One-dimensional plasma

One-Dimensional Plasma (Prager). One-Electron Theory of w-Electron Systems, New Develop- 4 201... 

The idea of treating in one dimension a system which has proved intractable in three is of course not new, and a number of authors have treated one-dimensional solutions. The results have proved to be semi-quantitatively applicable to the corresponding three-dimensional situation, and constitute the justification of the so-called quasichemical approximation. In view of this it might be hoped that the one-dimensional plasma would also serve as a model for the actual three-dimensional system, but it will appear that the equations of state for the two cases are quite different. 

The one-dimensional plasma must therefore be regarded as a somewhat fictitious system. Nevertheless it does have one very important feature in common with its three-dimensional counterpart, and that is the presence of long-range forces. It is these forces which make the statistical mechanics of pleismas and electrolyte solutions so extraordinarily difficult to treat. Where charged particles are involved it is not even approximately correct to consider only interactions between nearest neighbors—the interaction of every pair of particles must be taken into account. The one-dimensional plasma, where this can be done exactly, should thus serve as a useful testing-ground for approximations developed to treat the three-dimensioneil ceise. 

Manuscript received Sept. ig6o The One-Dimensional Plasma... 

As an example, we look at tire etching of silicon in a CF plasma in more detail. Flat Si wafers are typically etched using quasi-one-dimensional homogeneous capacitively or inductively coupled RF-plasmas. The important process in tire bulk plasma is tire fonnation of fluorine atoms in collisions of CF molecules witli tire plasma electrons... 

Of course, care should be taken when comparing the experimental data and the modeling results the model is an approximation, and the experiment has its uncertainties. The most important approximation is that the model is one-dimensional. A main uncertainty of the experiment is the relation between source power and plasma power (see Section 1.3.2.3). The source power is defined as the power delivered by the power generator. In experiments, the source power is a discharge setting (Table IV). The plasma power is the power dissipated by the plasma. As a rule, this plasma power is smaller than the source power, due to losses in the matching network, which matches the plasma impedance to the impedance of the source power generator, viz., 50 [180]. From comparison of experimental data... 

In order to be able to explain the observed results plasma modeling was applied. A one-dimensional fluid model was used, which solves the particle balances for both the charged and neutral species, using the drift-diffusion approximation for the particle fluxes, the Poisson equation for the electric field, and the energy balance for the electrons [191] (see also Section 1.4.1). 

Earlier the velocity distribution function of quasi particles of a relativistic ideal gas for a one dimensional system, for example, fluxons in thermalized Josephson systems and electrons in a high temperature plasma was found. 

Plasma, One-Dimensional (Prager). Point Interactions in Solids, Statistical Mechanics of 4 201... 

P Gimsing, E Nexo, E Hippe. Determination of cobalamins in biological material. II. The cobalamins in human plasma and erythrocytes after desalting on nonpolar adsorbent material, and separation by one-dimensional thin-layer chromatography. Anal Biochem 129 296-304, 1983. 

Modeling EM solitary waves in a plasma is quite a challenging problem due to the intrinsic nonlinearity of these objects. Most of the theories have been developed for one-dimensional quasi-stationary EM energy distributions, which represent the asymptotic equilibrium states that are achieved by the radiation-plasma system after long interaction times. The analytical modeling of the phase of formation of an EM soliton, which we qualitatively described in the previous section, is still an open problem. What are usually called solitons are asymptotic quasi-stationary solutions of the Maxwell equations that is, the amplitude of the associated vector potential is either an harmonic function of time (for example, for linear polarization) or it is a constant (circular polarization). Let s briefly review the theory of one-dimensional RES. 

Following the same procedure outlined for the cold plasma, we can specialize the system of (10.17) and (10.18) in Part I to the one-dimensional case with circular polarization and zero group velocity. The explicit forms of the relevant equations are given in [39], where RES in an electron-positron plasma were studied. Since the two species have equal masses and absolute values of charge, the plasma does not develop any charge separation for Te = Tp = T0 and so (j> 0. A single second-order nonlinear differential equa-... 

A kinetic approach to the study of one-dimensional RES in a hot plasma was developed in [44] and applied to RES in an electron-positron plasma [44], electron-ion plasma [45], and electron-positron-ion plasma [46]. A highly anisotropic particle distribution function for each plasma species j (where j = e for electrons and j = i for ions) was considered, with a finite constant... 

The Drude parameters in Table 4 have been derived by fitting the reflectance spectra with the Drude-like dielectric constant, Eq. (33). It has been stressed by Jacobsen [98] and Yamaji [68b] that in the limit of highly anisotropic one-dimensional conductors the ratio of transfer integrals is not proportional to the ratio of plasma frequencies but to its square instead. 

A number of one dimensional computer models have been developed to analyze thermionic converters. These numerical models solve the nonlinear differential equations for the thermionic plasma either by setting up a finite element mesh or by propagating across the plasma and iterating until the boundary conditions are matched on both sides. The second of these approaches is used in an analytical model developed at Rasor Associates. A highly refined "shooting technique" computer program, known as IMD-4 is used to calculate converter characteristics with the model ( ). 

Because amounts of vitamin B12 are very low in foods, tissues, and body fluids, bioautography is used before densitometry. A selected strain of Escherichia coli is used as a microorganism for the bioautography. Growth spots are enhanced by the addition of 2,3,5-triphenyltetrazolium chloride, which is converted to the red-colored formazan by E. coli growth. Determination of vitamin B12 in human plasma and erythrocytes was accomplished by one-dimensional bioautography.A... 

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