Don Melrose

The University of Sydney · School of Physics

We propose and discuss an alternative pulsar radio emission mechanism that relies on rotation-driven plasma oscillations, rather than on a beam-driven instability, and suggest that it may be the generic radio emission mechanism for pulsars. We identify these oscillations as superluminal longitudinal waves in the pulsar plasma, and point out that th...

We consider critically the three most widely favored pulsar radio emission mechanisms: coherent curvature emission (CCE), beam-driven relativistic plasma emission (RPE) and anomalous Doppler emission (ADE). We assume that the pulsar plasma is one dimensional (1D), streaming outward with a bulk Lorentz factor γs ≫ 〈γ〉 − 1 ≳ 1, where 〈γ〉 is the intri...

We propose and discuss an alternative pulsar radio emission mechanism that relies on rotation-driven plasma oscillations, rather than on a beam-driven instability, and suggest that it may be the generic radio emission mechanism for pulsars. We identify these oscillations as superluminal longitudinal waves in the pulsar plasma, and point out that th...

We consider critically the three most widely favored pulsar radio emission mechanisms: coherent curvature emission (CCE), beam-driven relativistic plasma emission (RPE) and anomalous Doppler emission (ADE). We assume that the pulsar plasma is one dimensional (1D), streaming outward with a bulk Lorentz factor $\gamma_{\rm s} \gg \langle\gamma\rangle...

Beam-driven instabilities are considered in a pulsar plasma assuming that both the background plasma and the beam are relativistic Jüttner distributions. In the rest frame of the background, the only waves that can satisfy the resonance condition are in a tiny range of slightly subluminal phase speeds. The growth rate for the kinetic (or maser) ver...

Beam-driven instabilities are considered in a pulsar plasma assuming that both the background plasma and the beam are relativistic J\"uttner distributions. In the rest frame of the background, the only waves that can satisfy the resonance condition are in a tiny range of slightly subluminal phase speeds. The growth rate for the kinetic (or maser) v...

Wave dispersion in a pulsar plasma (a one-dimensional, strongly magnetized, pair plasma streaming highly relativistically with a large spread in Lorentz factors in its rest frame) is discussed, motivated by interest in beam-driven wave turbulence and the pulsar radio emission mechanism. In the rest frame of the pulsar plasma there are three wave mo...

Wave dispersion in a pulsar plasma is discussed emphasizing the relevance of different inertial frames, notably the plasma rest frame ${\mathcal{K}}$ and the pulsar frame ${\mathcal{K}}^{\prime }$ in which the plasma is streaming with speed $\unicode[STIX]{x1D6FD}_{\text{s}}$ . The effect of a Lorentz transformation on both subluminal, $|z| , and s...

Wave dispersion in a pulsar plasma is discussed emphasizing the relevance of different inertial frames, notably the plasma rest frame ${\cal K}$ and the pulsar frame ${\cal K}'$ in which the plasma is streaming with speed $\beta_{\rm s}$. The effect of a Lorentz transformation on both subluminal, $|z|<1$, and superluminal, $|z|>1$, waves is discuss...

Wave dispersion in a pulsar plasma (a 1D, strongly magnetized, pair plasma streaming highly relativistically with a large spread in Lorentz factors in its rest frame) is discussed, motivated by interest in beam-driven wave turbulence and the pulsar radio emission mechanism. In the rest frame of the pulsar plasma there are three wave modes in the lo...

Observations during the main phase of geomagnetic storms reveal an anti-correlation between the occurrence of broadband low frequency electromagnetic waves and outer radiation belt electron flux. We show that the drift-bounce motion of electrons in the magnetic field of these waves leads to rapid electron transport. For observed spectral energy den...

Type III solar radio bursts are the Sun's most intense and frequent nonthermal radio emissions. They involve two critical problems in astrophysics, plasma physics, and space physics: how collective processes produce nonthermal radiation and how magnetic reconnection occurs and changes magnetic energy into kinetic energy. Here magnetic reconnection...

A purely magnetospheric model is introduced for observed abrupt changes in pulsar radio profile. Motion of magnetospheric plasma is described by a drift frequency, ω dr, that depends on a parameter 0 ≤ y ≤ 1, and a change in the magnetospheric state corresponds to a change in y. Emission is assumed to arise from m spots distributed uniformly around...

Pulsar radio emission involves a coherent emission mechanism involving relativistic particles, but there is no consensus on what the specific emission mechanism is. There are arguments for and against several suggested mechanisms of long-standing, including two, relativistic plasma emission and anomalous Doppler emission, that depend explicitly on...

