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Fast electron beams (FEBs) are one of the main products of various active events and are ubiquitous in solar, space and cosmic plasmas. They reveal themselves in hard X-ray and radio emissions. The observed characteristics of X-ray and radio emissions sensitively depend on the energy distribution of FEBs, which usually have a power-law energy spectrum. As FEBs travel in the solar atmosphere, their energy distribution can considerably vary due to the interaction with ambient plasmas. Tang et al. investigated the evolution of the energy spectrum of the FEBs traveling along a flare loop and discussed the possible effects on associated hard X-ray (HXR) and radio emissions. Considering the ubiquitous coronal loops in active regions, in the present paper, we investigate the parametric evolution of the energy spectra of FEBs when propagating along coronal loops. Here, we take the sunpot atmospheric model as an approximate coronal loop atmosphere model. The results show that the energy loss has an important impact on the cutoff behavior and energy spectra of FEBs when precipitating in a coronal loop with density ratio n b /n e = 0.01. The initially single power-law spectrum with a steepness cutoff can evolve into a more complex double power-law spectrum or two “knees” power-law spectrum with a flattened steepness cutoff behavior or saturation cutoff behavior. Our calculations also demonstrate that the energy spectrum evolution is not obvious if n b /n 0 = 0.001 as Tang et al. asserted. The present results are helpful for a more comprehensive understanding of the dynamic spectra of HXR and radio emissions from FEBs.

Besides the sun shines on the earth there is an invisible direct interaction between the sun and the earth, that is the impact of the solar wind on the earth. The conception of intermittent plasma streams consisting of electrons and ions from the sun was introduced by Chapman and Ferraro (1930) to explain the cause of geomagnetic storms, and later the existence of the solar wind continuously blowing away from the sun was proposed successively by Biermann (1948, 1951, 1957) and Alfven (1957) in their studies on comet tails to explain the deviation of the comet tail direction from the solar-comet radial direction (i.e., the solar radiation pressure direction) found by Hoffmeister in 1943.

The existence of AWs, as electromagnetic hydrodynamic waves, was predicted first by Alfven in (1942), however, the experimental study in laboratory had not been made until 1949. One of important reasons for this delay is that the long wavelength and low frequency characteristics of AWs make them very difficult to study experimentally in laboratory. The similar case happened on KAWs. When KAWs were discovered in 1970’s, their ability to heat plasma particles attracted attention of researches.

Plasma turbulence is a stochastic state of the plasma and its electromagnetic fluctuations in spatial and temporal structures. Unlike the randomness of thermal fluctuations (or i.e., thermal noise) that is caused by the discrete randomness of microscopic particles (or i.e., the hypothesis of molecular chaos), however, the turbulent stochasticity of the plasma turbulence should be attributed to the chaotic nondeterminacy of plasma collective modes when dynamically evolving into the chaos state via their nonlinear coupling (Ruelle and Takens 1971; Gollub and Swinney 1975). Plasmas, consisting of charged particles, are intrinsically different from neutral fluids, consisting of neutral atoms or molecules, and can have a number of various collective eigenmodes due to the interparticle electromagnetic interaction.

In the companion volume, Kinetic Alfven Wave: Theory, Experiment, and Application, we have presented the systematic theories and basic principles of kinetic Alfven waves (KAWs) based on both kinetic and fluid descriptions of magnetic plasmas. The present volume builds upon that and proceeds into the in-depth analyses and discussions of observation, generation, and application of KAWs in various plasma environments in the solar-terrestrial coupling system, which is a unique natural laboratory for the comprehensive and thorough study of KAWs. However, first of all, in this introductory chapter we concisely review main physical properties of KAWs without proving, which are from the companion volume and set up the basis for the following chapters.

