Overcoming the Child-Langmuir law via the magnetic mirror effect

The maximum current in a vacuum tube prescribed by the classical Child-Langmuir law can be overcome, when the space-charge effect of the induced potential is mitigated by the mirror effect in a spatially varying magnetic field. The current could exceed the Child-Langmuir value by as much as a few factors. The regime of practical interest is examined

Space Charge Limited 2-d Electron Flow between Two Flat Electrodes in a Strong Magnetic Field

An approximate analytic solution is constructed for the 2-d space charge limited emission by a cathode surrounded by non emitting conducting ledges of width Lambda. An essentially exact solution (via conformal mapping) of the electrostatic problem in vacuum is matched to the solution of a linearized problem in the space charge region whose boundaries are sharp due to the presence of a strong magnetic field. The current density growth in a narrow interval near the edges of the cathode depends strongly on Lambda. We obtain an empirical formula for the total current as a function of Lambda which extends to more general cathode geometries.Comment: 4 pages, LaTex, e-mail addresses: [email protected], [email protected]

Modes of Growth in Dynamic Systems

Regardless of a system's complexity or scale, its growth can be considered to be a spontaneous thermodynamic response to a local convergence of down-gradient material flows. Here it is shown how growth can be constrained to a few distinct modes that depend on the availability of material and energetic resources. These modes include a law of diminishing returns, logistic behavior and, if resources are expanding very rapidly, super-exponential growth. For a case where a system has a resolved sink as well as a source, growth and decay can be characterized in terms of a slightly modified form of the predator-prey equations commonly employed in ecology, where the perturbation formulation of these equations is equivalent to a damped simple harmonic oscillator. Thus, the framework presented here suggests a common theoretical under-pinning for emergent behaviors in the physical and life sciences. Specific examples are described for phenomena as seemingly dissimilar as the development of rain and the evolution of fish stocks.Comment: 16 pages, 6 figures, including appendi

Mantle Source Variations beneath the Eastern Lau Spreading Center and the Nature of Subduction Components in the Lau Basin-Tonga Arc System

New high-density sampling of the Eastern Lau Spreading Center provides constraints on the processes that affect the mantle wedge beneath a back-arc environment, including the effect of the subduction input on basalt petrogenesis and the change in subduction input with distance from the Tonga arc. We obtained trace element and Pb-Sr-Nd isotopic compositions of 64 samples distributed between 20.2 degree S and 22.3 degree S with an average spacing of ~3.6 km. The trace element and isotope variations do not vary simply with distance from the arc and reflect variations in the mantle wedge composition and the presence of multiple components in the subduction input. The mantle wedge composition varies form north to south, owing to the southward migration of Indian-like mantle, progressively replacing the initially Pacific-like mantle wedge. The mantle wedge compositions also require an enriched mid-ocean ridge basalt-like trace element enrichment that has little effect on isotope ratios, suggesting recent low-degree melt enrichment events. The composition of the subduction input added to the mantle wedge is geographically variable and mirrors the changes observed in the Tonga arc island lavas. The combination of the back-arc and arc data allows identification of several components contributing to the subduction input. These are a fluid derived from the altered oceanic crust with a possible sedimentary contribution, a pelagic sediment partial melt, and, in the southern Lau basin, a volcaniclastic sediment partial melt. While on a regional scale, there is a rough decrease in subduction influence with the distance from the arc, on smaller scales, the distribution of the subduction input reflects different mechanisms of the addition of the subduction input to a variable mantle wedge.Earth and Planetary Science

Volcanic glasses at the Izu arc volcanic front : new perspectives on fluid and sediment melt recycling in subduction zones

Author Posting. © American Geophysical Union, 2004. This article is posted here by permission of American Geophysical Union for personal use, not for redistribution. The definitive version was published in Geochemistry Geophysics Geosystems 5 (2004): Q01007, doi:10.1029/2002GC000408.Volcanic glasses contained in distal fallout tephras from the Izu arc volcanic front (Izu VF) provide unique perspectives on general problems of arc volcanism. Unlike cogenetic lavas, these glasses are liquid compositions where element concentrations as well as ratios have significance. Isotopic evidence and previous work show that there is no sediment melt contribution to the sources of the Izu VF tephras, and hence their trace element characteristics permit determination of the trace element contents of slab fluids. The slab fluid is a composite of metasediment (∼5% of total fluid) and metabasalt (∼95%) component fluids, and carries large ion lithophile elements (LILE) with high LILE/Th and LILE/U, and low Th and U relative to source. Except for Sr and K, the metabasalt fluid is much less enriched than the metasediment fluid, but its large relative proportions make it an important carrier of many trace elements. The metabasalt fluid has the characteristics of the arc trace element signature, obviating the need for ubiquitous involvement of sediment in arc magma genesis. The fluid component in the tephras is remarkably constant in composition over fifteen million years, and hence appears to be a robust composition that may be applicable to other convergent margins. Assuming that the metabasalt fluid is a common component, and that distribution coefficients between sediment and fluid are similar from one arc to another, composite fluid compositions can be estimated for other arcs. Differences from this composition then would likely result from a sediment melt component. Comparison to arcs with sediment melt components in their source (Marianas, eastern Aleutians) shows that partial sediment melts may be so enriched, that they can completely mask the signature of the comingling slab fluids. Hence sediment melts can easily dominate the trace element and isotopic signature of many convergent margins. Since sediment melts inherit the LILE/LILE ratios of the trench sediment, Earth's surface processes must eventually influence the compositional diversity of arcs.This study was funded by the “Deutsche Forschungsgemeinschaft” (grants Str 441/3 and 441/4). The Northeast National Ion Microprobe Facility at WHOI was supported by grants EAR-9628749 and EAR-990440 from the National Science Foundation

