Erratum: Hydrodynamic stability of a laser-driven plasma

Brueckner, Keith A.; Jorna, S.; Janda, Ralph

doi:10.1063/1.862831

Cited by 9 publications

(10 citation statements)

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“…Concerning the value of the modified Rayleigh number, we may draw a comparison between Bassett et al (1987) and Brueckner et al (1974). One major point of difference is the choice of target: the former authors have Z = 13 and A = 27 (aluminium) whereas in the latter work Z = 1 and A -2 (deuterium).…”

Section: Discussionmentioning

confidence: 99%

“…The temporal behaviour of the unstable flow is not exponential, however; rather it evolves according to an hypergeometric law. Brueckner, Jorna & Janda (1974) considered the stability of a deuterium plasma ablating from a plane surface with vorticity again across the direction of irradiation. In their numerical calculations, ablation acts as a stabilizing effect.…”

Section: Introductionmentioning

confidence: 99%

“…A complete description of the phenomena occurring in such experiments would be of prohibitive complexity. For instance, we may expect that, early in its development, the plasma is Rayleigh-Taylor unstable (Brueckner et al 1974;Kull & Anisimov 1986;Kull 1989). These early stages of ablation are not addressed in our investigation.…”

Section: Introductionmentioning

confidence: 99%

“…One classical reference for our investigation is given by the many studies on the onset of marginal convection in liquids, known as Rayleigh-Be'nard convection theory (Chandrasekhar 1981;Turner 1979;Drazin & Reid 1981). Attempts to use this theory to calculate the critical value of the Rayleigh number at which marginal convection appears were made by Bassett (1987 personal communication) and Brueckner et al (1974) in order to justify the results of their numerical simulations: the latter authors conclude that the typical Rayleigh numbers provided by an atmosphere of ablating deuterium plasma are too small for convection to set in. However, our results suggest that mere application of the Rayleigh-Be'nard theory for marginal convection may not necessarily give the correct results.…”

Section: Introductionmentioning

confidence: 99%

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Convection in a plasma with opposed temperature and density gradients

Nocera¹

1991

J. Plasma Phys.

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The stability of a viscous and heat-conducting plasma is considered, with temperature and density gradients arranged so that the resulting pressure is homogeneous, as suggested by some experiments on laser-plasma interactions. Gravity and magnetic field effects are ignored throughout. A non-dissipative fluid is considered first. Under the assumption of an Epstein profile for the equilibrium temperature, the dispersion curves for the propagation of sound waves are determined using a relaxation technique applied to a second-order spheroidal boundary-value problem for mode numbers 1,…, 5: it is found that these modes may be destablized by inhomogeneity. The dynamics of vorticity is analysed in the framework of the WKB approximation, which allows reduction to a fourth-order boundary-value problem: this is tackled in the ‘quasi-classical’ limit by solution of the relevant Bohr-Sommerfeld eigenvalue problem. Convective flows arise in the classically accessible layers and evanesce outside. For the same Epstein temperature profile as above, two such layers are formed, in agreement with observation. Given the growth rate of the unstable flow, the modified Rayleigh number, the width of the convective layer and the temperature drop across it are calculated as functions of the transverse wavenumber and for mode numbers 1–5. Conversely, given the modified Rayleigh number, the growth rate is calculated. The modified Rayleigh number and the growth rate thus found have a minimum and a maximum respectively as functions of the wavenumber of the perturbation. These can be taken as the most favourable values for convection to develop. The value of the wavenumber at which these extrema are attained can be used to determine the aspect ratio of the convective cells.

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Section: Discussionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Convection in a plasma with opposed temperature and density gradients

Nocera¹

1991

J. Plasma Phys.

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“…The effective gravity g must be included in the energy equation as the product of force density pg with velocity v. It cannot be omitted, as by Brueckner, Jorna, and Janda. 7 The heat flux q at any point in the hot conduction region is considered to be the lesser in magnitude of the classical flux q cU^ = -KT 5/2 T' and limited flux q Um = lp(T/m i ) s/2 T f \T f \'" L .…”

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confidence: 99%

Steady-State Model of a Flat Laser-Driven Target

Felber

1977

Phys. Rev. Lett.

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so that a AI becomes comparable to a DI at relatively low energies. The estimated cross sections are plotted in Fig. 2. It shows the dominance of a AI for the incident kinetic energy of approximately 12 keV and higher, pa 0 >30. The energy parameters used in the evaluation of (3) and (5) are generated by the single-particle model 5 ; A 35 = 96.5 Ry and A 3^= 92.1 Ry for the DI, and A 2s = 180 Ry = A 2/> for the AI excitations. From the extrapolation fit of a discussed earlier, one obtains a L = 0.90, as compared with a L (Z r =Q) = 0.91. The AI contribution comes mainly from the 2p excitation followed by the Auger emission, while the 2s excitation contributes about 4% to the total AI. The contribution of the 3s electrons to the AI by excitations to states just below the ionization threshold is also estimated to be about 3% and less. For the DI cross section, the 3p ionization dominates over the 3s electrons by approximately 5 to 1.In summary, I have shown that, for reactions involving highly stripped ions, a DI alone can often lead to a gross underestimate of the impact ionization cross section. The relative magnitude of M c (outer shell) and M D (inner shell) is important, but not sufficient to make the AI process dominant, and the branching ratio a { plays an important role which warrants much further study. AsIn an earlier Letter 1 exact transmission coefficients were calculated for intense light incident on a plasma slab in which ions were frozen. In this paper a steady-state model of a plasma slab, accelerated by its interaction with laser radiation, is treated by one-dimensional (ID) steady-flow hydrodynamic equations in an accelerated frame of reference. The cold unablated fluid, the ablation layer, both classical and flux-limited hot conduction regions, the critical surface, and the underdense blowoff are all considered. A global description determines the temperature, density, Z c increases, we expect that the dominance of the AI process will be more prevalent even at fairly low Z r .The calculation presented here is only approximate and requires more extensive studies, but its qualitative conclusions are not expected to be seriously affected by the details, which will be reported elsewhere. 9 Phys. Rev. A 7, 491 (1973). 2 Y. Hahn, Phys. Rev. A (to be published). 3 H. A 0 Bethe and R. W. Jackiw, Intermediate Quantum Mechanics (Benjamin, New York, 1968). 4 Y. Hahn and K. M. Watson, Phys 0 Rev. A 6, 548 (1972); Y. Hahn, Phys, Rev. A 13, 1326 (1976). 5 P. P. Szydlik and A. E. S. Green, Phys. Rev. A 9, 1885 (1974). 6 W. Bambynek et al., Rev. Mod. Phys. 44, 716 (1972). 7 M. H. Chen and B. Crasemann, Phys. Rev. A 12, 959 (1975). 8 C. P. Bhalla, Phys. Rev. A JL2, 122 (1975), and J. Phys. B 8, 2792 (1975). 9 Y. Hahn, to be published. 10 U. Fano and M. Inokuti, ANL Report No. ANL-76-80, 1976 (unpublished).velocity, and boundaries as well. Approximate analytic solutions are given in each of the plasma regions.The ablation layer, containing a steep density gradient separating cold dense fluid from hot lowdensity p...

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