The attachment length in orificed hollow cathodes

2021 ◽  
Author(s):  
Christopher Wordingham ◽  
Pierre-Yves Taunay ◽  
Edgar Choueiri
Keyword(s):  
Electron Temperature ◽  
Plasma Density ◽  
Hollow Cathode ◽  
Computational Models ◽  
Closed Form Solution ◽  
Form Solution ◽  
Decay Length ◽  
Plasma Density Profile ◽  
Wide Range ◽  
Approximate Boundary Condition

Abstract A first-principles approach to obtain the attachment length within a hollow cathode with a constrictive orifice, and its scaling with internal cathode pressure, is developed. This parameter, defined herein as the plasma density decay length scale upstream of (away from) the cathode orifice, is critical because it controls the utilization of the hollow cathode insert and influences cathode life. A two-dimensional framework is developed from the ambipolar diffusion equation for the insert-region plasma. A closed-form solution for the plasma density is obtained using standard partial differential equation techniques by applying an approximate boundary condition at the cathode orifice plane. This approach also yields the attachment length and electron temperature without reliance on measured plasma property data or complex computational models. The predicted plasma density profile is validated against measurements from the NSTAR discharge cathode, and calculated electron temperatures and attachment lengths agree with published values. Nondimensionalization of the governing equations reveals that the solution depends almost exclusively on the neutral pressure-diameter product in the insert plasma region. Evaluation of analytical results over a wide range of input parameters yields scaling relations for the variation of the attachment length and electron temperature with the pressure-diameter product. For the range of orifice-to-insert diameter ratio studied, the influence of orifice size is shown to be small except through its effect on insert pressure, and the attachment length is shown to be proportional to the insert inner radius, suggesting high-pressure cathodes should be constructed with larger-diameter inserts.

scholarly journals A Stochastic Analysis of Hard Disk Drives

2011 ◽  
Vol 2011 ◽  
pp. 1-21 ◽  
Author(s):  
Field Cady ◽  
Yi Zhuang ◽  
Mor Harchol-Balter
Keyword(s):  
Stochastic Analysis ◽  
Hard Disk Drives ◽  
Closed Form Solution ◽  
Hard Disk ◽  
Form Solution ◽  
Access Time ◽  
Analytical Technique ◽  
Wide Range ◽  
Average Access Time ◽  
Memory Request

We provide a stochastic analysis of hard disk performance, including a closed form solution for the average access time of a memory request. The model we use covers a wide range of types and applications of disks, and in particular it captures modern innovations like zone bit recording. The derivation is based on an analytical technique we call “shuffling”, which greatly simplifies the analysis relative to previous work and provides a simple, easy-to-use formula for the average access time. Our analysis can predict performance of single disks for a wide range of disk types and workloads. Furthermore, it can predict the performance benefits of several optimizations, including short stroking and mirroring, which are common in disk arrays.

Analysis and Synthesis of Dynamic Response of a Flexibly Coupled Rotor Assembly

1997 ◽  
Author(s):  
Valdas Chaika
Keyword(s):  
Equations Of Motion ◽  
Excitation Frequency ◽  
Closed Form Solution ◽  
Form Solution ◽  
System Response ◽  
Wide Range ◽  
Analysis And Synthesis ◽  
Coupling Parameters ◽  
Elastic Couplings ◽  
Rotor Assembly

Abstract Torsional vibration of two flexibly coupled reciprocating machines is investigated. The rotors of the machines are connected by elastic couplings of several types. The system is excited by a harmonic torque. The excitation frequency is proportional to the rotational speed which varies within a wide range. The motion of the system is described by nonlinear ordinary differential equations. These are linearized for the specific case of the rotor assembly design. Applying impedance functions, a closed-form solution of the equations of motion is derived. Three different cases of the system response are analyzed in the frequency domain. The passive vibration control of the rotor assembly using the centrifugal coupling is investigated. An analytical synthesis technique of the coupling parameters is devised.

scholarly journals Biophysical comparison of ATP synthesis mechanisms shows a kinetic advantage for the rotary process

2016 ◽  
Vol 113 (40) ◽  
pp. 11220-11225 ◽  
Author(s):  
Ramu Anandakrishnan ◽  
Zining Zhang ◽  
Rory Donovan-Maiye ◽  
Daniel M. Zuckerman
Keyword(s):  
Closed Form Solution ◽  
Atp Synthesis ◽  
Form Solution ◽  
Energy Conditions ◽  
Rotary Machine ◽  
Wide Range ◽  
Steady State Rate ◽  
Systematic Enumeration ◽  
Kinetic Effects ◽  
Chemical Cycle

The ATP synthase (F-ATPase) is a highly complex rotary machine that synthesizes ATP, powered by a proton electrochemical gradient. Why did evolution select such an elaborate mechanism over arguably simpler alternating-access processes that can be reversed to perform ATP synthesis? We studied a systematic enumeration of alternative mechanisms, using numerical and theoretical means. When the alternative models are optimized subject to fundamental thermodynamic constraints, they fail to match the kinetic ability of the rotary mechanism over a wide range of conditions, particularly under low-energy conditions. We used a physically interpretable, closed-form solution for the steady-state rate for an arbitrary chemical cycle, which clarifies kinetic effects of complex free-energy landscapes. Our analysis also yields insights into the debated “kinetic equivalence” of ATP synthesis driven by transmembrane pH and potential difference. Overall, our study suggests that the complexity of the F-ATPase may have resulted from positive selection for its kinetic advantage.

