Solar Radio Bursts – I. Emission at a Single Location or Frequency

A model of type III solar radio bursts is developed that incorporates large-angle scattering and reabsorption of fundamental emission amid ambient density fluctuations in the corona and solar wind. Comparison with observations shows that this model accounts semiquantitatively for anomalous harmonic ratios, the exponential decay constant of bursts, burst rise times, and the directivity of fundamental emission. It is concluded that the long emission tail on interplanetary type III bursts is mostly fundamental emission, while much of the anomalous time delay of fundamental relative to harmonic emission from a given location must be ascribed to other causes.     

Stochastic-growth theory of Langmuir growth-rate fluctuations in type III solar radio sources

Fluctuations in type III beams are produced by quasilinear interactions with clumpy Langmuir waves in type III radio sources. The properties of these fluctuations are estimated and shown to yield Langmuir growth rates and growth-rate fluctuations consistent with those required by the recent stochastic-growth theory of type III radio bursts, with observations, and with existing theoretical constraints. This strengthens the basis of stochastic-growth theory and provides an essential consistency test for this model.     

由束流不稳定性直接激发电磁波来解释太阳射电Ⅲ型爆发

本文在用MHD理论研究等离子体束流不稳定性时发现:在电子等离子体频率附近可以激发出宽频带电磁波,其时间尺度、方向性、相对带宽、偏振特性及谐波结构等理论预期,在典型的日冕参数下,和米波段太阳射电Ⅲ型爆发的观测结果基本吻合.这一机制还可避免经典的等离子体辐射理论中由Langmuir波转换成横电磁波的效率较低的主要困难.     

Dynamics of a cloud of fast electrons travelling through the plasma

A simulation of normal type III radio bursts has been made in a whole frequency range of about 200 MHz to 30 kHz by the usage of the semi-analytical method as developed in previous papers for the plasma waves excited by a cloud of fast electrons. Three-dimensional plasma waves are computed, though the velocities of fast electrons are assumed to be one-dimensional. Many basic problems about type III radio bursts and associated solar electrons have been solved showing the following striking or unexpected results.Induced scattering of plasma waves, by thermal ions, into the plasma waves with opposite wave vectors is efficient even for a solar electron cloud of rather low number density. Therefore, the second harmonic radio emission as attributed to the coalescence of two plasma waves predominates in a whole range from meter waves to km waves. Fundamental radio emission as ascribed to the scattering of plasma waves by thermal ions is negligibly small almost in the whole range. On the other hand, third harmonic radio emission can be strong enough to be observed in a limited frequency range.If, however, the time integral of electron flux is, for example, 2 × 10¹³ cm^–2 (>5 keV) or more at the height of 4.3 × 10¹⁰ cm ( _p = 40 MHz) above the photosphere, the fundamental may be comparable with or greater than the second harmonic, but an effective area of cross-section of the electron beam is required to be very small, 10¹⁷ cm² or less, and hence much larger sizes of the observed radio sources must be attributed to the scattering alone of radio waves.The radio flux density expected at the Earth for the second harmonic can increase with decreasing frequencies giving high flux densities at low frequencies as observed, if x-dependence of the cross-sectional area of the electron beam is x ^1.5 or less instead of x ², at least at x 2 × 10¹² cm.The second harmonic radio waves are emitted predominantly into forward direction at first, but the direction of emission may reverse a few times in a course of a single burst showing a greater backward emission at the low frequencies.In a standard low frequency model, a total number of solar electrons above 18 keV arriving at the Earth orbit reduces to 12% of the initial value due mainly to the collisional decay of plasma waves before the waves are reabsorbed by the beam electrons arriving later. However, no deceleration of the apparent velocity of exciter appears. A change in the apparent velocity, if any, results from a change in growth rate of the plasma waves instead of the deceleration of individual electrons.Near the Earth, the peak of second harmonic radio flux as emitted from the local plasma appears well after the passage of a whole solar electron cloud through this layer. This is ascribed to the secondary and the third plasma waves as caused in non-resonant regions by the induced scattering of primary plasma waves in a resonant region.     

