Emission of solar radio spikes by beam-driven cyclotron resonance

The generation of bright solar radio spikes by the beam-driven cyclotron resonance maser mechanism (the resonant interaction of an electron beam with a circularly polarized wave in a background plasma under the action of a guide magnetic field) is studied. Nonlinear effects such as radiation damping and gyrophase bunching on electron energy and momentum are responsible for the enhanced direct energy conversion between the beam and the coherent wave. Factors such as beam energy spread and pitch angle distribution are analyzed. The intense maser radiation is carried at the source by the circularly polarized wave propagating along the magnetic field. Due to the magnetic field curvature, the outgoing maser radiation converts into extraordinary and ordinary modes. The extraordinary mode suffers from plasma absorption at the second harmonic layer, whereas the ordinary mode is likely to get through.     

Propagation and absorption of cyclotron maser radiation in solar microwave spike bursts

It has been argued that the loss-cone-driven electron cyclotron maser instability can account for the properties of millisecond microwave spike bursts observed during some solar flares. However, as it propagates outward from the corona, maser radiation undergoes gyroresonance absorption when its frequency is a harmonic of the local electron-cyclotron frequency. Existing analytical models using slab geometries predict that this absorption should be sufficiently strong to prevent the radiation from being seen at the observed levels, except under highly restrictive conditions or for unrealistic plasma parameters. A more comprehensive analysis is presented here to determine if and when maser radiation can escape to produce microwave spike bursts. This analysis employs numerical raytracing and incorporates propagation and absorption of fundamental maser emission in a realistic model of a coronal flux loop. It is found that ranges of physical conditions do exist under which maser radiation can escape to an observer and that these conditions are much more limiting for fundamental emission in the extraordinary ()-mode than in the ordinary (o)-mode. Detailed investigation implies that escaping radiation in the -mode is highly directional and chiefly observable toward the center of the solar disk, while escapingo-mode radiation is found to emerge from the corona over a much wider range of directions, with some cases corresponding to radiation observable near the solar limb.     

Non-thermal processes in large solar flares

We analyze particle acceleration processes in large solar flares, using observations of the August, 1972, series of large events. The energetic particle populations are estimated from the hard X-ray and γ-ray emission, and from direct interplanetary particle observations. The collisional energy losses of these particles are computed as a function of height, assuming that the particles are accelerated high in the solar atmosphere and then precipitate down into denser layers. We compare the computed energy input with the flare energy output in radiation, heating, and mass ejection, and find for large proton event flares that:

1. The ～10–10² keV electrons accelerated during the flash phase constitute the bulk of the total flare energy.
2. The flare can be divided into two regions depending on whether the electron energy input goes into radiation or explosive heating. The computed energy input to the radiative quasi-equilibrium region agrees with the observed flare energy output in optical, UV, and EUV radiation.
3. The electron energy input to the explosive heating region can produce evaporation of the upper chromosphere needed to form the soft X-ray flare plasma.
4. Very intense energetic electron fluxes can provide the energy and mass for interplanetary shock wave by heating the atmospheric gas to energies sufficient to escape the solar gravitational and magnetic fields. The threshold for shock formation appears to be ～10³¹ ergs total energy in >20 keV electrons, and all of the shock energy can be supplied by electrons if their spectrum extends down to 5–10 keV.
5. High energy protons are accelerated later than the 10–10² keV electrons and most of them escape to the interplanetary medium. The energetic protons are not a significant contributor to the energization of flare phenomena. The observations are consistent with shock-wave acceleration of the protons and other nuclei, and also of electrons to relativistic energies.
6. The flare white-light continuum emission is consistent with a model of free-bound transitions in a plasma with strong non-thermal ionization produced in the lower solar chromosphere by energetic electrons. The white-light continuum is inconsistent with models of photospheric heating by the energetic particles. A threshold energy of ～5×10³⁰ ergs in >20 keV electrons is required for detectable white-light emission.

The highly efficient electron energization required in these flares suggests that the flare mechanism consists of rapid dissipation of chromospheric and coronal field-aligned or sheet currents, due to the onset of current-driven Buneman anomalous resistivity. Large proton flares then result when the energy input from accelerated electrons is sufficient to form a shock wave.     

