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.     

An Estimation of the Coronal Magnetic Field Strength From Spectrographic Observations in the Microwave Range

Solar radio emission observations in the microwave frequency range show fine structures consisting of a number of almost parallel narrow-frequency bands. We interpret these bands as plasma emission at cyclotron harmonics. This emission is generated by the anisotropic electron beam, which excites longitudinal waves at a normal Doppler effect resonance. Subsequently, the longitudinal waves convert to radio emission at the second harmonic of the longitudinal wave frequency, and sometimes to the fundamental harmonic. The magnetic field strength is estimated on the basis of such a model in the microwave burst sources at 100–200 G. Estimates of the density variations are also made.     

Generation of Type U Bursts in Solar Radio Emission

If plasma waves propagate in the direction of the plasma density decrease, their spectrum shifts to large wave numbers (to small phase velocities). This means that the spectrum of plasma waves excited by an electron beam concentrates near the distribution function (“plateau”) border, which shifts in the region of low velocities in the process of quasilinear relaxation. As the spectrum of excited plasma waves shifts in the region of large wave numbers, their frequency grows in accordance with the dispersion equation, which describes these waves. When the growth of the plasma wave frequency exceeds the decrease of the frequency owing to the regular inhomogeneity in the corona, the branch with positive frequency drift appears on the dynamic spectrum of the radio emission. Our computations allow us to estimate the density and energy of electron beams generating type U bursts.     

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.     

Characteristic frequencies of a non-maxwellian plasma: A method for localizing the exact frequencies of magnetospheric intense natural waves near ƒpe

Intense natural waves are commonly observed, onboard satellites, in the outer Earth's magnetosphere, inside a narrow frequency range, including the electron plasma and upper hybrid frequencies. In order to progress in the understanding of their emission processes, it is necessary to determine precisely the relationship which exists between their frequencies and the characteristic frequencies of the magnetospheric plasma. For this purpose, it is necessary to take into account the fact that some of these characteristic frequencies ($\text{?}{}_{\mathrm{qN}}$), which are provided by active sounding of the plasma, not only depend on the total density, but also on the shape of the distribution function (which has generally been assumed, in previous studies, to be maxwellian). A method providing a fine diagnosis of general non-maxwellian plasmas is developed. This method of analysis of the experimental data is based on a theoretical study, which points out the influence of the shape of the distribution function on the dispersion curves (for wave vectors perpendicular to the static magnetic field).     

Vlasov – Maxwell,Self-consistent Electromagnetic Wave Emission Simulations in the Solar Corona

1.5D Vlasov – Maxwell simulations are employed to model electromagnetic emission generation in a fully self-consistent plasma kinetic model for the first time in the context of solar physics. The simulations mimic the plasma emission mechanism and Larmor-drift instability in a plasma thread that connects the Sun to Earth with the spatial scales compressed appropriately. The effects of spatial density gradients on the generation of electromagnetic radiation are investigated. It is shown that a 1.5D inhomogeneous plasma with a uniform background magnetic field directed transverse to the density gradient is aperiodically unstable to the Larmor-drift instability. The latter results in a novel effect of generation of electromagnetic emission at plasma frequency. The generated perturbations consist of two parts: i) non-escaping (trapped) Langmuir type oscillations, which are localised in the regions of density inhomogeneity, and are highly filamentary, with the period of appearance of the filaments close to electron plasma frequency in the dense regions; and ii) escaping electromagnetic radiation with phase speeds close to the speed of light. When the density gradient is removed (i.e. when plasma becomes stable to the Larmor-drift instability) and a low density super-thermal, hot beam is injected along the domain, in the direction perpendicular to the magnetic field, the plasma emission mechanism generates non-escaping Langmuir type oscillations, which in turn generate escaping electromagnetic radiation. It is found that in the spatial location where the beam is injected, standing waves, oscillating at the plasma frequency, are excited. These can be used to interpret the horizontal strips (the narrow-band line emission) observed in some dynamical spectra. Predictions of quasilinear theory are: i) the electron free streaming and ii) the long relaxation time of the beam, in accord with the analytic expressions. These are corroborated via direct, fully-kinetic simulation. Finally, the interplay of the Larmor-drift instability and plasma emission mechanism is studied by considering a dense electron beam in the Larmor-drift unstable (inhomogeneous) plasma. The latter case enables one to study the deviations from the quasilinear theory.     

