{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,4,13]],"date-time":"2026-04-13T03:24:37Z","timestamp":1776050677458,"version":"3.50.1"},"reference-count":53,"publisher":"MDPI AG","issue":"6","license":[{"start":{"date-parts":[[2022,6,19]],"date-time":"2022-06-19T00:00:00Z","timestamp":1655596800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"DOI":"10.13039\/501100002261","name":"Russian Foundation for Basic Research","doi-asserted-by":"publisher","award":["19-32-90281"],"award-info":[{"award-number":["19-32-90281"]}],"id":[{"id":"10.13039\/501100002261","id-type":"DOI","asserted-by":"publisher"}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>One of the most important properties of stochastic nonlinear processes, including the turbulence of the hydrodynamic motion of continuous media, is distant spatial correlations. To describe them, an approach was proposed by Shlesinger and colleagues based on a linear integro-differential equation with a slowly decaying kernel, which corresponds to superdiffusion (nonlocal) transfer in the regime of L\u00e9vy walks (L\u00e9vy flights when the finite velocity of the carriers is taken into account). In this paper, we formulate a similar approach that makes it possible to formulate the problem of determining these properties from the scattering spectra of electromagnetic (EM) waves and cross-correlation reflectometry. A universal description of the relationship between the observed symmetric quasi-coherent component in the spectrum of scattered EM waves in plasmas and a process of the Mandelstam\u2013Brillouin scattering type is obtained. It is shown that the nonlocality of spatial correlations of density fluctuations in a turbulent medium is due to long-free-path carriers of the medium\u2019s perturbations, for which the free path distribution function is described by the L\u00e9vy distribution. The effectiveness of the proposed method is shown by the example of the interpretation of the data of cross-correlation reflectometry of EM waves in the radio-frequency range for the diagnosis of turbulent plasma in magnetic confinement devices for axisymmetric toroidal thermonuclear plasma.<\/jats:p>","DOI":"10.3390\/sym14061265","type":"journal-article","created":{"date-parts":[[2022,6,19]],"date-time":"2022-06-19T21:19:26Z","timestamp":1655673566000},"page":"1265","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":4,"title":["New Approach to Cross-Correlation Reflectometry Diagnostics of Nonlocality of Plasma Turbulence"],"prefix":"10.3390","volume":"14","author":[{"given":"Alexander B.","family":"Kukushkin","sequence":"first","affiliation":[{"name":"National Research Center \u201cKurchatov Institute\u201d, 123182 Moscow, Russia"},{"name":"National Research Nuclear University MEPhI (Moscow Engineering Physics Institute), 115409 Moscow, Russia"},{"name":"Moscow Institute of Physics and Technology, National Research University, 141700 Dolgoprudny, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]},{"given":"Andrei A.","family":"Kulichenko","sequence":"additional","affiliation":[{"name":"National Research Center \u201cKurchatov Institute\u201d, 123182 Moscow, Russia"}],"role":[{"role":"author","vocabulary":"crossref"}]}],"member":"1968","published-online":{"date-parts":[[2022,6,19]]},"reference":[{"key":"ref_1","unstructured":"Mandelbrot, B.B. 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