This volume contains focus reviews, oral contributions and poster papers presented at the NATO Advanced Research Workshop ``Turbulence, Waves, and Instabilities in the Solar Plasma'', held at Hotel Normafa, Budapest, 16--20 September, 2002. The more exensive invited reviews presented at the same meeting are published by Kluwer in a companion volume, with the same title as that of the meeting.
The purpose of the workshop was to facilitate interchange and communication between diverse groups studying different layers and regions of the Sun but from the same aspect, concentrating on the study of small-scale motions. While the emphasis was on the common theoretical roots of these phenomena, observational aspects were not excluded either.
The selection of invited speakers concentrated on the researchers currently most active in the field, mostly on a post-doctoral/tenure/fresh faculty position level. A number of senior experts and PhD students were also invited. Scientists from NATO partner countries were especially encouraged to apply.
Altogether, 50 scientists from 11 different countries participated in the workshop. The relative isolation of the venue, as well as the fact that the participants all lived at the same place, where the conference was also held, contributed to the success of the meeting, offering plenty of opportunities to meet and exchange ideas.
We are convinced that many of the papers in the present volume will prove to be a very useful reference for some rarely discussed chapters of solar physics.

The Editors

K. B. MacGregor: Gravity Waves in the Radiative Zone and Tachocline

We review the properties of internal gravity waves under physical conditions like those of the solar radiative interior, and consider a few of the ways in which such disturbances might influence the dynamical structure of the tachocline region.

Keywords:

D. Nandy and A. R. Choudhuri: Insights on Turbulent Flows

Turbulent flows in the interior of the Sun, both at small and large scales, are believed to feed and sustain the solar hydromagnetic dynamo that generates the solar cycle. The solar cycle itself strikingly manifests in a 11-year periodic variation in the number of sunspots seen on the solar surface. Sunspots are regions of concentrated magnetic fields, occurring at low latitudes on the solar surface and are believed to be tracers of the underlying dynamo mechanism. An important ingredient in recent models of the dynamo mechanism is the meridional flow of material, which is believed to originate from turbulent stresses in the solar convection zone. This meridional circulation is observed to be poleward in the outer 15\% of the Sun and must be balanced by an equatorward counterflow in the interior. The nature and exact location of this counterflow, however, is unknown. We discuss here results from a dynamo model that reproduces the correct latitudinal distribution of sunspots and show that this requires a meridional counterflow of material that penetrates much deeper than hitherto believed -- into the radiative layers below the convection zone. We comment on the viability of such a deep counterflow of material and discuss its implications for turbulent convection and elemental abundance in the Sun and related stellar atmospheres.

Keywords: Sun, MHD, dynamo, turbulence, meridional circulation

Y. Zhugzhda: Waves and instabilities of periodical shear flows

The exact analytical solution of the extended Rayleigh (ER) equation for the case of the periodical compressible shear flow is found. The dispersion relation of the problem is the infinite Hill determinant. It is found that sound waves in a shear flow have a dispersion and its velocity field contains a solenoidal part. Besides sound waves, new wave modes such as phonon, waveguide and vortex wave modes are revealed. The vortex mode is a singular solenoidal mode. Such modes are negative energy waves for which a dissipative instability is possible. The absolute phonon-vortex instability appears for Mach number $Ma\gtrsim 0.4$.

Keywords:

A. Kerekes: Effect of meridional flow on Parker's interface dynamo

Parker's interface dynamo is generalized to the case of a transversal (i.e. meridional) flow of constant speed, limited to the high diffusivity volume. It is found that the Parker-Yoshimura sign law is much more difficult to violate in this case than for a homogeneous velocity field.

Keywords: Sun, MHD, plasma physics

D. Marik: A new model for the lower overshoot layer in the Sun

We present a model for the lower overshoot layer of the Sun, based on the realistic solar stratification, without the use of a ``mixing-length'' parameter, by solving the system of Reynolds momentum equations using the closure formalism of \citet{Canuto+Dubov:1,Canuto+Dubov:2}. A fixed value of velocity anisotropy is assumed, and the local convection model is assumed to be valid for the convectively unstable layer. In accordance with seismic constraints, overshoot (defined as the amount by which the convectively mixed zone extends beyond its boundary in local theory) is found to be as low as about 6 percent of the pressure scale height, and it is not bounded by a discontinuity from below.

