On the birational section conjecture with local conditions

A birationally liftable Galois section s of a hyperbolic curve X/k over a number field k yields an adelic point x(s) in the smooth completion of X. We show that x(s) is X-integral outside a set of places of Dirichlet density 0, or s is cuspidal. The proof relies on $GL_2(F_\ell)$-quotients of $\pi_1(U)$ for some open U of X. If k is totally real or imaginary quadratic, we prove that all birationally adelic, non-cuspidal Galois sections come from rational points as predicted by the section conjecture of anabelian geometry. As an aside we also obtain a strong approximation result for rational points on hyperbolic curves over Q or imaginary quadratic fields.Comment: Theorem C (and Section 7) of the original version have been deleted due to a gap in the proof. This is the journal versio

Kinetic instability of drift-Alfven waves in solar corona and stochastic heating

The solar atmosphere is structured and inhomogeneous both horizontally and vertically. The omnipresence of coronal magnetic loops implies gradients of the equilibrium plasma quantities like the density, magnetic field and temperature. These gradients are responsible for the excitation of drift waves that grow both within the two-component fluid description (in the presence of collisions and without it) and within the two-component kinetic descriptions (due to purely kinetic effects). In the present work the effects of the density gradient in the direction perpendicular to the magnetic field vector are investigated within the kinetic theory, in both electrostatic and electromagnetic regimes. The electromagnetic regime implies the coupling of the gradient-driven drift wave with the Alfven wave. The growth rates for the two cases are calculated and compared. It is found that, in general, the electrostatic regime is characterized by stronger growth rates, as compared with the electromagnetic perturbations. Also discussed is the stochastic heating associated with the drift wave. The released amount of energy density due to this heating should be more dependent on the magnitude of the background magnetic field than on the coupling of the drift and Alfven waves. The stochastic heating is expected to be much higher in regions with a stronger magnetic field. On the whole, the energy release rate caused by the stochastic heating can be several orders of magnitude above the value presently accepted as necessary for a sustainable coronal heating.Comment: To appear in ApJ (2010

Relativistic Landau damping of longitudinal waves in isotropic pair plasmas

Landau damping is described in relativistic electron-positron plasmas. Relativistic electron-positron plasma theory contains important new effects when compared with classical plasmas. For example, there are undamped superluminal wave modes arising from both a continuous and discrete mode structure, the former even in the classical limit. We present here a comprehensive analytical treatment of the general case resulting in a compact and useful form for the dispersion relation. The classical pair-plasma case is addressed, for completeness, in an appendix

The Sun's Preferred Longitudes and the Coupling of Magnetic Dynamo Modes

Observations show that solar activity is distributed non-axisymmetrically, concentrating at "preferred longitudes". This indicates the important role of non-axisymmetric magnetic fields in the origin of solar activity. We investigate the generation of the non-axisymmetric fields and their coupling with axisymmetric solar magnetic field. Our kinematic generation (dynamo) model operating in a sphere includes solar differential rotation, which approximates the differential rotation obtained by inversion of helioseismic data, modelled distributions of the turbulent resistivity, non-axisymmetric mean helicity, and meridional circulation in the convection zone. We find that (1) the non-axisymmetric modes are localised near the base of the convection zone, where the formation of active regions starts, and at latitudes around $30^{\circ}$; (2) the coupling of non-axisymmetric and axisymmetric modes causes the non-axisymmetric mode to follow the solar cycle; the phase relations between the modes are found. (3) The rate of rotation of the first non-axisymmetric mode is close to that determined in the interplanetary space.Comment: 22 pages, 18 figures. Accepted for publication in the Astrophysical Journa

High Resolution Ionization of Ultracold Neutral Plasmas

Collective effects, such as waves and instabilities, are integral to our understanding of most plasma phenomena. We have been able to study these in ultracold neutral plasmas by shaping the initial density distribution through spatial modulation of the ionizing laser intensity. We describe a relay imaging system for the photoionization beam that allows us to create higher resolution features and its application to extend the observation of ion acoustic waves to shorter wavelengths. We also describe the formation of sculpted density profiles to create fast expansion of plasma into vacuum and streaming plasmas