Unlike the magnetosphere-ionosphere coupling is concentrated mainly in the polar magnetosphere, especially in the auroral plasma and is performed via field-aligned currents, the solar wind-magnetosphere coupling can occur in all outer boundaries of the magnetosphere from the magnetopause on the day side to the magnetotail on the night side. On the day side, in fact, before the supersonic magnetized plasma flow of the solar wind directly impacts on the magnetosphere, a shock can be first formed in front of the magnetosphere due to the blunt obstacle of the magnetosphere, called the bow shock, and the magnetopause is the interface between the shocked solar wind and the magnetosphere.

In previous chapters we comprehensively introduced KAWs in space and solar plasmas, including their observational identifications and applications to related particle kinetic phenomena, such as the auroral energetic electron acceleration in auroral magnetospheric plasmas, the anomalous particle transport in the magnetopause, the kinetic turbulence in the solar wind, and the solar coronal heating problem. The solar and solar-system plasma, especially the solar-terrestrial coupling system, is a natural laboratory for plasma astrophysics.

The Sun is our nearest star and the energy released by nuclear reactions near its center is transported by photons inside the inner \({\sim }71\%\) of the solar radius (\(R_\odot \simeq 6.9\times 10^5\) km), called the radiative zone. Outside this radiative zone, called the convective zone, photons are no longer able to transfer energy efficiently, so convective instabilities set in and vertical flows carry nearly all the excess heat to the solar surface. This visible surface, called the photosphere, is the lowest layer of the solar outer atmosphere, emits almost all the solar light, and lowers its temperature by the radiation.

Kinetic Alfven Wave (KAW) is one of the low-frequency electromagnetic fluctuations that are identified extensively in space plasmas by in situ observations of satellites and has been an interesting topic for discussion widely in the fields of laboratory, space, and astrophysical plasmas because of its potential importance in plasma particle energization. Some satellite observations show that the number density ratio of the oxygen ions to the ambient plasma is 30% similar to 50%, sometimes, even as high as 80%. In this paper, effects of heavy ion species on KAWs are studied in a low-beta plasma. The results show that heavy ions not only considerably reduce the propagation speed of KAWs, but also remarkably influence the parallel component of perturbed electric field of KAWs (to the ambient magnetic field). The ratio of parallel to perpendicular components of perturbed field decreases (or increases) with the heavy ion abundance for KAWs dominated by the electron inertial length (or by ion acoustic gyroradius). In particular, the resonant condition of KAWs with thermal electrons is modified by the heavy ion species.

Kinetic Alfven wave (KAW) has been an interesting topic for discussion extensively in the fields of laboratory, space, and astrophysical plasmas. A general dispersion equation is derived from the exact two-fluid model in this paper. Based on this dispersion equation, dispersion of Alfven waves near the Alfven frequency omega(A) = v(A)k(parallel to) are discussed for arbitrary values of wavelength, where v(A) is the Alfven velocity, and k(parallel to) = 2pi/lambda(parallel to) is the wavenumber parallel to the ambient magnetic field. For the short wavelength cases of klambda(i), >>1, where lambda(i) = v(A)/omega(ci) and omega(ci) are the ion inertial length and gyrofrequency,, respectively, our dispersion relations are appropriate for discussing effects of the ion temperature and inertia on KAWs. The present results show that both the ion temperature and inertia can affect considerably the behaviors of KAWs in propagation, resonance, and polarization, In particular, our results may be a great help to understanding some salient features of the low-frequency (in comparison with the ion gyrofrequency omega(ci)) electromagnetic fluctuations frequently observed by the FREJA and FAST satellites in the auroral zone of the Earth's ionosphere and magnetosphere.

