Propagation of a Maxwellian Electron Cloud in a Plasma

We consider the dynamics of an electron cloud with an initially Maxwellian electron distribution and a temperature significantly exceeding that of the surrounding plasma. It is demonstrated that only the fastest electrons propagate into the plasma as a beam-plasma structure, whereas the main part of the cloud of electrons is locked by the Langmuir turbulence generated by the electrons remaining.     

太阳运动IV型射电爆发的相干辐射模型

为解释太阳运动IV型射电爆发的相干辐射机制提出一个理论模型．从耀斑中产生的高能电子，可以被扩展上升的太阳磁流管俘获．在磁流管顶部，这些高能电子的速度分布形成为类束流速度分布，激发束流等离子体的不稳定性，并且主要直接放大O模电磁波．不稳定性增长率敏锐地依赖了日冕等离子体参数，fpe／fce和射束温度Tb，这能定性解释在太阳运动IV型射电爆发中观测到的高亮温度和高偏振度，以及宽频谱的特性．     

Thin electron beam propagation in plasmas

The propagation of dense electron beams and the interaction with the ambient plasmas are studied by using two-dimensional electrostatic simulations. When the width of the beam is of the order of electron gyro-radius, the beam electrons move across the magnetic field lines and the beam-plasma interaction becomes prominent with the reduced beam density. When the width of the beam is of the order of ion gyro-radius, the propagation of beam electrons is possible only with the formation of the ion channel. However, since the time scale of the ionic motion is much longer than that of the electronic motion, most of the beam electrons return back to the original beam injection region     

Electron beam formation and stability

The dynamics of fast electrons streaming from the Sun through the interplanetary plasma is reviewed from the kinetic viewpoint. How can a bump appear on the tail of the electron distribution function? How can the beam survive the beam-plasma instability and propagate up to 1 AU as observed? These two questions are discussed in light of the recent data acquired in situ on electron distributions, Langmuir waves, ion acoustic waves, and background density fluctuations.     

Velocities of beam-plasma structures at their propagation in the solar corona

It was found recently that fast electrons travel through the plasma of the solar corona in the form of beam-plasma structure (BPS), which consists of electrons and Langmuir waves. In this paper the influence of scattering BPS Langmuir waves off plasma ions (l+i=l+i) on BPS velocity is studied. We show that the maximum BPS velocity equals 0.35c, which is close to the velocity of Type III bursts sources.     

Dynamics of electron beams in the inhomogeneous solar corona plasma

Dynamics of a spatially-limited electron beam in the inhomogeneous solar corona plasma is considered in the framework of weak turbulence theory when the temperature of the beam significantly exceeds that of surrounding plasma. The numerical solution of kinetic equations manifests that generally the beam accompanied by Langmuir waves propagates as a beam-plasma structure with a decreasing velocity. Unlike the uniform plasma case the structure propagates with the energy losses in the form of Langmuir waves. The results obtained are compared with the results of observations of type III bursts. It is shown that the deceleration of type III sources can be explained by corona inhomogeneity. The frequency drift rates of the type III sources are found to be in good agreement with the numerical results of beam dynamics.     

Dynamics of a cloud of fast electrons travelling through the plasma

Numerical analysis of quasi-linear relaxation has been made for four models of electron beam with a finite length travelling through the plasma. In Model 4, a model atmosphere of the corona is adopted and also an increase in the cross-section of the electron beam is taken into account. The electron velocity distribution generally becomes a quasi-plateau form in limited velocity and time ranges. If, however, collisional decay of the fast electrons is too strong and the initial beam density is not high enough, the plateau does not appear. Collisional damping of plasma waves cannot be neglected, since the growth rate of the waves is strongly suppressed by the appearance of the quasi-plateau.An approximate formula for the velocity distribution of the solar electrons passing through the corona has been derived analytically taking into account not only the interaction with plasma waves, but also the collisional damping of the plasma waves and collisions with thermal particles. By the use of this formula, we can easily compute the time profile of the plasma waves caused by these solar electrons at any given place in the interplanetary space. The validity of this semi-analytical approach is checked by the numerical analysis of Model 4, showing a satisfactory fit between the numerical and semi-analytical results.The direct application of this method to the problems of type III radio bursts is left to a later paper.     

