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.     

Spectral peculiarities of strong solar bursts

We have investigated spectral features of strong radio burst emission for the 21st cycle of solar activity. The maximum daily radio fluxes in 8 frequency ranges are analyzed. For every year, the classification of these daily spectra is obtained by the cluster analysis method.We have shown that strong bursts are characterized by the stable shape of the mean radio emission spectra. For these bursts the total level of radio emission does not depend on the phase of the solar 11-yr cycle and varies with the quasi-period of 4 yr.The basic features of burst spectra can be explained by the gyrosynchrotron radiation of nonthermal electrons and plasma radiation at the second harmonic of plasma frequency. We supposed that in the generation region of centimetric emission, if the strength of the magnetic field B 100 G, the number of microbursts can amount to (6–7) × 10³. In the generation region of decimetric emission, the energy of Langmuir waves changes as W _l n _e ^0.4.     

Energetic solar electrons in the interplanetary medium

ISEE-3 measurements extending down to 2 keV energy have provided a new perspective on energetic solar electrons in the interplanetary medium. Impulsive solar electron events are observed, on average, several times a day near solar maximum, with 40% detected only below 15 keV. The electron energy spectra have a nearly power-law shape extending smoothly down to 2 keV, indicating that the origin of these events is high in the corona. These coronal flare-like events often produced ³He-rich particle events.In large solar flares which accelerate electrons and ions to relativistic energies, the electron spectrum appears to be modified by a second acceleration which results in a double power-law shape above 10 keV with a break near 100 keV and flattening from 10–100 keV. Large flares result in long-lived (many days) streams of outflowing electrons which dominate the interplanetary fluxes at low energies. Even in the absence of solar activity, significant fluxes of low energy electrons flow out from the Sun.Solar type-III radio bursts are produced by the escaping 2–10² keV electrons through a beam-plasma instability. The detailed ISEE-3 measurements show that electron plasma waves are generated by the bump-on-tail distribution created by the faster electrons running ahead of the slower ones. These plasma waves appear to be converted into radio emission by nonlinear wave-wave interactions.     

Electrostatic Wave Instability and Plasma Radiation from Coronal Loops

Polarization properties of solar and stellar radio emission require, in some cases, emission below the third or fourth coronal electron gyro level, < 3,_c; 4, _c. In the context of plasma radiation, the source parameters should be such that the intermediate magnetic field condition 1 < _p ² / _c ² < 3 is satisfied. Supposing this condition, we investigate the generation of electrostatic waves in a warm background plasma with a high-energy component of magnetically trapped electrons. We invoke the conversion of upper-hybrid waves and Bernstein waves into electromagnetic radiation as being responsible for intense radio emission from a coronal magnetic loop. Moreover, odd-half harmonic emissions in the solar radio spectrum as well as the o-mode polarization at the second harmonic of the plasma frequency are natural consequence of this proposed model.     

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.     

Quantitative comparisons of type III radio burst intensity and fast electron flux at 1 AU

We compare the flux of fast solar electrons and the intensity of the type III radio emission generated by these particles at 1 AU. We find that there are two regimes in the generation of type III radiation: one where the radio intensity is linearly proportional to the electron flux, and the second regime, which occurs above a threshold electron flux, where the radio intensity is proportional to the 2.4 power of the electron flux. This threshold appears to reflect a transition to a different emission mechanism.     

Fast solar electrons,interplanetary plasma and km-wave type-III radio bursts observed from the IMP-6 spacecraft

IMP-6 spacecraft observations of low frequency radio emission, fast electrons, and solar wind plasma are used to examine the dynamics of the fast electron streams which generate solar type-III radio bursts. Of twenty solar electron events observed between April, 1971 and August, 1972, four were found to be amenable to detailed analysis. Observations of the direction of arrival of the radio emission at different frequencies were combined with the solar wind density and velocity measurements at 1 AU to define an Archimedean spiral trajectory for the radio burst exciter. The propagation characteristics of the exciter and of the fast electrons observed at 1 AU were then conpared. We find that: (1) the fast electrons excite the radio emission at the second harmonic; (2) the total distance travelled by the electrons was between 30 and 70% longer than the length of the smooth spiral defined by the radio observations; (3) this additional distance travelled is the result of scattering of the electrons in the interplanetary medium; (4) the observations are consistent with negligible true energy loss by the fast electrons.     

