Abstract. In this work we used Particle-In-Cell simulations to study the interaction of circularly polarised Alfvén waves with one dimensional plasma density inhomogeneities transverse to the uniform magnetic field (phase mixing) in collisionless plasmas. In our preliminary work we reported discovery of a new electron acceleration mechanism, in which progressive distortion of the Alfvén wave front, due to the differences in local Alfvén speed, generates an oblique (nearly parallel to the magnetic field) electrostatic field. The latter accelerates electrons through the Landau resonance. Here we report a detailed study of this novel mechanism, including: (i) analysis of broadening of the ion distribution function due to the presence of Alfvén waves; and (ii) the generation of compressive perturbations due to both weak non-linearity and plasma density inhomogeneity. The amplitude decay law in the inhomogeneous regions, in the kinetic regime, is demonstrated to be the same as in the MHD approximation described by Heyvaerts & Priest (1983, A&A, 117, 220).

Abstract. Evolution of a coronal loop in response to an impulsive energy release is numerically modelled. It is shown that the loop density evolution curves exhibit quasi-periodic perturbations with the periods given approximately by the ratio of the loop length to the average sound speed, associated with the second standing harmonics of an acoustic wave. The density perturbations have a maximum near the loop apex. The corresponding field-aligned flows have a node near the apex. We suggest that the quasi-periodic pulsations with periods in the range 10-300 s, frequently observed in flaring coronal loops in the radio, visible light and X-ray bands, may be produced by the second standing harmonic of the acoustic mode.

The ''coronal heating problem'' has been with us over 60 years, and hundreds of theoretical models have been proposed without an obvious solution in sight. In this paper we point out that observations show no evidence for local heating in the solar corona, but rather for heating below the corona in the transition region and upper chromosphere, with subsequent chromospheric evaporation as known in flares. New observational evidence for this scenario comes from (1) the temperature evolution of coronal loops, (2) the overdensity of hot coronal loops, (3) upflows in coronal loops, (4) the Doppler shift in coronal loops, (5) upward propagating waves, (6) the energy balance in coronal loops, (7) the magnetic complexity in the transition region, (8) the altitude of nanoflares and microflares, (9) the cross section of elementary loops, as well as (10) 3D MHD simulations of coronal heating. The phrase ''coronal heating problem'' is therefore a paradoxical misnomer for what should rather be addressed as the ''chromospheric heating problem'' and ''coronal loop filling process.'' This paradigm shift substantially reduces the number of relevant theoretical models for coronal heating in active regions and the quiet Sun, but our arguments do not apply to coronal holes and the extended heliospheric corona.

A new linear mechanism of reciprocal transformation of waves and a corresponding energy transfer in shear flows is discovered. The effect is demonstrated on the simplest example -the two-dimensional waves in unbounded, parallel hydromagnetic flow with uniform velocity shear. The phenomenon discovered is of importance for magnetohydrodynamics and fusion plasma devices and for various terrestrial and astrophysical shear flows. Grasping the result became possible thanks to the nonmodal analyses of the perturbation evolution in the flow. ͓S1063-651X͑96͒11605-6͔PACS number͑s͒: 52.35. Bj, 03.40.Kf, 47.20.Ft Oscillatory systems are prevalent in the nature and play an important role in the wide variety of physical processes. It should be emphasized that: ͑i͒ these kinds of dynamical systems usually consist of coupled oscillators and have several degrees of freedom; ͑ii͒ parameters of the oscillators in most cases are not constant but vary slowly in time ͓1͔. The processes taking place in such systems are immensely complex and their study is applicable not only to the various branches of physics, but also to chemistry, biology, sociology, and other sciences. Investigation of these two key aspects of dynamics, closely related to each other in some physical situations, has become one of the most important interdisciplinary problems in applied mathematics ͓1-3͔. Hydrodynamical and plasma flows constitute such oscillatory systems, where coupling, as a rule, is associated with nonlinear processeswave decay processes ͓4͔, which ensures the mutual transformation of different wave modes. In plasma physics, a linear coupling phenomenon is also known: mutual transformation of different kinds of plasma waves arising due to a spatial inhomogeneity of a medium. For example, existence of the density inhomogeneity induces coupling between magnetohydrodynamic ͑MHD͒ oscillations ͓5͔ or the transformation of compressional-type waves into electromagnetic-type waves propagating across a density discontinuity ͓6͔, etc.In the present paper, we describe a mechanism of the linear reciprocal transformation of wave modes arising in flows due to a velocity inhomogeneity. The effect is demonstrated for the simplest example: MHD waves in twodimensional ͑2D͒, compressible, magnetized, unbounded parallel flow with uniform velocity shear ͑plane, magnetized Couette flow͒. The result is obtained by means of the nonmodal approach applied to the study of the evolution of small-scale perturbations in the flow. This effect makes more diverse the variety of processes taking place in shear flows. Under a traditional modal analysis, this phenomenon was not noticed for the following reason: the linear operators arising in shear flows ͑as becomes apparent in a number of recent contributions ͓7-13͔͒ are non-normal. It results in a set of nonorthogonal eigenfunctions strongly interfering with each other. That is why analysis of distinct eigenfunction evolution, performed in the framework of the modal approach ͑without adequate consideration of the interference͒, ...