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.     

A model exciter for type III solar radiobursts

In an earlier paper (Harvey and Aubier, 1973) the large scale radial electron density gradient in the corona and solar wind was shown to cause the phase velocity of plasma waves to decrease as they propagate away from the Sun, thus leading to appreciable Landau damping of the plasma waves. It is proposed here that this same phase velocity decrease creates conditions which facilitate the stabilisation of a beam of exciter electrons of finite duration, provided that three conditions are fulfilled. Two of these conditions concern the velocity-time distribution of the exciter electrons at their point of ejection from the Sun, while the third is simply that, above a certain altitude, the coronal electron density decreases with altitude r faster than r ^?2. The plasma wave source is then associated with the leading edge of the electron stream. The spatial density of the power converted into plasma waves is calculated as a function of position and time, and is shown to be independent of the nature of the stabilisation mechanism. The maximum of this power density is found to move outwards from the Sun at a uniform speed when a simple electron injection model with a Maxwellian velocity distribution is introduced.     

Time profile of type III bursts

On the hypothesis that the time profile of a type III burst corresponds directly to the flux of electron beam, the similarity of time profile is shown to be maintained even if the electron velocity decreases with distance provided that the time is normalized to unity at the time of maximum flux. The observed time profiles of type III bursts with simple shape seem to follow the similarity law in almost all frequency range. This evidence may indicate that the time profile, both the rising and decaying phases, of a type III burst should be attributed to a common origin, e.g., the time variation of exciter determined by the initial velocity distribution in the electron beam, instead of attributing the rising time to the beam length and the decay time to the damping of plasma waves after the passage of the electron beam.     

Beam propagation and Langmuir wave generation in a plasma with κ distribution function

Using a kappa velocity distribution function for the electrons of the background plasma, the dynamics of a beam of hot electrons streaming through the plasma and the generation of Langmuir waves are investigated in the frame work of quasilinear theory. It is shown that the Langmuir waves are strongly damped by high energy tail of the Kappa distribution function. The spatial expansion of the beam is reduced and the spectral density of Langmuir waves becomes narrower. The height of the plateau in the beam distribution function increases at small velocities and the average velocity of beam is larger than that of a Maxwellian distribution. The influence of Kappa velocity distribution function on the gasdynamical parameters is investigated. It is found that, the height of plateau in the beam distribution function, and its lower velocity boundary are enhanced while, the local beam width in velocity space decreases.     

POLAR 5—an electron accelerator experiment within an aurora. 3. Evidence for significant spacecraft charging by an electron accelerator at ionospheric altitudes

The POLAR 5 rocket experiment carried an electron accelerator on a “daughter” payload which injected a 0,1 A beam of 10 keV electrons in a pulsed mode every 410ms. With spin and precession, injections were made over a wide range of pitch angles. Measurements from a double probe electric field instrument and from particle detectors on the “mother” payload and from a crude R.P.A. on the “daughter” payload are interpreted to indicate that the “daughter” charges to a potential between several hundred volts and 1 kV. The neutralizing return current to the “daughter” is shown to be assymetrically distributed with the majority being collected from the direction of the beam. The additional electrons necessary to neutralize the daughter are thought to be produced and heated through beam-plasma interactions postulated by Maehlum et al. (1980b) and Grandal et al. (1980) to explain the particle and optical measurements. Significant electric fields emanating from the charged “daughter” and the beam are seen at distances exceeding 100 m at the “mother” payload.     

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

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

Observation of Hamiltonian chaos in wave–particle interaction

The motion of charged particle in longitudinal waves is a paradigm for the transition to large scale chaos in Hamiltonian systems. Recently a test cold electron beam has been used to observe its non-self-consistent interaction with externally excited wave(s) in a specially designed Traveling Wave Tube (TWT). The velocity distribution function of the electron beam is recorded with a trochoidal energy analyzer at the output of the TWT. An arbitrary waveform generator is used to launch a prescribed spectrum of waves along the slow wave structure (a 4 m long helix) of the TWT. The resonant velocity domain associated to a single wave is observed, as well as the transition to large scale chaos when the resonant domains of two waves and their secondary resonances overlap. This transition exhibits a “devil’s staircase” behavior when increasing the excitation amplitude in agreement with numerical simulation. A new strategy for control of chaos by building barriers of transport which prevent electrons to escape from a given velocity region as well as its robustness are also successfully tested. Thus generic features of Hamiltonian chaos have been experimentally observed.     

