The effect of retardation on the stability of current filaments

We investigate the influence of the finite Alfvén velocity on the evolution of an active region filament. In general, variations of a current result in variations of the magnetic fields which spread around with the Alfvén velocity. As a consequence of the fact that a magnetic field can only change with the Alfvén velocity, a filament will experience the photospheric boundary conditions as these were at an Alfvén travel time back in time. The inclusion of this retardation effect in the momentum equation of a filament leads effectively to an extra force term. This force contribution acts in the direction in which the filament moves and has therefore a destabilizing effect on the filament. Because a moving filament acts as an antenna of Alfvén waves, the filament loses energy by the emission process. This leads to a radiative damping term in the equation of motion of the filament. In general, the radiative damping will be sufficiently strong to counteract the retardation instability. Numerical simulations show that during the energy build-up phase a filament follows the van Tend-Kuperus equilibrium curve. After the van Tend-Kuperus equilibrium has disappeared the filament goes through a transient phase moving with a sub-Alfvénic velocity upward. At greater heights the repulsive Lorentz force of the photospheric surface current magnetic field is balanced by the radiative damping, resulting in a decreasing filament velocity.Parts of this paper were presented at the 4th CESRA Workshop in Ouranopolis (Greece) in 1991.     

Nonlinear Alfvén wave modulation in the solar atmosphere

Nonlinear interaction of finite-amplitude Alfvén waves with non-resonant finite-frequency electrostatic and stationary electromagnetic perturbations is considered. This interaction is governed by a pair of coupled equations consisting of nonlinear Schrödinger equation for the Alfvén wave envelope and an equation for the plasma slow response that is driven by the ponderomotive force of the Alfvén wave packets. The modulational instability of a constant amplitude Alfvén pump is investigated and some new results for the growth rate of the instability are presented. It is found that a possible stationary state of the modulated Alfvén wave packets could lead to localized structures. The relevance of our investigation to the solar atmosphere is discussed.     

Parallel electric fields accelerating ions and electrons in the same direction

In this contribution we present Viking observations of electrons and positive ions which move upward along the magnetic field lines with energies of the same order of magnitude. We propose that both ions and electrons are accelerated by an electric field which has low-frequency temporal variations such that the ions experience an average electrostatic potential drop along the magnetic field lines whereas the upward streaming electrons are accelerated in periods of downward pointing electric field which is quasi-static for the electrons and forces them to beam out of the field region before the field changes direction.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Electron-acoustic instability driven by a crossfield hot electron-beam

On the basis of kinetic theory, the electron-acoustic instability is studied in a three component plasma consisting of a hot electron-beam and stationary cool electrons and ions. The transformation of the instability into the modified two-stream instability for wave propagation oblique to the confining magnetic field is also investigated. In our model both the electrons and ions are magnetized, with the beam drifting across the external magnetic field. The dependence of the growth rate on plasma parameters, such as electron-beam density, electron-beam speed, magnetic field strength and propagation angle, is examined. In addition, we investigate the effect of anisotropies in the velocity distributions of the hot electron-beam and the cool electrons on the instability growth rate.     

Obliquely Propagating Shear Alfvén Waves Excited by Newborn Ions in the Chromosphere – Corona Transition Region

A source mechanism for the generation of shear Alfvén waves in the low solar corona is suggested. It is attributed to newly created ions associated with the ionization of neutral atoms in the chromosphere – corona transition region. In the present discussion attention is mainly paid to the excitation of shear Alfvén waves rather than compressional Alfvén waves, i.e., fast and slow magnetosonic waves. A kinetic instability, which amplifies Alfvén waves propagating in an arbitrary direction, due to the newborn ions, is studied. In the present analysis heavy ion species are emphasized.     

Turbulence Heating for Protons in High-Speed Solar Wind

In high-speed solar wind, propagating Alfvén waves can be transferred into fast magnetosonic waves. When both the magnetic field strength and Alfvén wave velocity approach zero, fast magnetosonic waves will be transferred into ion-acoustic waves. As the phase velocity of ion-acoustic waves is slightly greater than the thermal velocity of protons, the turbulence energy of ion-acoustic waves can largely be absorbed by protons and can cause the mean temperature of protons to be greater than that of electrons by stochastic turbulence heating of ion-acoustic waves for protons.     