We study the influence of kinetic-scale Alfv\'enic turbulence on the generation of plasma radio emission in the solar coronal regions where the plasma/magnetic pressure ratio $\beta $ is smaller than the electron/ion mass ratio $m_{e}/m_{i}$. The present study is motivated by the phenomenon of solar type I radio storms associated with the strong ma...

Roles played by the currents in the impulsive phase of a solar flare and in a coronal mass ejection (CME) are reviewed. Solar flares are magnetic explosions: magnetic energy stored in unneutralized currents in coronal loops is released into energetic electrons in the impulsive phase and into mass motion in a CME. The energy release is due to a chan...

Three known examples of coherent emission in radio astronomical sources are reviewed: plasma emission, electron cyclotron maser emission (ECME) and pulsar radio emission.

A representative case study from the Van Allen Probes during a geomagnetic storm recovery phase reveals enhanced electron fluxes at intermediate pitch angles over energies from ~100 keV to 5 MeV coincident with broadband low frequency electromagnetic waves. The statistical properties of these waves are used to build a model for radial diffusion via...

Since the early 1980s, decimetric spike bursts have been attributed to electron cyclotron maser emission (ECME) by the electrons that produce hard X-ray bursts as they precipitate into the chromosphere in the impulsive phase of a solar flare. Spike bursts are regarded as analogous to the auroral kilometric radiation (AKR), which is associated with...

Pulsar electrodynamics is reviewed emphasizing the role of the inductive electric field in an oblique rotator and the incomplete screening of its parallel component by charges, leaving ‘gaps’ with $E_{\Vert }\neq 0$ . The response of the plasma leads to a self-consistent electric field that complements the inductive electric field with a potentia...

We develop a model for subpulse separation period, P2, taking into account both the apparent motion of the visible point as a function of pulsar phase, ψ, and the possibility of abrupt jumps between different rotation states in non-corotating pulsar magnetospheres. We identify three frequencies: (i) the spin frequency of the star, (ii) the drift fr...

A conventional astrophysical treatment of synchrotron emission is modified to include the refractive index of air, written as n = 1 + 1/(2γ 02), with γ0 ⪢ 1. The angular distribution of emission by an electron with Lorentz factor γ is broadened, from a range of |θ - α| ≈ 1/γ in vacuo (θ = emission angle, α = pitch angle) to |θ - α| ≈ max{1/γ, 1/γ0}...

A standard model for the visibility of pulsar radio emission is based on the assumption that the emission is confined to a narrow cone about the tangent to a dipolar field line. The widely accepted rotating vector model (RVM) is an approximation in which the line of sight is fixed and the field line is not strictly tangent to it. We refer to an exa...

We reconsider pulsar electrodynamics for an obliquely rotating pulsar, and propose a way of synthesizing the vacuum dipole model (VDM) and the rotating magnetosphere model (RMM). We first modify the VDM by assuming that the parallel component of the inductive electric field is screened by charges. We refer to the resulting model as the minimal mode...

Bulk energization of electrons to $10\,-\,20\,$keV in solar flares is attributed to dissipation of Alfv\'en waves that transport energy and potential downward to an acceleration region near the chromosphere. The acceleration involves the parallel electric field that develops in the limit of inertial Alfv\'en waves (IAWs). A two-potential model for...

The magnetized vacuum has dispersive properties similar to a material medium. Its response may be described by a hierarchy of response tensors, which are functions of B∕B c . The linear response tensor, referred to as the vacuum polarization tensor, has a relatively simple form, first derived in the 1930s, that applies at frequencies, ω≪2m, well be...

First order processes are described by a Feynman diagram with a single electron-photon vertex. In the presence of a static magnetic field, such a diagram describes six allowed processes: emission and absorption of a photon by an electron or a positron, and one-photon pair creation or annihilation. These are referred to here as the first-order gyrom...

Existing global models for flares do not include an essential ingredient in the electrodynamics: the inductive electric field due to the time-varying magnetic field. How the large (≈ 1010 V) electromotive force and the current it drives can be included in a model is discussed. Alfvén waves play an important role in transporting energy and potential...

Alfv\'en waves play three related roles in the impulsive phase of a solar flare: they transport energy from a generator region to an acceleration region; they map the cross-field potential (associated with the driven energy release) from the generator region onto the acceleration region; and within the acceleration region they damp by setting up a...

