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

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

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