Low frequency turbulence in the solar corona and fundamental radiation of type III solar radio burst

On the basis of the previous numerical simulations, a new mechanism for the emission of the fundamental radio waves of solar radio type III bursts is presented. This hypothesis is to attribute the fundamental radio emission to the coalescence of the plasma waves with the low frequency turbulence, whistler or ion acoustic waves, pre-existing on the way of the electron beam which excite the plasma waves.It is estimated that ion acoustic waves could be occasionally unstable in the solar corona due to that drifting bi-Maxwellian distribution of electrons as observed in the solar wind, which is probably caused by collision-less heat conduction.It is also suggested that the reduced damping of the ion acoustic waves in such a distorted electron distribution in the corona may decrease the threshold electric current to cause the anomalous resistivity to be the onset of the solar flares.     

Plasma emission due to isotropic fast electrons,and types I,II, and V solar radio bursts

The theory of plasma emission is developed under the assumption that the Langmuir waves are generated by an isotropic distribution of fast electrons. Emission from inverse power-law distributions tend to favor emission at the second harmonic with brightness temperatures up to about 10⁸ K at 100 MHz. The concept of a gap (in velocity space) distribution is developed. Very bright plasma emission can result from a gap distribution. For brightness temperatures between 10⁹ K and 10¹¹ K for the second harmonic the fundamental has a brightness temperature between 10⁸ K and 10⁹ K. For higher brightness temperatures the fundamental is amplified and can be very much brighter than the second harmonic. The maximum brightness temperatures for the fundamental and second harmonic at 100 MHz are about 10¹⁶ K and 10¹³ K respectively. Mechanisms by which a gap distribution might be formed are discussed and two effective mechanisms are identified. The theory is applied to the interpretation of radio bursts of types I, II, stationary IV and V. In each case the suggested mechanism appears to be favorable.     

Plasma radiation diagnostics of the primary energy release region in solar flares

The possibility is investigated that the plasma turbulence used in many recent models of the primary energy release and acceleration in solar flares should be detectable by radiation near the fundamental and second harmonic of the plasma frequency. Formulae are derived for fundamental emission due to the combination of ion-acoustic and Langmuir plasma turbulence and for second harmonic emission due to the combination of two Langmuir waves. These results are applied to recent primary energy release and acceleration models which shows that either such radiation should be detectable and possibly distinguishable with suitable microwave interferometers or that its absence places fairly stringent constraints on the possible level of Langmuir or Langmuir and ion-acoustic waves in these models.The National Center for Atmospheric Research is sponsored by the National Science Foundation.     

A relationship between the brightness temperatures for type III bursts

Type III bursts often have brightness temperatures at the fundamental greater than 10⁹K. If the fundamental emission is due to scattering of Langmuir waves into transverse waves by thermal ions, this implies that induced scattering dominates over spontaneous scattering, which in turn requires that the energy density in Langmuir waves be greater than some minimum value, e.g. W ^l > 3 × 10^-10 erg cm^-3 for bursts at f _p = 100 MHz. Such Langmuir waves become isotropic on a time-scale shorter than the rise-time of type III bursts, e.g. < l s at f _p = 100 MHz. Consequently, their coalescence, leading to emission at the second harmonic, proceeds. The above inequalities would imply a brightness temperature at the second harmonic in excess of 10⁹K at f = 200 MHz.The predicted values of the brightness temperatures _T1 ^t and _T2 ^t (at the fundamental and second harmonic respectively) can be expressed in terms of an optical depth . After is eliminated a functional relation between _T1 ^t , _T2 ^t and the plasma frequency, f _p , remains. The form of this relation is not dependent on a quantitative theory of how the Langmuir waves are generated by the stream of electrons. Consequently, comparison with observed quantities should provide further insight into the detailed properties of the emission processes.     

