Table of contents

This Topical Issue of Physica Scripta is dedicated to Professor Hannes Alfvén (1908–1995). In order to review the state-of-the-art on Alfvén waves in cosmic and laboratory plasmas, an International Workshop on Alfvén Waves was organized at the State University of Rio de Janeiro (UERJ), Brazil, during November 8–10, 1994. The Alfvén waves that Professor Alfvén predicted in the 1940s are of fundamental importance to laboratory plasma physics, space plasma physics, and plasma astrophysics. It is remarkable that after half a century of its discovery, the subject of Alfvén waves is still an active area of research in all branches of plasma physics.

This Topical Issue consists of invited lectures delivered at the International Workshop on Alfvén Waves. In addition, a number of leading experts on Alfvén waves have been invited to contribute papers to this special issue. With the assistance of these colleagues, this issue has a good coverage of most aspects of Alfvén wave research today.

The workshop was made possible by the kind support of Professor H Cordeiro (Rector of UERJ), Miss G S Dutra (Workshop Secretary), the State University of Rio de Janeiro and the Research Foundation of State of Rio de Janeiro (FAPERJ).

Invited Opening Lecture at the International Workshop on Alfvén Waves Rio de Janeiro 8-10 November 1994

It has been studied the quantitative modification of the electron runaway flux due to a spectrum of kinetic Alfvén waves (kAw), using the quasilinear (waves) and Fokker-Planck (collisions) equations. It is shown that these modes enhance the runaway production rate via their Cherenkov dissipation. The runaway flux for narrow and broad band spectrum for low and high phase velocities is calculated, and it is found as a general feature that its enhancement is the larger the weaker the background electric field, while for its absolute enhancement it is just the opposite. In some cases, the runaway production rate is found to be enhanced by many orders of magnitude over that without kinetic Alfvén waves. It has also been discussed the consequences of this study for cosmic plasmas, namely: amplification of nonthermal emissions from stellar atmospheres, and planetary magnetospheres, (radio frequency waves, and x-ray), life extension of stellar radio bursts, enhancement of Langmuir turbulence, depletion of thermal population in extragalactic jets, and enhancement of auroral electrons precipitation.

The non-uniformity of plasma density and magnetic fields is an important feature of the magnetospheric plasma. An Alfvén wave acquires very unique features while propagating in such a plasma and exhibits interesting new phenomena like resonant mode coupling, resonant absorption and resonant mode conversion. The theoretical analysis of the Alfvén wave equation governing the dynamics of a linear inhomogeneous plasma system at low frequencies is discussed to understand these phenomena associated with the Alfvén wave.

The resonant mode coupling of shear Alfvén waves both to steady and time-dependent sources is then related to understand the origin and characteristics features of micropulsations.

The resonant mode conversion of an Alfvén wave to a kinetic Alfvén wave (KAW) having a wavelength comparable to the ion gyroradius in a direction perpendicular to the magnetic field is discussed. As a KAW has a component of its electric field in the direction of the ambient magnetic field it can accelerate plasma particles along the field. The basic theory of the mechanism of particle acceleration by KAW and a possible application of this type of acceleration mechanism to the formation of the aurora arcs is discussed.

Some important nonlinear effects involving Alfvén waves in plasmas are presented. For illustrative purposes, we start with small amplitude Alfvén waves and their relation with other low-frequency plasma modes. We then show that Alfvén and magnetosonic waves can be nonlinearly excited by a high-frequency external pump wave. Finite-amplitude Alfvén waves can either interact with the background plasma or with themselves, giving rise to a number of nonlinear phenomena such as wave- amplitude modulation or filamentation, density profile modification, as well as self-organization in vortical structures. The nonlinear effects that are described here are of relevance to the large-amplitude disturbances which are frequently observed in laboratory and space plasmas.

Three nonlinear Alfvén wave phenomena in the planetary magnetosphere are discussed: (1) magnetohydrodynamic parametric instabilities induced by a nonlinear standing Alfvén wave, (2) parametric excitation of Alfvén and Langmuir waves by a nonlinear electromagnetic whistler wave, and (3) parametric generation of electromagnetic waves in the vicinity of electron plasma frequency via nonlinear coupling of Langmuir and Alfvén waves. Observational evidence in support of these nonlinear Alfvén wave phenomena, such as the auroral Alfvén-acoustic turbulence and the auroral Langmuir-Alfvén-whistler (LAW) events, in the planetary magnetosphere is presented.

