Continuum Mechanics and Thermodynamics

, Volume 30, Issue 2, pp 365–380 | Cite as

The reflection of an ionized shock wave

Original Article


In a previous paper, we studied the thermodynamic and kinetic theory for an ionized gas, in one space dimension; in this paper, we provide an application of those results to the reflection of a shock wave in an electromagnetic shock tube. Under some reasonable limitations, which fully agree with experimental data, we prove that both the incident and the reflected shock waves satisfy the Lax entropy conditions; this result holds even outside genuinely nonlinear regions, which are present in the model. We show that the temperature increases in a significant way behind the incident shock front but the degree of ionization does not undergo a similar growth. On the contrary, the degree of ionization increases substantially behind the reflected shock front. We explain these phenomena by means of the concavity of the Hugoniot loci. Therefore, our results not only fit perfectly but explain what was remarked in experiments.


Systems of conservation laws Ionized gas Shock reflection 


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Supplementary material

161_2017_607_MOESM1_ESM.pdf (690 kb)
Supplementary material 1 (pdf 690 KB)


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Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2017

Authors and Affiliations

  1. 1.Center of Physics and MathematicsOsaka Electro-Communication UniversityNeyagawaJapan
  2. 2.Department of Mathematics and Computer ScienceUniversity of FerraraFerraraItaly

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