Polar 5—an electron accelerator experiment within an aurora. 4. Measurements of the 391.4 nm light produced by an artificial electron beam in the upper atmosphere

The POLAR 5 sounding rocket, launched from Andøya, Norway, on February 1, 1976, was of the “mother-daughter” configuration.A rocket-borne electron accelerator, mounted on the “daughter,” produced a pulsed electron beam with a maximum current of 130 mA and electron energies up to 10 kev.Using a photometer the luminescence at 391.4nm produced by electrons colliding with ambient nitrogen molecules was studied. The observed light at 391.4 nm consisted of low background, with occasional flashes due to the natural auroral excitations, and intense sparkles when the electron beam was emitted.Below 130 km the light observed during beam injection can be explained by excitations of ambient N₂ due to high energy beam electrons.In the altitude range from 150 km to apogee at 220 km, the observed light level during beam emission is fairly constant and much larger than that produced by the high energy beam electrons. A possible source of this light is the excitation of ambient N₂ by an enhanced population of low energy electrons, created by the presence of a beam plasma discharge in the vicinity of the “daughter” payload.     

The existence of stationary ion-acoustic double layers in a plasma with an electron beam

The stationary ion-acoustic double layer is investigated in a plasma with an electron beam. The condition of the existence sensitively depends on the parameters such as the electron beam temperature, the ion temperature, the beam density and the effect of the trapped electrons. The properties of the double layer are also depicted. It turns out that the electron beam velocity is relatively small. This investigation predicts new findings of the ion-acoustic double layers in a plasma with an electron beam.     

The Energetic Spectrum of Non-Thermal Electrons in an Acceleration Region Calculated From a Solar Microwave Type III Burst with both Positive and Negative Frequency Drifts

A typical event of solar microwave type III burst with both positive and negative frequency drifts was observed by the 1–2 GHz spectrograph at Beijing Observatory on January 5, 1994. The separatrix frequency (1.3 GHz) may correspond to an acceleration region. The energy of the electron beam responsible for the burst is calculated from the drift rate and the height of the source above the photosphere. Moreover, if the solar microwave type III burst is explained by the beam-plasma instability as suggested by Huang (1998), the energy density as well as the particle density of the electron beam may be estimated from the burst flux, the growth rates and the modularity (Huang et al., 1996). So that, a very good power- law distribution is simulated for the energetic spectrum of the electron beam in this event with a spectrum index 4.5. The electron beam may be accelerated by an electric field with a length of 10⁷ m and a strength of <10-4 V m- 1. These results are necessary for understanding the acceleration process in solar flares. This revised version was published online in July 2006 with corrections to the Cover Date.     

On the production of hard X-rays in solar flares

The problem of producing the hard X-ray burst at the onset of solar flares may be thought of in terms of the problem of producing the non-thermal electrons which emit the X-rays via bremsstrahlung. Electron acceleration to relativistic energies without similar ion acceleration is difficult to achieve, even in an ad hoc theoretical model. Yet from global energetic considerations, it is not feasible to accelerate the electrons as a minor constituent of the total energetic particle population. Therefore, it is necessary to invoke a more sophisticated process for the electron acceleration. In this paper we describe a mechanism for achieving this via an initial acceleration of a neutralized ion beam. When such a beam impacts the chromosphere, the electrons start to scatter while the ions continue downwards, rapidly setting up an electric field which is either cancelled by the inflow of background chromospheric electrons or results in the runaway acceleration of beam electrons. In the former case the result is simply heating, whereas in the latter case much of the ion kinetic energy is transferred into electron kinetic energy. The final electron energy may be similar to the typical energy of the ions. The electrons that are accelerated are those in the neutral beam that experience an electric field greater than the critical Dreicer field. Thus there will be a low-energy cut-off to the electron spectrum which overcomes the well-known energetics problem at low energies with certain other spectral forms.     

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.