Low-frequency plasma turbulence during solar wind-comet interaction

The pick up cometary ion distributions are shown to excite Alfvénic mode instabilities, slow ion-acoustic mode instability and a lower hybrid instability during solar wind-comet interaction. The growth rates of all these instabilities become larger as the comet is approached. The lower hybrid instability is shown to account for the low-frequency 0–300 Hz electrostatic turbulence observed near comet Halley. The Alfvén modes can grow to large amplitudes and become modulationally unstable, in the presence of low-frequency density fluctuations, going over to envelope Alfvén solitons. A model consisting of a gas of Alfvén solitons is suggested to explain the hydromagnetic turbulence observed near comet Halley and comet Giacobini-Zinner.     

Criteria for shear flow instability in the magnetopause boundary layer region

Shear flow instability is studied in the planar magnetopause boundary layer region by treating the plasma as compressible. A necessary criterion for instability near the Alfvén resonance is obtained. Sufficient criterion for instability is derived from the solution of a six degree polynomial for the cases of constant and antisymmetric velocity profiles when there is no Alfvén resonance. Both the criteria are obtained analytically for the first time. The necessary criterion generalises the well-known inflexion point theorem and Rayleigh's criterion in the hydrodynamic case to magnetohydrodynamic case for incompressible plasma provided both the Alfvén surfaces lie in the boundary layer. The Alfvén resonant surfaces are similar to the boundary walls in hydrodynamics. A semi-hyperbola theorem for the unstable situation is derived which represents the domain of Doppler shifted real frequency and imaginary frequency. From the sufficient criterion for instability it is observed that plasma shear should be more for a compressible plasma in order to make the plasma unstable. The growth rate for instability is obtained. A thin layer around Alfvén resonance effectively determines how fast the flow could attain instability.     

Two-stream instability in plasmas with arbitrary orientation of magnetic field

The problem of two-stream instability in plasmas where electrons move through ions with arbitrary orientation of the magnetic field is discussed. Electrostatic and electromagnetic instabilities have both been discussed. It is found that the strength and orientation of the magnetic field both affect the electrostatic waves propagating along the streaming direction to a considerable extent. The electromagnetic instability with a cross-field orientation is associated with a larger range of unstable wavenumber and larger growth rates compared to any other coexisting electrostatic instability.     

Excitation of high-frequency Alfvén waves by plasma outflows from coronal reconnection events

We study a kinetic excitation mechanism for high-frequency dispersive Alfvén waves in the solar corona by magnetic reconnection events. The ion-cyclotron and Cerenkov kinetic effects are important for these waves which we call the ion-cyclotron kinetic Alfvén waves (IC KAWs). The plasma outflowing from the reconnection site sets up a neutralized proton beam in the surrounding plasma, providing free energy for the excitation of waves. The dependence of the phase velocity of the IC KAW on the parallel wavenumber is different from that on the perpendicular wavenumber. The phase velocity is an increasing function of the perpendicular wavenumber and overtakes the Alfvén velocity for sufficiently large values of k . However, the phase velocity is a decreasing function of k , and sufficiently large values of k result in a phase velocity below the Alfvén velocity. As a result, the IC KAWs can undergo the Cerenkov resonance with both super- and sub-Alfvénic particles, and for the waves to be excited the outflow velocity does not need to be super-Alfvénic, as for KAWs, but the beam/Alfvén velocity ratio can span a wide range of values. High growth rates of the order of 10⁴ s^–1 are found for the values of the plasma parameters typical for the low solar corona. The waves excited by (sub-)Alfvénic beams are damped mainly due to kinetic wave-particle interactions with ions at the cyclotron resonance (ion-cyclotron damping), and with ions and electrons at the Cerenkov resonance (Landau damping). Therefore, IC KAWs can heat the plasma species of the corona in both the parallel and perpendicular direction, giving rise to an anisotropic heating of the ions. The observational consequences of the processes under study are discussed.     