Estimation of Stress Intensity Factor for Circumferential Through-Wall Cracked Elbows Subjected to In-Plane Bending

2015 ◽  
Author(s):  
Han-Bum Surh ◽  
Jong Wook Kim ◽  
Min Kyu Kim ◽  
Min-Gu Won ◽  
Moon Ki Kim ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Nuclear Power ◽  
Closed Form Solution ◽  
Form Solution ◽  
Accurate Estimation ◽  
Wide Range ◽  
Plane Bending ◽  
Geometric Variables

The stress intensity factor (SIF) is the major fracture mechanics parameter in LEFM concept. Since the SIF can be used for not only calculation of J-integral based on the GE/EPRI and reference stress method but also evaluation of fatigue crack growth, an accurate estimation of the SIF is an important issue for the piping in nuclear power plant. Recently, there is a need to develop the SIF solution which can cover wide geometric variables since there are on-going efforts that are developing next generation reactors in Korea, which is designed to thin-walled structures. For the through-wall cracked straight pipes, many researchers have proposed the SIF solutions which can cover wide range of wall thickness. However, since only limited solutions have been proposed yet for the through-wall cracked elbows, a research related to the SIF estimation for the elbows with wide geometric variables should be performed. In this study, the extended SIF solution for circumferential through-wall cracked elbows subjected to in-plane bending is proposed as the tabulated form through the finite element (FE) analyses. Wide elbow geometries are selected to range between 5 and 50 of Rm/t and range between 2∼20 of Rb/Rm. The existing solutions are then reviewed by comparing with the FE results. Furthermore, effects of geometric variables on the SIF are addressed through systematic investigation of FE based SIF results. These investigated results are expected to contribute to the development of closed form solution for the circumferential through-wall cracked elbows subjected to in-plane bending.

Plasma parameters of RF capacitively coupled discharge: comparative study between a plane cathode and a large hole dimensions multi-hollow cathode

2019 ◽  
Vol 85 (1) ◽  
pp. 10801 ◽  
Author(s):  
Samira Djerourou ◽  
Mourad Djebli ◽  
Mohamed Ouchabane
Keyword(s):  
Comparative Study ◽  
Electron Temperature ◽  
Hollow Cathode ◽  
Gas Pressure ◽  
Incident Power ◽  
Plasma Parameters ◽  
Large Hole ◽  
Capacitively Coupled ◽  
Self Bias ◽  
Wide Range

This work deals with a comparative study of plasma discharge generated by two geometrical configurations of cathodes through an investigation of their plasma parameters. A large hole diameter and depth (D = 40 mm, W = 50 mm) multi-hollow (MH) cathode compared with a plane (PL) cathode are presented for argon capacitively coupled radiofrequency discharge. The electrical characteristics of MH and PL cathodes have been measured in terms of the self-bias voltage (Vdc) while the Langmuir probe was used to measure electron density (ne) and electron temperature (Te) for a wide range of gas pressure (60–400 mTorr) and incident power (50–300 W). It is found that the hollow cathode effect (HCE) is optimum at 60 mTorr with 220 mTorr as a critical gas pressure for which a transition from HCE to insufficient HCE is seen. The electron temperature varies from 3 to 5 eV in the case of MH and PL cathodes with respect to incident power and gas pressure.

NEUROFUZZY MODELING OF NATURAL FREQUENCIES OF CYLINDRICAL SHELLS APPLIED TO EVOLUTIONARY BASED OPTIMAL DESIGN OF SR MOTORS

2006 ◽  
Vol 03 (03) ◽  
pp. 263-277 ◽  
Author(s):  
HOSSEIN ROUHANI ◽  
MANSOUR NIKKHAH BAHRAMI ◽  
BABAK NADJAR ARAABI ◽  
CARO LUCAS
Keyword(s):  
Finite Element ◽  
Optimal Design ◽  
Closed Form ◽  
Natural Frequencies ◽  
Cylindrical Shells ◽  
Closed Form Solution ◽  
Form Solution ◽  
Design Problems ◽  
Special Cases ◽  
Wide Range

A thorough analysis of cylindrical shells' dynamical behavior is essential in many different industrial design problems, and particularly in electric motor design. Shell vibration equations form a set of partial differential equations of order eight, where their closed form solution is only known for few special cases with a few known boundary conditions along with many not necessarily realistic assumptions. On the other hand, finite element based numerical solutions does not yield a lumped model that can be regarded as a general solution for natural frequencies of cylindrical shells. In this paper, a neurofuzzy model for natural frequencies of cylindrical shells is developed. At first, natural frequencies are calculated for a wide range of cylindrical shells' dimensions, using either closed form solution or finite element method. Gathered data is exploited for training of a Locally Linear Neurofuzzy Network, which yields a general model for calculation of natural frequencies of cylindrical shells. While the developed neurofuzzy model may be used in different design problems that deals with cylindrical shells, as a case study, the proposed model along with an evolutionary algorithm are utilized in the optimal design of a Switched Reluctance motor.

