Converging cylindrical shocks in ideal magnetohydrodynamics
We consider a cylindrically symmetrical shock converging onto an axis within the framework of ideal, compressiblegas nondissipative magnetohydrodynamics (MHD). In cylindrical polar coordinates we restrict attention to either constant axial magnetic field or to the azimuthal but singular magnetic field produced by a line current on the axis. Under the constraint of zero normal magnetic field and zero tangential fluid speed at the shock, a set of restricted shockjump conditions are obtained as functions of the shock Mach number, defined as the ratio of the local shock speed to the unique magnetohydrodynamic wave speed ahead of the shock, and also of a parameter measuring the local strength of the magnetic field. For the line current case, two approaches are explored and the results compared in detail. The first is geometrical shockdynamics where the restricted shockjump conditions are applied directly to the equation on the characteristic entering the shock from behind. This gives an ordinarydifferential equation for the shock Mach number as a function of radius which is integrated numerically to provide profiles of the shock implosion. Also, analytic, asymptotic results are obtained for the shock trajectory at small radius. The second approach is direct numerical solution of the radially symmetricmore »
 Authors:

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 Graduate Aerospace Laboratories, California Institute of Technology, Pasadena, California 91125 (United States)
 School of Mechanical and Mining Engineering, University of Queensland, Queensland 4072 (Australia)
 Mechanical Engineering, Physical Sciences and Engineering Division, King Abdullah University of Science and Technology, Thuwal (Saudi Arabia)
 Publication Date:
 OSTI Identifier:
 22311059
 Resource Type:
 Journal Article
 Resource Relation:
 Journal Name: Physics of Fluids (1994); Journal Volume: 26; Journal Issue: 9; Other Information: (c) 2014 AIP Publishing LLC; Country of input: International Atomic Energy Agency (IAEA)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; ASYMPTOTIC SOLUTIONS; COMPARATIVE EVALUATIONS; CURRENTS; CYLINDRICAL CONFIGURATION; DIFFERENTIAL EQUATIONS; HYDROMAGNETIC WAVES; IMPLOSIONS; INERTIAL CONFINEMENT; MACH NUMBER; MAGNETIC FIELDS; MAGNETOHYDRODYNAMICS; NUMERICAL SOLUTION