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.     

Alfvén waves in a space plasma and its role in the solar wind interaction with comets

The importance of Alfvén wave generation in interacting plasmas is discussed in general and illustrated by the example of solar wind interaction with cometary plasma. The quasi-linear theory of Alfvén wave generation by cometary ions at distances far from the cometary nucleus is reviewed. The incorporation of a diabatic plasma compression effects into this theory modifies the spectrum of Alfvén waves and the integral intensity of magnetic field fluctuations previously published. These results are in quantitative agreement with thein situ observations near the comets Giacobini-Zinner and Halley. However, the polarization of quasi-linearly excited waves needs further detailed comparison with observations.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

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.     

Modeling a cometary nucleus

Considerations are summarized concerning the physical properties of and plasma phenomena around a cometary nucleus aiming at a new model of the nucleus and its interaction with the solar wind.Paper dedicated to Professor Hannes Alfvén on the occasion of his 80th birthday, 30 May 1988.     

Frequency-energy distributions of flares and active region transient brightenings

In 1988, Uchida and Shibata proposed a model for compact loop flares as due to the collision of two large amplitude torsional Alfvén wave packets coming up along a coronal magnetic loop, leaking out from the subphotospheric convective layers of the solar atmosphere. We investigate the possibility that active region transient brightenings occur when a single torsional Alfvén wave packet transits a coronal loop. Assuming this related origin for flares and transient brightenings, the statistics of the two phenomena must also be closely related. It is shown that the observed power-law frequency-energy distributions of flares and transient brightenings may be accounted for in a natural way if the energy distribution of the underlying torsional Alfvén wave packets is itself a power law.     

Loop models of solar flares: Revisions and comparisons

Due to developments in solar flare observations which appear to show that a particular class of solar flares result from instabilities occurring in magnetic loops we re-examine the Alfvén-Carlqvist flare model to show that it is workable and we update the Spicer loop model of a flare. It is noted that the Alfvén-Carlqvist model of necessity requires an external current driver which must maintain the current driven instability at marginal stability during the duration of the flare. In addition, it is argued that if the Alfvén-Carlqvist model is to work the current density must rise in a time shorter than an MHD or resistive tearing mode time scale. Otherwise, the dominant flare mechanism must be an ideal MHD or tearing type instability. Further, the distinctions between the two models are highlighted and a new hybrid model of the Alfvén-Carlqvist and Spicer models is introduced.     

Physical conditions in the plasma tail of comet C/1987 P1 bradfield

Photometric measurements of photographic images of comet C/1987 P1 Bradfield have been carried out with a flat-bed scanner equipped with a slide module. Lengthwise and transverse photometric profiles of the cometary plasma tail have been obtained. Magnetic field induction and some other physical characteristics of the cometary plasma tail observed in November 1987 have been estimated with the use of the diffusion model for a cometary tail by Shul’man and Nazarchuk (1968). It has been shown that the scanned images of comets can be used for estimating the physical characteristics of cometary tails.     

Resonant Absorption of Alfvén Waves in Steady Coronal Loops

The effect of equilibrium flow on linear Alfvén resonances in coronal loops is studied in the compressible viscous MHD model. By means of a finite element code, the full set of linearised driven MHD equations are solved for a one-dimensional equilibrium model in which the equilibrium quantities depend only on the radial coordinate. Computations of resonant absorption of Alfvén waves for two classes of coronal loop models show that the efficiency of the process of resonant absorption strongly depends on both the equilibrium parameters and the characteristics of the resonant wave. We find that a steady equilibrium shear flow can also significantly influence the resonant absorption of Alfvén waves in coronal magnetic flux tubes. The presence of an equilibrium flow may therefore be important for resonant Alfvén waves and coronal heating. A parametric analysis also shows that the resonant absorption can be strongly enhanced by the equilibrium flow, even up to total dissipation of the incoming wave.     

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.     

Coronal loop heating by Alfvén waves

The excitation and dissipation of global and surface Alfvén waves and their conversion into kinetic Alfvén waves have been analyzed for solar coronal loops using a cylindrical model of a magnetized plasma. Also the optimal conditions for coronal loop heating regimes with density of dissipated power 10³ erg cm^–3 s^–1 by the new scheme named combined Alfvén wave resonance are found. Combined Alfvén wave heating regime appears when the global Alfvén wave is immersed into the Alfvén continuum with the condition of not-so-sharp distribution of axial current.Instituto de Matemática, Universidade Federal Fluminense, Niterói, RJ, Brazil     

Alfvén-magnetosonic waves interaction in the solar corona

The nonlinear propagation of the Alfvén and magnetosonic waves in the solar corona is investigated in terms of model equations. Due to viscous effects taken into account the propagation of the fast wave itself is governed by Burgers type equations possessing both expansion and compression shock solutions. Numerical simulations show that both parallely and perpendicularly propagating fast waves can steepen into shocks if their amplitudes are in excess of some sizeable fraction of the Alfvén velocity. However, if the magnetic field changes linearly in the perpendicular direction, then formation of perpendicular shocks can be hindered. The Alfvén waves exhibit a tendency to drive both the slow and fast magnetosonic waves whose propagation is described by linearized Boussinesq type equations with ponderomotive terms due to the Alfvén wave. The limits of the slow and fast waves are investigated.     

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.     

Coronal loop heating by discrete Alfvén waves

We have modeled the solar coronal active loop heating by discrete Alfvén waves. Discrete Alfvén waves (DAW) are a new class of Alfvén waves which can be described by the two-fluid model with finite ion-cyclotron frequency, or the MHD model with plasma current along the magnetic field line as shown by Appert, Vaclavik, and Villar (1984). We have modeled the coronal loop as a semi-toroidal plasma with the major toroidal radius much larger than the plasma radius. We have shown that the absorption of discrete Alfvén waves by the plasma through viscosity can account for at least 30% of the coronal heating rate density of 10^–4 J m^–3 s^–1.     