Alfvén waves in fusion plasmas play an important role in a number of situations. First, in Alfvén Wave Heating (AWH) schemes. Second, both theory and experiment have demonstrated the existence of Global Alfvén Eigenmodes (GAEs). GAEs have been observed in different tokamaks (PRETEXT, TCA, TEXTOR, etc.) and, more recently, in a stellarator (Wendelstein 7-AS) where they were shown to become unstable under intense Neutral Beam injection. Third, the existence and possible destabilization by fast ions of Toroidicity induced Alfvén Eigenmodes (TAEs) has been evidenced both theoretically and experimentally. This destabilization could hamper the operation of a magnetically confined fusion reactor by setting a limit on the number of fusion alpha particles in the plasma. It is therefore crucial to understand the mechanisms leading to the occurrence of the instability and also those that can stabilize the TAEs by increasing the strength of the damping. The aim is to be able to devise possible ways to avoid the instability of Alfvén eigenmodes in a region of parameter space that is compatible with the functioning of a fusion reactor. A global perturbative approach is presented to tackle the problem of the linear stability of TAEs. Our model computes the overall wave particle power transfers to the different species and thus could also be applied to the study of alpha power extraction in the presence of Alfvén waves. We indicate also how to go beyond the perturbative approach.

The effect of resistivity on the stable part of the Alfvén spectrum of a plasma is described with reference to a slab model and an exactly solvable cylindrical model. Toroidal effects are examined by using a numerical code, SPECTOR. This also enables a study of the damping of toroidicity-induced Alfvén eigenmodes due to resistivity.

Ion energies in reversed-field pinch plasmas are observed to be considerably higher than expected from ohmic heating and collisional transfer from electrons. Other mechanisms must be involved and seem to be related to tearing-mode fluctuations. Observations of ion heating and fluctuation spectra are reviewed here as well as various mechanisms proposed to be responsible for the ion heating. A mechanism is proposed, where induced currents due to rotating tearing-mode perturbations passing by irregularities in the wall structure excite plasma waves, which in turn are absorbed at the Alfvén-wave resonance. The partition of energy between electrons and ions is discussed.

The resonant and nonresonant current drive produced by the Alfvén and fast waves are discussed both for collision and collisionless magnetized plasmas. The magneto-hydrodynamics approach is used to study collision plasma regimes, and the purely kinetic model, with the Landau and transit time magnetic pumping (TTMP) damping, is considered in the weak collision plasma case. The general form of the time-averaged ponderomotive force (and current drive as a result) generated by waves in magnetized plasma configurations is presented. It has been shown that standing Alfvén waves can drive non-inductive and nonresonant current in a magnetized plasma through Landau and TTMP damping. If all oscillations of the solar corona loops are related to standing Alfvén waves, which can introduce the density of dissipated wave power that is necessary to keep the plasma hot, the axial nonresonant current drive has been estimated to be enough for equilibrium and stability of corona loops. Experimental evidence of the Alfvén wave current drive in tokamaks and stellarators is demonstrated.

Alfvén's results for the charged-particle drift motions in a non-uniform magnetic field have been generalized

Fundamental wave and stability properties of shear Alfvén waves in nonuniform axisymmetric toroidal plasmas are reviewed. Using a slab model with nonuniform density, concepts such as continuous spectrum, resonant absorption, and linear mode conversion to kinetic Alfvén wave are first discussed. We then analyze the formation of frequency gaps in the continuous spectrum due to the finite toroidicity-induced coupling between the poloidal harmonics in an axisymmetric torus. Existence of discrete eigenmodes both inside the frequency gap and the continuous spectra are further demonstrated. Kinetic excitations of collective toroidal shear Alfvén instabilities via resonances with energetic particles are also reviewed; first in the one-dimensional radially local limit and then with a full two-dimensional global analysis. Effects due to the non-perturbative nature of the energetic-particle drive and the global extent of the eigenmodes are emphasized.

Identification of Alfvén waves in the solar wind by means of spacecraft measurements was first achieved in late 1960s. Subsequent study of these waves has found that Alfvén waves in interplanetary space is a very complicated topic. Two and half decades after the first discovery there are still many issues unresolved. The only agreement reached by scientists is that the predominant component of the Alfvén waves observed in the solar wind is of solar origin. What is the generation mechanism and how these waves evolve in interplanetary space are still unclear. But on the other hand there exists another family of Alfvén waves which are not of solar origin. The best example is those waves generated in the exosphere of a comet. For these waves the physics is much better understood. In the present paper we discuss the two families of Alfvén waves separately.