The electron–cyclotron maser for astrophysical application

The electron–cyclotron maser is a process that generates coherent radiation from plasma. In the last two decades, it has gained increasing attention as a dominant mechanism of producing high-power radiation in natural high-temperature magnetized plasmas. Originally proposed as a somewhat exotic idea and subsequently applied to include non-relativistic plasmas, the electron–cyclotron maser was considered as an alternative to turbulent though coherent wave–wave interaction which results in radio emission. However, when it was recognized that weak relativistic corrections had to be taken into account in the radiation process, the importance of the electron–cyclotron maser rose to the recognition it deserves. Here we review the theory and application of the electron–cyclotron maser to the directly accessible plasmas in our immediate terrestrial and planetary environments. In situ access to the radiating plasmas has turned out to be crucial in identifying the conditions under which the electron–cyclotron maser mechanism is working. Under extreme astrophysical conditions, radiation from plasmas may provide a major energy loss; however, for generating the powerful radiation in which the electron–cyclotron maser mechanism is capable, the plasma must be in a state where release of susceptible amounts of energy in the form of radiation is favorable. Such conditions are realized when the plasma is unable to digest the available free energy that is imposed from outside and stored in its particle distribution. The lack of dissipative processes is a common property of collisionless plasmas. When, in addition, the plasma density becomes so low that the amount of free energy per particle is large, direct emission becomes favorable. This can be expressed as negative absorption of the plasma which, like in conventional masers, leads to coherent emission even though no quantum correlations are involved. The physical basis of this formal analogy between a quantum maser and the electron–cyclotron maser is that in the electron–cyclotron maser the free-space radiation modes can be amplified directly. Several models have been proposed for such a process. The most famous one is the so-called loss-cone maser. However, as argued in this review, the loss-cone maser is rather inefficient. Available in situ measurements indicate that the loss-cone maser plays only a minor role. Instead, the main source for any strong electron–cyclotron maser is found in the presence of a magnetic-field-aligned electric potential drop which has several effects: (1) it dilutes the local plasma to such an extent that the plasma enters the regime in which the electron–cyclotron maser becomes effective; (2) it generates energetic relativistic electron beams and field-aligned currents; (3) it deforms, together with the magnetic mirror force, the electron distribution function, thereby mimicking a high energy level sufficiently far above the Maxwellian ground state of an equilibrium plasma; (4) it favors emission in the free-space RX mode in a direction roughly perpendicular to the ambient magnetic field; (5) this emission is the most intense, since it implies the coherent resonant contribution of a maximum number of electrons in the distribution function to the radiation (i.e., to the generation of negative absorption); (6) it generates a large number of electron holes via the two-stream instability, and ion holes via the current-driven ion-acoustic instability which manifest themselves as subtle fine structures moving across the radiation spectrum and being typical for the electron–cyclotron maser emission process. These fine structures can thus be taken as the ultimate identifier of the electron–cyclotron maser. The auroral kilometric radiation of Earth is taken here as the paradigm for other manifestations of intense radio emissions such as the radiation from other planets in the solar system, from exoplanets, the Sun and other astrophysical objects.     

Simulation studies of electron acceleration by ion ring distributions in solar flares

Using a 2 1/2-D fully relativistic electromagnetic particle-in-cell code (PIC) we have investigated a potential electron acceleration mechanism in solar flares. The free energy is provided by ions which have a ring velocity distribution about the magnetic field direction. Ion rings may be produced by perpendicular shocks, which could in turn be generated by the super-Alfvénic motion of magnetic flux tubes emerging from the photosphere or by coronal mass ejections (CMEs). Such ion distributions are known to be unstable to the generation of lower hybrid waves, which have phase velocities in excess of the electron thermal speed parallel to the field and can, therefore, resonantly accelerate electrons in that direction. The simulations show the transfer of perpendicular ion energy to energetic electrons via lower hybrid wave turbulence. With plausible ion ring velocities, the process can account for the observationally inferred fluxes and energies of non-thermal electrons during the impulsive phase of flares. Our results also show electrostatic wave generation close to the plasma frequency: we suggest that this is due to a bump-in-tail instability of the electron distribution.     

太阳射电毫秒Spike辐射窄带宽的理论探讨

在磁拱底部非线性等离子体密度波传播期间,损失锥分布的反射电子驱动着电子迴旋maser不稳定性的增长,激励出二次谐频波模,支配着太阳射电毫秒Spike辐射。根据这个理论模型,本文着重研究了太阳射电毫秒Spike辐射的频带宽度问题。对于典型参数,计算结果发现:辐射带宽一般为几MHz到几十MHz,最高为100MHz。而且通常折射出的二次谐频z模辐射带宽较窄,而二次谐频o模辐射带宽较宽。     