Transport across nanogaps using semiclassically consistent boundary conditions

Charge particle transport across nanogaps is studied theoretically within the Schrodinger-Poisson mean field framework and the existence of limiting current investigated. It is shown that the choice of a first order WKB wavefunction as the transmitted wave leads to self consistent boundary conditions and gives results that are significantly different in the non-classical regime from those obtained using a plane transmitted wave. At zero injection energies, the quantum limiting current density, J_c, is found to obey the local scaling law J_c ~ (V_g)^alpha/(D)^{5-2alpha} with the gap separation D and voltage V_g. The exponent alpha > 1.1 with alpha --> 3/2 in the classical regime of small de Broglie wavelengths. These results are consistent with recent experiments using nanogaps most of which are found to be in a parameter regime where classical space charge limited scaling holds away from the emission dominated regime.Comment: 4 pages, 4 ps figure

Dynamic Scaling of an Adsorption-Diffusion Process on Fractals

A dynamic scaling of a diffusion process involving the Langmuir type adsorption is studied. We find dynamic scaling functions in one and two dimensions and compare them with direct numerical simulations, and we further study the dynamic scaling law on fractal surfaces. The adsorption-diffusion process obeys the fracton dynamics on the fractal surfaces.Comment: 9 pages, 7 figure

Diffusion-limited reactions and mortal random walkers in confined geometries

Motivated by the diffusion-reaction kinetics on interstellar dust grains, we study a first-passage problem of mortal random walkers in a confined two-dimensional geometry. We provide an exact expression for the encounter probability of two walkers, which is evaluated in limiting cases and checked against extensive kinetic Monte Carlo simulations. We analyze the continuum limit which is approached very slowly, with corrections that vanish logarithmically with the lattice size. We then examine the influence of the shape of the lattice on the first-passage probability, where we focus on the aspect ratio dependence: Distorting the lattice always reduces the encounter probability of two walkers and can exhibit a crossover to the behavior of a genuinely one-dimensional random walk. The nature of this transition is also explained qualitatively.Comment: 18 pages, 16 figure

Geodynamics and Rate of Volcanism on Massive Earth-like Planets

We provide estimates of volcanism versus time for planets with Earth-like composition and masses from 0.25 to 25 times Earth, as a step toward predicting atmospheric mass on extrasolar rocky planets. Volcanism requires melting of the silicate mantle. We use a thermal evolution model, calibrated against Earth, in combination with standard melting models, to explore the dependence of convection-driven decompression mantle melting on planet mass. Here we show that (1) volcanism is likely to proceed on massive planets with plate tectonics over the main-sequence lifetime of the parent star; (2) crustal thickness (and melting rate normalized to planet mass) is weakly dependent on planet mass; (3) stagnant lid planets live fast (they have higher rates of melting than their plate tectonic counterparts early in their thermal evolution) but die young (melting shuts down after a few Gyr); (4) plate tectonics may not operate on high mass planets because of the production of buoyant crust which is difficult to subduct; and (5) melting is necessary but insufficient for efficient volcanic degassing - volatiles partition into the earliest, deepest melts, which may be denser than the residue and sink to the base of the mantle on young, massive planets. Magma must also crystallize at or near the surface, and the pressure of overlying volatiles must be fairly low, if volatiles are to reach the surface. If volcanism is detected in the Tau Ceti system, and tidal forcing can be shown to be weak, this would be evidence for plate tectonics.Comment: Revised version, accepted by Astrophysical Journa

Development of a thermal ionizer as ion catcher

An effective ion catcher is an important part of a radioactive beam facility that is based on in-flight production. The catcher stops fast radioactive products and emits them as singly charged slow ions. Current ion catchers are based on stopping in He and H$_2$ gas. However, with increasing intensity of the secondary beam the amount of ion-electron pairs created eventually prevents the electromagnetic extraction of the radioactive ions from the gas cell. In contrast, such limitations are not present in thermal ionizers used with the ISOL production technique. Therefore, at least for alkaline and alkaline earth elements, a thermal ionizer should then be preferred. An important use of the TRI$\mu$P facility will be for precision measurements using atom traps. Atom trapping is particularly possible for alkaline and alkaline earth isotopes. The facility can produce up to 10$^9$ s$^{-1}$ of various Na isotopes with the in-flight method. Therefore, we have built and tested a thermal ionizer. An overview of the operation, design, construction, and commissioning of the thermal ionizer for TRI$\mu$P will be presented along with first results for $^{20}$Na and $^{21}$Na.Comment: 10 pages, 4 figures, XVth International Conference on Electromagnetic Isotope Separators and Techniques Related to their Applications (EMIS 2007