Dynamic stabilization of Rayleigh–Taylor instability in an ablation front

Abstract

Dynamic stabilization of Rayleigh-Taylor instability in an ablation front is studied by considering a modulation in the acceleration that consists of sequences of Dirac deltas. This allows obtaining explicit analytical expressions for the instability growth rate as well as for the boundaries of the stability region. As a general rule, it is found that it is possible to stabilize all wave numbers above a certain minimum value k m , but the requirements in the modulation amplitude and frequency become more exigent with smaller k m . The essential role of compressibility is phenomenologically addressed in order to find the constraint it imposes on the stability region. The results for some different wave forms of the acceleration modulation are also presented.

Vibration waveform effects on dynamic stabilization of ablative Rayleigh-Taylor instability

“…Instead, the effect equivalent to the surface tension that in the ablative RTI appears when the front is at least partially driven by thermal conduction, resulted to be beneficial but not essential for the dynamic stabilization. 15 This result was of special relevance for the scenario of ICF ablatively driven by ion beams recently considered by Logan et al 16 in which the driver energy is transported up to the front mostly by classical Coulombian collisions. In such a case, the absence of transport by thermal conduction prevents the surface tension-like effect that stabilize the wave numbers larger than the cut-off value k c .…”

“…Recently, we have shown that the essence of the problem can be captured by using the simplest possible driving waveform which consists in a sequence of Dirac deltas. 13,15 In such a way, we have been able to develop a completely analytical treatment that yields explicit expressions for the stability regions and for the instability growth rates as functions of the parameters of the acceleration modulation as well as of the parameters of the steady ablation front. As in the case of Newtonian fluids, we have found that the damping effect equivalent to the viscosity produced by the ablation process by itself is crucial for the dynamic stabilization of the front.…”

Dynamic Stabilization of the Ablative Rayleigh-Taylor Instability for Heavy Ion Fusion

“…If δh(s) is piece-wise constant or a series of δ-functions, then the solution of Eq. (7) can be constructed piece-wise [20].…”

“…For heavy ion fusion application, Kawata et al [11,18,19] showed that time-dependent acceleration effectively reduces the growth of the RT instability. On the other hand, Piriz et al [20] concluded that time-modulation of the acceleration is ineffective using a model of time-modulation consisting of a sequence of pulsed accelerations with the shape of δ-functions.…”

Dynamic stabilization of the ablative Rayleigh–Taylor instability for heavy ion fusion

“…For heavy ion fusion application, Kawata et al [11,18,19] showed that time-dependent acceleration effectively reduces the growth of the RT instability. On the other hand, Piriz et al [20] concluded that time-modulation of the acceleration is ineffective using a model of time-modulation consisting of a sequence of pulsed accelerations with the shape of δ-functions.…”