Nonlocal transport models of the self‐consistent potential distribution in a plasma sheath with charge transfer collisions

1988 ◽  
Vol 64 (11) ◽  
pp. 6200-6209 ◽  
Author(s):  
Charles W. Jurgensen ◽  
Eric S. G. Shaqfeh
Keyword(s):  
Charge Transfer ◽  
Potential Distribution ◽  
Plasma Sheath ◽  
The Self ◽  
Transport Models ◽  
Self Consistent ◽  
Nonlocal Transport

Theoretical and Computational Problems in Modeling Glow Discharges

1986 ◽  
Vol 68 ◽  
Author(s):  
David B. Graves ◽  
Klavs F. Jensen
Keyword(s):  
Plasma Reactor ◽  
Physical Structure ◽  
Plasma Sheath ◽  
The Self ◽  
Rf Discharge ◽  
Fluid Equation ◽  
Complex Interactions ◽  
Self Consistent ◽  
Self Consistent Field ◽  
The Many

AbstractIt is desirable to develop detailed models of glow discharge chemical reactors in order to understand the many complex interactions that govern reactor performance.One important part of an overall model of the plasma reactor is the description of the discharge physical structure including charged particle densities, energies and the self-consistent electric field.The continuum or fluid equation approach to this problem is presented in this paper and potential problems with this approach are discussed.Results from recent simulations of a 13.56 MHz rf discharge are presented.The behavior of the electrons in the quasineutral plasma and their interaction with the self-consistent field are highlighted.It is shown that the rf power dissipation peaks at the plasma-sheath boundary, and the implications of this for the validity of estimates of mean electron density from equivalent rf rcircuit models is discussed.

Tetrel bonding interaction: an analysis with the block-localized wavefunction (BLW) approach

2019 ◽  
Vol 21 (22) ◽  
pp. 11776-11784 ◽  
Author(s):  
Changwei Wang ◽  
Yama Aman ◽  
Xiaoxi Ji ◽  
Yirong Mo
Keyword(s):  
Wave Function ◽  
Charge Transfer ◽  
The Self ◽  
Bonding Interaction ◽  
Self Consistent

In this study, fifty-one iconic tetrel bonding complexes were studied using the block localized wave function (BLW) method which can derive the self-consistent wavefunction for an electron-localized (diabatic) state where charge transfer is strictly deactivated.

scholarly journals The relativistic self-consistent field

1935 ◽  
Vol 152 (877) ◽  
pp. 625-649 ◽  
Keyword(s):  
Wave Equation ◽  
Field Equation ◽  
Wave Functions ◽  
The Self ◽  
Magnetic Interactions ◽  
Consistent Field ◽  
Exchange Effects ◽  
Self Consistent ◽  
Self Consistent Field ◽  
Schrödinger's Equation

1—The method of the self-consistent field for determining the wave functions and energy levels of an atom with many electrons was developed by Hartree, and later derived from a variation principle and modified to take account of exchange and of Pauli’s exclusion principle by Slater* and Fock. No attempt was made to consider relativity effects, and the use of “ spin ” wave functions was purely formal. Since, in the solution of Dirac’s equation for a hydrogen-like atom of nuclear charge Z, the difference of the radial wave functions from the solutions of Schrodinger’s equation depends on the ratio Z/137, it appears that for heavy atoms the relativity correction will be of importance; in fact, it may in some cases be of more importance as a modification of Hartree’s original self-nsistent field equation than “ exchange ” effects. The relativistic self-consistent field equation neglecting “ exchange ” terms can be formed from Dirac’s equation by a method completely analogous to Hartree’s original derivation of the non-relativistic self-consistent field equation from Schrodinger’s equation. Here we are concerned with including both relativity and “ exchange ” effects and we show how Slater’s varia-tional method may be extended for this purpose. A difficulty arises in considering the relativistic theory of any problem concerning more than one electron since the correct wave equation for such a system is not known. Formulae have been given for the inter-action energy of two electrons, taking account of magnetic interactions and retardation, by Gaunt, Breit, and others. Since, however, none of these is to be regarded as exact, in the present paper the crude electrostatic expression for the potential energy will be used. The neglect of the magnetic interactions is not likely to lead to any great error for an atom consisting mainly of closed groups, since the magnetic field of a closed group vanishes. Also, since the self-consistent field type of approximation is concerned with the interaction of average distributions of electrons in one-electron wave functions, it seems probable that retardation does not play an important part. These effects are in any case likely to be of less importance than the improvement in the grouping of the wave functions which arises from using a wave equation which involves the spins implicitly.

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