Direct observations of low-energy solar electrons associated with a type III solar radio burst

A highly anisotropic packet of solar electron intensities was observed on 6 April 1971 with a sensitive electrostatic analyzer array on the Earth-orbiting satellite IMP-6. The anisotropies of intensities at electron energies of several keV were factors 10 favoring the expected direction of the interplanetary magnetic lines of force from the Sun. The directional, differential intensities of solar electrons were determined over the energy range 1–40 keV and peak intensities were 10² cm^–2 s^–1 sr^–1 eV^–1 at 2–6 keV. This anisotropic packet of solar electrons was detected at the sattelite for a period of 4200 s and was soon followed by isotropic intensities for a relatively prolonged period. This impulsive emission was associated with the onsets of an optical flare, soft X-ray emission and a radio noise storm at centimeter wavelengths on the western limb of the Sun. Simultaneous measurements of a type III radio noise burst at kilometric wavelengths with a plasma wave instrument on the same satellite showed that the onsets for detectable noise levels ranged from 500 s at 178 kHz to 2700 s at 31.1 kHz. The corresponding drift rate requires a speed of 0.15c for the exciting particles if the emission is at the electron plasma frequency. The corresponding electron energy of 6 keV is in excellent agreement with the above direct observations of the anisotropic electron packet. Further supporting evidence that several-keV solar electrons in the anisotropic packet are associated with the emission of type III radio noise beyond 50R is provided by their time-of-arrival at Earth and the relative durations of the radio noise and the solar electron packet. Electron intensities at E 45 keV and the isotropic intensities of lower-energy solar electrons are relatively uncorrelated with the measurements of type III radio noise at these low frequencies. The implications of these observations relative to those at higher frequencies, and heliocentric radial distances 50R , include apparent deceleration of the exciting electron beam with increasing heliocentric radial distance.Research supported in part by the National Aeronautics and Space Administration under contracts NAS5-11039 and NAS5-11074 and grant NGL16-001-002 and by the Office of Naval Research under contract N000-14-68-A-0196-0003.     

Nonlinear treatment for solar radio spikes

We emphasize that a nonlinear treatment is required to realize the diagnostic potentiality of solar spiky emission. The observational constraints including the latest data on the harmonic structure, degree, and sense of polarization are discussed. A set of coupled equations for energy density of high-frequency normal modes of a magneto-active plasma involving the most important nonlinear effects within the three-wave approximation is deduced. The equations include both previously known and new effects. The qualitative evaluations of the equations obtained have provided a few new findings: (i) quasi-linear relaxation of fast electrons on quasi-potential waves (_) occurs in a characteristic time scale of the order of 10 ms if the frequency,f, is about 1 GHz; (ii) the stimulated scattering of the transverse waves on the background plasma particles is shown to be important if the brightness temperature of the spiky emission exceeds 10¹⁵–10¹⁶ K; (iii) the Raman scattering of the transverse waves on background plasma density inhomogeneities may suppress the electron cyclotron maser instability if n _e ² /n _e ² 3 × (10^–4–10^–5).     

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.     

A theory of the origin of the split pair burst emission from the solar corona

The radio emissions caused by electron streams in a non-isothermal plasma are studied quantitatively. It is proposed that conversion of the stream-excited plasma waves into electromagnetic waves by scattering on the thermal fluctuations at nonisothermal sonic oscillation frequency is the origin of the emission of the split-pair burst near the plasma frequency. The occurrence of the split-pair bursts near the second harmonic of the plasma frequency can be due to combination scattering of the stream-excited plasma waves by electron density fluctuations which are produced by the scattered plasma waves. With a streamer model in which the electron densities are two times those in Newkirk's model, both the observed frequency splitting and the rate of drift of the split pair can be explained as the result of plasma radiation caused by a stream of 10 keV electrons. A tentative model for the split-pair emission is suggested.     