Keywords: Sun, MHD, plasma physics

Kwing L. Chan: Turbulence in Rotating Convection

Rotation plays vital roles in a great number of solar phenomena. Here we discuss results of a large eddy simulation study that illustrates the behavior of convective turbulence spanning over a wide range of Coriolis numbers.

Keywords: Sun, rotation, convection, turbulence

K. Murawski: Turbulent effects on solar acoustic waves

The effect of space- and time-dependent random mass density, velocity, and pressure fields on frequencies and amplitudes of solar acoustic waves is considered by means of the analytical perturbative method. The analytical results, which are valid for weak fluctuations and long wavelength waves, reveal frequency and amplitude alteration, the effect which depends on the type of a random field. In particular, short-wavelength frequencies of the sound waves that propagate along the constant gravity in an isothermal atmosphere are lifted up (reduced) by a space-dependent random mass density (pressure) field. Higher values of the acoustic cut-off frequency result in an increase of wave frequencies. This effect is stronger for longer waves. As a consequence of that in the case of the random pressure field the frequency correction exhibits a cross-over at intermediate values of wavenumber; long (short) sound waves experience a positive (negative) frequency shift. In the limit of a gravity-free medium, the effect of a random mass density field is to increase wave frequencies. Space-dependent random velocity and pressure fields reduce wave frequencies. While space-dependent random fields attenuate wave amplitudes, their time-dependent counterparts lead to wave amplification.

In the other example, the sound waves that are trapped in the vertical direction but are free to propagate horizontally are effected by a space-dependent random mass density field. This effect depends on a direction along which this field is varying. A random field, which varies along the horizontal direction, does not couple standing modes but increase their frequencies and attenuates amplitudes. These modes are coupled by a random field which depends on the vertical coordinate but the dispersion relation remains the same as in the case of the deterministic medium.

Keywords: Sun, MHD, plasma physics, turbulence, random fields

M. T. Homem and R. Erdélyi: Absolute and Convective Instabilities in Open Shear Flow Layers

In the present paper we study the absolute and convective nature of instabilities in open shear flows by carrying out fully non-linear adiabatic 2-D hydrodynamic numerical simulations. We found the value of mean flow for which perturbations change from absolute to convective unstable. We fully recover the results of a previous analytic solution. We found that (i) an inviscid incompressible fluid is the most unstable configuration; (b) compressibility and viscosity decrease the value of mean flow necessary for the transition from absolute to convective instability; (c) even a viscosity has dominant influence over compressibility.

Keywords: Instability, Absolute, Convective

Yu. Kyzyurov: Electron-Density Fluctuations

On the basis of quasi-hydrodynamic equations we consider formation of electron-density fluctuations by turbulent mixing of weakly-ionized plasma in the solar atmosphere. An expression for the power spectrum of the fluctuations is obtained, assuming quasi-neutrality and isothermality. The expression is used to predict the shape of the spatial spectrum and the rms level of the plasma fluctuations in the lower part of the solar atmosphere.

Keywords: solar atmosphere, turbulence, plasma fluctuations

D. Schmitt and A. Ferriz-Mas: Variable Solar and Stellar Activity by a Flux Tube Dynamo

The dynamo action of unstable magnetic flux tubes due to magnetic buoyancy in a rotating stellar convection zone is summarized and the implications of a flux tube dynamo with a threshold in field strength for dynamo action is discussed in connection with the observed variability of solar and stellar magnetic activity.

Keywords: Sun, stars, magnetic activity, dynamo, stability, MHD

L. Tóth and O. Gerlei: On the Orientational Relaxation of Bipolar Active Regions

Our work on the basis of selected regular bipolar magnetic regions (BMRs) strengthens the assumption that the scatter of tilt angles of BMRs around Joy`s law is determined by the convective turbulence. Furthermore, regular BMRs grouped by age do not show the phenomenon of toroidal relaxation, which may probably mean the disconnection of $\Omega$-loops from the bottom of the convection zone.