Second order processes are described by Feynman diagrams with two electron-photon vertices. Such processes include Compton scattering, two-photon emission, two-photon pair creation and annihilation, Møller and Bhabha scattering, and the trident process. These processes have counterparts in the absence of a magnetic field, and an important motivatio...

Dispersion in a magnetized, quantum electron gas was first discussed in the nonrelativistic case in the 1960s and 1970s [24, 15, 7, 6, 2]. Extension to the relativistic case, with one early exception [20], was carried out mainly in the 1980s [3, 5, 13, 8] and continues to the present [14, 22, 11]. An exact expression for the linear response tensor...

The generalization of the covariant classical kinetic theory of plasma responses from an unmagnetized to a magnetized plasma involves a considerable increase in algebraic complexity. As in the unmagnetized case, two different methods of calculation are available and both are useful: the forward-scattering and Vlasov methods. In the forward-scatteri...

The linear response tensor contains all information on the linear response of a medium. In particular, it determines the properties of the natural wave modes of the medium. Magnetized plasmas can support a large variety of different wave modes. There is no systematic classification of wave modes, leading to a confusing variety of names. Some modes...

Three applications of covariant fluid theory are discussed in this chapter: a covariant form of cold-plasma theory, covariant MHD theory, and a covariant form of quantum fluid theory.

Gyromagnetic emission is the generic name for emission due to the spiraling motion of a particle in a magnetic field. Gyromagnetic emission by nonrelativistic particles is referred to as cyclotron emission, which is dominated by the fundamental and first few harmonics of the cyclotron frequency. Gyromagnetic emission by highly relativistic particle...

In this chapter the Dirac equation is solved for an electron in the presence of a magnetostatic field. To solve the Dirac equation requires a specific choice of gauge for the magnetostatic field, and a specific choice of the spin operator. It is then possible to separate the wavefunction into a gauge- and spin-dependent factor and a reduced wavefun...

The generalization of the covariant classical kinetic theory of plasma responses from an unmagnetized to a magnetized plasma involves a considerable increase in algebraic complexity. As in the unmagnetized case, two different methods of calculation are available and both are useful: the forward-scattering and Vlasov methods. In the forward-scatteri...

Second order processes are described by Feynman diagrams with two electron-photon vertices. Such processes include Compton scattering, two-photon emission, two-photon pair creation and annihilation, Moller and Bhabha scattering, and the trident process. These processes have counterparts in the absence of a magnetic field, and an important motivatio...

Three applications of covariant fluid theory are discussed in this chapter: a covariant form of cold-plasma theory, covariant MHD theory, and a covariant form of quantum fluid theory.

In this chapter the Dirac equation is solved for an electron in the presence of a magnetostatic field. To solve the Dirac equation requires a specific choice of gauge for the magnetostatic field, and a specific choice of the spin operator. It is then possible to separate the wavefunction into a gauge- and spin-dependent factor and a reduced wavefun...

Dispersion in a magnetized, quantum electron gas was first discussed in the nonrelativistic case in the 1960s and 1970s [24, 15, 7, 6, 2]. Extension to the relativistic case, with one early exception [20], was carried out mainly in the 1980s [3, 5, 13, 8] and continues to the present [14, 22, 11]. An exact expression for the linear response tensor...

Gyromagnetic emission is the generic name for emission due to the spiraling motion of a particle in a magnetic field. Gyromagnetic emission by nonrelativistic particles is referred to as cyclotron emission, which is dominated by the fundamental and first few harmonics of the cyclotron frequency. Gyromagnetic emission by highly relativistic particle...

The linear response tensor contains all information on the linear response of a medium. In particular, it determines the properties of the natural wave modes of the medium. Magnetized plasmas can support a large variety of different wave modes. There is no systematic classification of wave modes, leading to a confusing variety of names. Some modes...

The parametric decay instability of upper hybrid wave into low-frequency electromagnetic Shear Alfv�en wave and Ordinary mode radiation (O-mode) has been investigated in an electron-ion plasma immersed in the uniform external magnetic field. Incorporating quantum effect due to electron spin, the fluid model has been used to investigate the linear a...

The inductive electric field is unjustifiably neglected in most models for pulsar electrodynamics; it cannot be screened by the magnetospheric plasma, and it is not small in comparison with the corotation electric field. The perpendicular component of the inductive electric field implies a drift motion that is inconsistent with corotation at any an...

