Magnetic explosions: role of the inductive electric field

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 ${\bf E}_{\rm ind}\times{\bf B}$ drift is identified with the inflow of magnetic field lines into a reconnection region; the polarization current, associated with $\partial{\bf E}_{\rm ind}/\partial t$, implies a ${\bf J}\times{\bf B}$ force that accelerates this inflow; and the component of ${\bf E}_{\rm ind}$ parallel to ${\bf B}$ accelerates the energetic electrons that cause hard X-ray emission and type III radio bursts. Some simple models that describe these effects are presented. A resolution of the long-standing "number problem" in solar flares is suggested

Current-driven flare and CME models

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 change in current configuration effectively reducing the net current path. A flare is driven by the electromotive force (EMF) due to the changing magnetic flux. The EMF drives a flare-associated current whose cross-field closure is achieved by redirection along field lines to the chromosphere and back. The essential roles that currents play are obscured in the "standard" model and are described incorrectly in circuit models. A semi-quantitative treatment of the energy and the EMF is provided by a multi-current model, in which the currents are constant and the change in the current paths is described by time-dependent inductances. There is no self-consistent model that includes the intrinsic time dependence, the EMF, the flare-associated current and the internal energy transport during a flare. The current, through magnetic helicity, plays an important role in a CME, with twist converted into writhe allowing the kink instability plus reconnection to lead to a new closed loop, and with the current-current force accelerating the CME through the torus instability

Faraday rotation: effect of magnetic field reversals

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 ray path reverses sign (called QT regions) the modes are nearly linearly polarized. The neglect of QT regions in estimating RM is not well justified at frequencies below a transition frequency where mode coupling changes from strong to weak. By integrating the polarization transfer equation across a QT region in the latter limit, I estimate the additional contribution $\Delta\psi$ needed to correct this omission. In contrast with a result proposed by \cite{BB10}, $\Delta\psi$ is small and probably unobservable. I identify a new source of circular polarization, due to mode coupling in an asymmetric QT region. I also identify a new circular-polarization-dependent correction to the dispersion measure at low frequencies.Comment: 25 pages 1 figure, accepted for publication in The Astrophysical Journa

Dynamics of spin 1/2 quantum plasmas

The fully nonlinear governing equations for spin 1/2 quantum plasmas are presented. Starting from the Pauli equation, the relevant plasma equations are derived, and it is shown that nontrivial quantum spin couplings arise, enabling studies of the combined collective and spin dynamics. The linear response of the quantum plasma in an electron--ion system is obtained and analyzed. Applications of the theory to solid state and astrophysical systems as well as dusty plasmas are pointed out.Comment: 4 pages, 2 figures, to appear in Physical Review Letter

Acceleration Mechanisms

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. BibliographyComment: To be published in Meyers, Robert (Ed.) Encyclopedia of complexity and systems science, Springer review completed late 200

Linear acceleration emission: 2 Power spectrum

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 emissivity is derived for an individual particle and is integrated over frequency and solid angle to find the power radiated per particle. The result is different from that implied by the generalized Larmor formula which, we argue, is not valid in this case. We also discuss a mathematical inconsistency that arises when one evaluates the power spectrum by integrating the emissivity over solid angle. The correct power spectrum increases as the 4/3rd power of the frequency at low frequencies, and falls off exponentially above a characteristic frequency. We discuss application of linear acceleration emission to the emission of high frequency photons in an oscillating model for pulsars. We conclude that it cannot account for gamma-ray emission, but can play a role in secondary pair creation.Comment: 25 pages; Accepted for publication in Ap

Bulk Energization of Electrons in Solar Flares by Alfv\'en Waves

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 IAWs is used to relate the parallel potential to the cross-field potential transported by the waves. We identify a maximum parallel potential in terms of a maximum current density that corresponds to the threshold for the onset of anomalous resistivity. This maximum is of order $10\,$kV when the threshold is that for the Buneman instability. We argue that this restricts the cross-field potential in an Alfv\'en wave to about $10\,$kV. Effective dissipation requires a large number of up- and down-current paths associated with multiple Alfv\'en waves. The electron acceleration occurs in localized, transient, anomalously-conducting regions (LTACRs) and is associated with the parallel electric field determined by Ohm's law with an anomalous resistivity. We introduce an idealized model in which the LTACRs are (upward-)current sheets, a few skin depths in thickness, separated by much-larger regions of weaker return current. We show that this model can account semi-quantitatively for bulk energization.Comment: 20 pages, 1 figur