A new numerical method for simulating the solar wind Alfvén waves: Development of the Vlasov-MHD model

A novel scheme of plasma simulation particularly suited for computing the one-dimensional nonlinear evolution of parallel propagating solar wind Alfvén waves is presented. The scheme is based on the Vlasov and the MHD models, for solving the longitudinal and the transverse components, respectively. As long as the nonlinearity is not very large (so that the longitudinal and transverse components are well separated), our Vlasov-MHD model can correctly describe evolution of finite amplitude parallel Alfvén waves, which are typical in the solar wind, both in the linear and nonlinear stages. The present model can be applied to discussions of phenomena where the parallel Alfvén waves play major roles, for example, the solar coronal heating and solar wind acceleration by the Alfvén waves propagating from the photosphere.     

Kelvin-Helmholtz instability in an Alfvén resonant layer of a solar coronal loop

A Kelvin-Helmholtz instability has been identified numerically on an azimuthally symmetric Alfvén resonant layer in an axially bounded, straight cylindrical coronal loop. The physical model employed is an incompressible, reduced magnetohydrodynamic (MHD) model including resistivity, viscosity, and density variation. The set of equations is solved numerically as an initial value problem. The linear growth rate of this instability is shown to be approximately proportional to the Alfvén driving amplitude and inversely proportional to the width of the Alfvén resonant layer. It is also shown that the linear growth rate increases linearly with m - 1 up to a certain m, reaches its maximum value for the mode whose half wavelength is comparable to the Alfvén resonant layer width, and decreases at higher m's. (m is the azimuthal mode number.)     

Helical waves in type-1 comet tails

Oscillations of type-1 comet tails with plasma compressibility taken into account are studied. A comet tail is treated as a plasma cylinder separated by a tangential discontinuity surface from the solar wind. The dispersion equation obtained in the linear approximation is solved numerically with typical plasma parameters. A sufficient condition for instability of the cylindrical tangential discontinuity in the compressible fluid is obtained. The phase velocity of helical waves is shown to be approximately coincident with Alfvén speed in the tail in the reference system moving with the bulk velocity of the plasma outflow in the tail. The instability growth rate is calculated.This theory is shown to be in good agreement with observations in the tails of Comets Kohoutek, Morehouse and Arend-Roland. Hence we conclude that helical waves observed in type-1 comet tails are produced due to the Kelvin-Helmholtz instability, and the model under consideration is justified. If so, one may estimate comet tail magnetic field from the pressure balance at the tangential discontinuity; it turns out to be of the order of the interplanetary magnetic field.     

Alfvén waves in the solar atmosphere

The nonlinear propagation of Alfvén waves on open solar magnetic flux tubes is considered. The flux tubes are taken to be vertical and axisymmetric, and they are initially untwisted. The Alfvén waves are time-dependent axisymmetric twists. Their propagation into the chromosphere and corona is investigated by solving numerically a set of nonlinear time-dependent equations, which couple the Alfvén waves into motions parallel to the initial magnetic field (motion in the third coordinate direction is artificially suppressed). The principal conclusions are: (1) Alfvén waves can steepen into fast shocks in the chromosphere. These shocks can pass through the transition region into the corona, and heat the corona. (2) As the fast shocks pass through the transition region, they produce large-velocity pulses in the direction transverse to B _o. The pulses typically have amplitudes of 60 km s^–1 or so and durations of a few tens of seconds. Such features may have been observed, suggesting that the corona is in fact heated by fast shocks. (3) Alfvén waves exhibit a strong tendency to drive upward flows, with many of the properties of spicules. Spicules, and the observed corrugated nature of the transition region, may therefore be by-products of magnetic heating of the corona. (4) It is qualitatively suggested that Alfvén waves may heat the upper chromosphere indirectly by exerting time-dependent forces on the plasma, rather than by directly depositing heat into the plasma.     

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.     

Alfvén wave heating and acceleration of plasmas in the solar transition region producing jet-like eruptive activity

We present an analysis of observations and theory of selected transition-region phenomena, concentrating on small scale jet-like structures known as spicules and macrospicules. We examine a number of mechanisms that may be responsible for their formation and conclude that Alfvén waves could provide the necessary acceleration through the ponderomotive force and dissipation for heating forming a beam or jet like structure. In applying the Alfvén wave model we make no fundamental distinction between spicules and macrospicules. In this respect we consider them to be manifestations of the same phenomenon on different scales. We predict that the most effective Alfvén waves have frequencies around 1 Hz and amplitudes of 1 V m^–1. The resulting plasma jet sets up plasma conditions suitable for creating rotating structures which are also observed.     

Nonlinear dissipation of Alfvén waves

Alfvén waves are generated easily in many cosmic plasmas, but they possess no linear damping mechanism since they are not compressive. The most prominent nonlinear damping occurs when one Alfvén wave decays into another plus a slow magnetosonic wave, or two Alfvén waves combine into one fast magnetosonic wave; the resulting magnetosonic waves can then be dissipated. The nonlinear coupling rates are presented, with special emphasis on the astrophysically important case of sound speed Alfvén speed. Streaming cosmic rays generate Alfvén waves moving in the direction of streaming, but they reabsorb the backward moving waves then produced by wave decay. The possible steady states for this system of cosmic rays and Alfvén waves turn out to be highly restricted.Supported by NSF grant GP-15218.