Numerical simulation of electromagnetic emissions in the solar wind plasma with non-thermal electron distribution

Dynamics of fundamental and second harmonic electromagnetic emissions are simulated in the solar wind plasma in the presence of non-thermal electron distribution function in which primary Langmuir waves are driven by an electron beam. The electron velocity distribution function is separated into two distributions representing the distribution of the ambient electrons (Maxwellian) and the suprathermal electrons (non-thermal electrons). The effects of the non-thermal electrons on the generation of primary Langmuir waves, emission rates of the fundamental (F) and harmonic waves (H) and their distributions are investigated. The both of the F and H emissions are sensitive to the characterizes of the non-thermal electrons. It is found that in the presence of non-thermal electrons the production of the Langmuir waves decreases and consequently the levels of fundamental and second harmonic waves are reduced. The emission rate of the fundamental transverse waves decreases and its peak moves slightly toward smaller wave-numbers.     

The brightness temperatures of solar type III bursts

There is a characteristic maximum brightness temperature T _B 10¹⁵K for type III solar radio bursts in the solar wind. The suggestion is explored that the maximum observed values of T _Bmay be attributed to saturation of the processes involved in the plasma emission. The processes leading to fundamental and second harmonic emission saturate when T _Bis approximately equal to the effective temperature T _Lof the Langmuir waves. The expected maximum value of T _Bis estimated for this saturation model in two ways: from the growth rate for the beam instability, and from the maximum amplitude of the observed Langmuir turbulence. The agreement with the observed values is satisfactory in view of the uncertainties in the estimates (a) of the intrinsic brightness temperature from the observed brightness temperature, (b) of the actual growth rate of the beam instability, which must be driven by local, transient features (that are unobservable using available instruments) in the electron distribution, and (c) in the k-space volume filled by the Langmuir waves, and this is consistent with the observational data on two well-studied events at the orbit of the Earth and with statistical data for events over a range of radial distances from the Sun.     

Type III solar radio bursts and the fundamental-harmonic hypothesis

The observational evidence is reviewed for the occurrence of type III solar radio bursts in pairs with frequency ratio two to one. We show that the observations can be explained under the hypothesis that there is a tendency for a type III burst to be followed by a second burst within approximately one second. This explanation leads to fewer difficulties than the hypothesis that type III bursts occur in pairs, one member being emitted at the fundamental of the local coronal plasma frequency, the other at its second harmonic. We conclude that in general, type III bursts are emitted at the second harmonic of the plasma frequency and that type III theories should account for this and only under very special circumstances (which are rare) for the emission at the fundamental and the second harmonic.     

Progress and problems in the theory of type III solar radio emission

The experimental and theoretical status of type III solar radio emission is considered in detail. We emphasize very recent developments which are relevant to the underlying plasma physics. In particular we discuss the identity of the sub-megahertz emissions as fundamental, or second harmonic, the degree of correlation between emissivities, electron streams, and plasma (Langmuir) waves, paradoxes concerned with the time-ordering of these phenomena, and the role of background density irregularities and ion-acoustic turbulence in the solar wind. From the theoretical point of view we discuss the current picture of the underlying Langmuir turbulence, including such effects as the interaction between Langmuir waves and stream electrons, induced scatter off ions, and strong turbulence effects such as modulational instability and soliton collapse.     

Bidirectional Type III Solar Radio Bursts

Bidirectional coronal type III bursts are modeled by combining a model of coronal electron heating and beam generation via time-of-flight effects with semiquantitative estimates of quasilinear relaxation. Electromagnetic emissivities are estimated by extending the recently developed theory of interplanetary type III bursts to coronal emissions, including its features of stochastic Langmuir-wave growth and three-wave interactions. The results are investigated for heating on open and closed coronal field lines and are compared with observations of normal, reverse-slope, bidirectional, and inverted-J and -U coronal type III radio bursts. Harmonic emission is predicted to dominate at plasma frequencies above roughly 100 MHz where the efficiency of fundamental emission falls off steeply, while its free-free reabsorption rises. The model also explains the observed trends in the likelihood of occurrence of normal, reverse-slope, and bidirectional coronal type III bursts.