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We show that the linearized Vlasov-Poisson equations around self-similarnon-homogeneous states near zero contain the full plasma echo mechanism,yielding Gevrey 3 as a critical stability class. Moreover, here Landau dampingmay persist despite blow-up: We construct a critical Gevrey regularity class inwhich the force field converges in $L^2$. Thus, on the one hand, the physicalphenomenon of Landau damping holds. On the other hand, the density diverges toinfinity in Sobolev regularity. Hence, ``strong damping'' cannot hold.

On Echo Chains in Landau damping: Self-similar Solutions and Gevrey 3 as a Linear Stability Threshold