Keywords: Sun, $\Omega$-loop, convective turbulence, dinamic disconnection, tilt angle

K. Jahn: Dynamics of thin flux tubes in sunspot penumbrae

A model for the fine structure of a sunspot penumbra can be constructed in a form of an ensemble of magnetic flux tubes moving in their own background. As a first step the evolution of a single flux tube in a penumbra of the magnetostatic sunspot model is studied numerically. Properties of such solutions are briefly recalled and some of new results are presented with a qualitative discussion of dynamic features of emerging tubes as compared with the observed behaviour of bright penumbral grains. Limitations of the model and problems related to a quantitative comparison with observations are also commented.

Keywords: Sunspots, penumbrae, magnetic flux tubes

A. A. Norton and H. Uitenbroek: Observing MHD Oscillations in Sunspot

Attempts to detect magnetohydrodynamic waves in the solar photosphere by identifying oscillations in the magnetic field have proved problematic due to suspected contributions from systematic temperature and density fluctuations causing the spectral line formation height to vary, which in turn samples a vertical gradient in the magnetic field strength. We investigate this effect in sunspot umbrae and penumbrae through the analysis of data obtained with the Advanced Stokes Polarimeter in spectral lines with notoriously different temperature sensitivities. The temporal behavior of the magnetic field strength in sunspot is presented with special consideration to line formation physics occurring in the dynamic solar atmosphere. These results are compared to forward modeling of Stokes profiles with a radiative transfer code given a sunspot atmosphere perturbed by an MHD oscillation.

Keywords: Sun, MHD waves, observations

I. Ballai and R. Erdélyi: Challenges in Coronal Moreton waves

Observations with the Extreme Ultraviolet Imaging Telescope (EIT) onboard SOHO have revealed the existence of transient coronal waves which propagate across the visible solar disc and are generated by an impulsive event. Using observational quantities (propagation speed, attenuation length) we derive average values for magnetic field intensity and viscosity in the low corona, i.e. we develop global coronal seismology.

Keywords: Sun, MHD, waves

I. De Moortel and A.W. Hood: Thermal conduction damping of longitudinal waves in coronal loops

High cadence TRACE observations show that outward propagating intensity disturbances are a common feature in large coronal loops. An overview is given of measured parameters of such longitudinal waves in coronal loops. We found that loops that are situated above sunspot regions display intensity oscillations with periods centred around 3 minutes, whereas oscillations in `non-sunspot' loops show periods centred around 5 minutes. The observed longitudinal waves are interpreted as propagating slow magneto-acoustic waves and we show that the disturbances are not flare-driven but are most likely caused by an underlying driver exciting the loop footpoints. We found that (slightly enhanced) thermal conduction could account for the observed damping lengths.

Keywords: Sun, corona, oscillations

S. P. James and R. Erdélyi: Spicule Formation by Ion-neutral Damping

The possible generation of spicules by Alfvénic waves is studied in MHD where dissipation is mainly caused by ion-neutral collision damping, as suggested by \citet{haerendel}. The propagation of high frequency Alfvén waves on vertically open solar magnetic flux tubes is considered by numerically solving a set of fully nonlinear, dissipative 1.5D MHD equations with the waves being generated by a continuous sinusoidal driver in the low atmosphere of the Sun. Spicule-like structures with heights of around $4\,000-10\,000\unit{km}$ were formed, primarily by the impact of a series of slow shocks generated by the continuous interaction between the upward propagating driven and reflected wave trains rather than the predicted ion-neutral damping mechanism.

Keywords: Sun, MHD, plasma physics

A. Ludmány, B. Major and V. M. Nakariakov: Quasi-periodic behaviour of a flare ribbon system

A series of quasi-periodic pulsations have been detected in the flare of 19th July 1999. The total area occupied by the flare ribbons exhibited temporary increases in the declining phase of the flare at certain moments, the period of the pulses was about 20-30 minutes. The phenomenon has been recognized in the center, as well as at 0.5 and 1.0 \AA\ wings on both sides of the H-alpha line.

