Stable and unstable supersonic stagnation of an axisymmetric rotating magnetized plasma

Beresnyak, Andrey; Velikovich, A. L.; Giuliani, J. L.; Dasgupta, A.

doi:10.1017/jfm.2022.77

Cited by 6 publications

(3 citation statements)

References 55 publications

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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%

“…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%

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Simulating a pulsed power-driven plasma with ideal MHD

Beresnyak,

Velikovich,

Giuliani

et al. 2022

Preprint

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We describe a simple practical numerical method for simulating plasma driven within a vacuum chamber by a pulsed power generator. Typically, in this type of simulation, the vacuum region adjacent to the plasma is approximated as a highly resistive, light fluid; this involves computationally expensive solvers describing the diffusion of the magnetic field through this fluid. Instead, we provide a recipe for coupling pulsed power generators to the MHD domain by approximating the perfectly insulating vacuum as a light, perfectly conducting, inviscid MHD fluid and discuss the applicability of this counter-intuitive technique. This, much more affordable ideal MHD representation, is particularly useful in situations where a plasma exhibits interesting three-dimensional phenomena, either due to the design of the experiment or due to developing instabilities. We verified that this coupling recipe works by modeling an exactly solvable flux compression generator as well as a self-similar Noh-like solution and demonstrated convergence to the theoretical solution. We also showed examples of simulating complex three-dimensional pulsed power devices with this technique. We release our code implementation to the public 1 .

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Section: Mag Noh Verification Problemmentioning

confidence: 99%

Section: Mag Noh Verification Problemmentioning

confidence: 99%

Simulating a pulsed power-driven plasma with ideal MHD

Beresnyak,

Velikovich,

Giuliani

et al. 2022

Preprint

View full text Add to dashboard Cite

show abstract

“…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%

The stability of expanding reactive shocks in a van der Waals fluid

2022

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Despite the extensive literature accumulated since the pioneering works of D'yakov and Kontorovich in the 1950s, the stability of steady shocks is still an open question when realistic boundary conditions are accounted. The consideration of a supporting mechanism, which is indeed a necessary condition for shock steadiness, modifies the perturbation shock dynamics in the unstable range. The Noh problem is a suitable example to form steady expanding shocks. This configuration is of great interest to the high-energy-density-physics community because of its direct application to inertial confinement fusion and astrophysics, for which the stagnation of a supersonically converging material via an accretion shock front is ubiquitous. In this work, we extend the generalized Noh problem, both base-flow solution and linear stability analysis, to conditions where endothermic or exothermic transformations undergo across the shock. Within the spontaneous acoustic emission conditions found for a van der Waals gas [J. W. Bates and D. C. Montgomery, “The D'yakov-Kontorovich instability of shock waves in real gases,” Phys. Rev. Lett. 84, 1180 (2000)], we find that cylindrical and spherical expanding shocks become literally unstable for sufficiently high mode numbers. Counterintuitively, the effect of exothermicity or endothermicity across the shock is found to be stabilizing or destabilizing, respectively.

show abstract

Simulating a pulsed-power-driven plasma with ideal MHD

et al. 2022

View full text Add to dashboard Cite

We describe a simple practical numerical method for simulating plasma driven within a vacuum chamber by a pulsed power generator. Typically, in this type of simulation, the vacuum region adjacent to the plasma is approximated as a highly resistive, light fluid; this involves computationally expensive solvers describing the diffusion of the magnetic field through this fluid. Instead, we provide a recipe for coupling pulsed power generators to the magnetohydrodynamics (MHD) domain by approximating the perfectly insulating vacuum as a light, perfectly conducting, inviscid MHD fluid and discuss the applicability of this counter-intuitive technique. This much more affordable ideal MHD representation is particularly useful in situations where a plasma exhibits interesting three-dimensional phenomena, either due to the design of the experiment or due to developing instabilities. We verified that this coupling recipe works by modeling an exactly solvable flux compression generator as well as a self-similar Noh-like solution and demonstrated convergence to the theoretical solution. We also showed examples of simulating complex three-dimensional pulsed power devices with this technique. We release our code implementation to the public (see https://github.com/beresnyak/verif_coupling ).

show abstract

Stable and unstable supersonic stagnation of an axisymmetric rotating magnetized plasma

Cited by 6 publications

References 55 publications

Simulating a pulsed power-driven plasma with ideal MHD

Simulating a pulsed power-driven plasma with ideal MHD

The stability of expanding reactive shocks in a van der Waals fluid

Simulating a pulsed-power-driven plasma with ideal MHD

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