Empirical Equations for Planing Hull Bottom Pressures

2014 ◽  
Vol 58 (04) ◽  
pp. 185-200 ◽  
Author(s):  
M. G. Morabito
Keyword(s):  
Closed Form Solution ◽  
Empirical Method ◽  
Form Solution ◽  
Empirical Equations ◽  
Planing Craft ◽  
Wide Range ◽  
Hydrodynamic Effects ◽  
The Impact ◽  
Interaction Problem ◽  
Impact Problem

Recently there has been increasing interest in the fluid-structure interaction problem of planning hull bottom structure during slamming events. Significant work has been done in estimating the bottom pressures that occur during a slam and incorporating this into structural models of planing craft. In this article, empirical equations for the pressure distribution on prismatic planing hulls are developed, including both hydrostatic and hydrodynamic effects, deadrise variation, trim, and wetted length. The empirical method is based on relevant experimental measurements of planing hull bottom pressures that have been made over an 80-year period. This analysis may readily be extended to the impact problem by substitution of an equivalent planing velocity, which is discussed in the article. The end result is a closed form solution for bottom pressures on prismatic planing craft that can be rapidly calculated using a simple spreadsheet. The method is applicable for deadrise angles from 0 to 40, trim angles up to 30, and wetted lengths up to five beams. This wide range of parameters is significantly larger than most current models. The empirical method is modular, allowing for substitution of more accurate formulae as more data become available in the future.

scholarly journals First results from the Sweeping Langmuir Probe (SLP) instrument on board PICASSO

2021 ◽  
Author(s):  
Sylvain Ranvier ◽  
Johan De Keyser ◽  
Jean-Pierre Lebreton
Keyword(s):  
Electron Temperature ◽  
Spatial Resolution ◽  
Plasma Density ◽  
Langmuir Probe ◽  
Floating Potential ◽  
Polar Caps ◽  
Spacecraft Potential ◽  
Wide Range ◽  
First Results ◽  
Fixed Bias

<p>The Sweeping Langmuir Probe (SLP) instrument on board the Pico-Satellite for Atmospheric and Space Science Observations (PICASSO) has been developed at the Royal Belgian Institute for Space Aeronomy.  PICASSO, an ESA in-orbit demonstrator launched in September 2020, is a triple unit CubeSat orbiting at about 540 km altitude with 97 degrees inclination. The SLP instrument includes four independent cylindrical probes that are used to measure the plasma density and electron temperature as well as the floating potential of the spacecraft. Along the orbit of PICASSO the plasma density is expected to fluctuate over a wide range, from about 1e8/m<sup>3</sup> at high latitude up to more than 1e12/m<sup>3</sup> at low/mid latitude. SLP can measure plasma density from 1e8/m<sup>3</sup> to 1e13/m<sup>3</sup>. The electron temperature is expected to lie between approximately 1000 K and 10.000 K. Given the high inclination of the orbit, SLP will allow a global monitoring of the ionosphere. Using the traditional sweeping mode, the maximum spatial resolution is of the order of a few hundred meters for the plasma density, electron temperature and spacecraft potential. With the fixed-bias mode, the electron density can be measured with a spatial resolution of about 1.5 m. The main goals are to study the ionosphere-plasmasphere coupling, the subauroral ionosphere and corresponding magnetospheric features together with auroral structures and polar caps, by combining SLP data with other complementary data sources (space- or ground-based instruments). The first results from SLP will be presented.</p>

Evaluation of vertical effective stress and pile lateral capacities considering scour-hole dimensions

2019 ◽  
Vol 56 (1) ◽  
pp. 135-143 ◽  
Author(s):  
Cheng Lin ◽  
Randall Wu
Keyword(s):  
Effective Stress ◽  
Slope Angle ◽  
Closed Form Solution ◽  
Form Solution ◽  
Lateral Capacity ◽  
Wide Range ◽  
Scour Hole ◽  
Vertical Effective Stress ◽  
Scour Hole Dimensions ◽  
Hole Dimensions

Determination of vertical effective stress along piles is an essential part of calculation of both pile axial and lateral capacities under scour conditions. However, the current design manuals including those from the US Federal Highway Administration (FHWA) and American Petroleum Institute (API) recommend different methods for calculating vertical effective stress. Moreover, they are effective only for restricted scour-hole dimensions. This study presents an improved closed-form solution that allows estimation of the vertical effective stress for a wide range of scour-hole dimensions including scour depth, width, and slope angle. Using the improved analytical solution for stress, API p–y curves for sand were modified to compute pile lateral capacity at different scour-hole conditions. Based on a series of parametric analyses for laterally loaded piles in sand, errors of calculation using the existing methods were quantified and a simplified method was proposed for practical applications. Effects of different scour-hole dimensions on both vertical effective stress and pile lateral capacity were also discussed.

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