Nonlinear theory of ion-acoustic waves in an ideal plasma with degenerate electrons |
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Authors: | A E Dubinov A A Dubinova |
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Institution: | (1) All-Russia Research Institute of Experimental Physics, Russian Federal Nuclear Center, Sarov, Nizhni Novgorod oblast, 607188, Russia;(2) Advanced School of General and Applied Physics, Lobachevsky Nizhni Novgorod State University, ul. Ul’yanova 46, Nizhni Novgorod, 603950, Russia |
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Abstract: | A nonlinear theory is constructed that describes steady-state ion-acoustic waves in an ideal plasma in which the electron component is a degenerate Fermi gas and the ion component is a classical gas. The parameter ranges in which such a plasma can exist are determined, and dispersion relations for ion-acoustic waves are obtained that make it possible to find the linear ion-acoustic velocity. Analytic gas-dynamic models of ion sound are developed for a plasma with the ion component as a cold, an isothermal, or an adiabatic gas, and moreover, the solutions to the equations of all the models are brought to a quadrature form. Profiles of a subsonic periodic and a supersonic solitary wave are calculated, and the upper critical Mach numbers of a solitary wave are determined. For a plasma with cold ions, the critical Mach number is expressed by an explicit exact formula. |
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