Recent results of zebra patterns in solar radio bursts

This review covers the most recent experimental results and theoretical research on zebra patterns(ZPs)in solar radio bursts.The basic attention is given to events with new peculiar elements of zebra patterns received over the last few years.All new properties are considered in light of both what was known earlier and new theoretical models.Large-scale ZPs consisting of small-scale fiber bursts could be explained by simultaneous inclusion of two mechanisms when whistler waves"highlight"the levels of double plasma resonance(DPR).A unique fine structure was observed in the event on 2006 December 13: spikes in absorption formed dark ZP stripes against the absorptive type Ⅲ-like bursts.The spikes in absorption can appear in accordance with well known mechanisms of absorptive bursts.The additional injection of fast particles filled the loss-cone(breaking the loss-cone distribution),and the generation of the continuum was quenched at these moments.The maximum absorptive effect occurs at the DPR levels.The parameters of millisecond spikes are determined by small dimensions of the particle beams and local scale heights in the radio source.Thus,the DPR model helps to understand several aspects of unusual elements of ZPs.However,the simultaneous existence of several tens of the DPR levels in the corona is impossible for any realistic profile of the plasma density and magnetic field.Three new theories of ZPs are examined.The formation of eigenmodes of transparency and opacity during the propagation of radio waves through regular coronal inhomogeneities is the most natural and promising mechanism.Two other models(nonlinear periodic space-charge waves and scattering of fast protons on ion-sound harmonics)could happen in large radio bursts.     

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.     

Excitation of Langmuir waves by the lower energy cutoff behavior of power-law electrons

Langmuir waves (LWs), which are believed to play a crucial role in the plasma emission of solar radio bursts, can be excited by streaming instability of energetic electron beams. However, solar hard X-ray observations imply that the energetic flare electrons usually have a power-law energy distribution with a lower energy cutoff. In this paper, we investigate LWs driven by the power-law electrons. The results show that power-law electrons with the steepness cutoff behavior can excite LWs effectively because of the population inversion distribution below the cutoff energy (E _c ). The growth rate of LWs increases with the steepness index (δ) and decreases with the power-law index (α). The wave number of the fastest growing LWs (kλ _D ), decreases with the characteristic velocity of the power-law electrons ( \(v_{c}=\sqrt{2E_{c}/m_{e}}\) ) and increases with the thermal velocity of ambient electrons (v _T ). This can be helpful for us to understand better the physics of LWs and the dynamics of energetic electron beams in space and astrophysical plasmas.     

Hydrodynamic response of the solar chromosphere to an elementary flare burst

The problem of hydrodynamic response of the solar chromosphere on impulsive heating by energetic electrons is discussed. All basic physical processes are considered in a one-dimensional approximation, due to presence of a strong magnetic field. The calculations are performed for the heating of the chromosphere by electrons having a power-law energetic spectrum. In the upper chromosphere the electron temperature rises rapidly to values of order 10⁷ K. The ion temperature is more than the order of magnitude less than the temperature of electrons. The heated high-temperature chromospheric plasma expands into corona with a velocity up to 1500 km s^–1. In more dense layers, the fast re-emission of supplied energy takes place. This process gives rise to short-lived EUV flash. Just below the flare transition layer the thermal instability produces cold plasma condensation which moves downward at a velocity exceeding the sonic one in the quiet chromosphere.     

Relation between X-ray flux and radio flux from cosmic objects

The relationship between the X-ray flux and the radio flux from cosmic objects is investigated. We consider the emission from energetic electrons on the condition in which a plasma and a magnetic field exist. As energetic electrons under the circumstances emit both X-rays by the bremsstrahlung mechanism and radio waves by the gyrosynchrotron mechanism simultaneously, it is shown that the radio flux density is closely related to the X-ray flux density. Solving an integral equation describing the X-ray flux density at Earth, we obtain the energy spectrum of electrons in the emitting region. Inserting the result into equation of the radio flux density at Earth, we obtain the direct formula between the X-ray flux density and the radio flux density. The relation is independent of the distance between Earth and cosmic sources. Assuming a power-law X-ray spectrum, we evaluate the numerical relation between two flux densities.     

The efficiency of electron acceleration in solar type-IV radio pulsations with a zebra pattern

Based on a comprehensive analysis of the October 25, 1994 event, we consider the balance of energetic particles in a type-IV solar radio emission source with a zebra-type fine structure (in a coronal magnetic loop). The zebra pattern is formed through the injection of fast electrons into a trap and the formation of a ring-type nonequilibrium electron distribution function. We estimated the characteristic zebra-pattern lifetime, which is determined by the escape of fast particles from the trap into the loss cone. In addition, we determined the number of fast particles that must be injected into the trap to provide the observed radio brightness temperature in zebra-pattern stripes by analyzing the plasma emission mechanism responsible for the zebra-pattern generation. As a result, we estimated the efficiency of the electron acceleration mechanism in coronal magnetic loops at the post-flare evolutionary phase of an active region.     

