Abstract
We revisit the applications of quasi-linear theory as a paradigmatic model for weak plasma turbulence and the associated bump-on-tail problem. The work, presented here, is built around the idea that large-amplitude or strongly shaped beams do not relax through diffusion only and that there exists an intermediate time scale where the relaxations are convective (ballistic-like). We cast this novel idea in the rigorous form of a self-consistent nonlinear dynamical model, which generalizes the classic equations of the quasi-linear theory to "broad" beams with internal structure. We also present numerical simulation results of the relaxation of a broad beam of energetic particles in cold plasma. These generally demonstrate the mixed diffusive-convective features of supra-thermal particle transport; and essentially depend on nonlinear wave-particle interactions and phase-space structures. Taking into account modes of the stable linear spectrum is crucial for the self-consistent evolution of the distribution function and the fluctuation intensity spectrum.
Highlights
The relaxation of supra-thermal particle beams in plasmas is a problem of fundamental significance
The relevance of the BoT problem for fusion plasma research was revived in the 1990s by Berk and Breizman [18,19,20], who proposed it as a paradigmatic model to investigate and understand the nonlinear interaction of supra-thermal particles with Alfvén fluctuations [20,21,22,23]
We address the role of nonlinearity in supra-thermal particle transport by a fluctuation spectrum that is not necessarily “broad”
Summary
The relaxation of supra-thermal particle beams in plasmas is a problem of fundamental significance. The relevance of the BoT problem for fusion plasma research was revived in the 1990s by Berk and Breizman [18,19,20], who proposed it as a paradigmatic model to investigate and understand the nonlinear interaction of supra-thermal particles with Alfvén fluctuations [20,21,22,23]. Accounting for modes of the linear stable spectrum is crucial [40,41] Posing these issues for the BoT problem becomes an interesting and relevant research topic, in light of its possible implications as a paradigm for Alfvénic fluctuation-induced supra-thermal particle transport in fusion plasmas near marginal stability. Convective relaxation is found to occur for small nonlinearity parameter as a result of a self-consistent evolution of the fluctuation spectrum on the same time scales of particle transport We support these findings with a simplified theory model.
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