Recent investigations have focused attention on the role of intermediate shocks in MHD. It has been shown that intermediate shocks are admissible and can be formed through nonlinear wave steepening process. The intermediate shocks can have a family of shock structure; the shock structure and the evolution are related. Furthermore, there exists a class of time-dependent intermediate shocks. In this review paper, these properties are discussed based on the small-amplitude MHD equation.

Hannes Alfvén developed concepts over a half-century ago that continue to influence and guide modern space plasma physics. He derived the guiding center approximation for determining the motion of charged particles in a magnetic field and introduced the idea of a partial ring current formed from trapped radiation in the Earth's magnetic field. He expanded on the suggestion of electric currents flowing into and away from the auroral regions along geomagnetic field lines that was made at the turn of the century by the Norwegian scientist, Kristian Birkeland. Alfvén introduced the concept of a new type of wave motion that involved the coupling between mechanical and electromagnetic fields. These waves are called magnetohydrodynamic waves and are also commonly referred to as "Alfvén waves." In his theory of the origin of the solar system, Alfvén proposed that when a neutral gas streams through a plasma across magnetic field lines at sufficiently high velocity, a discharge-like process can occur in which the neutral gas begins to ionize rapidly. His "Critical Ionization Velocity" (CIV) effect has been demonstrated in laboratory experiments and in space. He applied Langmuir's theory of a probe in a plasma to explain the acceleration of electrons along geomagnetic field lines by "double layers" which produced aurora. Alfvén's ideas were not immediately accepted. His view of Birkeland currents became a source of controversy and intense debate for decades, which could be resolved only after the dawn of the space age. Alfvén regarded the space age as being a revolution in science, comparable to the introduction of the telescope by Galileo. He pointed out the ability of spacecraft to observe a wide range of physical parameters in comparison to the limited "visual light universe" based on ground based telescopes. An enormous amount of data is collected every day from a fleet of international satellite missions which depend upon the plasma physics principles introduced by Hannes Alfvén for interpretation and analysis. This paper describes a small fraction of the ever-increasing knowledge base derived from these space missions, concerning our understanding of Birkeland currents and Alfvén waves.

We discuss some of the astrophysical problems in which Alfvén waves can play an important role. The problems that we focus in are: (i) Alfvén waves in stellar winds; (ii) formation of extragalactic jets by Alfvén waves, and (iii) formation of quasar clouds by a thermal instability and Alfvén waves.

This paper reviews the theory of classical garden-hose instability in high-beta plasmas. The garden-hose (or fire-hose) instability is a hydromagnetic instability that is due to the nonresonant wave-particle interaction. Therefore, to the lowest order, it is customary to describe the instability under the assumption of hydromagnetic perturbation. The hydromagnetic assumption implies that the characteristic wave frequency (or the growth rate) is much lower than the ion gyrofrequency, and that the ion gyroradius is sufficiently smaller than the characteristic wavelength associated with the perturbation. As a result, the ion gyroradius is often taken to be zero at the outset. However, it was recently discovered that keeping the ion gyroradius finite (however small it may be) results in a fundamental alteration of the basic property of the instability. The article also reviews the nonlinear theory of the garden-hose instability.

Low-frequency, long-wavelength, non-resonant electromagnetic fluctuations are studied in a multibeam dusty plasma with anisotropic pressures, by taking the momentum and pressure changes due to fluctuations in the dust charges into account. Equilibrium drifts are included, leading to a dispersion law for Alfvén modes in the firehose-like limit. Possible instabilities are discussed, including their quailinear evolution. This analysis has relevance for cometary and planetary plasmas.

A review of the geomagnetic response to large-amplitude interplanetary Alfvén-wave trains (LAIAWT) is presented, highlighting its dependence on solar activity level and its role in the storm/substorm relationship problem. Also some recent observations obtained by the Ulysses spacecraft at high heliospheric latitudes dealing with the origin and dynamics of these wave trains are discussed.