Theory of solar radio pulsation

We show that the observed modulation of some coronal microwave, X-ray and Type III emission into pulses of 10 sec intervals is a consequence of the stimulation of electron cyclotron waves propagated in the whistler mode in dipole-like bipolar regions of dimension 0.2 R . Assuming that a power law spectrum of 10 keV electrons with a slope similar to solar flare protons can be trapped in a bipolar region, we show that whistlers can be generated by pitch angle instability. The resultant 10 sec bounce motion of whistler wave trains leads to enhanced, modulated emission in microwave and X-ray frequencies by pitch angle scattering of MeV electrons, and to modulated Type III emission by scattering with coherent plasma waves. A direct prediction of the theory is the existence of sympathetic pulsations at two sources a fraction of a solar radius apart. A second test of the theory is that modulated Type III emission should show strong polarization.This work was conducted under U.S. Air Force Space and Missile Systems Organization (SAMSO) Contract No. F04701-69-C-0066.     

The relationship of electron plasma oscillations to type III radio emissions and low-energy solar electrons

An extensive study of the IMP-6 and IMP-8 plasma and radio wave data has been performed to try to find electron plasma oscillations associated with type III radio noise bursts and low energy solar electrons. This study shows that electron plasma oscillations are seldom observed in association with solar electron events and type III radio bursts at 1.0 AU. In nearly four years of observations only one event was found in which electron plasma oscillations are clearly associated with solar electrons. Numerous cases were found in which no electron plasma oscillations with field strengths greater than 1 V/m could be detected even though electrons from the solar flare were clearly detected at the spacecraft.For the one case in which electron plasma oscillations are definitely produced by the electrons ejected by the solar flare, the electric field strength is very small, only about 100 V/m. This field strength is about a factor of ten smaller than the amplitude of electron plasma oscillations generated by electrons streaming into the solar wind from the bow shock. Electromagnetic radiation, believed to be similar to the type III radio emission, is also observed coming from the region of more intense electron plasma oscillations upstream of the bow shock. Quantitative calculations of the rate of conversion of the plasma oscillation energy to electromagnetic radiation are presented for plasma oscillations excited by both solar electrons and electrons from the bow shock. These calculations show that neither the type III radio emissions nor the radiation from upstream of the bow shock can be adequately explained by a current theory for the coupling of electron plasma oscillations to electromagnetic radiation. Possible ways of resolving these difficulties are discussed.     

Ray-type spectra of plasma turbulence in coronal magnetic loops

The problem of stationary spectra of Langmuir, l, and electromagnetic, t, waves excited in a magnetic trap (loop) by a group of suprathermal electrons, whose velocity distribution includes a loss cone, is considered. Within the framework of weak turbulence theory, accurate spectra of l- and t-waves are found. These spectra have the form of thin rays in wavevector space. Forms of plasma emission radio lines of a homogeneous source near the plasma frequency and its second harmonic are determined.     

Towards a theory for type III solar radio bursts

The mechanisms for the transformation of plasma waves into radiation near the fundamental and second harmonic of the plasma frequency are reviewed and equations are given for both the emission and absorption coefficients for these mechanisms. Near the fundamental the process is the scattering of plasma waves on the polarization clouds of ions and the absorption coefficient can be negative, i.e. the radiation can be amplified. Near the second harmonic the process is the combination of two excited plasma waves for which the absorption coefficient can only be positive. These results are applied to construct models of the radiation source for type III solar radio bursts both at high frequencies where the fundamental is dominant and at low frequencies where the second harmonic is dominant using two model plasma wave spectra, one being one-dimensional, the other isotropic. At high frequencies second harmonic radiation is used to determine the source area for a given energy density in plasma waves W _p . The source size and W _p are detrmined uniquely for a given plasma wave spectrum by tracing rays in a model source taking into account amplification of the fundamental. The results for a strong source at the 80 MHz plasma level with a ratio of emissivities of the fundamental to second harmonic P(ω _p )/P(2ω _p ) ≈ 10 are that the source with a one-dimensional plasma wave spectrum is about 14000 km in diameter and W _p = 10^?6.52 erg cm^?3, and the source with an isotropic distribution of plasma waves is about 200 km in diameter and W _p = 10^?6.3 erg cm^?3. It is shown that at low frequencies, where amplification of the fundamental is no longer possible, second harmonic radiation must be dominant and thus very little information about the source can obtained from the radiation.     