Cyclotron wave instability in the corona and origin of solar radio emission with fine structure

The longitudinal waves (Bernstein modes and plasma waves near the hybrid frequency) in a mixture of equilibrium coronal plasma and a small group of energetic electrons are investigated. The energetic electrons have a nonequilibrium momentum distribution inherent in trapped particles. The frequency dependence of the cyclotron instability increments is studied. Attention is paid to a significant role of the relativistic effects for the cyclotron instability of longitudinal waves. For sufficiently large velocity of nonequilibrium electrons the increments are shown to increase when the hybrid frequency coincides with one of the gyrofrequency harmonics (double plasma resonance). The results obtained are used in Parts II and III to explain tadpoles and zebra-pattern in solar radio bursts.     

Propagation of energetic electron streams in solar flares

The microscopic stability of an electron stream flowing down to the photosphere from the corona is examined. It is found that, while a power-law distribution is stable in the low-density corona, it is unstable against the generation of magnetized electron plasma waves in the high-density photosphere. The scattering of these energetic electrons may alter their radiation signatures.     

The loss-cone driven instability for Langmuir waves in an unmagnetized plasma

Analytic and numerical results are presented for the growth rate of Langmuir waves due to a loss-cone distribution of energetic electrons. The effect of the magnetic field on the wave-particle interaction is ignored, and the resonance condition is described in terms of a resonance hyperboloid in momentum space. The collisional evolution of a distribution of magnetically trapped electrons is followed numerically to show how a gap distribution develops. The growth is most favorable for an intermediate sized loss cone ( 45 °) and a gap distribution in which the mean energy of the suprathermal electrons is much larger than the thermal energy of the background electrons. It is plausible that loss-cone gap distributions do develop in the solar corona, and that they should lead to second harmonic plasma emission weakly polarized in the x-mode.     

The Growth rate of upper-hybrid waves and dynamics of microwave zebra structures

The growth rate of the upper-hybrid waves with different velocities of superthermal electrons is computed considering a finite temperature of the background plasma and relativistic corrections. Based on these computations two examples of high-frequency zebra structures are interpreted. The sequence of the continuum, zebra structure, and continuum observed in the 29 October 2000, event is explained as an increase and following decrease of the velocity of superthermal electrons in the range of v=0.1–0.3 c. On the other hand, the zebra structure observed during the 18 March 2003 event represents an example with fast electron acceleration.     

Electromagnetic wave propagation and instabilities in the magnetosphere

Growth rates for both the RH- and LH-modes of an EM wave propagating along a magnetic field through an isotropic loss-cone plasma have been obtained. It is found that growing modes can exist, and are found to depend critically on the mirror ratioR, and the specific details of the distribution function of the energetic component. To study the energetic-particle distribution observed at low energies by satellites within the magnetosphere, an isotropic double-humped loss-cone velocity distribution is then studied with a view to determining whether the secondary hump can introduce an instability not present for monotonic distribution. It is found that such a distribution can be unstable in a mirror geometry if the energetic component is sufficiently monoenergetic. Within the magnetosphere, nearly monoenergetic fluxes are observed, peaking in the energy range 1–10 keV, depending on the McIlwain parameterL. It is possible that the initial injection of monoenergetic particles may have been much more sharply peaked than the one presently observed, and, as a result of wave-particle interactions, subsequently relaxed to the presently observed distribution. It is seen here that the EM waves within the magnetosphere can contribute to the relaxation of such an initial injection.     

A Theoretical Study Of The Whistler Mode Instability At The Uranian Bow Shock

Relativistic whistler wave mode with a perpendicular AC electric field has been studied for generalized distribution function with an index j, which is reducible to bi-Maxwellian for j = 0, loss-cone for j = 1 and delta function for j = ∞. Based on particle trajectories, the dispersionrelation is obtained using the techniques of a kinetic approach anda method of characteristic solutions Calculations are compassed with observations of low frequency waves of Voyager 2 The growth rates for the plasma parameters suited to the magnetosphere of Uranus are obtained. It is inferred that, not the magnitude but the frequency of the AC field, influences the growth rate. In addition to the temperature anisotropy, plasma particles having a loss-cone provide an additional source of energy. The relativistic electrons along with increasing the growth rate, widen the band width so as to cover a wide frequency range thus may explain the entire spectrum of whistler emissions at Uranian bow shock. This revised version was published online in July 2006 with corrections to the Cover Date.     

