2022
DOI: 10.1017/jfm.2022.77
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Stable and unstable supersonic stagnation of an axisymmetric rotating magnetized plasma

Abstract: The Naval Research Laboratory ‘Mag Noh problem’, described in this paper, is a self-similar magnetized implosion flow, which contains a fast magnetohydrodynamic (MHD) outward propagating shock of constant velocity. We generalize the classic Noh (OSTI Tech. Rep. 577058, 1983) problem to include azimuthal and axial magnetic fields as well as rotation. Our family of ideal MHD solutions is five parametric, each solution having its own self-similarity index, gas gamma, magnetization, the ratio of axial to the azimu… Show more

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Cited by 6 publications
(3 citation statements)
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“…The convergence to high accuracy was also slow because our solution, formally, had a mass distribution in a form of a delta function in x or r, which was subject to fast numerical diffusion. Recently we developed a suite of exact self-similar solutions of MHD equations with a fast MHD shock, resembling plasma driven by magnetic field in Z-pinches 28,29 . We released the code to produce such solutions to the public 30 and already used these solutions to test stability and accuracy of various codes, such as Athena, Mach2 and Flash.…”
Section: Mag Noh Verification Problemmentioning
confidence: 99%
See 1 more Smart Citation
“…The convergence to high accuracy was also slow because our solution, formally, had a mass distribution in a form of a delta function in x or r, which was subject to fast numerical diffusion. Recently we developed a suite of exact self-similar solutions of MHD equations with a fast MHD shock, resembling plasma driven by magnetic field in Z-pinches 28,29 . We released the code to produce such solutions to the public 30 and already used these solutions to test stability and accuracy of various codes, such as Athena, Mach2 and Flash.…”
Section: Mag Noh Verification Problemmentioning
confidence: 99%
“…The self-similarity of these functions is expressed in the following way -for any two r 1 ,t 1 and r 2 ,t 2 satisfying r 1 /t 1 = r 2 /t 2 we have v ss (r 1 ,t 1 ) = v ss (r 2 ,t 2 ), B {φ ,z}ss (r 1 ,t 1 ) = (t 1 /t 2 ) 1.5 B {φ ,z}ss (r 2 ,t 2 ), ρ ss (r 1 ,t 1 ) = (t 1 /t 2 ) 3 ρ ss (r 2 ,t 2 ). For more detail see 28,29 . Our solution, therefore, is a self-similar solution stitched to the vacuum solution.…”
Section: Mag Noh Verification Problemmentioning
confidence: 99%
“…Spherically imploding flows are produced in ICF configurations 62,63 , where the stagnation of a lowdensity fuel via the accretion shock front expanding from the centre of an imploded capsule, back into the converging once-shocked deuterium-tritium plasma, constitutes the first stage of the central hot spot's compression and heating. Fast Z pinches [64][65][66] implode cylindrically to produce keV x-rays or neutrons 67 . It has been argued 68 that most of the x-ray and neutron yields from Z pinches are generated during the stagnation of magnetically driven, cylindrically imploded mass via an expanding accretion shock.…”
Section: Introductionmentioning
confidence: 99%