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An experimental study of transverse ionizing MHD shock waves

Published online by Cambridge University Press:  13 March 2009

Charlles F. Stebbins
Affiliation:
Aerospace Engineering Sciences Department, University of Colorado, and Frank J. Sailer Research Laboratory, U.S. Air Force Academy
George C. Vlases
Affiliation:
Aerospace Engineering Sciences Department, University of Colorado

Extract

The jump conditions across a transverse ionizing MHD shock wave, where the magnetic field is in the plane of the shock, are examined. The conservation laws, in conjunction with Maxwell's laws and the equation of state, yield three jump equations in four unknowns. To uniquely describe jumps across an ionizing wave requires an additional descriptive relationship. The theory of Kulikovskii & Lyubimov and, later, Chu, in which the internal structure of the shock itself supplies the missing relationship, is examined. In particular, Kulikovskii & Lyubimov show, for appropriate ratios of thermal to magnetic diffusivities, that for low-speed waves the magnetic field compression across the shock is unity and the jump equations reduce to the ordinary Rankine—Hugoniot relations. For high-speed shock waves, the magnetic field compression, B2/B1, equals the gas compression across the wave, p2/p1, and the jump equations become the magnetohydrodynamic shock jump relations. Furthermore, intermediate speed shocks induce magnetic field compressions between 1 and p2/p1. An experiment was performed in an inverse pinch where E behind the shock, the shock and piston velocities, and the magnetic field compression across the shock, were measured over a wide range of initial conditions and shock velocities in hydrogen. The jump relations were written with B2/B1 as a parameter and programmed into a digital computer. The program was written for real, equilibrium hydrogen. The program provided easy access to a unique solution of the jump equations for any B2/B1. The experiment tends to confirm the Kulikovskii—Lyubimov—Chu theory. Ordinary shock waves were observed at low speeds and near-MilD shocks were observed at high speeds. Further, the relation was verified for the plasma behind the shock for low-speed shock waves, and was verified to within experimental accuracy for the intermediate class of shock waves.

Type
Research Article
Copyright
Copyright © Cambridge University Press 1968

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References

REFERENCES

Chu, C. K. 1964 Phys. Fluids 7, 1349.CrossRefGoogle Scholar
Cowley, M. D. 1967 J. Plasma Phys. 1, 39.CrossRefGoogle Scholar
Greifinger, C. & Cole, J. D. 1961 Phys. Fluids 4, 527.CrossRefGoogle Scholar
Helliwell, J. B. 1962 J. Fluid Mech. 14, 405.CrossRefGoogle Scholar
Huddlestone, R. H. & Leonard, S. L. 1965 Plasma Diagnostic Techniques.Google Scholar
Jones, T. G. & Vlases, G. C. 1967 Rev. Sci. Instrum. 38, 1038.CrossRefGoogle Scholar
Kulikovskii, A. G. & Lyubimov, G. A. 1959 Doki. Akad. Nauk SSSR 129, 525.Google Scholar
Kulikovskii, A. G. & Lyubimov, G. A. 1960 Rev. Mod. Phys. 32, 977.CrossRefGoogle Scholar
Marshall, W. 1955 Proc. Roy. Soc. A 233, 367.Google Scholar
May, R. M. & Tendys, J. 1965 Nucl. Fusion 5, 144.CrossRefGoogle Scholar
McLean, E. A., Faneuff, C. E., Kolb, A. C. & Griem, H. R. 1960 Phys. Fluids, 3 843.CrossRefGoogle Scholar
Patrick, R. M. & Pugh, E. R. 1965 Phys. Fluids 8, 636.CrossRefGoogle Scholar
Soubbaramayer, M. 1962 Comptes Rendus 254, 2135.Google Scholar
Stebbins, C. F. & Clawson, D. W. 1968 FJSRL Report 68–0006.Google Scholar
Taussig, R. T. 1967 Phys. Fluids 10, 1145.CrossRefGoogle Scholar
Vlases, G. C. 1963 J. Fluid Mech. 16, 82.CrossRefGoogle Scholar
Vlases, G. C. 1964 Phys. Fluids 7 1358.CrossRefGoogle Scholar
Vlases, G. C. 1965 Proc. 5th Int. Shock Tube Symp. p. 351.Google Scholar
Vlases, G. C. 1967 Phys. Fluids 11, 2351.CrossRefGoogle Scholar
Zhilin, Iu. L. 1960 Prikl. Mat. Mekh. 24, 543.Google Scholar