Generation of Intermediate Drift Bursts by Magnetohydrodynamic Waves in the Solar Corona

The plasma mechanism of radio emission generation in an inhomogeneous medium is investigated. In the model under study, the electron beam with loss-cone distribution generates upper-hybrid waves that, in turn, are transformed into radio emission. It is shown that the influence of the plasma density inhomogeneity limits the plasma waves’ intensity considerably due to variation in their wave vector. The results are used to interpret the intermediate drift (IMD) bursts. A model is proposed in which these bursts are reflections of propagating small-scale (with amplitudes of about 1% and sizes of hundreds of kilometers) magnetohydrodynamic (MHD) disturbances of magnetic tubes. It is shown that this model allows us to explain the spectral parameters of the bursts in question. At present, the lack of precise and independent data about the magnetic field does not allow us to decide definitively between the existing models (whistler or MHD waves) of the IMD bursts; nevertheless, if the proposed model is correct, it can be used to determine the characteristics of the coronal MHD waves.     

Theory of decametric radio emissions from Jupiter

It is suggested that the Jovian decametric emissions (DAM) originate in a cyclotron instability of weakly relativistic electrons trapped in the Jovian magnetic field. The resulting radiation has a group velocity in the magnetosphheric plasma which may be of order 10²km/sec, and thus takes much more time to escape the magnetosphere than if the group velocity were at or near the speed of light. Therefore, the asymmetry of the Io phase with respect to sources east and west of the Earth-Jupiter line does not imply an asymmetric beaming of DAM; it is caused by the delay the waves experience in traversing the magnetosphere. The frequency drifts of milli- and decasecond bursts are also explained. It is found that the rotation of the magnetosphere can play an important role, since the observer views the propagation velocity of the waves as the sum of their group velocity and the velocity of the medium itself. The rotation velocity is in opposite directions, relative to the observer, for sources east and west of the Earth-Jupiter line; the resultant vector addition gives positive frequency drifts for decasecond bursts from the early and fourth sources, and negative drifts for bursts from the main and third sources. The negative drifts of millisecond bursts may be the result of large density gradients of plasma in a temporarily compressed magnetosphere.     

A model for drift pair and hook burst emission from the solar corona

Combination scattering of the Cerenkov plasma waves generated by a fast electron beam on the electron density fluctuations in a magnetoactive plasma is assumed to be the cause of the emission of the drift pair (or the hook burst) from the solar corona. The features of the combination emission are studied numerically with parameters appropriate to the solar corona condition. It is found that the major properties of the drift pair and the hook burst can be accounted for.     

Non-linear effects of VLF noise generation by electron beams in the polar magnetosphere

A theory of VLF noise excitation by electron beams in the polar magnetosphere is proposed. Two modes of excited oscillations are considered: waves with frequencies in the vicinity of the lower hybrid resonance (LHR) from about 50 to 1000 kHz and whistler-mode waves in the frequency range of several kHz.The spectral distribution and the level of turbulent noise, having been excited by means of two counterstreaming electron beams, are deduced in magnetized plasma at the LHR frequency. It is also shown that the growth of noise up to the quasistationary level oscillates with time. Energy density of oscillations at the LHR frequency in the region of the dayside polar cusp agrees with the experimental data.The processes of whistler excitation by electron beams are discussed. The growth rate of excitation of whistler-mode by electrostatic oscillations at the LHR frequency is calculated.     

Polar observations of plasma waves in and near the dayside magnetopause/magnetosheath

