Phase-Mixing and Dissipation of Standing Shear Alfven waves

We study the phase mixing and dissipation of a packet of standing shear Alfv\'en waves localized in a region with non-uniform Alfv\'en background velocity. We investigate the validity of the exponential damping law in time, $\exp(-At^3)$, presented by Heyvaerts & Priest (1983) for different ranges of Lundquist, $S$, and Reynolds, $R$, numbers. Our numerical results shows that it is valid for $(R,S)\geq 10^7$.Comment: 11 pages, 8 figure

Review Article: MHD Wave propagation near coronal null points of magnetic fields

We present a comprehensive review of MHD wave behaviour in the neighbourhood of coronal null points: locations where the magnetic field, and hence the local Alfvén speed, is zero. The behaviour of all three MHD wave modes, i.e. the Alfvén wave and the fast and slow magnetoacoustic waves, has been investigated in the neighbourhood of 2D, 2.5D and (to a certain extent) 3D magnetic null points, for a variety of assumptions, configurations and geometries. In general, it is found that the fast magnetoacoustic wave behaviour is dictated by the Alfvén-speed profile. In a β=0 plasma, the fast wave is focused towards the null point by a refraction effect and all the wave energy, and thus current density, accumulates close to the null point. Thus, null points will be locations for preferential heating by fast waves. Independently, the Alfvén wave is found to propagate along magnetic fieldlines and is confined to the fieldlines it is generated on. As the wave approaches the null point, it spreads out due to the diverging fieldlines. Eventually, the Alfvén wave accumulates along the separatrices (in 2D) or along the spine or fan-plane (in 3D). Hence, Alfvén wave energy will be preferentially dissipated at these locations. It is clear that the magnetic field plays a fundamental role in the propagation and properties of MHD waves in the neighbourhood of coronal null points. This topic is a fundamental plasma process and results so far have also lead to critical insights into reconnection, mode-coupling, quasi-periodic pulsations and phase-mixing

Alfv\`en wave phase-mixing and damping in the ion cyclotron range of frequencies

Aims. To determine the effect of the Hall term in the generalised Ohm's law on the damping and phase mixing of Alfven waves in the ion cyclotron range of frequencies in uniform and non-uniform equilibrium plasmas. Methods. Wave damping in a uniform plasma is treated analytically, whilst a Lagrangian remap code (Lare2d) is used to study Hall effects on damping and phase mixing in the presence of an equilibrium density gradient. Results. The magnetic energy associated with an initially Gaussian field perturbation in a uniform resistive plasma is shown to decay algebraically at a rate that is unaffected by the Hall term to leading order in k^2di^2 where k is wavenumber and di is ion skin depth. A similar algebraic decay law applies to whistler perturbations in the limit k^2di^2>>1. In a non-uniform plasma it is found that the spatially-integrated damping rate due to phase mixing is lower in Hall MHD than it is in MHD, but the reduction in the damping rate, which can be attributed to the effects of wave dispersion, tends to zero in both the weak and strong phase mixing limits

Chinese Flower

https://digitalcommons.library.umaine.edu/mmb-vp/3856/thumbnail.jp

The moon shines on the moonshine : song

https://digitalcommons.library.umaine.edu/mmb-vp/3289/thumbnail.jp

Magnetohydrodynamics dynamical relaxation of coronal magnetic fields. I. Parallel untwisted magnetic fields in 2D

Context. For the last thirty years, most of the studies on the relaxation of stressed magnetic fields in the solar environment have onlyconsidered the Lorentz force, neglecting plasma contributions, and therefore, limiting every equilibrium to that of a force-free field. Aims. Here we begin a study of the non-resistive evolution of finite beta plasmas and their relaxation to magnetohydrostatic states, where magnetic forces are balanced by plasma-pressure gradients, by using a simple 2D scenario involving a hydromagnetic disturbance to a uniform magnetic field. The final equilibrium state is predicted as a function of the initial disturbances, with aims to demonstrate what happens to the plasma during the relaxation process and to see what effects it has on the final equilibrium state. Methods. A set of numerical experiments are run using a full MHD code, with the relaxation driven by magnetoacoustic waves damped by viscous effects. The numerical results are compared with analytical calculations made within the linear regime, in which the whole process must remain adiabatic. Particular attention is paid to the thermodynamic behaviour of the plasma during the relaxation. Results. The analytical predictions for the final non force-free equilibrium depend only on the initial perturbations and the total pressure of the system. It is found that these predictions hold surprisingly well even for amplitudes of the perturbation far outside the linear regime. Conclusions. Including the effects of a finite plasma beta in relaxation experiments leads to significant differences from the force-free case