One of the most puzzling problems in astrophysics is to understand the anomalous resistivity in collisionless magnetic reconnection that is believed extensively to be responsible for the energy release in various eruptive phenomena. The magnetic null point in the reconnecting current sheet, acting as a scattering center, can lead to chaotic motions of particles in the current sheet, which is one of the possible mechanisms for anomalous resistivity and is called chaos-induced resistivity. In many interesting cases, however, instead of the magnetic null point, there is a nonzero magnetic field perpendicular to the merging field lines, usually called the guide field, whose effect on chaos-induced resistivity has been an open problem. By use of the test particle simulation method and statistical analysis, we investigate chaos-induced resistivity in the presence of a constant guide field. The characteristics of particle motion in the reconnecting region, in particular, the chaotic behavior of particle orbits and evolving statistical features, are analyzed. The results show that as the guide field increases, the radius of the chaos region increases and the Lyapunov index decreases. However, the effective collision frequency, and hence the chaos-induced resistivity, reach their peak values when the guide field approaches half of the characteristic strength of the reconnection magnetic field. The presence of a guide field can significantly influence the chaos of the particle orbits and hence the chaos-induced resistivity in the reconnection sheet, which decides the collisionless reconnection rate. The present result is helpful for us to understand the microphysics of anomalous resistivity in collisionless reconnection with a guide field.

The physical nature of the auroral electron acceleration has been an outstanding problem in space physics for decades. Some recent observations from the auroral orbit satellites, FREJA and FAST, showed that large amplitude solitary kinetic Alfven waves (SKAWs) are a common electromagnetic active phenomenon in the auroral magnetosphere. In a low-beta (i.e., beta /2 << m(e)/m(i) << 1) plasma, the drift velocity of electrons relative to ions within SKAWs is much larger than thermal velocities of both electrons and ions. This leads to instabilities and causes dissipations of SKAWs. in the present work, based on the analogy of classical particle motion in a potential well, it is shown that a shock-like structure can be formed from SKAWs if dissipation effects are included. The reformed SKAWs with a shock-like structure have a local density jump and a net field-aligned electric potential drop of order of m(e)v(A)(2)/e over a characteristic width of several lambda (e). As a consequence, the reformed SKAWs can efficiently accelerate electrons field-aligned to the order of the local Alfven velocity. In particular, we argue that this electron acceleration mechanism by reformed SKAWs can play an important role in the auroral electron acceleration problem. The result shows that not only the location of acceleration regions predicted by this model is well consistent with the observed auroral electron acceleration region of 1-2 R-E above the auroral ionosphere, but also the accelerated electrons from this region can obtain an energy of several keV and carry a field-aligned current of several muA/m(2) which are comparable to the observations of auroral electrons.

The properties of the solitary kinetic Alfven waves (SKAWs) observed by Freja satellite are studied statistically for a typical event on March 7, 1994. The eigenmode of the SKAWs observed is still recognized by their anisotropic structure (1000 km x 1 km), their waveform which is similar to that of a wave packet and their frequency close to the local oxygen ion cyclotron frequency. If these, spatial structures really exist, they may have resulted from the evolution of the SKAWs or some envelope solitons of ion cyclotron and magnetosonic waves, which is supported by four statistical results: (1) The phase velocity is directly proportional to the Alfven velocity. (2) The amplitudes of the electric filed, magnetic field and density fluctuations are directly proportional to the timescales of the pulsations. (3) The amplitudes as well as the timescales are directly proportional to the phase velocity. (4) The polarization sense is both of right circular and left circular mode with different phase relation among the electric field, magnetic field, and density fluctuations. Moreover, the SKAWs are often superposed by a strong electrostatic fluctuations at several hundred hertz, the causal relation between the SKAWs and superposed waves is still unknown.

A new type of density soliton, which we call “dipole density soliton,’’ is discovered in data from the Freja satellite. Like the dip or hump density solitons that were recently discovered in the Freja data [D.-J. Wu, G.-L. Huang, and D.-Y. Wang, Phys. Plasmas 3, 2879 (1996)], the dipole density solitons are also associated with strong electric spikes (∼ a few 100 mV/m) and have a spatial scale length of a few 100 m. This indicates that the three types of density solitons (dip, hump, and dipole) probably have the same physical nature. In this paper, a two-dimensional solitary kinetic Alfven wave (SKAW) model with a dipole vortex structure is proposed to account for the three kinds of density solitons (dip, hump, and dipole), in which the differences in their appearances can naturally be attributed to differences in the positions and directions at which the satellite crosses dipole vortex structures. Some features of this two-dimensional SKAW model are discussed, and the results are compared to the one-dimensional cases.