The plasma wave instrument (PWI) on board the Polar spacecraft made numerous passages of the dayside magnetopause and several probable encounters with the magnetosheath during the years 1996 and 1997. During periods of relatively high density, the PWI antenna-receiver system is coupled to the plasma and oscillates. The oscillations have been shown (cf. Radio Sci. 36 (2001) 203) to be indicative of periods of higher plasma density and plasma flows, possibly associated with magnetic reconnection. We have studied the plasma waves observed on three distinct magnetopause passes distinguished by the presence of these oscillations of the PWI receivers, and we report on the data obtained near, but not during, the times of the oscillations and the possible role of these waves in magnetic reconnection. Sweep-frequency receiver and high-resolution waveform data for some of these times are presented. The plasma wave measurements on each of the passes are characterized by turbulence. The most stable waves are whistler mode emissions typically of several hundred hertz that are seen intermittently in these regions. The data indicate the presence of impulsive solitary-like wave structures with strong electric fields both parallel and perpendicular to the magnetic field near, but not always within, suspected reconnection sites. The solitary waves show the highest occurrence when observed with electrostatic electron cyclotron waves. These latter waves have been observed in the past in the cusp, polar magnetosphere, and auroral regions and therefore may represent excursions into the cusp, but also indicate the presence of low-energy electron beams. Turbulence near the lower hybrid frequency, low-frequency EM waves, and impulsive monopolar electrostatic pulses are seen throughout the magnetopause and particularly near regions of large decrease in the local magnetic field and enhanced field-aligned flows, the suspected reconnection sites. The absence of significant solitary wave signatures within suspected reconnection sites may require modifications to some reconnection models.     

Coherent Emission Mechanisms in Radio Pulsars

A theory of pulsar radio emission generation, in which the observed waves are produced directly by the maser-type plasma instabilities on the anomalous cyclotron-Cherenkov resonance and the Cherenkov-drift resonance , is capable of explaining the main observational characteristics of pulsar radio emission. The instabilities are due to the interaction of the fast particles of the primary beam and from the tail of the distribution with the normal modes of a strongly magnetized one-dimensional electron-positron plasma. The waves emitted at these resonances are vacuum-like electromagnetic waves that may leave the magnetosphere directly. The cyclotron-Cherenkov instability is responsible for core emission pattern and the Cherenkov-drift instability produces conal emission. The conditions for the development of the cyclotron-Cherenkov instability are satisfied for the both typical and millisecond pulsars provided that the streaming energy of the bulk plasma is not very high γ _p = 5 ÷ 10. In a typical pulsar the cyclotron-Cherenkov and Cherenkov-drift resonances occur in the outer parts of magnetosphere at r _res ≈ 10⁹cm. This theory can account for various aspects of pulsar phenomenology including the morphology of the pulses, their polarization properties and spectral behavior. This revised version was published online in July 2006 with corrections to the Cover Date.     

Stochastic wave growth, power balance, and beam evolution in type III solar radio sources

Energy-balance arguments are combined with the stochastic-growth theory of type III radio sources to determine the properties of the source in average dynamical equilibrium with the beam, and the beam's long-term evolution. Purely linear stochastic-growth theory has previously emphasized that the beam evolves to a state close to marginal stability. Small mean residual deviations from marginal stability are present at dynamical equilibrium and these lead to residual energy flows that feed the waves observed in situ and by remote receivers; consequently the beam energy is depleted. Here, dynamical equilibrium beam and wave levels are estimated for the first time and it is found that the main sink of beam-driven Langmuir waves is either via electrostatic decay into product Langmuir and ion-sound waves or via scattering by short-wavelength density fluctuations, depending on the conditions. Improved estimates of energy branching ratios imply that, at 1 AU from the Sun, typically 20% of the beam energy is converted to Langmuir waves that are scattered off low-frequency density fluctuations and then dissipated, with almost all the remaining waves undergoing electrostatic decay, although as little as one-third of the Langmuir waves may decay in atypical circumstances. Of order 10^–3 of the beam energy is converted into sound waves, which are mostly dissipated, and of order 10^–5 is converted into potentially observable electromagnetic waves. The mean lifetime of the Langmuir waves at 1 AU is 1–40 s, while that of the beam is of order 1000 s. The beam density decreases relative to that of the background as the beam propagates. For most parameters, analysis of energy losses from the beam to the waves shows that the beam velocity decreases at roughly the same rate as the thermal velocity of the background plasma. It is argued from these considerations, and from in situ observations at 1 AU, that these trends imply that only the densest and fastest type III beams will be able to penetrate much past 1 AU from the Sun. This implies a low-frequency cutoff to type III emission at roughly 10 kHz, in good agreement with recent Ulysses remote observations, showing their consistency with in situ measurements.     