The covariant form of the response 4-tensor is derived for a spin-dependent, relativistic magnetized quantum electron gas. The electron gas is described by its occupation number, nns(pz), where = ±1 labels electron and positron states, n the Landau level, pz the parallel momentum, and s = ±1 the spin, which corresponds to the parallel component of...

We investigate the changes in polarization position angle in radiation from pulsar A around the eclipse in the Double Pulsar system PSR J0737-3039A/B at the 20 cm and 50 cm wavelengths using the Parkes 64-m telescope. The changes are ~2\sigma\ during and shortly after the eclipse at 20 cm but less significant at 50 cm. We show that the changes in p...

An accepted model for magnetospheric substorms is proposed as the basis for a generic model for magnetic explosions, and is applied to solar flares. The model involves widely separated energy-release and particle-acceleration regions, with energy transported Alfv\'enically between them. On a global scale, these regions are coupled by a large-scale...

Inclusion of the inductive electric field, ${\bf E}_{\rm ind}$ due to the temporally changing ${\bf B}$, in magnetic explosions is discussed, with emphasis on solar flares. Several roles played by ${\bf E}_{\rm ind}$ are identified: on a global scale, ${\bf E}_{\rm ind}$ produces the EMF that drives the explosion; the associated ${\bf E}_{\rm ind}\...

We present 13 and 20 cm radio observations of the magnetic chemically peculiar star CU Virginis taken with the Australia Telescope Compact Array. We detect two circularly polarized radio pulses every rotation period which confirm previous detections. In the first pulse, the lower frequency emission arrives before the higher frequency emission and t...

Hans Buchdahl, who died in Adelaide on 7 January 2010 at the age of 90, contributed extensively to three fields of theoretical physics: geometric optics, general relativity and thermodynamics. His early work on optical aberration coefficients was motivated by a wartime need; through this work he rejuvenated a field that had been moribund for close...

An accepted model for magnetospheric substorms is used as the basis for a generic model for magnetic explosions, Emphasis is placed on the role of the inductive electric field and the displacement current. It is pointed out that these are unjustifiably neglected in conventional models, with this neglect being implicit in the assumptions of magnetoh...

The solar activity cycle entered a prolonged quiet phase that started in 2008 and ended in 2010. This minimum lasted for a year longer than expected and all activity proxies, as measured from Earth and from Space, reached minimum values never observed before (de Toma, 2012). The number of spotless days from 2006 to 2009 totals 800, the largest ever...

The resistive instabilities and dispersion of obliquely propagating waves near the lower hybrid (LH) frequency are studied in plasma carrying a current parallel to the magnetic field. Possible applications of these instabilities include magnetic reconnection regions where LH-like waves may accelerate and heat both ions and electrons. A resistive in...

Pulsar electrodynamics has been built up by taking ingredients from two models, the vacuum-dipole model, which ignores the magnetosphere but includes the inductive electric field due to the obliquely rotating magnetic dipole, and the corotating-magnetosphere model, which neglects the vacuum inductive electric field and assumes a corotating magnetos...

The dispersion and reactive instabilities of obliquely propagating waves near the lower hybrid (LH) frequency are studied in plasma carrying a current parallel to the magnetic field. Possible applications of these instabilities include magnetic reconnection regions, where LH-like waves may accelerate and heat both ions and electrons. In plasmas wit...

The response of a cold electron gas is generalized to include the spin of the electron described by the relativistically correct quasiclassical Bargmann-Michel-Telegdi (BMT) equation. The magnetization of the electron gas is assumed to be along the background magnetic field B and the spin-dependent contribution to the response tensor is proportiona...

The dispersion equation is analyzed for waves in a strongly magnetized, electron-positron plasma in which counterstreaming electrons and positrons have a relativistic thermal distribution in their respective rest frames, for propagation parallel to the magnetic field. We derive the response tensor for the medium, demonstrate the dispersion curves f...

Australia has a small but world-class solar physics research community, with strong international ties, working in areas of particular strength defined by the research interests of individuals and small groups. Most research occurs at the major universities, and a small number of Ph.D. students are trained in the field each year. This paper surveys...

Pulsar electrodynamics has been built up by taking ingredients from two models, the vacuum-dipole model, which ignores the magnetosphere but includes the inductive electric field due to the obliquely rotating magnetic dipole, and the corotating-magnetosphere model, which neglects the inductive electric field and assumes a corotating magnetosphere....