Plasma emission and the decimetre portion of type-IV solar bursts

An attempt is made to account for the decimetre portion of the Type-IV solar radio bursts by plasma emission. Non-thermal electrons (E ～ 500 keV) trapped in a magnetic mirror (IV_dm, burst source) having loss-cone gap distribution excite plasma waves which are transformed into transverse waves through non-linear scattering by ions. A good agreement was reached between the calculated spectrum and the observed fluxes for the event of 1972 August 2. A distribution of the number of non-thermal electrons with height, and a total number of 10³², were obtained. Also it was found that the Langmuir waves can accelerate some background thermal electrons to the MeV range.     

Depolarization of solar bursts due to scattering by low-frequency waves

The possibility is explored that fundamental plasma emission in solar radio bursts of types I, II, and III is depolarized due to scattering off low-frequency waves. Three ways in which depolarization might occur are identified: (1) one or several large-angle scatters, (2) several small-angle scatters close to the plasma level, and (3) many small-angle scatters well above the plasma level. It is pointed out that the degree p of polarization (p = 1 initially) may be approximated by p() = cos after one large-angle scatter through an angle , and that for backscatter ( > /2) the sense of polarization changes (from o-mode to x-mode senses). Possibility (2) involves coupling between the o- and x-mode components through their longitudinal parts, and is explored in some detail. The wave vectors k required for the scatterings are identified, and it is suggested that ion-sound waves are suitable for possibility (1) and whistlers for possibility (2). The whistlers may be generated by the streaming electrons themselves.Large-angle scattering is favourable for depolarizing type I emission, as proposed by Wentzel, Zlobec, and Messerotti (1986). Scattering by whistlers near the plasma level is favourable for depolarizing type III bursts. Several predictions are made based on these possibilities.     

Electron plasma oscillations associated with type III radio emissions and solar electrons

An extensive study of the IMP-6 and IMP-8 plasma and radio wave data has been performed to try to find electron plasma oscillations associated with type III radio noise bursts and low-energy solar electrons. This study shows that electron plasma oscillations are seldom observed in association with solar electron events and type III radio bursts at 1.0 AU. In nearly four years of observations only one event was found in which electron plasma oscillations are clearly associated with solar electrons. For this event the plasma oscillations appeared coincident with the development of a secondary maximum in the electron velocity distribution functions due to solar electrons streaming outwards from the Sun. Numerous cases were found in which no electron plasma oscillations with field strengths greater than 1 μV m^?1 could be detected even though electrons from the solar flare were clearly detected at the spacecraft. For the one case in which electron plasma oscillations are definitely produced by the electrons ejected by the solar flare the electric field strength is relatively small, only about 100 μV m^?1. This field strength is about a factor of ten smaller than the amplitude of electron plasma oscillations generated by electrons streaming into the solar wind from the bow shock. Electromagnetic radiation, believed to be similar to the type III radio emission, is also observed coming from the region of the more intense electron plasma oscillations upstream of the bow shock. Quantitative calculations of the rate of conversion of the plasma oscillation energy to electromagnetic radiation are presented for plasma oscillations excited by both solar electrons and electrons from the bow shock. These calculations show that neither the type III radio emissions nor the radiation from upstream of the bow shock can be adequately explained by a current theory for the coupling of electron plasma oscillations to electromagnetic radiation. Possible ways of resolving these difficulties are discussed.     

Magnetic fields,bremsstrahlung and synchrotron emission in the flare of 24 October 1969

An impulsive flare October 24, 1969 produced two bursts with virtually identical time profiles of 8800 MHz emission and X-rays above 48 keV. The two spikes of hard X-rays correspond in time to the times of sharp brightening and expansion in the H flare. The first burst was not observed at frequencies below 3000 MHz. This cut off is ascribed to plasma cutoff above the low-lying flare.A model of the flare based on H observations at Big Bear shows that the density of electrons with energy above 10 keV is 5 × 10⁷ if the field density is 10¹¹. The observed radio flux would be produced by this electron distribution with the observed field of 200 G. The H emission accompanying the hard electron acceleration is presumed due to excitation of the field atoms by the hard electrons.