Revisiting Reading: Exploring an intensive reading pedagogy in adult literacy

Applied linguistic research into genres of written communication hashad a considerable impact in recent decades on the pedagogy of writing inall sectors of education in Australia, from early schooling to post-secondaryand workplace contexts (eg. Christie and Martin 1997). Attending to thesocial purpose of language and modelling and deconstructing texts inpreparation for supported writing has become a common feature of manyprograms, including those in the field of adult English as a SecondLanguage (ESL) and adult literacy. However, effective engagement withmodel texts for writing is dependent on students being able to read thosetexts. While reading continues to be explicitly identified as a component ofmost adult literacy programs, there is evidence to suggest that less attentionmay be given to the deliberate supported development of reading skills(Burns and de Silva Joyce 2000, 2005). This paper reports on a projectfunded by the National Centre for Vocational Education Research(NCVER) in Australia. The study, Investigating the impact of intensive readingpedagogy in adult literacy, was designed to explore the relevance and thepotential of an intensive, explicit reading pedagogy, Reading-to-Learn, in adultand community education (ACE) and TAFE colleges in metropolitanSydney, teaching literacy in ESL and adult basic education (ABE) classes.The study was a partnership between practising teachers andresearcher/teacher educators. It identified positive outcomes for students,with advances in reading abilities for many students well beyond thoseanticipated by teachers and students alike. Teachers also reported verypositive outcomes for their own professional development. Importantly, thestudy also identified a number of system-level features that would need to bein place to support a broader adoption of the pedagogy

Phase mixing of Alfvén waves propagating in non-reflective magnetic plasma configurations

The ability of phase mixing to provide efficient damping of Alfvén waves even in weakly dissipative plasmas made it a popular mechanism for explaining the solar coronal heating. Initially it was studied in the equilibrium configurations with the straight magnetic field lines and the Alfvén speed only varying in the direction perpendicular to the magnetic field. Later the analysis of the Alfvén wave phase mixing was extended in various directions. In particular it was studied in two-dimensional planar magnetic plasma equilibria. Analytical investigation was carried out under the assumption that the wavelength is much smaller than the characteristic scale of the background quantity variation. This assumption enabled using the Wentzel, Kramers, and Brillouin (WKB) method. When it is not satisfied the study was only carried out numerically. In general, even the wave propagation in a one-dimensional inhomogeneous equilibrium can be only studied numerically. However there is one important exception, so-called non-reflective equilibria. In these equilibria the wave equation with the variable phase speed reduces to the Klein-Gordon equation with constant coefficients. In this paper we apply the theory of non-reflective wave propagation to studying the Alfvén wave phase mixing in two-dimensional planar magnetic plasma equilibria. Using curvilinear coordinates we reduce the equation describing the Alfvén wave phase mixing to the equation that becomes a one-dimensional wave equation in the absence of dissipation. This equation is further reduced to the equation which is the one-dimensional Klein-Gordon equation in the absence of dissipation. Then we show that this equation has constant coefficients when a particular relation between the plasma density and magnetic field magnitude is satisfied. Using the derived Klein-Gordon-type equation we study the phase mixing in various non-reflective equilibria. We emphasise that our analysis is valid even when the wavelength is comparable with the characteristic scale of the background quantity variation. In particular, we study the Alfvén wave damping due to phase mixing in an equilibrium with constant plasma density and exponentially divergent magnetic field lines. We confirm the result previously obtained in the WKB approximation that there is enhanced Alfvén wave damping in this equilibrium with the damping length proportional to ln(Re), where Re is the Reynolds number. Our theoretical results are applied to heating of coronal plumes. We show that, in spite of enhanced damping, Alfvén waves with periods of the order of one minute can be efficiently damped in the lower corona, at the height about 200 Mm, only if the shear viscosity is increased by about 6 orders of magnitude in comparison with its value given by the classical plasma theory. We believe that such increase of the shear viscosity can be provided by the turbulence