Response tensor for a spin-dependent electron gas: Dependence on the choice of spin operator.

It is shown that the choice of spin operator affects the form of the response tensor describing a spin-dependent electron gas. The covariant, spin-dependent response tensor for a magnetic dipole moment-polarized electron gas (statistical distribution of electrons and positrons) is evaluated. A simultaneous eigenfunction of both the magnetic-moment spin operator and the Dirac Hamiltonian is constructed, from which explicit expressions for the magnetic-moment states and the corresponding vertex functions are derived. It is shown that a gas of electrons having a preferred magnetic-moment spin has a rotatory-type response that is gyrotropic. In contrast, when the helicity is chosen as the spin operator, the response of an electron gas with a preferred helicity spin has a rotatory response that is analogous to an optically active medium. The distinction between these spin operators does not appear in conventional treatments of spin dependence in quantum plasmas.

Low Altitude Solar Magnetic Reconnection, Type III Solar Radio Bursts, and X-ray Emissions.

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 events are identified definitively in Solar Dynamics Observatory UV-EUV data, with strong upward and downward pairs of jets, current sheets, and cusp-like geometries on top of time-varying magnetic loops, and strong outflows along pairs of open magnetic field lines. Type III bursts imaged by the Murchison Widefield Array and detected by the Learmonth radiospectrograph and STEREO B spacecraft are demonstrated to be in very good temporal and spatial coincidence with specific reconnection events and with bursts of X-rays detected by the RHESSI spacecraft. The reconnection sites are low, near heights of 5-10 Mm. These images and event timings provide the long-desired direct evidence that semi-relativistic electrons energized in magnetic reconnection regions produce type III radio bursts. Not all the observed reconnection events produce X-ray events or coronal or interplanetary type III bursts; thus different special conditions exist for electrons leaving reconnection regions to produce observable radio, EUV, UV, and X-ray bursts.

Classical relativistic model for spin dependence in a magnetized electron gas.

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 proportional to the magnitude of the magnetization. The dispersion equation is shown to be quadratic in the refractive index squared, and dispersion curves for the two wave modes are plotted for cases where the magnetic field associated with magnetization is comparable with B. Two intrinsically spin-dependent wave modes are identified: one bounded by two resonances and the other by two cutoffs. The counterpart of the z mode can escape without encountering a resonance or a cutoff.

Wave dispersion in a counterstreaming, relativistic thermal, magnetized, electron-positron plasma.

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 for different temperatures, and discuss the differences from the cold-plasma case. Application to the case of pulsar magnetospheres is discussed.

Dispersion in a thermal plasma including arbitrary degeneracy and quantum recoil.

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 function to arbitrary order in this parameter. The infinite sum is performed in terms of polylogarithms in the long-wavelength and quasistatic limits, giving results that apply for arbitrary degeneracy. The results are applied to the dispersion relations for Langmuir waves and to screening, reproducing known results in the nondegenerate and completely degenerate limits, and generalizing them to arbitrary degeneracy.

Wave dispersion in a counterstreaming, cold, magnetized, electron-positron plasma.

The dispersion equation is analyzed for waves in a strongly magnetized, electron-positron plasma in which counterstreaming electrons are cold in their respective rest frames. For propagation parallel to the magnetic field the dispersion equation factorizes into equations for two longitudinal modes and four transverse modes. Instabilities occur in both longitudinal and transverse modes, with the most notable being at low wave numbers where a longitudinal branch has purely imaginary frequency. For oblique propagation at small angles, the modes reconnect at points where the parallel modes intersect, either deviating away from each another, or being separated by a pair of complex modes. In addition, intrinsically oblique branches of the dispersion equation appear. The results are applied to an oscillating model for a pulsar magnetosphere, in which the oscillations are purely temporal with a frequency well below relevant wave frequencies, and in which the counterstreaming becomes highly relativistic. We assume that the medium may be treated as time stationary in treating the wave dispersion and wave growth. The wave properties, including the wave frequency, vary periodically with the phase of the oscillations. The fastest growing instability is when the counterstreaming is nonrelativistic or mildly relativistic. A given wave can experience bursts of growth over many oscillations. Mode coupling associated with the cyclotron resonance may be effective in generating the observed orthogonally polarized modes at phases of the oscillation where the (relativistic) cyclotron and wave frequencies are comparable.

Polarized maser growth.

