The stochastic structures of the material surface observed in thermonuclear plasma devices, formed irradiated with hot plasma, have the property of statistical self-similarity — scale invariance from tens of nanometers to hundreds of micrometers. Plasma-surface interaction in thermonuclear devices is characterized not only by high energy content, but also by collective effects under the influence of strong turbulence of the near-wall plasma. The problem of the observed surface shaping relates to the growth of stochastic interface boundaries under the influence of several competing agglomeration mechanisms. In thermonuclear plasma devices, this leads to the growth of unique forms of stochastic relief with a self-similar structure and hierarchical granularity of the material with a long-range order in the structure, differing from both crystalline and amorphous bodies.