Location and parameters of a microwave millisecond spike event

A typical microwave millisecond spike event on November 2, 1997 was observed by the radio spectrograph of National Astronomical Observatories (NAOs) at 2.6–3.8 GHz with high time and frequency resolution. This event was also recorded by Nobeyama Radio Polarimeters (NoRP) at 1–35 GHz and Radio Heliograph (NoRH) at 17 GHz. The source at 17 GHz is located in one foot-point of a small bright coronal loop of YOHKOH SXT and SOHO EIT images with strong photospheric magnetic field in SOHO MDI magnetograph. It is assumed that the electron cyclotron maser instability and gyro-resonance absorption dominate, respectively, the rising and decay phase of the spike event. For different harmonic number of gyro-frequency or magnetic field strength, a fitting program with free plasma parameters is used to minimize the difference between the observational and theoretical values of the exponential growth and decay rates for a given spike. The plasma parameters at third harmonic number are more comparable to their typical values in solar corona. Hence, it is able to provide a diagnosis for the source parameters (magnetic field, density, and temperature), the properties of radiations (wave vector and propagation angle), and the properties of non-thermal electrons (density, pitch angle, and energy). The results are also comparable with the diagnosis of the gyro-synchrotron radiation model, the frequency drift rates and a dipole magnetic field model, as well as the YOHKOH SXT and SOHO MDI data. This study is supported by the NFSC project nos. 10333030 and 10273025, and “973” program with no. G2000078403.     

A theoretical study of the direction and polarization of solar radio millisecond spike radiation

We investigated the angular direction and polarization of the solar radio millisecond spike emission in the model in which the spike emission is due to the second harmonic instability modes driven by electron cyclotron maser of loss cone distributed electrons during the propagation of a nonlinear plasma density wave near the magnetic mirror. We found that, when the angle θ between the wave vector and the magnetic field is > 60 °, the emission is in 100% X-mode polarization; when 40 ° < θ<60 °, the emission is in 100% O-mode polarization provided the amplitude of the density wave is below a certain limit; above that limit, the polarization will fall from 100% O-mode to even the X-mode. We also found that only 0.1% of the free energy of energy carrying electrons in the source region is converted into radiation wave energy.     

Nonthermal Electron Energy Deposition in the Chromosphere and the Accompanying Soft x-ray Flare Emission

We analyse four solar flares which have energetic hard X-ray emissions, but unusually low soft X-ray flux and GOES class (C1.0–C5.5). These are compared with two other flares that have soft and hard X-ray emission consistent with a generally observed correlation that shows increasing hard X-ray accompanied by increasing soft X-ray flux. We find that in the four small flares only a small percentage of the nonthermal electron beam energy is deposited in a location where the heating rate of the electron beam exceeds the radiative cooling rate of the ambient plasma. Most of the beam energy is subsequently radiated away into the cool chromosphere and so cannot power chromospheric evaporation thus reducing the soft X-ray emission. We also demonstrate that in the four small flares the nonthermal electron beam energy is insufficient to power the soft X-ray emitting plasma. We deduce that an additional energy source is required, and this could be provided by a DC-electric field (where quasi-static electric field channels in the coronal loops accelerate electrons, and those electrons with velocity below a critical velocity will heat the ambient plasma via Joule heating) in preference to a loop-top thermal source (where heat flux deposited in the corona is conducted along magnetic field lines to the chromosphere, heating the coronal plasma and giving rise to further chromospheric evaporation).     

Radio and soft X-ray investigation of the solar flares of February 4, 1986

In this paper, the 3B flare of February 4, 1986 is studied comprehensively. The escape electrons accelerated to 10–100 keV at the top of coronal loop are confirmed by III type bursts. The energetic electron beams moved downward trigger the eruptions in the low layer of solar atmosphere. The radio and soft X-ray bursts are interpreted, respectively, by the maser mechanism and evaporation effect. Finally, the important role of energetic electron beams in solar flares is pointed out.     

1997年11月2日微波尖峰源背景参数的诊断

利用北京天文台高时间和高频率分辨率的射电频谱仪对射电尖峰的测量,可以对背景等离子体参数进行的自洽诊断（ 磁场,密度,温度,波矢,及非热电子的性质） 。该诊断基于电子回旋脉塞不稳定性和回旋共振吸收。最后从诊断结果和太阳日冕典型参数的比较以确定尖峰辐射的谐波数。     

Sub-terahertz emission from solar flares: The plasma mechanism of chromospheric emission