A polarized maser is assumed to operate in an anisotropic medium with natural modes polarized differently to the maser. It is shown that when the spatial growth rate and the generalized Faraday rotation rate are comparable, the polarization of the growing radiation is different from those of the maser and medium. In particular, for a lineary polarized maser operating in a medium with linearly polarized natural modes, the growing radiation is partially circularly polarized. This provides a previously unrecognized source of circular polarization that may be relevant to pulsar radio emission.

Wave dispersion near cyclotron resonance in pulsar plasmas.

In a standard pulsar model, the radio emission is produced in the relativistic, strongly magnetized electron-positron plasma in the polar-cap region of the magnetosphere. Waves are generated well below the cyclotron frequency and must propagate through the cyclotron resonance region where they are affected by the resonance. Wave dispersion near the cyclotron resonance is discussed in the formalism of the weak anisotropy approximation in which the relevant waves are treated as transverse. Analytical approximations for the two orthogonal modes are derived, in the rest frame of the plasma, for nearly parallel, nearly antiparallel and nearly perpendicular propagation with respect to the magnetic field direction. It is shown that due to the relativistic distribution the wave dispersion varies smoothly across the resonance with initially elliptical polarization evolving to linear and then elliptical polarization with opposite handedness. The relevance of such a change in handedness to the interpretation of circular polarization is discussed.

Optical activity in an isotropic gas of electrons with a preferred helicity.

An isotropic gas of electrons with a preferred spin helicity is shown to be optically active. Simultaneous eigenfunctions of the Dirac Hamiltonian and the helicity operator are constructed and used to derive explicit expressions for vertex functions for helicity states. The (covariant) response tensor is calculated for an electron gas described in terms of a spin-dependent occupation number. The possibility of detecting optical activity in an electron gas is discussed briefly.

Wave dispersion in gyrotropic relativistic pulsar plasmas.

Wave dispersion in a gyrotropic relativistic pulsar plasma is discussed. A pulsar plasma in general contains electrons, positrons, and possibly ions. Although electron-positron pairs are dominant in number density, charge neutrality is generally not satisfied and the gyrotropic terms need to be considered. These gyrotropic terms can lead to elliptical polarization that may be relevant for the observed circular polarization of pulsar radio emission. The wave dispersion and polarization are obtained numerically by calculating the response in terms of the three relativistic plasma dispersion functions. For waves propagating at an oblique angle (to the ambient magnetic field) a significant ellipticity requires the plasma to deviate substantially from the neutrality condition.

Quasilinear diffusion as a result of modulational instability in the pulsar plasma.

Quasilinear diffusion due to modulational instability is considered in this paper. Interaction between the high-frequency, nearly transverse O mode (or the transverse X mode) and the low-frequency, nearly longitudinal L-O mode in a pulsar magnetospheric pair plasma can lead to modulational instability. The low-frequency L-O mode is superluminal, which is not subjected to usual Landau damping, and it is possible that excess wave energy is stored in this superluminal mode. The superluminal low-frequency L-O mode can dissipate in a way similar to the process of Langmuir wave collapse, that is, it cascades from the long- to short-wavelength regimes. When the phase speed becomes less than c, the waves can be damped through various resonances. We consider, in particular, damping through cyclotron resonance, which can lead to particle acceleration. The energetic beam particles, which have a very small spread initially, can develop a high-energy distribution tail, acquiring pitch angles through quasilinear diffusion. These particles can emit gamma rays through synchrotron radiation, contributing to the observed pulsar high-energy emission.

New mechanism of pulsar radio emission.

It is shown that pulsar radio emission can be generated effectively through a streaming motion in the polar-cap regions of a pulsar magnetosphere causing non-resonant growth of waves that can escape directly. As in other beam models, a relatively low-energy high-density beam is required. The instability generates quasitransverse waves in a beam mode at frequencies that can be well below the resonant frequency. As the waves propagate outward, growth continues until the height at which the wave frequency is equal to the resonant frequency. Beyond this point, the waves escape in a natural plasma mode (LO mode). This one-step mechanism is much more efficient than previously widely considered multistep mechanisms.

Waves in strongly magnetized relativistic plasmas: generally covariant approach.

A dispersion relation for long waves in strongly magnetized multifluid plasma in a curved spacetime is derived in a covariant form. A generally covariant form for the ray equations is obtained. The results are applicable to ray propagation in relativistic plasmas in the vicinity of strongly gravitating (black holes) or rapidly rotating (pulsars) systems.