Generation of ULF waves in the polar cusp region by velocity shear-driven kinetic Alfvén modes

The velocity shear of ion beams observed in the polar cusp region can drive the kinetic Alfvén modes unstable. A hot ion beam can excite both a resonant kinetic Alfvén wave instability and a nonresonant coupled Alfvén ion-acoustic wave instability. For the case of a cold ion beam only the latter instability is excited. For the altitude range of 5–7R _e , velocity shearS0.04–1.0 is needed to excite the kinetic Alfvén wave instabilities. HereS=(dV _B / _cB dx), whereV _b is the streaming velocity,and _cB is the gyrofrequency of the bean ions. The excited modes have frequencies, in the satellite frame of reference, in the ULF frequency range. The noise generated by the velocity shear-driven Alfvén modes is electromagnetic in nature. These modes have a substantial component of parallel electric fields and, therefore, they can play an important role in the ionosphere-magnetosphere coupling process occurring in the polar cusp region.     

Alfvén wave plasma turbulence during solar wind-comet interaction

The large differences in drift velocities between the solar wind protons and the picked-up ions of cometary origin cause the Alfvén waves (among others) to become unstable and generate turbulence. A self-consistent treatment of such instabilities has to take into account that these cometary ions affect the solar wind plasma in a decisive way. With the help of a previously developed formalism one finds the correct Alfvén instability criterion, which is here nondispersive, in contrast to recent calculations where the cometary ions are treated as a low-density, high-speed, and non-neutral beam through an otherwise undisturbed solar wind. The true bulk speed of the combined solar wind plus cometary ion plasma clearly shows the mass-loading and deceleration of the solar wind near the cometary nucleus, indicating a bow shock. The instability criterion is also used to determine the region upstream where the Alfvén waves can be unstable, based upon recent observations near comet Halley.     

Band structure of the solar system: An objective test of the grouping of planets and satellites

Alfvén in his early work on the origin of the solar system (1942–1946) noted a pronounced band structure in the gravitational potential distribution of secondary bodies, and suggested this feature to be directly related to the formation process. When the critical velocity phenomenon was later discovered, a close agreement was found between the planet-satellite bands on one hand, and the critical velocity limits of the major compound elements in the interstellar medium on the other, suggesting a specific emplacement mechanism for the dusty plasma which presumably constituted the solar nebula.Since the originally perceived band structure was outlined in a qualitative fashion, an attempt is made here to analyze the distribution by a statistical technique, testing the significance of clustering of the observational data in the bands. The results show that, with proper scaling of the parameters, such a band structure indeed appears, with features closely similar to those originally conceived. Some deviations are indicated by the cluster analysis, however; their significance is discussed in terms of process involved in the formation of the solar system.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Spatial structure and stability of coupled Alfvén and drift compressional modes in non-uniform magnetosphere: Gyrokinetic treatment

The spatial structure and stability properties of the coupled Alfvén and drift compressional modes in a space plasma are studied in a gyrokinetic framework in a model taking into account field-line curvature and plasma and magnetic field inhomogeneity across the magnetic shells. The perturbation is found to be localized in two transparent regions, the Alfvén and drift compressional transparent regions, where the wave vector radial component squared is positive. Both regions are bounded by the resonance and cut-off surfaces, where the wave vector radial component turns into infinity and zero, respectively. An existence of the drift compressional resonance is one of the most important results of this work. It is argued that on the surface of this resonance the longitudinal and azimuthal components of the wave's magnetic field have a pole and logarithmic singularities, respectively. The instability conditions and expressions for the growth rate of the coupled modes have been obtained. In the Alfvénic transparent region, an instability occurs in the presence of the negative plasma temperature gradient. This instability does not lead to a non-stationary wave behavior: all the energy gained from the resonance particles was finally absorbed owing to any dissipation process. In a drift compressional transparent region, a necessary condition for the instability is the growth of the temperature with the radial coordinate. The growth rate is almost independent of the radial coordinate, which means that the wave energy gained from the particles cannot disappear. It will lead to an ever increasing wave amplitude, and no stationary picture for the unstable drift compressional mode is possible.     