Effects of the magnetic field model and wave polarisation on the estimation of proton number densities in the magnetosphere using field line resonances

The cold, core plasma mass density in the Earth's magnetosphere may be deduced from the resonant behaviour of ultra-low frequency (ULF; 1–100 mHz), magnetohydrodynamic (MHD) waves. Ground-based magnetometers are the most widely used instruments for recording the signature of ULF wave activity in the magnetosphere. For a suitable model of the background magnetic field and a functional form for the variation of the proton number density with radial distance, the resonant frequencies of ULF waves provide estimates of the equatorial plasma mass density. At high latitudes, the magnetic field model becomes critical when estimating the plasma mass density from FLR data. We show that a dipole field model is generally inadequate for latitudes greater than ∼65° geomagnetic compared with models that are keyed to magnetic activity, interplanetary magnetic field and solar wind properties. Furthermore, the method often relies on the detection of the fundamental ULF resonance, which changes frequency depending on the polarisation of the oscillation. Using idealised toroidal and poloidal oscillation modes, the range of the derived densities as the ULF wave polarisation changes is of the same order as changing the density function from a constant value throughout the magnetosphere to assuming constant Alfven speed in a dipole geometry.     

The mechanism of magnetospheric substorm and the MHD waves of the solar wind

A mechanism of the Earth's magnetospheric substorm is proposed. It is suggested that the MHD waves may propagate across the magnetopause from the magnetosheath into the magnetotail and will be dissipated in the plasma sheet, heating the plasma and accelerating the particles. When the solar wind parameters change, the Poynting flux of the waves transferred from the magnetosheath into the tail, may be greater than 10¹⁸ erg s^?1. The heated plasma and accelerated particles in the plasma sheet will be injected into the inner magnetosphere, and this may explain the process of the ring current formation and auroral substorm.The Alfvén wave can only propagate along the magnetic force line into the magnetosphere in the open magnetosphere, but the magnetosonic wave can propagate in both the open and closed magnetosphere. When the IMF turns southward, the configuration of the magnetosphere will change from a nearly closed model into some kind of open one. The energy flux of Alfvén waves is generally larger than that of the magnetosonic wave. This implies that it is easy to produce substorms when the interplanetary magnetic field (IMF) has a large southward component, but the substorm can also be produced even if the IMF is directed northward.     

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.     

Electrostatic waves at electron gyrofrequency

An attempt to give theoretical foundation for understanding the origin of electrostatic waves at electron gyrofrequency in the magnetosphere is presented. The electrostatic dispersion equation describ- ing wave propagation at electron gyrofrequency is investigated in different limiting cases. It is pointed out that this equation can describe weakly damped waves when the electron plasma frequency is above electron gyrofrequency.     

Observations of waves artificially stimulated by an electron beam inside a region with auroral precipitation

The POLAR 5 sounding rocket, launched from Andøya, Norway on 1 February, 1976 was of a “mother-daughter” configuration. An electron accelerator, mounted on the “daughter,” produced a pulsed electron beam with currents up to 130 mA and electron energies up to 10 keV. The waves, artificially stimulated by the injected electron beam, was studied using wave receivers, mounted on the “mother.” The receivers covered the frequency range from 0.1 kHz to 5 MHz.

In addition to the stimulated waves observed during beam injection, enhanced wave emissions were observed 10–20 ms after the end of beam injection. This emission seemed to be relatively independent of whether the electron beam is launched up or down along the geomagnetic field.

The high frequency emission observed after beam injection is found to be correlated with the passage through an auroral arc. In particular this emission is closely correlated with the flux of 4–5 keV auroral electrons.

The low frequency emissions observed after beam injection are concentrated in two bands below the lower hybrid frequency.

Different mechanisms for explaining the observed time delays between the beam injection and the observation of the emissions are discussed.     

Dynamics of a cloud of fast electrons travelling through the plasma

Numerical analysis has been carried out on the one-dimensional quasi-linear relaxation of a group of fast electrons travelling through the plasma. It is demonstrated that the electron velocity distribution of fast electrons tends to be a plateau form exciting the electron plasma waves and that the plasma waves are almost completely reabsorbed later by electrons arriving later. Both the velocity range and time interval in which quasi-plateau distribution is formed increase with distance from the origin of the fast electrons. There is no net energy loss of the electron cloud during the travel through the plasma if we neglect both the collisional losses and the scattering of plasma waves. Although the present computation is preliminary and limited to rather low beam density, we can see that the characteristics of both the electron beam and the plasma waves tend, with distance, to those of the analytical solution given by Ryutov and Sagdeev; though a modification to set a low velocity cutoff on the plasma waves due to the thermal electrons is necessary.