Thermodynamik

Schottky, Walter

doi:10.1007/978-3-642-88482-5

Cited by 46 publications

(13 citation statements)

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“…They are the bulk plasma and the ion sheath, which are closely coupled with each other. A self-consistent continuum theory is highly desired in modeling both dc and rf discharges in order to overcome the limits of classical theories applied to the sheath and the bulk plasma, respectively [42][43][44][45]. The historical development of the modeling of dc glow discharges has been reviewed [46 -49].…”

Section: Introductionmentioning

confidence: 99%

Modeling and diagnostics of the structure of rf glow discharges in Ar at 13.56 MHz

Makabe

Nakano

Yamaguchi³

1992

Phys. Rev. A

135

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The structure of rf glow discharges in Ar at 13.56 MHz is described, making use of a relaxation continuum model. The model includes consideration of the relaxation kinetics for the momentum and energy of charged particles. The discharge structure and plasma property are modeled using molecular quantities (i.e. , collision cross sections, radiative lifetimes, etc.) and macroscopic transport quantities for charged particles. Spatiotemporal distributions for the field and the net production rate and density of particles are studied in detail in the bulk plasma as well as the ion sheath under periodic steady-state conditions. In particular, the temporal profiles including phase shift and nonlinear variation with respect to the applied-voltage wave form are discussed. Each type of excited atom shows a different spatiotemporal density distribution due to different loss mechanisms, although the production profiles are similar. That is, Ar( ps) is controlled by a radiative decay and quenching in collisions with Ar( So), while Ar( Po & ) is controlled by diffusion. The validity of the relaxation continuum model is investigated by the observation of external electric properties and the measurement of spatiotemporally resolved optical emission from the rf glow. Quantitative comparison of the results from theory and experiment supports the validity of the relaxation continuum model. The relaxation continuum model is simple and physically reasonable.PACS number(s): 52.80. Hc, 52.25.Fi, 52.70.Kz

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Section: Introductionmentioning

confidence: 99%

Modeling and diagnostics of the structure of rf glow discharges in Ar at 13.56 MHz

Makabe

Nakano

Yamaguchi³

1992

Phys. Rev. A

135

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“…The interaction between G and G * can be described by exchange quantities. We call G a Schottky system [Schottky (1929)], if the interaction with its environment consists of heat exchangeQ, of power exchangeẆ , and of mass exchange described by time rates of mole numbersṅ e of the different species (Fig. A.1).…”

Section: A11 Contact Quantitiesmentioning

confidence: 99%

Back Matter

2008

World Scientific Series on Nonlinear Science Series A

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Appendix A Thermodynamic interaction between two discrete systems in non-equilibrium 0 There are two different descriptions of thermodynamic systems: the field formulation and the description as a discrete (or lumped) system. The field formulation or continuum thermodynamics deals with balance equations [Wilmanski (1988);Jou, Casas-Vazquez and Lebon (2001); Muschik, Papenfuss and Ehrentraut (2001)], which model together with the constitutive relations (equations of state) and the initial and boundary conditions of the process going on in the system. After having inserted the constitutive relations into the balance equations, we obtain a system of partial differential equations whose analytical solutions can be calculated only in sufficiently simple cases. In numerous practical applications, these continuous models are replaced by approximations usually obtained by means of finite differences or finite elements. Calculations are carried out after having chosen an appropriate algorithm with respect to the problems of stability and convergence. Consequently for practical reasons it seems to be more convenient to have a direct description of the coupled thermodynamic behavior of a finite number of interacting elements or cells. This is just one of the reasons for introducing the concept of discrete systems [Muschik (1990)] because this gives a simple and effective possibility for describing thermodynamics and interactions of elements being in non-equilibrium. But here we encounter the analogous difficulties, which appears in classical thermodynamics, as noted by Truesdell and Bharatha [Truesdell and Bharatha (1977)] "the formal structure of classical thermodynamics describes the effects of changes undergone by 0 This Appendix represents results of the paper by W. Muschik and A. Berezovski (Thermodynamic interaction between two discrete systems in non-equilibrium. J. NonEquilib. Thermodyn., 29, (2004)

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“…Discrete systems. A system which is separated by a partition from its surroundings is called a discrete thermodynamic system or a Schottky system [28], if the interaction between the system and its environment can be described by the heat exchangeQ, the power exchangeẆ and the material exchangeṅ e , represented by the external rates of the mole numbers [29].…”

Section: Thermodynamics Of Irreversible Processesmentioning

confidence: 99%

Why so many “schools” of thermodynamics?

Muschik

2007

Forsch Ingenieurwes

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ABSTRACT. A classification representing some main branches of phenomenological nonequilibrium thermodynamics is discussed. Differences and similarities of these selected branches are explained. Starting out with basic concepts of phenomenological thermodynamics, more developed theories with different back-grounds contributing to contemporary thermodynamics are considered. Because of its vast extent, this field cannot be presented completely in a single reasonably sized paper without any omissions.

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Thermodynamik

Cited by 46 publications

References 0 publications

Modeling and diagnostics of the structure of rf glow discharges in Ar at 13.56 MHz

Modeling and diagnostics of the structure of rf glow discharges in Ar at 13.56 MHz

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Why so many “schools” of thermodynamics?

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