The linear and nonlinear theory of circularly-polarized Alfvén and ion-cyclotron waves in multicomponent plasmas is reviewed. It is shown that minor heavy-ion components play an important role in the dispersive properties of space plasmas. In the nonlinear theory, the presence of minor heavy-ion components leads to a number of new wave couplings which in turn, can lead to new instabilities. These instabilities are of various kinds: modulational, beat wave and decay instabilities. It is shown that the new instabilities can be very efficient in the energy transfer from the pump wave to the heavy-ion species. This can occur through the Landau damping of electro-acoustic daughter waves, and/or resonance absorption of sideband waves. These processes can help us to understand a number of properties observed in high-speed solar wind streams and in the magnetosphere.

Salient aspects of the Alfvén wave spectrum in hot confined plasmas are presented.

This paper reviews a recent development in the theory of resonant MHD waves in non-uniform plasmas. An asymptotic analysis of the equations for MHD waves in plasmas with high magnetic Reynolds numbers has shown that resonant slow and Alfvén waves obey conservation laws and jump conditions across the dissipative layer. These conservation laws specify the dominant dynamics of the resonant MHD waves. In combination with the jump conditions they enable us to understand the basic physics of resonant MHD waves and also help us with the interpretation of results of large scale numerical simulations in resistive MHD. They also can be used to design an accurate and computationally simple methods for numerical studying resonant MHD waves in non-uniform plasmas.

Conservation laws and jump conditions for resonant MHD waves are first discussed in linear MHD for 1-dimensional equilibrium states. Subsequently the generalization of these results to 2-dimensional equilibrium state in linear MHD and to nonlinear MHD is reviewed. The interaction of sound waves with an inhomogeneous plasma is discussed as an application of the theory. Firstly the results of linear theory are used to consider the interaction of sound waves with 1-dimensional magnetic tubes. The phenomenon of total resonant absorption is discussed. Secondly the nonlinear theory of cusp dissipative layers is used to study the interaction of sound waves with 1-dimensional inhomogeneous plasmas in planar geometry. New effects that owe their existence to nonlinearity in the cusp dissipative layer are reviewed.

The effects of non-ideal terms on the dispersion relation of magnetohydrodynamic surface waves in nonuniform, magnetised plasmas are examined. These wave modes play an important role in wave heating processes in laboratory and astrophysical plasmas. Recent results for surface waves in cold and warm plasmas at frequencies less than and equal to the ion-cyclotron frequency are presented. The plasma is modelled by fluid equations and kinetic theory, and the non-ideal effects enter via finite ion cyclotron frequency, multiple ion species, dust, the finite pressure of the ions and electrons, and collisional processes such as resistivity. The cases of low and high plasma β (gas pressure/magnetic pressure) are considered, and it is shown that the thermal and other non-ideal effects give rise to additional short-wavelength modes which can lead to damping of modes localized on a sharp surface, via leakage of energy into the short-wavelength modes. The process of resonance absorption of surface waves at the Alfvén resonance in a smoothed-out surface is examined, and a number of ways of calculating the absorption are summarised. The status of the theory of nonlinear Alfvén surface waves is also reviewed.

In this report we address the present knowledge of plasma vortex structures and how that impacts on cosmogony, the evolution of the solar system, as it was conceived by Hannes Alfvén in 1954. Although plasma vortex structures are well known phenomena in contemporary space plasma physics, few attempts have been made to associate plasma vortices with large astrophysical objects. Indeed, Hannes Alfvén was a pioneer in this respect by associating the early solar system with a plasma vortex. Despite obvious merits from an observational and theoretical point of view, Alfvén-cosmogony based on a synthesis between space plasma physics and contemporary planetology have had few proponents. In fact, few people outside the space plasma physics community appear to appreciate the evolutionary thesis by Hannes Alfvén and his coworker Gustaf Arrhenius.

Alfvén cosmogony is based on three principles. (1) The evolution of the solar nebula into the early sun and its planets was a plasma-physics process where electromagnetic forces combine with gravitational forces. (2) Chemical separation of matter in the solar system was governed by the critical velocity ionization effect. (3) The transfer of angular momentum from the magnetized sun to the planets was due to partial plasma corotation in the early solar nebula. In this report some important aspects of plasma vortex structures and the Alfvén cosmogony will be addressed and it will be shown that a number of new observations within the plasma environment of planets and in interplanetary space corroborate cosmogony as envisaged by Hannes Alfvén.