Simulations of electrothermal instability growth in solid aluminum rods

Peterson, Kyle; Yu, Edmund; Sinars, Daniel Brian; Cuneo, M. E.; Slutz, Stephen A.; Koning, J. M.; Marinak, M. M.; Nakhleh, Charles; Herrmann, Mark

doi:10.1063/1.4802836

Cited by 64 publications

(44 citation statements)

References 34 publications

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“…It is also possible these modes collude with electrothermal instability which tends to occur for short wavelengths (<200 lm) at these early times. 21,22 (iv) As the azimuthal magnetic field further increases much beyond the axial magnetic field (from the current rise after 55 ns), both the m ¼ 0 and m ¼ 1 mode are unstable, but the m ¼ 0 mode becomes dominant. At this point g is large, such that MRT is the dominant driver of instability decreasing the e-folding time substantially.…”

Section: Equilibrium and Stabilitymentioning

confidence: 98%

Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner

et al. 2015

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This paper analyzes the coupling of magneto-Rayleigh-Taylor (MRT), sausage, and kink modes in an imploding cylindrical liner, using ideal MHD. A uniform axial magnetic field of arbitrary value is included in each region: liner, its interior, and its exterior. The dispersion relation is solved exactly, for arbitrary radial acceleration (-g), axial wavenumber (k), azimuthal mode number (m), liner aspect ratio, and equilibrium quantities in each region. For small k, a positive g (inward radial acceleration in the lab frame) tends to stabilize the sausage mode, but destabilize the kink mode. For large k, a positive g destabilizes both the kink and sausage mode. Using the 1D-HYDRA simulation results for an equilibrium model that includes a pre-existing axial magnetic field and a preheated fuel, we identify several stages of MRT-sausage-kink mode evolution. We find that the m ¼ 1 kink-MRT mode has a higher growth rate at the initial stage and stagnation stage of the implosion, and that the m ¼ 0 sausage-MRT mode dominates at the main part of implosion. This analysis also sheds light on a puzzling feature in Harris' classic paper of MRT [E. G. Harris, Phys. Fluids 5, 1057(1962]. An attempt is made to interpret the persistence of the observed helical structures [Awe et al., Phys. Rev. Lett. 111, 235005 (2013)] in terms of non-axisymmetric eigenmode. V C 2015 AIP Publishing LLC. [http://dx.

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Section: Equilibrium and Stabilitymentioning

confidence: 98%

Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner

et al. 2015

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“…One such mechanism is the electro-thermal instability (ETI). 13,14 This instability is driven by temperature dependent resistivity and alters the distribution of both current density and temperature within the liner. In the solid state, the current forms azimuthally correlated bands, which have the same orientation of wavevector as the fastest growing MRT modes.…”

Section: Introductionmentioning

confidence: 99%

Instability growth for magnetized liner inertial fusion seeded by electro-thermal, electro-choric, and material strength effects

Pecover

Chittenden

2015

Physics of Plasmas

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A critical limitation of magnetically imploded systems such as magnetized liner inertial fusion (MagLIF) [Slutz et al., Phys. Plasmas 17, 056303 (2010)] is the magneto-Rayleigh-Taylor (MRT) instability which primarily disrupts the outer surface of the liner. MagLIF-relevant experiments have showed large amplitude multi-mode MRT instability growth growing from surface roughness [McBride et al., Phys. Rev. Lett. 109, 135004 (2012)], which is only reproduced by 3D simulations using our MHD code Gorgon when an artificially azimuthally correlated initialisation is added. We have shown that the missing azimuthal correlation could be provided by a combination of the electro-thermal instability (ETI) and an "electro-choric" instability (ECI); describing, respectively, the tendency of current to correlate azimuthally early in time due to temperature dependent Ohmic heating; and an amplification of the ETI driven by density dependent resistivity around vapourisation. We developed and implemented a material strength model in Gorgon to improve simulation of the solid phase of liner implosions which, when applied to simulations exhibiting the ETI and ECI, gave a significant increase in wavelength and amplitude. Full circumference simulations of the MRT instability provided a significant improvement on previous randomly initialised results and approached agreement with experiment. V C 2015 AIP Publishing LLC.

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“…It is long-ranged magnetic fluctuation that gives rise to collective perturbation. It is worthwhile noting that a theory recently proposed by Peterson suggests that the initial seed of MRT instability is not liner surface roughness, but electrothermal instability that arises from the dependence of electrical resistivity on temperature [6,7]. The prominent seeds of electrothermal instability are surface contaminants and small radial surface perturbations which cause nonuniform of electrical resistivity and current density in space respectively, consequently leading to significant variations in Joule heating.…”

Section: Introductionmentioning

confidence: 99%

Role of electromagnetic wave in mode selection of magnetically driven instabilities

Dan¹,

Ren²,

Shuchao³

et al. 2014

AIP Conference Proceedings

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Abstract. The fundamental wavelength of the instability along two 25-m-diameter aluminum wires using a 100 ns rise time, 220 kA pulsed power facility is measured for two different load configurations. In one case the wires are perpendicular to end surface of electrodes, and in another case the wires are oblique to electrode's end surface. The primary diagnostic used to measure time revolution of instability wavelength and amplitude is laser shadowgraphy. The role of end surface of electrodes appears to be responsible for the differences in dominant wavelength of instability between two types of load configurations. The experimental results that the fundamental wavelength in oblique case is about one half of that in perpendicular case indicates the ionic electromagnetic waves may play a key role in mode selection of magnetically driven instabilities. Conclusions drew from this paper may help us to understand the original reason why instabilities along wires manifest itself as a quasiperiodic pattern.

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Simulations of electrothermal instability growth in solid aluminum rods

Cited by 64 publications

References 34 publications

Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner

Coupling of sausage, kink, and magneto-Rayleigh-Taylor instabilities in a cylindrical liner

Instability growth for magnetized liner inertial fusion seeded by electro-thermal, electro-choric, and material strength effects

Role of electromagnetic wave in mode selection of magnetically driven instabilities

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