Beyond the Child–Langmuir law: A review of recent results on multidimensional space-charge-limited flow

Space-charge-limited (SCL) flows in diodes have been an area of active research since the pioneering work of Child and Langmuir in the early part of the last century. Indeed, the scaling of current density with the voltage to the 3/2’s power is one of the best-known limits in the fields of non-neutral plasma physics, accelerator physics, sheath physics, vacuum electronics, and high power microwaves. In the past five years, there has been renewed interest in the physics and characteristics of SCL emission in physically realizable configurations. This research has focused on characterizing the current and current density enhancement possible from two- and three-dimensional geometries, such as field-emitting arrays. In 1996, computational efforts led to the development of a scaling law that described the increased current drawn due to two-dimensional effects. Recently, this scaling has been analytically derived from first principles. In parallel efforts, computational work has characterized the edge enhancement of the current density, leading to a better understanding of the physics of explosive emission cathodes. In this paper, the analytic and computational extensions to the one-dimensional Child–Langmuir law will be reviewed, the accuracy of SCL emission algorithms will be assessed, and the experimental implications of multidimensional SCL flows will be discussed. © 2002 American Institute of Physics.Peer Reviewedhttp://deepblue.lib.umich.edu/bitstream/2027.42/69652/2/PHPAEN-9-5-2371-1.pd

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]

The international universities walking project:Development of a framework for workplace intervention using the Delphi technique

Background: This paper aimed to use the Delphi technique to develop a consensus framework for a multinational, workplace walking intervention. Methods: Ideas were gathered and ranked from eight recognized and emerging experts in the fields of physical activity and health, from universities in Australia, Canada, England, the Netherlands, Northern Ireland, and Spain. Members of the panel were asked to consider the key characteristics of a successful campus walking intervention. Consensus was reached by an inductive, content analytic approach, conducted through an anonymous, three-round, e-mail process. Results: The resulting framework consisted of three interlinking themes defined as "design, implementation, and evaluation." Top-ranked subitems in these themes included the need to generate research capacity (design), to respond to group needs through different walking approaches (implementation), and to undertake physical activity assessment (evaluation). Themes were set within an underpinning domain, referred to as the "institution" and sites are currently engaging with subitems in this domain, to provide sustainable interventions that reflect the practicalities of local contexts and needs. Conclusions: Findings provide a unique framework for designing, implementing, and evaluating walking projects in universities and highlight the value of adopting the Delphi technique for planning international, multisite health initiatives.</p