A plasma dispersion function (PDF) is defined for a nonrelativistic Fermi–Dirac distribution and its properties are explored. The degree of degeneracy is described by a parameter ξ = eμe/Te, for electrons, with μe/Te large and negative in the nondegenerate limit, and large and positive in the completely degenerate limit. The PDF is denoted Z(y,ξ),...

Division II of the IAU provides a forum for astronomers studying a wide range of phenomena related to the structure, radiation and activity of the Sun, and its interaction with the Earth and the rest of the solar system. Division II encompasses three Commissions, 10, 12 and 49, and four working groups. During the last triennia the activities of the...

The longitudinal response function for a thermal electron gas is calculated including two quantum effects exactly, degeneracy, and the quantum recoil. The Fermi-Dirac distribution is expanded in powers of a parameter that is small in the nondegenerate limit and the response function is evaluated in terms of the conventional plasma dispersion functi...

The standard formula for the rotation measure, RM, which determines the position angle, $\psi={\rm RM}\lambda^2$, due to Faraday rotation, includes contributions only from the portions of the ray path where the natural modes of the plasma are circularly polarized. In small regions of the ray path where the projection of the magnetic field on the ra...

It is pointed out that the standard model for pulsar electrodynamics is based on a false premise, related to neglecting the displacement current, and the associated need for current screening. Wave dispersion in the standard model is reviewed, and its relation to the interpretation of pulsar radio emission and its polarization is discussed. Inclusi...

The pulsar current, in the $P$--$ {\dot P}$ plane where $P$ is the pulsar period and ${\dot P}$ is the period derivative, is used as a supposedly ``model free'' way to estimate the pulsar birthrate from statistical data on pulsars. We reconsider the derivation of the kinetic equation on which this is based, and argue that the interpretation of the...

The magnetic chemically peculiar star CU Virginis is a unique astrophysical laboratory for stellar magnetospheres and coherent emission processes. It is the only known main-sequence star to emit a radio pulse every rotation period. Here we report on new observations of the CU Virginis pulse profile in the 13- and 20-cm radio bands. The profile is k...

We propose the first volume-limited survey for transient and quiescent radio emission from ultracool dwarf stars. Ultracool dwarfs are the coolest stars, and include the sub-stellar brown dwarfs. Transient radio emission, as periodic pulses and isolated flares on timescales of minutes, along with quiescence, was recently discovered from some ultrac...

Division II of the IAU provides a forum for astronomers studying a wide range of phenomena related to the structure, radiation and activity of the Sun, and its interaction with the Earth and the rest of the solar system. Division II encompasses three Commissions, 10, 12 and 49, and four working groups. During the last triennia the activities of the...

Pair modes were identified by Hines and collaborators as longitudinal waves in a relativistic quantum plasma of spin 0 particles in the completely degenerate limit. Pair modes with both longitudinal and transverse polarization also exist in spin 1 plasmas in the completely degenerate limit. We consider the possible existence of pair modes in comple...

The longitudinal response function for an isotropic, nonrelativistic, thermal plasma with the quantum recoil included exactly is used to generalize the dispersion relation for ion acoustic waves and the absorption coefficient for Landau damping to include the quantum recoil. The results are compared to recent treatment of the dispersion relation de...

It is argued that the inclusion of the Bohm potential in quantum fluid equations is equivalent to inclusion of a nonrelativistic form of the quantum recoil in plasma kinetic theory. The Bohm term is incorrect when applied to waves with phase speed greater than the speed of light.

The response 4-tensor is derived for a spin-independent, relativistic magnetized quantum electron gas. The sum over spins is carried out both directly and using a procedure due to Ritus. The 4-tensor components are written in terms of a sum over the two solutions of the resonance condition for the particle 4-momentum. It is shown that the dispersiv...

This book is a collection of lecture notes for seven courses presented at the Astrophysics School VII, organized by the European Astrophysics Doctoral Network and held at San Miniato, Italy, in October 1994. The topics of each of the seven courses are independent of each other. This has the advantage that most readers with a general interest in ast...

We consider the motion of a charge in a large-amplitude electrostatic wave with a triangular waveform relevant to an oscillating model of a pulsar magnetosphere. The (one-dimensional) orbit of a particle in such a wave is found exactly in terms of Weierstrass functions. The result is used to discuss linear acceleration emission (at both low and hig...