An exact nonlinear equation governing the coupling Alfvenic aad ion-acoustic solitons and criterion for their existence are presented. For the case of low-beta plasmas. the two modes decouple. In the small amplitude limit, the analytical results lead to KdV solitons.

An analytical solution of finite‐amplitude solitary kinetic Alfven waves (SKAWs) in a low‐β (β≪me/mi≪1) plasma is presented. This solution has been compared with the solution of the Korteweg–de Vries (KdV) equation in the small‐amplitude limit. It is found that the KdV soliton solution is valid only for the maximum relative density perturbation Nm

Self‐excited dust density waves (DDWs) are studied in a striped electrode device. In addition to the usual perpendicularly (with respect to the electrode) propagating DDWs, which have been frequently observed in dusty plasma experiments on the ground, a low‐frequency oblique mode is also observed. This low‐frequency oblique DDW has a frequency much lower than the dust plasma frequency and its spontaneous excitation is observed even with a very low dust density. It is found that the low‐frequency oblique mode can exist either separately or together with the usual perpendicular mode. In the latter case, a new mode arises as a result of the interactions between the perpendicular and the oblique modes. The experiments show that these three modes satisfy the wave coupling conditions in both the frequencies and the wave‐vectors.

Starting with an exact nonlinear equation governing solitary kinetic Alfven waves (SKAWs), a new type of SKAW on the ion‐acoustic velocity branch is obtained in a low‐β plasma. It propagates in a direction oblique to the ambient magnetic field, has a dispersion originating from the finite perpendicular wavelength, and is accompanied by a density hump soliton similar to that of the SKAWs on the Alfven velocity branch in the case of 1≫β≫me/mi. It has a perturbed electric field with the same order as that of the latter SKAWs, but its perturbed magnetic field is weaker by a factor of (β/2)1/2, and in the small amplitude limit, the analytical result also leads to the Korteweg–de Vries soliton.

The new data set of 1901 bow shock crossings by Geotail and Wind satellites in period 1999-2000 is selected for a wide range of distances and solar wind conditions observed by Wind and ACE upstream monitors. The data set is applied for verification of the semi-empirical bow shock model developed in the last solar minimum (1995-1997), using Geotail crossings of the bow shock and Wind upstream solar wind data. In general, the model accuracy is reasonably good in the dayside and flank regions of the bow shock. But, the model extrapolation in the tail region has much less accuracy due to restriction of the bow' shock crossing distances used in the model development. Some difference between the data of ACE and Wind upstream solar wind monitors leads also to the model discrepancies. Analysis of long time variations of the bow shock parameters during last three solar cycles shows noticeable difference in the heliospheric conditions controlling the bow shock size and shape in the solar minimum and maximum. In the solar maximum, the variations of the interplanetary conditions are much higher than in the solar minimum. This difference produces additional disagreement in prediction of the bow shock crossings in the current solar maximum by the model developed using a data set obtained in the solar minimum.

In their comment, Shukla and Stenflo proposed a completeset of equations @i.e., Eqs. ~1!–~4! in Ref. 1# to describe thesolitary kinetic Alfve´n wave ~SKAW! data from the Frejasatellite, in which the equilibrium electron and ion velocitygradients, the parallel ion dynamics and the electron–ion andion–ion collision effects are included. It is easy to find thatthe equation system proposed by Shukla and Stenflo is es-sentially no different from that presented in our paper ~i.e.,Ref. 2! if neglecting above the effects in Shukla andStenflo’s equation system.With regard to the points criticized by Shukla and Sten-flo, we would like to explain in turn as follows: First, ne-glecting magnetic field perturbations and electron inertialcontribution ~the