scholarly journals Electron shock waves moving into an ionized medium

1995 ◽  
Vol 13 (3) ◽  
pp. 377-382
Author(s):  
Mostafa Hemmati
Keyword(s):  
Shock Waves ◽  
Electric Field ◽  
Boundary Conditions ◽  
Transition Region ◽  
Fluid Model ◽  
Class Ii ◽  
Poisson’S Equation ◽  
Electron Velocity ◽  
Poisson's Equation ◽  
Dynamical Transition

The propagation of electron driven shock waves has been investigated by employing a one-dimensional, three-component fluid model. In the fluid model, the basic set of equations consists of equations of conservation of mass, momentum, and energy, plus Poisson's equation. The wave is assumed to be a shock front followed by a dynamical transition region. Following Fowler's (1976) categorization of breakdown waves, the waves propagating into a preionized medium will be referred to as Class II Waves. To describe the breakdown waves, Shelton and Fowler (1968) used the terms proforce and antiforce waves, depending on whether the applied electric field force on electrons was with or against the direction of wave propagation. Breakdown waves, i.e., return strokes of lightning flashes, therefore, will be referred to as Antiforce Class II waves. The shock boundary conditions and Poisson's equation for Antiforce Class II waves are different from those for Antiforce Waves. The use of a newly derived set of boundary conditions and Poisson's equation for Antiforce Class II waves allows for a successful integration of the set of fluid equations through the dynamical transition region. The wave structure, i.e., electric field, electron concentration, electron temperature, and electron velocity, are very sensitive to the ion concentration ahead of the wave.

Electric field distribution and voltage breakdown modeling for any PN junction

2016 ◽  
Vol 35 (1) ◽  
pp. 137-156 ◽  
Author(s):  
N. Rouger
Keyword(s):  
Numerical Methods ◽  
Electric Field ◽  
Field Distribution ◽  
Electric Field Distribution ◽  
Poisson’S Equation ◽  
Doping Profile ◽  
Distribution Analysis ◽  
Poisson's Equation ◽  
Content Type ◽  
Pn Junction

Purpose – Scientists and engineers have been solving Poisson’s equation in PN junctions following two approaches: analytical solving or numerical methods. Although several efforts have been accomplished to offer accurate and fast analyses of the electric field distribution as a function of voltage bias and doping profiles, so far none achieved an analytic or semi-analytic solution to describe neither a double diffused PN junction nor a general case for any doping profile. The paper aims to discuss these issues. Design/methodology/approach – In this work, a double Gaussian doping distribution is first considered. However, such a doping profile leads to an implicit problem where Poisson’s equation cannot be solved analytically. A method is introduced and successfully applied, and compared to a finite element analysis. The approach is then generalized, where any doping profile can be considered. 2D and 3D extensions are also presented, when symmetries occur for the doping profile. Findings – These results and the approach here presented offer an efficient and accurate alternative to numerical methods for the modeling and simulation of mathematical equations arising in physics of semiconductor devices. Research limitations/implications – A general 3D extension in the case where no symmetry exists can be considered for further developments. Practical implications – The paper strongly simplify and ease the optimization and design of any PN junction. Originality/value – This paper provides a novel method for electric field distribution analysis.

Existence of Solutions to Poisson's Equation

2008 ◽  
Vol 51 (2) ◽  
pp. 229-235
Author(s):  
Mary Hanley
Keyword(s):  
Boundary Conditions ◽  
Poisson Equation ◽  
Existence Of Solutions ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
The Poisson Equation ◽  
Topological Condition ◽  
Necessary And Sufficient

AbstractLet Ω be a domain in ℝn (n ≥ 2). We find a necessary and sufficient topological condition on Ω such that, for anymeasure μ on ℝn, there is a function u with specified boundary conditions that satisfies the Poisson equation Δu = μ on Δ in the sense of distributions.

scholarly journals Efficient and accurate solver of the three-dimensional screened and unscreened Poisson's equation with generic boundary conditions

2012 ◽  
Vol 137 (13) ◽  
pp. 134108 ◽  
Author(s):  
Alessandro Cerioni ◽  
Luigi Genovese ◽  
Alessandro Mirone ◽  
Vicente Armando Sole
Keyword(s):  
Boundary Conditions ◽  
Three Dimensional ◽  
Poisson’S Equation ◽  
Poisson's Equation ◽  
Generic Boundary

Generalized theory of the stabifity of shock waves in magnetogasdynamics

1971 ◽  
Vol 6 (3) ◽  
pp. 615-627 ◽  
Author(s):  
L. C. Woods
Keyword(s):  
Shock Waves ◽  
Electric Field ◽  
Boundary Conditions ◽  
Wave Interaction ◽  
Shock Structure ◽  
Interaction Theory ◽  
Single Treatment ◽  
Special Cases ◽  
The Stability ◽  
Incident Waves

Stability of MGD shock waves can be investigated either by disturbing the shock discontinuity by incident waves and then considering whether the response of the shock is unique and determinate or not, or by studying the behaviour of the dissipative shock structure with variations in the magnitudes of the dissipations. Both approaches yield the same results, which appears at first sight to be a coincidence. In this paper we show, from a single treatment that includes each as special cases, why the two methods yield the same conclusions.Also, by including the Hall term on Ohm's law, we are able to resolve the uncertainty about the stability of switch-on and switch-off shocks that occurs in the usual MHD treatment of the problem. Finally, it is shown that the Hall term also introduces the possibility of electric field layers in the unsteady shock and thereby reduces the number of shock boundary conditions. This throws some doubt on the value of the wave-interaction theory for shocks in real plasmas.

Sign in / Sign up

Export Citation Format

Share Document