Electrostatic wave noise in the neutral sheet in the earth's geomagnetic tail

Numerical solutions are obtained from analytic dispersion relations for electrostatic waves in a self-consistent, one-dimensional magnetic neutral sheet. The dispersion relations are solved in the real wave number and complex frequency domain. The properties of wave modes will be described, with special emphasis on instability. Several regimes of instability are identified which may generally be divided into two classes. Wave growth is associated firstly with counterstreaming between ions and electrons, giving rise to low frequency waves similar to the usual electrostatic two-stream mode. In addition, high frequency growing waves occur, associated with harmonics of the electron oscillation frequency across the neutral plane.     

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.     

Space charge sheath in plasma-neutral gas interaction

A space charge sheath is found to be formed whenever a high-velocity magnetized plasma stream penetrates a gas cloud. The sheath is always located at the head of the plasma stream, and its thickness is very small compared to the length of the plasma stream. Soon after the sheath is formed it quickly slows down to the Alfvén critical velocity. The plasma behind the sheath continues to move at higher velocity until the whole plasma stream is retarded to the critical velocity. In the interaction at gas density 10¹⁹ m^–3 the sheaths are observed to be accompanied by a single loop of current with current density of 10⁵ Å m^–2. Maximum potential in the sheath ranges between 50 and 200 V.Presently available models for the sheath may explain the initiation of the sheath formation. Physical processes like heating of the electrons and ionization of the gas cloud which come into play at a later stage of the interaction are not included in these models. These processes considerably alter the potential structure in the sheath region. A schematic model of the observed sheath is presented here.Experiments reveal a threshold value of the magnetic field for plasma retardation to occur. This seems to correspond to the threshold condition for excitation of the modified two-stream instability which can lead to the electron heating. The observed current are found sufficient to account for the plasma retardation at a gas density of 10¹⁷ m^–3.     

On Alfvén's critical velocity for the interaction of a neutral gas with a moving magnetized plasma

A theory for the interaction of a neutral gas with a moving magnetized plasma is given. The Alfvén expression for the critical velocity is identified with that for the terminal velocity while another expression for the threshold velocity for interaction is given. The implications of these results to the Alfvén-Arrhenius model for the solar system are discussed.Paper dedicated to Professor Hannes Alfvén on the occasion of his 70th birthday, 30 May, 1978.     

Kinetic Alfvén waves in extended radio sources

Electric current generation by kinetic Alfvén waves (KAW) is discussed for the case of extended radio sources (ERS), in particular, extragalactic jets (EJ). These currents are generated parallel to the background magnetic field due to Landau damping by which KAW accelerate electrons. We find that the KAW generated currents are in excess of the currents necessary for an EJ to be magnetically self-confined. We address the problem of determining the process that can maintain ERS inhomogeneous. We study the stability of a plasma which has: (1) the average local current density due to KAW given by our calculations; (2) the average local electrical conductivity (anomalous) due to KAW indicated by our calculations and the calculations of Hasegawa and Mima (1978); and (3) wave heating by surface Alfvén waves, independent of plasma temperature. We show that this plasma is subject to the thermal Joule instability. We suggest the thermal Joule instability as the process that maintains ERS inhomogeneous. Our KAW analysis correlates the important problems of ERS of (re)acceleration, current generation, collimation, and maintenance of inhomogeneities.     

Electrostatic ion cyclotron waves in an anisotropic plasma

In the solar wind, electrostatic ion cyclotron waves can be excited, by electrons or ions when the flow velocity becomes supersonic. The instability of these waves is investigated for a situation in which ions are streaming in opposite directions along the interplanetary magnetic field in a uniform background of relatively stationary electrons. Many modes become unstable under the existing conditions. It is conjectured that the excitation of this instability may lead to a steady state electrostatic turbulence in the solar wind.