We consider the plasma mechanism of sub-terahertz emission from solar flares and determine the conditions for its realization in the solar atmosphere. The source is assumed to be localized at the chromospheric footpoints of coronal magnetic loops, where the electron density should reach n ≈ 10¹⁵ cm^?3. This requires chromospheric heating at heights h ? 500 km to coronal temperatures, which provides a high degree of ionization needed for Langmuir frequencies ν _p ≈ 200–400 GHz and reduces the bremsstrahlung absorption of the sub-THz emission as it escapes from the source. The plasma wave excitation threshold for electron-ion collisions imposes a constraint on the lower density limit for energetic electrons in the source, n ₁ > 4 × 10⁹ cm^?3. The generation of emission at the plasma frequency harmonic ν ≈ 2ν _p rather than the fundamental tone turns out to be preferred. We show that the electron acceleration and plasma heating in the sub-THz emission source can be realized when the ballooning mode of the flute instability develops at the chromospheric footpoints of a flare loop. The flute instability leads to the penetration of external chromospheric plasma into the loop and causes the generation of an inductive electric field that efficiently accelerates the electrons and heats the chromosphere in situ. We show that the ultraviolet radiation from the heated chromosphere emerging in this case does not exceed the level observed during flares.     

On the theory of astronomical masers – II. Polarization of maser radiation

In this paper, we investigate the polarization property of the radiation amplified by astronomical masers in the presence of a strong magnetic field. Our model explicitly takes into account the broad-band nature of the radiation field and the interaction of the radiation with the maser transition   J = 1–0  . The amplification of different realizations of the background continuum radiation by the maser is directly simulated and the Stokes parameters of the radiation field are then obtained by averaging over the ensemble of emerging maser radiation. For isotropic pumping and partially saturated masers, we find that the maser radiation is linearly polarized in two representative cases where the magnetic field   B   makes an angle  θ= 30°  and  90°  to the maser axis. The linear polarization for maser radiation obtained in our simulations for both cases is in agreement with the results of the standard model. Furthermore, no instability during amplification is seen in our simulations. Therefore, we conclude that there is no problem with the previous numerical investigations of maser polarization in the unsaturated and partially saturated regime.     

A model of fast radio bursts: collisions between episodic magnetic blobs

Fast radio bursts(FRBs) are bright radio pulses from the sky with millisecond durations and Jansky-level flux densities. Their origins are still largely uncertain. Here we suggest a new model for FRBs. We argue that the collision of a white dwarf with a black hole can generate a transient accretion disk, from which powerful episodic magnetic blobs will be launched. The collision between two consecutive magnetic blobs can result in a catastrophic magnetic reconnection, which releases a large amount of free magnetic energy and forms a forward shock. The shock propagates through the cold magnetized plasma within the blob in the collision region, radiating through the synchrotron maser mechanism,which is responsible for a non-repeating FRB signal. Our calculations show that the theoretical energetics, radiation frequency, duration timescale and event rate can be very consistent with the observational characteristics of FRBs.     

Evidence for cyclotron maser emission from the Sun and stars

In recent years radiation has been observed from planets, Sun and stars that is best explained by the cyclotron maser instability; in fact, all celestial bodies that might feasibly emit and be detected by their cyclotron maser radiation have been detected. Here we review those observations, the developments in the theory, the recent work on the effiency of energy transfer by cyclotron maser radiation, and some recent and future observations that might demonstrate whether the mechanism is energetically important in solar and stellar flares.This work was supported in part by NASA's Solar Heliospheric Physics and Solar Terrestrial Theory Programs under grants NSG-7287 and NAGW-91 to the University of Colorado. The numerical simulations were performed on the Cray XMP at the San Diego Supercomputer Center which is funded by the National Science Foundation.     

On the saturation of electron-cyclotron masers in solar flares

We consider the relaxation of an unstable distribution of fast non-relativistic electrons. Langmuir turbulence generated by the electrons is found to determine the saturation of an electron-cyclotron maser. The important role of nonlinear processes in Langmuir and electromagnetic waves is shown. The characteristic saturation time is about 1 ms. It is shown that both cyclotron maser emission and the transformation of plasma waves to transverse ones can be essential in the formation of observable radio spectra from solar flares.     

Is Cyclotron Maser Emission in Solar Flares Driven by a Horseshoe Distribution?

