Plasma kinetic equation

In the second part we will consider the formulation of kinetic equations for partially ionized plasmas including ionization and recombination of the atoms. 

Owing to the long-range character of Coulomb forces, the formulation of kinetic equations for plasmas is more complicated than that for neutral gases. Therefore, the Coulomb systems show a collective behavior, and we observe for example, the dynamical screening of the Coulomb potential. 

However, a justification of the screening can only be found by a consequent derivation of kinetic equations for plasmas. In the subsequent sections we will deal with kinetic equations of charged particles and with that of bound state between charged particles. 

Until now we considered the limiting situation in which the plasma consists only of atoms. The kinetic equation was given by Eq. (4.62). However, we are also interested in describing the partially ionized plasma, and especially the ionization and recombination reactions. Formally, this corresponds to taking into account scattering states in Eq. (4.44). This means that the quantum numbers a may be discrete numbers and. may also run over the continuous spectrum. Taking into account scattering states, we are faced with difficulties. These are connected essentially with the application of Eq. (4.28) in the equation of motion. 

Since there is a directly proportionate relationship between administered drug dose and steady-state plasma levels Equations 2.2 and 2.3 provide a straightforward guide to dose adjustment for drugs that are eliminated by first-order kinetics. Thus, to double the plasma levels the dose simply should be doubled. Con-versely to halve the plasma level, the dose should be halved. It is for this reason that Equations 2.2 and 2.3 are the most clinically important pharmacokinetic equations. Note that, as is apparent from Eigure 2.6, these equations also stipulate that the steady-state level is determined only by the maintenance dose and elimination clearance. The loading dose does not appear in the equations and does not influence the eventual steady-state level. 

W. Y. Zhang and R. Balescu (1988) Statistical-mechanics of a spin-polarized plasma. J. Plasma Phys. 40, pp. 199-213 ibid. (1988) Kinetic-equation, spin hydrodynamics and collisional depolarization rate in a spin-polarized plasma. J. Plasma Phys. 40, pp. 215-234... 

The kinetic equation is very complex and covers a tremendous number of special electron kinetic problems. Consequently, there does not seem to be any chance of finding some kind of general solution of this equation that can later be adapted to the specific plasma conditions of interest. 

Another important point, closely connected with electron kinetics, concerns the self-consistent treatment of electron kinetics, of the particle and/or power balance equations for heavy particles (such as different ions and excited atoms or molecules), and of the Maxwell equations (or a reduced version such as the Poisson equation or appropriate electric circuit equations) to obtain a more complete description of all important plasma components as well as of the internal electric field. This self-consistent treatment is usually tricky and is based on an iterative approach to the solution of the various types of equations involved (Loffhagen and Winkler, 1994 Uhrlandt and Winkler, 1996 Yang and Wu, 1996). To integrate the electron kinetic equation in such an approach adequately, a very effective solution procedure for this equation is of particular importance, although remarkable progress with respect to the speed of computation has been achieved in recent years. 

Vibrational distributions in non-equilibrium plasma are mostly controlled by W-exchange and VT-relaxation processes, while excitation by electron impact, chemical reactions, radiation, and so on determine averaged energy balance and temperatures. At steady state, the Fokker-Planck kinetic equation (3-116) gives J(E) = const. At E oo = 0,... 

One-Temperature Approach to Vibrational Kinetics and Energy Balance of CO2 Dissociation in Non-Equilibrium Plasma Major Equations... 

Analysis of kinetic equation (5-131) shows the effective Maxwellization of plasma electrons, generated by a high-crrrrent relativistic electron beam, and as a result /x 1 becomes possible when ionization degrees are sufficiently high ... 

All these factors explain why quenching of products of direct UFg decomposition in thermal plasma is such a challenging task. The condensed products should be separated from fluorine before heterogeneous reverse reactions take place. For example, the heterogeneous reverse reaction of tetrafluoride gasification, UF4 + F2 UFg, decreases the mass of a UF4 particulate in accordance with the following kinetic equation ... 

Quenching of Products of Direct UFe Decomposition in Thermal Plasma. Integrating kinetic equation (7-48), derive formula (7-49) for the mass decrease of uranium-containing product particles due to their gasification by fluorine. Analyze the effect of initial particulate size on the rate and characteristic time of the heterogeneous reverse reactions. Compare the efficiencies of quenching of UF4 and metallic uranium. 

This situation does not qualify for use of the high dose equation (Eq. 15.15). Neither are the plasma drug concentrations obtained small enough to warrant use of the low dose (linear kinetic) equation (Eq. 15.13). This leaves the requirement to use the general equation for Michaelis-Menten elimination kinetics (Eq. 15.14) ... 

Contents Introduction. - Classical Theoty Free Charged Particles and a Field. Atoms and Field. The Kinetic Equations for a System of Free Charged Particles and a Field. Brownian Motioa Kinetic Equations for an Atom-Field System. - Quantum Theory Microscopic Equations. The Kinetic Equations for Partially Ionized Plasma The Coulomb Approximation. Kinetic Equations for Partially Ionized Plasma The Processes Conditioned by a Transverse Electromagnetic Field. Spectral Emission Line Broadening of Atoms in Partially Ionized Plasma. Fluctuations and Kinetic Processes in Systems Composed of Strongly Interacting Particles. Fluctuations in Quantum Self-Osdllatory Systems. Phie Transitions in a System Composed of Atoms and a Field. Conclusion. -References. - Subject Index. 

In a plasma, the constituent atoms, ions, and electrons are made to move faster by an electromagnetic field and not by application of heat externally or through combustion processes. Nevertheless, the result is the same as if the plasma had been heated externally the constituent atoms, ions, and electrons are made to move faster and faster, eventually reaching a distribution of kinetic energies that would be characteristic of the Boltzmann equation applied to a gas that had been... 

Figure 4. The Brownian ratchet model of lamellar protrusion (Peskin et al., 1993). According to this hypothesis, the distance between the plasma membrane (PM) and the filament end fluctuates randomly. At a point in time when the PM is most distant from the filament end, a new monomer is able to add on. Consequently, the PM is no longer able to return to its former position since the filament is now longer. The filament cannot be pushed backwards by the returning PM as it is locked into the mass of the cell cortex by actin binding proteins. In this way, the PM is permitted to diffuse only in an outward direction. The maximum force which a single filament can exert (the stalling force) is related to the thermal energy of the actin monomer by kinetic theory according to the following equation ...

Since all the kinetic characteristics of the disappearance of a drug from plasma are the same as those for the pseudo-first-order disappearance of a substance from a solution by hydrolysis, the same working equations [Eqs. (11) and (13)] and the same approach to solving problems can be used. 

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