scholarly journals Influence of ablation-to-critical surface distance upon Rayleigh–Taylor instability

1991 ◽  
Vol 9 (2) ◽  
pp. 273-281 ◽  
Author(s):  
J. Sanz ◽  
A. Estevez

The Rayleigh—Taylor instability is studied by means of a slab model and when slab thickness D is comparable to the ablation-to-critical surface distance. Under these conditions the perturbations originating at the ablation front reach the critical surface, and in order to determine the instability growth rate, we must impose boundary conditions at the corona. Stabilization occurs for perturbation wave numbers such that kD ˜ 10.

1996 ◽  
Vol 14 (3) ◽  
pp. 449-471
Author(s):  
A. Estévez

A modelization of the Rayleigh–Taylor instability, in the context of inertial confinement fusion, is made by means of a planar slab model whose main features are a sharp ablation front separating the slab and the expanding corona, absorption of constant intensity laser light at a critical surface, profiles for background flow variables consistent with hydrodynamic equations, and heat conduction present in the expanding corona. A sharp ablation front assumption (density at the critical surface is much less than the slab density, ρc/ρs ≪ 1) supposes that the ablated mass is small, so the model is valid for thick targets. Two main regimes are modelized, subsonic and sonic absorption. The growth rate of the instability is obtained, and its variation with kD and kxc is studied (k = perturbation wavenumber; D = slab thickness; xc = ablation to critical surfaces distance). The model shows stabilization over the classical Rayleigh–Taylor growth rate (γ = √kg). The stabilization mechanism is based on heat conduction near the ablation front.


1989 ◽  
Vol 7 (1) ◽  
pp. 27-54 ◽  
Author(s):  
N. K. Gupta ◽  
S. V. Lawande

A formalism for the analysis of the Rayleigh–Taylor instability in the multi-structured solid or shell targets is presented. The formulation covers both the plane and the curved geometry targets. A generalized eigenvalue equation for the exponential growth rate of the instability is derived along with the necessary boundary conditions. Analytical solutions for the growth rate are presented for some elementary density profiles and a comparative study is made between the plane, cylindrical and spherical targets. The solution for the step function density profile is generalized for any number Nof zones forming an arbitrary density profile. This general formulation is illustrated with the explicit calculations for N = 3 and 4. A qualitative treatment of the effects of the ablative flow is also presented. This study predicts a stabilizing effect of the ablative flow on the growth of the instability. Further, a dynamic analysis of the instability growth rate is presented for a representative inertial confinement fusion spherical solid target driven by the laser beams. This study demonstrates that an approximate analysis of the instability with the time independent initial density profile gives the conservative results for the instability growth rate.


1996 ◽  
Author(s):  
S.A. Bel`kov ◽  
S.V. Bondarenko ◽  
O.A. Vinokurov ◽  
G.G. Kochemasov ◽  
L.S. Mkhitarian

2010 ◽  
Vol 14 (1) ◽  
pp. 11-29 ◽  
Author(s):  
Praveen Sharma ◽  
Ram Prajapati ◽  
Rajendra Chhajlani

The linear Rayleigh-Taylor instability of two superposed incompressible magnetized fluids is investigated incorporating the effects of suspended dust particles and viscosity. The basic magnetohydrodynamic set of equations have been constructed and linearized. The dispersion relation for 2-D and 3-D perturbations is obtained by applying the appropriate boundary conditions. The condition of Rayleigh-Taylor instability is investigated for potentially stable and unstable modes, which depends upon magnetic field, viscosity and suspended dust particles. The stability of the system is discussed by applying the Routh-Hurwitz criterion. It is found that the Alfven mode comes into the dispersion relation for perturbations in x, y-directions and in only x-direction, while it does not come into y-directional perturbation. The stable configuration is found to remain stable even in the presence of suspended dust particles. Numerical calculations have been performed to see the effects of various parameters on the growth rate of Rayleigh-Taylor instability. It is found that magnetic field and relaxation frequency of suspended dust particles both have destabilizing influence on the growth rate of Rayleigh-Taylor instability. The effects of kinematic viscosity and mass concentration of dust particles are found to have stabilized the growth rate of linear Rayleigh-Taylor instability.


1976 ◽  
Vol 15 (2) ◽  
pp. 239-244 ◽  
Author(s):  
G. L. Kalra ◽  
S. N. Kathuria

Nonlinear theory of Rayleigh—Taylor instability in plasma supported by a vacuum magnetic field shows that the growth rate of the mode, unstable in the linear theory, increases if the wavelength of perturbation π lies betweenand 2πcrit. This might have an important bearing on the proposed thermonuclear MHD power generation experiments.


2004 ◽  
Vol 22 (1) ◽  
pp. 29-33 ◽  
Author(s):  
N. RUDRAIAH ◽  
B.S. KRISHNAMURTHY ◽  
A.S. JALAJA ◽  
TARA DESAI

The Rayleigh–Taylor instability (RTI) of a laser-accelerated ablative surface of a thin plasma layer in an inertial fusion energy (IFE) target with incompressible electrically conducting plasma in the presence of a transverse magnetic field is investigated using linear stability analysis. A simple theory based on Stokes-lubrication approximation is proposed. It is shown that the effect of a transverse magnetic field is to reduce the growth rate of RTI considerably over the value it would have in the absence of a magnetic field. This is useful in the extraction of IFE efficiently.


2020 ◽  
Vol 634 ◽  
pp. A96
Author(s):  
E. Vickers ◽  
I. Ballai ◽  
R. Erdélyi

Aims. We investigate the nature of the magnetic Rayleigh–Taylor instability at a density interface that is permeated by an oblique homogeneous magnetic field in an incompressible limit. Methods. Using the system of linearised ideal incompressible magnetohydrodynamics equations, we derive the dispersion relation for perturbations of the contact discontinuity by imposing the necessary continuity conditions at the interface. The imaginary part of the frequency describes the growth rate of waves due to instability. The growth rate of waves is studied by numerically solving the dispersion relation. Results. The critical wavenumber at which waves become unstable, which is present for a parallel magnetic field, disappears because the magnetic field is inclined. Instead, waves are shown to be unstable for all wavenumbers. Theoretical results are applied to diagnose the structure of the magnetic field in prominence threads. When we apply our theoretical results to observed waves in prominence plumes, we obtain a wide range of field inclination angles, from 0.5° up to 30°. These results highlight the diagnostic possibilities that our study offers.


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