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Fluid simulations show that when a sinusoidal density modulation is superimposed on a linear density profile, convective instabilities can become absolutely unstable. This conversion can occur for two-plasmon-decay and stimulated Raman Scattering instabilities under realistic direct-drive inertial confinement fusion conditions and can affect hot electron generation and laser energy deposition. Analysis of the three-wave model shows that a sufficiently large change of the density gradient in a linear density profile can turn convective instabilities into absolute ones. An analytical expression is given for the threshold of the gradient change, which depends on the convective gain only.

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