Since the early 1980s, decimetric spike bursts have been attributed to electron cyclotron maser emission (ECME) by the electrons that produce hard X-ray bursts as they precipitate into the chromosphere in the impulsive phase of a solar flare. Spike bursts are regarded as analogous to the auroral kilometric radiation (AKR), which is associated with the precipitation of auroral electrons in a geomagnetic substorm. Originally, a loss-cone-driven version of ECME, developed for AKR, was applied to spike bursts, but it is now widely accepted that the measured distribution function is horseshoe-like (an isotropic distribution with a one-sided loss cone), and that a horseshoe-driven version of ECME applies to AKR. We explore the implications of the assumption that horseshoe-driven ECME also applies to spike bursts. We develop a 1D model for the acceleration of the electrons by a parallel electric field, and show that under plausible assumptions it leads to a horseshoe distribution of electrons in a solar flare. A second requirement for horseshoe-driven ECME is an extremely low plasma density, referred to as a density cavity. We argue that a coronal density cavity should develop in association with a hard X-ray burst, and that such a density cavity can overcome a long-standing problem with the escape of ECME through the second-harmonic absorption layer. Both the horseshoe distribution and the associated coronal density cavity are highly localized, and could not be resolved in the statistically large number of local precipitation regions needed to explain a hard X-ray burst. The model highlights the “number problem” in the supply of the electrons needed to explain a hard X-ray burst.     

On the heat conduction in a high-temperature plasma in solar flares

We have developed three types of mathematical models to describe the mechanisms of plasma heating in the corona by intense heat fluxes from a super-hot (T _e ? 10⁸ K) reconnecting current layer in connection with the problem of energy transport in solar flares. We show that the heat fluxes calculated within the framework of self-similar solutions using Fourier’s classical law exceed considerably the real energy fluxes known from present-day multi-wavelength observations of flares. This is because the conditions for the applicability of ordinary heat conduction due to Coulomb collisions of thermal plasma electrons are violated. Introducing anomalous heat conduction due to the interaction of thermal runaway electrons with ion-acoustic turbulence does not give a simple solution of the problem, because it produces unstable temperature profiles. Themodels incorporating the effect of collisional heat flux relaxation describe better the heat transport in flares than Fourier’s law and anomalous heat conduction.     

Loop heating by D.C. electric current and electromagnetic wave emissions simulated by 3-D EM particle code

We have shown that a current-carrying plasma loop can be heated by magnetic pinch driven by the pressure imbalance between inside and outside the loop, using a 3-dimensional electromagnetic (EM) particle code. Both electrons and ions in the loop can be heated in the direction perpendicular to the ambient magnetic field, therefore the perpendicular temperature can be increased about 10 times compared with the parallel temperature. This temperature anisotropy produced by the magnetic pinch heating can induce a plasma instability, by which high-frequency electromagnetic waves can be excited. The plasma current which is enhanced by the magnetic pinch can also excite a kinetic kink instability, which can heat ions perpendicular to the magnetic field. The heating mechanism of ions as well as the electromagnetic emission could be important for an understanding of the coronal loop heating and the electromagnetic wave emissions from active coronal regions.     

The Mechanisms of Particle Kinetics and Dynamics Leading to Seismic Emission and Sunquakes

In this paper the mechanisms responsible for observational features associated with sunquakes induced by different classes of solar flares are compared. The role of high-energy particle beams via Coulomb and Ohmic heating of the ambient plasma and nonthermal excitation and ionization is explored for different beam parameters at various atmospheric depths. On the one hand, only hard electron beams with high-energy fluxes are found producing extensive nonthermal hydrogen ionization, four orders of magnitude higher than in the quiet atmosphere. This excess ionization leads to the white-light flares associated with the seismic emission appearing simultaneously with hard X-ray emission and, consequently, to a strong increase of Ni-line emission observed as the seismic emission measured with the holographic technique. On the other hand, the ambient plasma hydrodynamic response to heating by such beam electrons forms hydrodynamic shocks just below the transition region, in the upper chromosphere, and they travel with supersonic velocity for up to five minutes before reaching the photosphere. These hydrodynamic responses caused by the beam electrons are maximized in the lower chromosphere for moderate electron beams because of their smaller Ohmic losses in the upper atmosphere compared to those for higher-energy electron beams whose bulk energy is deposited in the transition region. These shocks caused by electron beams can explain the observations of seismic emission by time?–?distance (TD) diagrams and the holographic method in M- and C-class flares, whereas to account for the quakes in X-class flares, high-energy quasi-thermal protons or power-law proton beams either by themselves or blended with electron beams are the most likely agents. Nonthermal ionization and excitation of lower atmospheric levels during the beam injection followed by thermo-conductive heating after the beam is stopped can contribute to the seismic signatures observed with the holographic technique caused by strong nonthermal ionization and back-warming heating occurring in the shock while it loses its energy by optically-thick radiation in the photospheric lines and continua.