V.P. Budaev
Stochastic clustering of materials by plasma - surface interaction


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: : 105 : 5 : 2017

Recently stochastic clustering with statistical self-similarity (fractality) has been found on material surface exposed under extreme plasma thermal loads in fusion devices (see [1]). In such devices, multiple processes of erosion and redeposition of the eroded material, surface melting and motion of the surface layers lead to a stochastic surface growth on the scales from tens of nanometers to hundreds of micrometers. The moving of eroded material species during redeposition from plasma and agglomeration on the surface is governed by stochastic electric fields generated by the high-temperature plasma. The specific property of the near-wall plasma in fusion device is the non-Gaussian statistics of electric field fluctuations with long-range correlations [2]. It leads to the stochastic agglomerate growth with a self- similar structure (hierarchical granularity - fractality) of non-Gaussian statistics contrary to a trivial roughness observed in ordinary processes of stochastic agglomeration. The dominant factor in such process in fusion device is the collective effect during stochastic clustering rather than the chemical element composition and physical characteristics of the solid material. In support of this view it is reported in this Letter, that such similar stochastic fractal structure with hierarchical granularity and self- similarity is formed on various materials, such as tungsten, carbon materials and stainless steel exposed to high-temperature plasma in fusion devices. In the literature it is discussed hypotheses of universal scalings of stochastic objects and processes with multi-scale invariance property (statistical self- similarity), see e.g. [3]. The kinetic models propose the describing of the stochastic clustering with a self- similar structure and considering the power law solutions for the number N of agglomerating clusters with mass m (see e.g. [4]), N(m)=Cm-(3+ η)/2, where η is a self-similarity exponent of the agglomeration kinetic model, C is a constant factor. It is surprisingly found in this Letter that such the power laws (with power exponents from -2.4 to -2.8) describing the roughness of the test specimens from fusion devices are strictly deviated from that of the reference samples formed in a trivial agglomeration process forming Brownian-like rough surface (such as samples exposed to low-temperature glow discharge plasma and rough steel casting with the power law exponent in the range of -1.97 to -2.2). Statistics of stochastic clustering samples from fusion devices is typically non-Gaussian and has a "heavy" tails of probability distribution functions (PDF) of stochastic surface heights (of the Hurst exponent from 0.68 to 0.86). It is contrary to the Gaussian PDF of the reference samples with trivial stochastic surface. Stochastic clustering of materials from fusion devices is characterised by multifractal statistics. Quantitative characteristics of statistical inhomogeneity of such material structure, including multifractal spectrum with broadening of 0.5 1.2, are in the range observed for typical multifractal objects and processes in nature. This may indicate a universal mechanism of stochastic clustering of materials under the influence of high-temperature plasma.


1. V.P. Budaev et al., JETP Letters vol. 95, 2, 78 (2012).
2. V.P. Budaev, S.P. Savin, L.M. Zelenyi, Physics-Uspekhi 54 (9), 875 (2011)
3. A. L. Barabasi and H. E. Stanley, Fractal Concepts in Surface Growth (Cambridge Univ. Press, Cambridge, 1995).
4. C. Connaughton, R. Rajesh, O. Zaboronski, PRL 94 (19), 194503 (2005).