Keywords: flare, oscillations

V. Fedun, A. Yukhimuk and A. Voitsekhovskaja: Transformation of the Alfvén Waves in the Low Beta Plasma

The nonlinear mechanism of the transformation of magnetohydrodynamic (MHD) Alfvén waves to kinetic Alfvén waves (KAW) in the homogeneous magnetized plasma with small plasma parameter beta << 1 is investigated. As the generation mechanism, the parametric instability, where the MHD Alfvén wave is the pumping wave is considered. On the basis of the two-fluid MHD and Vlasov equation the nonlinear dispersion relation describing three-wave interaction, the instability growth rate and the threshold of the instability are found. The theoretical results are used for the interpretation of plasma heating in the solar corona.

Keywords: Sun, MHD, Alfvén wave, instability

Y. Voitenko and M. Goossens: Nonlinear wave dynamics in the dissipation range

There is abundant observational evidence that the ions in the solar corona (in particular, $O^{+5}$) are heated anisotropicaly, predominantly across the background magnetic field. This heating is usually attributed to the dissipation of ion-cyclotron waves. We study an alternative possibility with the dissipation range in the solar corona formed by the kinetic Alfv\'{e}n waves (KAWs) which are very short- wavelengths across the magnetic field. Instead of transport of MHD wave energy towards to the range of ion-cyclotron waves, we study transport into the dissipation range of KAWs. We show that the nonlinear excitation of short-wavelength (of the order 10 m) KAWs in the extended solar corona and solar wind can be provided by upward-propagating fast and Alfv\'{e}n MHD waves launched from the coronal base by the convection or magnetic reconnection. KAWs are very efficient in the energy exchange with plasma particles, providing plasma heating and particles acceleration. In particular, these transversal wavelengths make KAWs accessible for the stochastic perpendicular heating of oxygen ions when the wave/background magnetic field ratio exceeds 0.005. Both the quasi-steady coronal heating and the transient heating events observed by Yohkoh and SOHO may be due to KAWs that are nonlinearly excited by MHD waves.

Keywords: solar corona, waves, instabilities

D. Marik: Nano-scale reconnection in the solar transition layer

Magnetic reconnection in the lower transition region of the solar atmosphere is numerically simulated by solving the fully nonlinear, time-dependent, dissipative, radiative 2D MHD equations. Setting the initial parameters describing transition region explosive events, we computed the evolution of the reconnection jets. Taking into account the limit of the spatial and temporal resolution of the CDS camera and converting the high-resolution numerical results into `CDS-resolution', the propagating reconnection jets are found to have similar properties as those described by CDS blinker observations. These results suggest SOHO CDS may actually observe reconnection driven explosive events as blinkers.

Keywords: Sun, MHD, blinkers, explosive events, transition region

C. A. Mendoza-Briceno and R. Erdélyi: Impulsive heating in the solar atmosphere

Observations of the solar chromosphere-corona transition region plasma show evidence of small, short-lived dynamic phenomena called e.g., explosive events, blinkers, micro- and nano-flares. These events may serve as the basic building blocks of the heating mechanism(s) of the solar atmosphere. In this paper we study the heating of the solar corona by numerous micro-scale randomly highly localized events representing the energy dissipation found by observations. We found, that typical loop temperature structures seen by e.g. TRACE are recovered when the energy release occurs close to the footpoints of the loop. Implications of these results upon the latest coronal loop observations are addressed.

Keywords: Sun, atmosphere, transition region, corona, hydrodynamics

Y. Taroyan: Global Resonant MHD Waves in the Magnetosphere

A major shortcoming of theories of long-period magnetic pulsations is the separate treatment of the problems of wave excitation and resonant coupling. This could account for many substantial discrepancies between the waveguide/cavity theories and observations. A unified approach leading to a new type of field line resonance (FLR) excitation mechanism is presented. It is shown that in a steady state the direct coupling of the waveguide modes to the local field line oscillations provides a natural and a very efficient transport of energy from the magnetosheath flow to the shear Alfvén waves even in the ideal MHD limit. Many well-known observational features are recovered.

Keywords: Magnetosphere, MHD, plasma physics