Constrained Transport Algorithms for Numerical Relativity. I. Development of a Finite Difference Scheme

A scheme is presented for accurately propagating the gravitational field constraints in finite difference implementations of numerical relativity. The method is based on similar techniques used in astrophysical magnetohydrodynamics and engineering electromagnetics, and has properties of a finite differential calculus on a four-dimensional manifold. It is motivated by the arguments that 1) an evolutionary scheme that naturally satisfies the Bianchi identities will propagate the constraints, and 2) methods in which temporal and spatial derivatives commute will satisfy the Bianchi identities implicitly. The proposed algorithm exactly propagates the constraints in a local Riemann normal coordinate system; {\it i.e.}, all terms in the Bianchi identities (which all vary as $\partial^3 g$) cancel to machine roundoff accuracy at each time step. In a general coordinate basis, these terms, and those that vary as $\partial g\partial^2 g$, also can be made to cancel, but differences of connection terms, proportional to $(\partial g)^3$, will remain, resulting in a net truncation error. Detailed and complex numerical experiments with four-dimensional staggered grids will be needed to completely examine the stability and convergence properties of this method. If such techniques are successful for finite difference implementations of numerical relativity, other implementations, such as finite element (and eventually pseudo-spectral) techniques, might benefit from schemes that use four-dimensional grids and that have temporal and spatial derivatives that commute.Comment: 27 pages, 5 figure

Development of high-efficiency solar cells on silicon web

Achievement of higher efficiency cells by directing efforts toward identifying carrier loss mechanisms; design of cell structures; and development of processing techniques are described. Use of techniques such as deep-level transient spectroscopy (DLTS), laser-beam-induced current (LBIC), and transmission electron microscopy (TEM) indicated that dislocations in web material rather than twin planes were primarily responsible for limiting diffusion lengths in the web. Lifetimes and cell efficiencies can be improved from 19 to 120 microns, and 8 to 10.3% (no AR), respectively, by implanting hydrogen at 1500 eV and a beam current density of 2.0 mA/sq cm. Some of the processing improvements included use of a double-layer AR coating (ZnS and MgF2) and an addition of an aluminum back surface reflectors. Cells of more than 16% efficiency were achieved

Laser-assisted solar cell metallization processing

The status of the laser-assisted solar cell metallization processing is described. Metallo-organic silver films were spun-on by argon ion laser beam pyrolysis. The metallo-organic decomposition (MOD) film was spun-on an evaporated Ti/Pd film to produce tood adhesion. In a maskless process, the argon ion laser writes the contact pattern. The film is then built up to obtain the required conductivity using conventional silverplating process. The Ti/Pd film in the field is chemically etched using the plated silver film as the mask. The width of the contact pattern is determined by the power of the laser. Widths as thin as 20 microns were obtained using 0.66 W of laser power. Cells fabricated with the 50 micron line widths of 4 ohm-cm floating zone (Fz) silicon-produced efficiencies of 16.6% (no passivation) which were equivalent to the best cells using conventional metallization/lithography and no passivation

Poynting Flux Dominated Jets in Decreasing Density Atmospheres. I. The Non-relativistic Current-driven Kink Instability and the Formation of "Wiggled" Structures

Non-relativistic three-dimensional magnetohydrodynamical (MHD) simulations of Poynting flux dominated (PFD) jets are presented. Our study focuses on the propagation of strongly magnetized hypersonic, but sub-Alfv\'enic ($C^{2}_{\rm s} \ll V^{2}_{\rm jet} < V^{2}_{\rm A}$) flow and on the subsequent development of a current-driven (CD) kink instability. This instability may be responsible for the ``wiggled'' structures seen in sub-parsec scale (VLBI) jets. In the present paper, we investigate the nonlinear behavior of PFD jets in a variety of external ambient magnetized gas distributions, including those with density, pressure, and temperature gradients. Our numerical results show that the jets can develop CD distortions in the trans-Alfv\'enic flow case, even when the flow itself is still strongly magnetically dominated. An internal non-axisymmetric body mode grows on time scales of order of the Alfv\'en crossing time and distorts the structure and magnetic configuration of the jet. The kink ($m=1$) mode of the CD instability, driven by the radial component of the Lorentz force, grows faster than other higher order modes ($m>1$). In the jet frame the mode grows locally and expands radially at each axial position where the jet is unstable: the instability, therefore, does not propagate as a wave along the jet length. A naturally-occurring, external helically magnetized wind, which is (quasi-) axially current-free, surrounds the well-collimated current-carrying jet and reduces velocity shear between the jet and external medium. This stabilizes the growth of MHD Kelvin-Helmholtz surface modes in the inner jet flow.Comment: 70 pages, 23 figures, 3 tables, Appendix, submitted to Ap

3-D Simulations of MHD Jets - The Stability Problem

Non-relativistic three-dimensional magnetohydrodynamic simulations of Poynting-flux-dominated (PFD) jets are presented. Our study focuses on the propagation of strongly magnetized hypersonic but sub-Alfv\'enic flow ($C_{\rm s}^2 << V_{\rm jet}^2 < V_{\rm A}^2$) and the development of a current-driven (CD) kink instability. This instability may be responsible for the "wiggled" structures seen in VLBI-scale AGN jets. In the present paper we investigate the nonlinear behavior of PFD jets in a variety of external ambient magnetized gas distributions, including those with density, pressure, and temperature gradients. Our numerical results show that PFD jets can develop kink distortions in the trans-Alfv\'enic flow case, even when the flow itself is still strongly magnetically dominated. In the nonlinear development of the instability, a non-axisymmetric mode grows on time scales of order the Alfv\'en crossing time (in the jet frame) and proceeds to disrupt the kinematic and magnetic structure of the jet. Because of a large scale poloidal magnetic field in the ambient medium, the growth of surface modes ({\it i.e.}, MHD Kelvin-Helmholtz instabilities) is suppressed. The CD kink mode ($m = 1$) grows faster than the other higher order modes ($m > 1$), driven in large part by the radial component of the Lorentz force.Comment: 6 pages, 3 figures; to appear in Plasmas in the Laboratory and in the Universe, Como, Italy, 16-19 Sep, 200