Emergence of Classical Orbits in Few-Cycle Above-Threshold Ionization

The time-dependent Schr\"odinger equation for atomic hydrogen in few-cycle laser pulses is solved numerically. Introducing a positive definite quantum distribution function in energy-position space, a straightforward comparison of the numerical ab initio results with classical orbit theory is facilitated. Integration over position space yields directly the photoelectron spectra so that the various pathways contributing to a certain energy in the photoelectron spectra can be established in an unprecedented direct and transparent way.Comment: 4 pages, 4 figures REVTeX (manuscript with higher resolution figures available at http://www.dieterbauer.de/publist.html

Implicit Solutions of PDE's

Further investigations of implicit solutions to non-linear partial differential equations are pursued. Of particular interest are the equations which are Lorentz invariant. The question of which differential equations of second order for a single unknown $\phi$ are solved by the imposition of an inhomogeneous quadratic relationship among the independent variables, whose coefficients are functions of $\phi$ is discussed, and it is shown that if the discriminant of the quadratic vanishes, then an implicit solution of the so-called Universal Field Equation is obtained. The relation to the general solution is discussed.Comment: 11 pages LaTeX2

Observation of explosive collisionless reconnection in 3D nonlinear gyrofluid simulations

The nonlinear dynamics of collisionless reconnecting modes is investigated, in the framework of a three-dimensional gyrofluid model. This is the relevant regime of high-temperature plasmas, where reconnection is made possible by electron inertia and has higher growth rates than resistive reconnection. The presence of a strong guide field is assumed, in a background slab model, with Dirichlet boundary conditions in the direction of nonuniformity. Values of ion sound gyro-radius and electron collisionless skin depth much smaller than the current layer width are considered. Strong acceleration of growth is found at the onset to nonlinearity, while at all times the energy functional is well conserved. Nonlinear growth rates more than one order of magnitude higher than linear growth rates are observed when entering into the small-$\Delta'$ regime

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

Arithmetic lattices and weak spectral geometry

This note is an expansion of three lectures given at the workshop "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces" held at Kyoto University in December of 2006 and will appear in the proceedings for this workshop.Comment: To appear in workshop proceedings for "Topology, Complex Analysis and Arithmetic of Hyperbolic Spaces". Comments welcom

Concept for improved vacuum pressure measuring device

To measure vacuum pressures in the range of 5 times 10 to the minus 7 to 5 times 10 to the minus 16, a semiconductor resistor composed of sintered zinc oxide is used. Through the effect of surface absorbed gases on the resistance of the semiconductor material, very low pressures are measured

Cusps of arithmetic orbifolds

This thesis investigates cusp cross-sections of arithmetic real, complex, and quaternionic hyperbolic $n$--orbifolds. We give a smooth classification of these submanifolds and analyze their induced geometry. One of the primary tools is a new subgroup separability result for general arithmetic lattices.Comment: 76 pages; Ph.D. thesi