Lower hybrid (LH) waves can interact resonantly with both electrons and ions transferring energy between the species. For this reason the properties of LH waves are of interest. Most treatments of LH waves include either electromagnetic (EM) or warm plasma effects but not both. Here a new analytic dispersion relation for LH waves, including both EM...

Cosmic-ray streaming instabilities at supernova shocks are discussed in the quasilinear diffusion formalism which takes into account the feedback effect of wave growth on the cosmic ray streaming motion. In particular, the nonresonant instability that leads to magnetic field amplification in the short wavelength regime is considered. The linear gro...

A generic interpretation of pulsar radio emission that does not rely on the identification of a specific emission mechanism is explored. Coherence is quantified in terms of a coherence factor, which implies a maximum brightness temperature; the possible significance of Poincaré invariants is pointed out, and the potential use of higher order moment...

Astrophysical applications of electron cyclotron maser emission (ECME) are reviewed with emphasis placed on planetary radio emissions. The early history of the field, and the relevant theory of ECME are summarized. Some emphasis is given to the problem of escape of ECME from an astrophysical source.

The theory of linear acceleration emission is developed for a large amplitude electrostatic wave in which all particles become highly relativistic in much less than a wave period. An Airy integral approximation is shown to apply near the phases where the electric field passes through zero and the Lorentz factors of all particles have their maxima....

The theory of plasma emission and of electron cyclotron maser emission, and their applications to solar radio bursts and to Jupiter's DAM and the Earth's AKR are reviewed, emphasizing the early literature and problems that remain unresolved. It is pointed out that there are quantitative measures of coherence in radio astronomy that have yet to be e...

Glossary I. Background and context of the subject II. Stochastic acceleration III. Resonant scattering IV. Diffusive shock acceleration V. DSA at multiple shocks VI. Applications of DSA VII. Acceleration by parallel electric fields VIII. Other acceleration mechanisms IX. Future directions X. Appendix: Quasilinear equations XI. Bibliography Comment:...

There are three important points on which a recent paper by E. N. Parker implies disagreement with a previous paper by this author where none actually exists: (1) The way dynamics should be treated in magnetohydrodynamics (MHD), (2) the speed of energy propagation in a plasma, and (3) the conditions under which line tying is valid. Points on which...

We analyze the three-dimensional geometry of solar flares that show so-called interacting flare loops in soft X-ray, hard X-ray, and radio emission, as previously identified by Hanaoka and Nishio. The two flare loops that appear brightest after the flare are assumed to represent the outcome of a quadrupolar magnetic reconnection process, during whi...

Relativistic plasma emission due to a beam instability in the polar cap regions is examined critically as a pulsar radio emission mechanism. Wave dispersion in the pulsar plasma is discussed, based on the use of a relativistic plasma dispersion function. The growth rate for the beam instability is estimated in the rest frame of the plasma for paral...

An oscillating model for the magnetospheres of pulsars suggests the presence of a counter-streaming electron-positron pair plasma, where the Lorentz factor of the streams varies over several orders of magnitude. The relativistically correct response of the plasma is calculated analytically, and numeric calculations of the dispersion functions perfo...

Commission 10 aims at the study of various forms of solar activity, including networks, plages, pores, spots, fibrils, surges, jets, filaments/prominences, coronal loops, flares, coronal mass ejections (CMEs), solar cycle, microflares, nanoflares, coronal heating etc., which are all manifestation of the interplay of magnetic fields and solar plasma...

The role of caustics in the scintillation of radio sources due to thin-screen scattering is explored. The classical stationary phase treatment of this type of scattering implies singular behavior at the caustics. Physically, this singularity is resolved by diffractive effects, and a smooth but highly peaked intensity distribution is expected, analo...

Scintillation of a radio source can be treated relatively simply by making the stationary phase point (SPP) approximation to the Fresnel-Kirchhoff integral, but the range of validity of the SPP approximation is not well determined. We identify three idealized models for the phase variation for which there are accurate approximations ("exact" result...

Commission 10 deals with solar activity in all of its forms, ranging from the smallest nanoflares to the largest coronal mass ejections. This report reviews scientific progress over the roughly two-year period ending in the middle of 2008. This has been an exciting time in solar physics, highlighted by the launches of the Hinode and STEREO missions...

Most treatments of lower hybrid waves include either electromagnetic or warm-plasma effects, but not both. Here we compare numerical dispersion curves for lower hybrid waves with a new analytic dispersion relation that includes both warm and electromagnetic effects. Very good agreement is obtained over significant ranges in wavenumber and plasma pa...