Statistics of beam-driven waves in plasmas with ambient fluctuations: Reduced-parameter approach

Tyshetskiy, Yu.; Cairns, I. H.; Robinson, P. A.
September 2008
Physics of Plasmas;Sep2008, Vol. 15 Issue 9, p092110
Academic Journal
A reduced-parameter (RP) model of quasilinear wave-plasma interactions is used to analyze statistical properties of beam-driven waves in plasmas with ambient density fluctuations. The probability distribution of wave energies in such a system is shown to have a relatively narrow peak just above the thermal wave level, and a power-law tail at high energies, the latter becoming progressively more evident for increasing characteristic amplitude of the ambient fluctuations. To better understand the physics behind these statistical features of the waves, a simplified model of stochastically driven thermal waves is developed on the basis of the RP model. An approximate analytic solution for stationary statistical distribution of wave energies W is constructed, showing a good agreement with that of the original RP model. The “peak” and “tail” features of the wave energy distribution are shown to be a result of contributions of two groups of wave clumps: those subject to either very slow or very fast random variations of total wave growth rate (due to fluctuations of ambient plasma density), respectively. In the case of significant ambient plasma fluctuations, the overall wave energy distribution is shown to have a clear power-law tail at high energies, P(W)∝W-α, with nontrivial exponent 1<α<2, while for weak fluctuations it is close to the lognormal distribution predicted by pure stochastic growth theory. The model’s wave statistics resemble the statistics of plasma waves observed by the Ulysses spacecraft in some interplanetary type III burst sources. This resemblance is discussed qualitatively, and it is suggested that the stochastically driven thermal waves might be a candidate for explaining the power-law tails in the observed wave statistics without invoking mechanisms such as self-organized criticality or nonlinear wave collapse.


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