Conservation of both current and helicity in a quadrupolar model for solar flares

A model for a solar flare, involving magnetic reconnection transferring flux and current between current-carrying magnetic loops connecting two pairs of footpoints, is generalized to include conservation of magnetic helicity during reconnection, as well as conservation of current at all four footpoints. For a set of force-free loops, with the $i$th loop having flux $F_i$ and current $I_i$, the self and mutual helicities are proportional to the self and mutual inductances with the constant of proportionality determined by $\alpha_i=F_i/\mu_0I_i$. In a constant-$\alpha$ model, the change in magnetic energy is proportional to the change in helicity, and conservation of helicity implies conservation of magnetic energy, so that a flare cannot occur. In a quadrupolar model, with $\alpha_1>\alpha_2$ initially, $\alpha_1$ increases and $\alpha_2$ decreases when flux and current are transferred from loops~1 and~2 to loops~3 and~4. A model that conserves both current and helicity is constructed; it depends on the initial $\alpha$s, and otherwise is somewhat simpler than when helicity is neglected.Comment: 14 pages, 1 figure. Solar Physics (in press

Large-Amplitude, Pair-Creating Oscillations in Pulsar and Black Hole Magnetospheres

A time-dependent model for pair creation in a pulsar magnetosphere is developed. It is argued that the parallel electric field that develops in a charge-starved region (a gap) of a pulsar magnetosphere oscillates with large amplitude. Electrons and positrons are accelerated periodically and the amplitude of the oscillations is assumed large enough to cause creation of upgoing and downgoing pairs at different phases of the oscillation. With a charge-starved initial condition, we find that the oscillations result in bursts of pair creation in which the pair density rises exponentially with time. The pair density saturates at $N_\pm\simeq E_{0}^2/(8\pi m_ec^2\Gamma_{\rm thr})$, where $E_0$ is the parallel electric field in the charge-starved initial state, and $\Gamma_{\rm thr}$ is the Lorentz factor for effec tive pair creation. The frequency of oscillations following the pair creation burst is given roughly by $\omega_{\rm osc}=eE_0/(8m_ec\Gamma_{\rm thr})$. A positive feedback keeps the system stable, such that the average pair creation rate balances the loss rate due to pairs escaping the magnetosphere.Comment: 21 pages, 6 figures, ApJ submitte

Anisotropic weak turbulence of Alfven waves in collisionless astrophysical plasmas

The evolution of Alfven turbulence due to three-wave interactions is discussed using kinetic theory for a collisionless, thermal plasma. There are three low-frequency modes, analogous to the three modes of compressible MHD. When only Alfven waves are considered, the known anisotropy of turbulence in incompressible MHD theory is reproduced. Inclusion of a fast mode wave leads to separation of turbulence into two regimes: small wave numbers where three-wave processes involving a fast mode is dominant, and large wave numbers where the three Alfven wave process is dominant. Possible application of the anisotropic Alfven turbulence to the interstellar medium and dissipation of magnetic energy in magnetars is discussed.Comment: 9 pages, accepted for publication in MNRA

Saturated magnetic field amplification at supernova shocks

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 growth rate is calculated using kinetic theory for a streaming distribution. We show that the nonresonant instability is actually driven by a compensating current in the background plasma. The nonresonant instability can develop into a nonlinear regime generating turbulence. The saturation of the amplified magnetic fields due to particle diffusion in the turbulence is derived analytically. It is shown that the evolution of parallel and perpendicular cosmic-ray pressures is predominantly determined by nonresonant diffusion. However, the saturation is determined by resonant diffusion which tends to reduce the streaming motion through pitch angle scattering. The saturated level can exceed the mean background magnetic field.Comment: 8 pages. Accepted for publication in MNRA

Oscillating pulsar polar gaps

An analytical model for oscillating pair creation above the pulsar polar cap is presented in which the parallel electric field is treated as a large amplitude, superluminal, electrostatic wave. An exact formalism for such wave is derived in one-dimension and applied to both the low-density regime in which the pair plasma density is much lower than the corotating charge density and the high-density regime in which the pair plasma density is much higher than the corotating charge density. In the low-density regime, which is relevant during the phase leading to a pair cascade, a parallel electric field develops resulting in rapid acceleration of particles. The rapid acceleration leads to bursts of pair production and the system switches to the oscillatory phase, corresponding to the high density regime, in which pairs oscillate with net drift motion in the direction of wave propagation. Oscillating pairs lead to a current that oscillates with large amplitude about the Goldreich-Julian current. The drift motion can be highly relativistic if the phase speed of large amplitude waves is moderately higher than the speed of light. Thus, the model predicts a relativistic outflow of pairs, a feature that is required for avoiding overheating of the pulsar polar cap and is also needed for the pulsar wind.Comment: 13 pages, 8 figures, accepted for publication in MNRA

Neurofascin 140 is an embryonic neuronal neurofascin isoform that promotes the assembly of the node of ranvier

Rapid nerve conduction in myelinated nerves requires the clustering of voltage-gated sodium channels at nodes of Ranvier. The Neurofascin (Nfasc) gene has a unique role in node formation because it encodes glial and neuronal isoforms of neurofascin (Nfasc155 and Nfasc186, respectively) with key functions in assembling the nodal macromolecular complex. A third neurofascin, Nfasc140, has also been described; however, neither the cellular origin nor function of this isoform was known. Here we show that Nfasc140 is a neuronal protein strongly expressed during mouse embryonic development. Expression of Nfasc140 persists but declines during the initial stages of node formation, in contrast to Nfasc155 and Nfasc186, which increase. Nevertheless, Nfasc140, like Nfasc186, can cluster voltage-gated sodium channels (Nav) at the developing node of Ranvier and can restore electrophysiological function independently of Nfasc155 and Nfasc186. This suggests that Nfasc140 complements the function of Nfasc155 and Nfasc186 in initial stages of the assembly and stabilization of the nodal complex. Further, Nfasc140 is reexpressed in demyelinated white matter lesions of postmortem brain tissue from human subjects with multiple sclerosis. This expands the critical role of the Nfasc gene in the function of myelinated axons and reveals further redundancy in the mechanisms required for the formation of this crucial structure in the vertebrate nervous system