Mechanisms of degassing at Nevado del Ruiz volcano, Colombia

Author Posting. © Geological Society, 2003. This article is posted here by permission of Geological Society for personal use, not for redistribution. The definitive version was published in Journal of the Geological Society 160 (2003): 507-521, doi:10.1144/0016-764902-028.Nevado del Ruiz volcano is an andesite stratovolcano located in the northern Andes of Colombia. The volcano erupted on 11 September 1985, 13 November 1985, and 1 September 1989. The last two eruptions emitted juvenile solid material. This paper examines the volatile and light lithophile trace element contents of melt inclusions and matrix glasses from this juvenile material, and proposes a model for degassing within the volcano. Major element distributions in the glasses show two evolutionary trends, with subsidiary points that lie between the two trends. The data suggest the existence of two separate magmas, which have interacted, mingled, and mixed during their ascent and eruption. Water contents in melt inclusions, as determined by secondary ionization mass spectrometric analysis, are generally low, averaging between 1.6 and 3.3 wt.%. Halogen concentrations in the glasses range from 400 to 1200 ppm for fluorine and from 1100 to 1500 ppm for chlorine. Sulphur contents are low, not exceeding 500 ppm, with most glasses containing <200 ppm. Lithium concentrations range from 20 to 40 ppm, beryllium from 1.5 to 2 ppm, and boron exhibits high variability from 30 to 100 ppm. The only significant difference between melt inclusions and matrix glasses is for water, with matrix glasses having significantly lower concentrations (<0.5 wt.%) than the melt inclusions. The generally elevated concentrations of boron in the magma may be a consequence of enrichment in the source region of the magma, i.e. by subduction of altered oceanic crust and/or sediments. Yet the large degree of boron heterogeneity in both melt inclusions and matrix glasses necessitates subsequent addition of boron at shallower depths as well, by the assimilation of crustal sedimentary rocks or by interaction with hydrothermal fluids. Evidence for pre-eruptive magma emplacement at shallow levels is provided by (1) anhydrous mineral assemblages of plagioclase and pyroxene, (2) high silica contents of glasses, and (3) low water contents in melt inclusions. When combined, these observations suggest a period of magma residence at shallow depths, probably <3 km beneath the summit of the volcano. A multistage model of magma transport and degassing involves alternating periods of magma ascent and magma ponding. Initially, volatile-bearing magma ascends from depths of 9–15 km, driven by buoyancy. During decompression, the magma loses gas, particularly CO2 and sulphur. The magma eventually ponds at its neutral buoyancy level. At this point, the gas-saturated magma cools and crystallizes, thereby liberating gas under isobaric conditions. As a result, CO2 is depleted from the magma whereas H2O and SiO2 are enriched. The H2O enrichment is caused by its increased solubility in the magma as CO2 is degassed, whereas SiO2 is enriched by fractional crystallization. The density of the magma decreases as the level of dissolved H2O increases, eventually causing the magma to become buoyant once more and to continue its ascent, either to erupt or to freeze at shallow depths.This work was funded with grants to J.S. by the Natural Sciences and Engineering Research Council of Canada and by the Fonds pour la formation de chercheurs et l’aide a` la recherche (Que´bec)

Quantum key distribution with higher-order alphabets using spatially-encoded qudits

We propose and demonstrate a quantum key distribution scheme in higher-order $d$-dimensional alphabets using spatial degrees of freedom of photons. Our implementation allows for the transmission of 4.56 bits per sifted photon, while providing improved security: an intercept-resend attack on all photons would induce an error rate of 0.47. Using our system, it should be possible to send more than a byte of information per sifted photon.Comment: 4 pages, 5 figures. Replaced with published versio

Vlasov equation and collisionless hydrodynamics adapted to curved spacetime

The modification of the Vlasov equation, in its standard form describing a charged particle distribution in the six-dimensional phase space, is derived explicitly within a formal Hamiltonian approach for arbitrarily curved spacetime. The equation accounts simultaneously for the Lorentz force and the effects of general relativity, with the latter appearing as the gravity force and an additional force due to the extrinsic curvature of spatial hypersurfaces. For an arbitrary spatial metric, the equations of collisionless hydrodynamics are also obtained in the usual three-vector form

Theoretical and numerical studies of wave-packet propagation in tokamak plasmas

Theoretical and numerical studies of wave-packet propagation are presented to analyze the time varying 2D mode structures of electrostatic fluctuations in tokamak plasmas, using general flux coordinates. Instead of solving the 2D wave equations directly, the solution of the initial value problem is used to obtain the 2D mode structure, following the propagation of wave-packets generated by a source and reconstructing the time varying field. As application, the 2D WKB method is applied to investigate the shaping effects (elongation and triangularity) of tokamak geometry on the lower hybrid wave propagation and absorbtion. Meanwhile, the Mode Structure Decomposition (MSD) method is used to handle the boundary conditions and simplify the 2D problem to two nested 1D problems. The MSD method is related to that discussed earlier by Zonca and Chen [Phys. Fluids B 5, 3668 (1993)], and reduces to the well-known "ballooning formalism" [J. W. Connor, R. J. Hastie, and J. B. Taylor, Phys. Rev. Lett. 40, 396 (1978)], when spatial scale separation applies. This method is used to investigate the time varying 2D electrostatic ITG mode structure with a mixed WKB-full-wave technique. The time varying field pattern is reconstructed and the time asymptotic structure of the wave-packet propagation gives the 2D eigenmode and the corresponding eigenvalue. As a general approach to investigate 2D mode structures in tokamak plasmas, our method also applies for electromagnetic waves with general source/sink terms, either by an internal/external antenna or nonlinear wave interaction with zonal structures.Comment: 24 pages, 14 figure

A Kinetic Alfven wave cascade subject to collisionless damping cannot reach electron scales in the solar wind at 1 AU

(Abridged) Turbulence in the solar wind is believed to generate an energy cascade that is supported primarily by Alfv\'en waves or Alfv\'enic fluctuations at MHD scales and by kinetic Alfv\'en waves (KAWs) at kinetic scales $k_\perp \rho_i\gtrsim 1$. Linear Landau damping of KAWs increases with increasing wavenumber and at some point the damping becomes so strong that the energy cascade is completely dissipated. A model of the energy cascade process that includes the effects of linear collisionless damping of KAWs and the associated compounding of this damping throughout the cascade process is used to determine the wavenumber where the energy cascade terminates. It is found that this wavenumber occurs approximately when $|\gamma/\omega|\simeq 0.25$, where $\omega(k)$ and $\gamma(k)$ are, respectively, the real frequency and damping rate of KAWs and the ratio $\gamma/\omega$ is evaluated in the limit as the propagation angle approaches 90 degrees relative to the direction of the mean magnetic field.Comment: Submitted to Ap