scholarly journals Intuitive calculation of the relativistic Rayleigh-Taylor instability linear growth rate

2011 ◽  
Vol 29 (2) ◽  
pp. 255-257 ◽  
Author(s):  
Antoine Bret
Keyword(s):  
Growth Rate ◽  
Inertial Confinement Fusion ◽  
Linear Growth ◽  
Taylor Instability ◽  
Linear Growth Rate ◽  
Inertial Confinement ◽  
Direct Derivation ◽  
Straightforward Calculation ◽  
Confinement Fusion ◽  
Rayleigh Taylor Instability

AbstractThe Rayleigh-Taylor instability is a key process in many fields of Physics ranging from astrophysics to inertial confinement fusion. It is usually analyzed deriving the linearized fluid equations, but the physics behind the instability is not always clear. Recent works on this instability allow for an very intuitive understanding of the phenomenon and for a straightforward calculation of the linear growth rate. In this Letter, it is shown that the same reasoning allows for a direct derivation of the relativistic expression of the linear growth rate for an incompressible fluid.

scholarly journals Rayleigh–Taylor instability in multi-structured inertial confinement fusion targets

1989 ◽  
Vol 7 (1) ◽  
pp. 27-54 ◽  
Author(s):  
N. K. Gupta ◽  
S. V. Lawande
Keyword(s):  
Growth Rate ◽  
Density Profile ◽  
Inertial Confinement Fusion ◽  
Initial Density ◽  
Taylor Instability ◽  
Instability Growth Rate ◽  
Inertial Confinement ◽  
Confinement Fusion ◽  
Instability Growth ◽  
Rayleigh Taylor Instability

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.

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