Exact self-similar solutions for the magnetized Noh Z pinch problem

Velikovich, A. L.; Giuliani, J. L.; Zalesak, S. T.; Thornhill, J. W.; Gardiner, Thomas A.

doi:10.1063/1.3678213

Cited by 25 publications

(28 citation statements)

References 43 publications

(70 reference statements)

Supporting

Mentioning

Contrasting

Order By: Relevance

“…[34][35][36] Purely gasdynamic stability analysis, like that done here and in Ref. 37, is, in turn, a pre-requisite for a more complete analysis accounting for additional physics, including MHD effects, 32,33 radiative energy losses from the stagnated cylindrical precursor plasma, 12,13 or both radiative losses and gravity in astrophysical accretion-shock flows. 17 Such study is obviously necessary for the analysis of the laboratory-astrophysics experiments proposed in Ref.…”

Section: Discussionmentioning

confidence: 99%

“…This code had originally been developed for astrophysical studies and is actively supported by a growing community. In fact, our choice of a Cartesian mesh rather than a cylindrical one was dictated in part by the confidence that we had developed in the Cartesian version of Athena during our previous work on the MHD version of the Noh problem, 32 and in part out of our curiosity about whether such a high-performance code could properly resolve decaying perturbations even on a non-aligned mesh. Our original intent had been to subsequently exercise the newly-added cylindrical mesh capabilities of Athena for this test, but we encountered some numerical difficulties with that effort which we have not yet been able to resolve.…”

Section: A Simulations On a Cartesian Gridmentioning

confidence: 99%

“…37, where such analysis has been done for a converging shock wave. Stability analysis of other hydrodynamic 31 and MHD 32,33 generalizations of the classic Noh solution could shed light on the stability of hot-spot formation and other cases of shock-wave stagnation in laser-fusion and Z-pinch implosions, in laboratory astrophysics experiments, 16 as well as guide verification of hydrodynamic and MHD codes.…”

Section: Introductionmentioning

confidence: 99%

“…31) and in MHD. 32,33 Stability analysis of the classic Noh solution is of interest for several reasons. First, the stability problem is solved analytically, so its explicit solution could be used for verification of hydrocodes in two and three dimensions.…”

Section: Introductionmentioning

confidence: 99%

See 3 more Smart Citations

Stability of stagnation via an expanding accretion shock wave

et al. 2016

Self Cite

View full text Add to dashboard Cite

Stagnation of a cold plasma streaming to the center or axis of symmetry via an expanding accretion shock wave is ubiquitous in inertial confinement fusion (ICF) and high-energy- (2014)]. Some experimental evidence indicates that stagnation via an expanding shock wave is stable, but its stability has never been studied theoretically. We present such analysis for the stagnation that does not involve a rarefaction wave behind the expanding shock front and is described by the classic ideal-gas Noh solution in spherical and cylindrical geometry. In either case the stagnated flow has been demonstrated to be stable, initial perturbations exhibiting a powerlaw, oscillatory or monotonic, decay with time for all the eigenmodes. This conclusion has been supported by our simulations done both on a Cartesian grid and on a curvilinear grid in spherical coordinates. Dispersion equation determining the eigenvalues of the problem and explicit formulas for the eigenfunction profiles corresponding to these eigenvalues are presented, making it possible to use the theory for hydro code verification in two and three dimensions.

show abstract

Section: Discussionmentioning

confidence: 99%

Section: A Simulations On a Cartesian Gridmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Stability of stagnation via an expanding accretion shock wave

et al. 2016

Self Cite

View full text Add to dashboard Cite

show abstract

“…Magnetic acceleration is the basis of magnetic pinch facilities where large magnetic pressure is used to compress material samples [21][22][23][24][25] . Magnetic field is also commonly used to process materials in industry.…”

mentioning

confidence: 99%

Anomalous wave structure in magnetized materials described by non-convex equations of state

Serna

Marquina

2014

Physics of Fluids

View full text Add to dashboard Cite

We analyze the anomalous wave structure appearing in flow dynamics under the influence of magnetic field in materials described by non-ideal equations of state. We consider the system of magnetohydrodynamics equations closed by a general equation of state (EOS) and propose a complete spectral decomposition of the fluxes that allows us to derive an expression of the nonlinearity factor as the mathematical tool to determine the nature of the wave phenomena. We prove that the possible formation of non-classical wave structure is determined by both the thermodynamic properties of the material and the magnetic field as well as its possible rotation. We demonstrate that phase transitions induced by material properties do not necessarily imply the loss of genuine nonlinearity of the wavefields as is the case in classical hydrodynamics. The analytical expression of the nonlinearity factor allows us to determine the specific amount of magnetic field necessary to prevent formation of complex structure induced by phase transition in the material. We illustrate our analytical approach by considering two non-convex EOS that exhibit phase transitions and anomalous behavior in the evolution. We present numerical experiments validating the analysis performed through a set of one-dimensional Riemann problems. In the examples we show how to determine the appropriate amount of magnetic field in the initial conditions of the Riemann problem to transform a thermodynamic composite wave into a simple nonlinear wave.

show abstract