Radioheliograph Observations of Microwave Bursts with Zebra Structures

The so-called zebra structures in radio dynamic spectra, specifically their frequencies and frequency drifts of emission stripes, contain information on the plasma parameters in the coronal part of flare loops. This paper presents observations of zebra structures in a microwave range. Dynamic spectra were recorded by Chinese spectro-polarimeters in the frequency band close to the working frequencies of the Siberian Solar Radio Telescope. The emission sources are localized in the flare regions, and we are able to estimate the plasma parameters in the generation sites using X-ray data. The interpretation of the zebra structures in terms of existing theories is discussed. The conclusion has been arrived at that the preferred generation mechanism of zebra structures in the microwave range is the conversion of plasma waves to electromagnetic emission on the double plasma resonance surfaces distributed across a flare loop.     

Fundamental Emission of Type III Bursts Produced in Non-Maxwellian Coronal Plasmas with Kappa-Distributed Background Particles

Detailed simulations based on quasi-linear theory are presented for fundamental ( $f_{\rm p}$ ) emission of type III bursts produced in non-Maxwellian, suprathermal, background coronal plasma by injection of energetic electrons during flares with a power-law or Maxwellian velocity distribution, where $f_{\rm p}$ is the electron plasma frequency. The background plasma is assumed to have a kappa (κ) distribution, as inferred from solar wind data and proposed by theories for the corona and solar wind. The predicted type III beam speeds, Langmuir wave levels, and the drift rate and flux of $f_{\rm p}$ emission are strongly sensitive to the presence of suprathermal background electrons in the corona. The simulations show the following results. i) Fast beams with speeds $v_{\rm b}>0.5c$ are produced for coronal background electrons with small κ (κ?5) by injected electrons with power-law spectra. ii) Moderately fast beams with $v_{\rm b} \approx0.3\,\mbox{--}\,0.5c$ are generated in coronal plasma with κ?8 by injections of power-law or Maxwellian electrons. iii) Slow beams with $v_{\rm b}<0.3c$ are produced for coronal background electrons with large κ (κ>8), including the asymptotic limit κ→∞ where the electrons are Maxwellian, for both power-law and Maxwellian injections. The observation of fast type III beams (with $v_{\rm b}>0.5c$ ) thus suggests that these beams are produced in coronal regions where the background electron distribution has small κ by injected electrons with power-law spectra, at least when such beams are observed. The simulations, from the viewpoint of type III bursts, thus support: i) the presence, at least sometimes, of suprathermal background electrons in the corona and the associated mechanisms for coronal heating and solar wind acceleration; ii) power-law spectra for injected energetic electrons, consistent with observations of such electrons in situ and of X-ray emission.     

Shear Driven Kinetic Alfven Wave with General Loss-Cone Distribution Function in the Plasma Sheet Boundary Layer

Expressions for the dispersion relation and growth rate of the KAW are derived for weak and strong shear regimes using the kinetic approach in view of the simultaneous observations of the large earthward Alfvenic Poynting flux, small-scale kinetic Alfven wave (KAW), earthward flowing electrons and upward flowing ions, at the substorm event in the plasma sheet boundary layer (PSBL). General loss-cone distribution function is adopted to describe the velocity distribution of the plasma particles. The results explain the generation of the observed KAW in the PSBL by the weak shear at the substorm onset. It is found that during the substorm expansion phase the cyclotron damping of KAW may lead to the upward flowing ion. Whereas, it’s Landau damping that may lead to the parallel energisation of the electrons that explains the observed loss of Alfvenic Poynting flux. It is also noted that the loss-cone distribution index changes the profiles of the frequency and growth rate plots of the shear-driven KAW. The loss-cone distribution function is therefore, an important factor for the excitation of KAW in the active region of the magnetosphere at the PSBL. Results are consistent with the finding of Wu and Seyler (J Geophys Res 108A6:1236, 2003) concerning kinetic Alfven wave generation and its stabilization by the sheared flow.     

