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

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.

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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).