Summary
On appealing to the recent well-established theory of mixtures, plasmas are described in a systematic way as mixtures of interacting charged-fluid constituents. Viscosity and heat conduction of the constituents are accounted for through the formalism of hidden variables so as to allow wave front propagation. A thermodynamic analysis is performed by having recourse to the second law in the form of the Clausius-Duhem inequality, thus providing a thorough scheme of dissipative effects in plasmas. For example, as an outstanding result of the investigation, it follows that, in the case of constituents at different temperatures, a transfer of linear momentum is unavoidably associated with a correspondent transfer of energy. It is then shown how, in the limiting approximation of magnetofluidodynamics, the process of electric conduction may be embodied into the framework of dissipative effects.
Riassunto
Sulla base della teoria delle misture elaborata negli ultimi anni si trattano i plasmi in maniera sistematica come misture di costituenti fluidi carichi interagenti. La viscosità e la conduzione di calore sono descritti mediante il formalismo delle variabili nascoste in modo da rendere ammissibile la propagazione di fronti d'onda. L'analisi della compatibilità del modello con la termodinamica è effettuata considerando la seconda legge nella forma della diseguaglianza di Clausius-Duhem; come risultato si ottiene uno schema completo di effetti dissipativi nei plasmi. Per esempio, si mostra che nel caso di costituenti a temperatura diversa un trasferimento d'impulso è inevitabilmente legato ad un corrispondente trasferimento di energia. Infine si mostra che, nel caso limite della magnetofluidodinamica, il fenomeno della conduzione elettrica può essere inglobato nel contesto degli effetti dissipativi.
Резюме
На основе недавно развитой теории смесей описывается плазма систематическим образом, как смесь взаимодействуюших заряженных жидких компонент. Вязкость и теплопроводность этих компонент объясняются с помошью формализма скрытых переменных, что позволяет описать распространение волнового фронта. Проводится анализ совместимости предложенной модели со вторым законом термодинамики в форме неравенства Клаузиуса-Духема. В результате этого получается полная схема диссипативных эффектов в плазме. Например, показывается, что в случае компонент при различных температурах перенос импульса неизбежно связан с соответствуюшим переносом энергии. Затем показывается, как в предельном случае магнитной гидродинамики процесс электропроводности может быть включен в рамки диссипативных явлений.
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Of course, owing to the principle of material-frame indifference, the response functions φ and the evolution functionh should depend onv α andW α only through the differencesv α-v β,W α-W β, α, β=−1, 0,..., ν.
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On appealing to the arbitrariness of the external-body forcesn β m β F β occurring in eq. (2.4), the accelerationsv′ β may be viewed as arbitrary vectors.
We remind the reader that the diagonal terms of the matricesN, M, K have no physical meaning.
To avoid misunderstandings, in this section we denote the constituents by the indices e (electrons), a (atoms), i (ions) instead of −1, 0, 1.
C. A. Truesdell:Rational Thermodynamics (New York, N. Y., 1969).
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Bampi, F., Morro, A. Mixture approach to plasmas with dissipative phenomena. Il Nuovo Cimento D 1, 169–185 (1982). https://doi.org/10.1007/BF02450076
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DOI: https://doi.org/10.1007/BF02450076