Electron acceleration in solar flares

We present observations of an intense solar flare hard X-ray burst on 1980 June 27, made with a balloon-borne array of liquid nitrogen-cooled germanium detectors which provided unprecedented spectral resolution (≲1 keV FWHM). The hard X-ray spectra throughout the impulsive phase burst fitted well to a double power-law form, and emission from an isothermal 10⁸–10⁹K plasma can be specifically excluded. The temporal variations of the spectrum indicate that the hard X-ray burst is made up of two superposed components: individual spikes lasting ∼3–15 s, whch have a hard spectrum and a break energy of 30–65 keV; and a slowly varying component characterized by a soft spectrum with a constant low-energy slope and a break energy which increases from 25 keV to ≳100 keV through the event. The double power-law shape indicates that acceleration by DC electric fields parallel to the magnetic field, similar to that occurring in the Earth's auroral zone, may be the source of the energetic electrons which produce the hard X-ray emission. The total potential drop required for flares is typically ∼10² kV compared to ∼10 kV for auroral substorms.

     

A Special Radio Spectral Fine Structure Used for Plasma Diagnostics in Coronal Magnetic Traps

A specific combination of spectral fine structures in meter –  decimeter dynamic spectra of solar radio burst emission is reported in observations carried out at the Astrophysical Institute Potsdam. We describe and interpret the occurrence of zebra patterns in fast drifting (type III burst-like) envelopes of absorbed continuum emission. A possible mechanism of the origin of such an involved spectral pattern is put forward, leading to a necessarily multinonequlibrium component coronal plasma. The suggested mechanism is based on the fact that during the passage of a fast electron beam through the corona the loss cone instability (which is caused by electrons captured in a magnetic trap generating the continuum) is quenched. As result, a fast drift burst appears in absorption, and the zebra pattern becomes visible on the low background emission. This zebra pattern is generated by a group of electrons with a nonequilibrium distribution over transverse velocities. In the absence of the beam the pattern is invisible against the background of the stronger continuum. It is shown that the mechanism is sensitive to the distribution parameters of the different electron ensembles. Therefore the effect in dynamic radio spectra is comparatively rare but its proper existence underlines that the simultaneous presence of different ensembles of electrons in the flaring corona can be quite a frequent situation. This can explain some problems in deconvolving X-ray photon spectra to electron energy spectra.     

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.     

On the analogy between the zebra patterns in radio emission from the sun and the crab pulsar

We investigate the close analogy between the solar radio emission with a quasi-harmonic spectrum structure and one of the microwave emission components of the Crab pulsar in the form of the so-called zebra pattern. The radio emission mechanism of this component can be provided by instability at double plasma resonance and can be realized in extraordinary (for a radio pulsar) conditions, namely in a nonrelativistic plasma with a relatively weak magnetic field. We point out possible models of the emission source in the form of a magnetic trap or a neutral current sheet with a transverse magnetic field localized in the corotating region of the pulsar magnetosphere far from the neutron star surface.     

Resonant Transition Radiation and Solar Radio Bursts

This paper presents general relations for the intensity of the resonant transition radiation (RTR) and their detailed analysis. This analysis shows that the spectrum amplitude of the x-mode at some frequencies for high-energy electrons can grow with the magnetic field increase in some interval from zero value; it can even dominate over that for the o-mode. With further magnetic field increase, the intensity of the RTR x-mode decreases in comparison with the intensity of the o-mode and this decrease is higher for higher velocities of energetic electrons. The polarization of the RTR depends on the velocity of energetic electrons, too. For velocities lower than some velocity limit v<v _i the RTR emission is unpolarized in a broad interval of magnetic field intensities in the radio source. For reasonable values of indices of the power-law distribution functions of energetic electrons, the RTR is broadband in frequencies (df/f≈0.2−0.4). Furthermore, we show various dependencies of the RTR and its spectral characteristics. Assuming the same radio flux of the transition radiation and the gyro-synchrotron one at the Razin frequency, we estimate the limit magnetic field in the radio source of the transition radiation. Then, we analyze possible sources of small-scale inhomogeneities (thermal density fluctuations, Langmuir and ion-sound waves), which are necessary for the transition radiation. Although the small-scale inhomogeneities connected with the Langmuir waves lead to the plasma radiation, which is essentially stronger than RTR, the inhomogeneities of the ion-sound waves are suitable for the RTR without any other radiation. We present the relations describing the RTR for anisotropic distribution functions of fast electrons. We consider the distribution functions of fast electrons in the form of the Legendre polynomials which depend on the pitch-angle. We analyze the influence of the degree of the anisotropy (an increase of the number of terms in the Legendre polynomial) on spectral characteristics of the RTR. A comparison with previous studies is made. As an example of the use of the derived formulas for the RTR, the 24 December 1991 event is studied. It is shown that the observed decimetric burst can be generated by the RTR in the plasma with the density inhomogeneities at the level 〈ΔN ²〉/N ²=2.5⋅10⁻⁵.