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dc.contributor.authorPullin, D. I.
dc.contributor.authorMostert, W.
dc.contributor.authorWheatley, V.
dc.contributor.authorSamtaney, Ravi
dc.date.accessioned2015-03-17T06:06:07Z
dc.date.available2015-03-17T06:06:07Z
dc.date.issued2014-09
dc.identifier.citationConverging cylindrical shocks in ideal magnetohydrodynamics 2014, 26 (9):097103 Physics of Fluids
dc.identifier.issn1070-6631
dc.identifier.issn1089-7666
dc.identifier.doi10.1063/1.4894743
dc.identifier.urihttp://hdl.handle.net/10754/346726
dc.description.abstractWe consider a cylindrically symmetrical shock converging onto an axis within the framework of ideal, compressible-gas non-dissipative magnetohydrodynamics (MHD). In cylindrical polar co-ordinates 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 shock-jump 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 shock-dynamics where the restricted shock-jump conditions are applied directly to the equation on the characteristic entering the shock from behind. This gives an ordinary-differential 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 symmetric MHD equations using a shock-capturing method. For the axial magnetic field case the shock implosion is of the Guderley power-law type with exponent that is not affected by the presence of a finite magnetic field. For the axial current case, however, the presence of a tangential magnetic field ahead of the shock with strength inversely proportional to radius introduces a length scale R = √μ0/p0 I/(2π) where I is the current, μ0 is the permeability, and p0 is the pressure ahead of the shock. For shocks initiated at r ≫ R, shock convergence is first accompanied by shock strengthening as for the strictly gas-dynamic implosion. The diverging magnetic field then slows the shock Mach number growth producing a maximum followed by monotonic reduction towards magnetosonic conditions, even as the shock accelerates toward the axis. A parameter space of initial shock Mach number at a given radius is explored and the implications of the present results for inertial confinement fusion are discussed.
dc.publisherAIP Publishing
dc.relation.urlhttp://scitation.aip.org/content/aip/journal/pof2/26/9/10.1063/1.4894743
dc.rightsArchived with thanks to Physics of Fluids
dc.titleConverging cylindrical shocks in ideal magnetohydrodynamics
dc.typeArticle
dc.contributor.departmentMechanical Engineering Program
dc.contributor.departmentPhysical Sciences and Engineering (PSE) Division
dc.identifier.journalPhysics of Fluids
dc.eprint.versionPublisher's Version/PDF
dc.contributor.institutionGraduate Aerospace Laboratories, California Institute of Technology, Pasadena, California 91125, USA
dc.contributor.institutionSchool of Mechanical and Mining Engineering, University of Queensland, Queensland 4072, Australia
dc.contributor.institutionSchool of Mechanical and Mining Engineering, University of Queensland, Queensland 4072, Australia
dc.contributor.affiliationKing Abdullah University of Science and Technology (KAUST)
kaust.personSamtaney, Ravi
refterms.dateFOA2018-06-13T16:16:14Z


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