$$\sqrt{\epsilon }$$ Law: Centennial of the First Exact Result of Classical Radiative Transfer Theory

Ivanov, V. V.

doi:10.1007/978-3-030-71254-9_1

Cited by 5 publications

(2 citation statements)

References 46 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…In conclusion, we note that the present work is the result of applying a general theoretical approach [28][29][30][31][32][33] to the practical problem of controlled thermonuclear fusion and demonstrates the relevance of the development of analytical approaches in the theory of nonlocal transfer (a modern review of the status and history of analytical approaches related to the theory of nonlocal transfer of radiation can be found in [53]).…”

Section: Discussionmentioning

confidence: 94%

New Approach to Cross-Correlation Reflectometry Diagnostics of Nonlocality of Plasma Turbulence

Kukushkin

Kulichenko

2022

Symmetry

View full text Add to dashboard Cite

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 Lévy walks (Lévy 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–Brillouin 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’s perturbations, for which the free path distribution function is described by the Lévy 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.

show abstract

Section: Discussionmentioning

confidence: 94%

New Approach to Cross-Correlation Reflectometry Diagnostics of Nonlocality of Plasma Turbulence

Kukushkin

Kulichenko

2022

Symmetry

View full text Add to dashboard Cite

show abstract

“…An alternative to the Biberman-Holstein equation, which is widely used to describe laboratory plasma, is an approach often used in astrophysics, in which the pair of differential kinetic equations for photons and excited atoms/ions is reduced to an integral, in spatial variables, equation for the radiation intensity (see, e.g., [31][32][33][34][35]). Here, the dominant role of long free travels (i.e., Lévy flights) is also recognized, although usually without a proper name.…”

Section: Introduction: Superdiffusion In the Biberman-holstein Modelmentioning

confidence: 99%

Lévy Walks as a Universal Mechanism of Turbulence Nonlocality

Kukushkin,

Kulichenko

2023

Foundations

View full text Add to dashboard Cite

The nonlocality (superdiffusion) of turbulence is expressed in the empiric Richardson t3 scaling law for the mean square of the mutual separation of a pair of particles in a fluid or gaseous medium. The development of the theory of nonlocality of various processes in physics and other sciences based on the concept of Lévy flights resulted in Shlesinger and colleagues’ about the possibility of describing the nonlocality of turbulence using a linear integro-differential equation with a slowly falling kernel. The approach developed by us made it possible to establish the closeness of the superdiffusion parameter of plasma density fluctuations moving across a strong magnetic field in a tokamak to the Richardson law. In this paper, we show the possibility of a universal description of the characteristics of nonlocality of transfer in a stochastic medium (including turbulence of gases and fluids) using the Biberman–Holstein approach to examine the transfer of excitation of a medium by photons, generalized in order to take into account the finiteness of the velocity of excitation carriers. This approach enables us to propose a scaling that generalizes Richardson’s t3 scaling law to the combined regime of Lévy flights and Lévy walks in fluids and gases.

show abstract

The $$\sqrt {\epsilon }$$ -law and the Nonlinear H-Equation

Frisch

2022

Radiative Transfer

View full text Add to dashboard Cite

$$\sqrt{\epsilon }$$ Law: Centennial of the First Exact Result of Classical Radiative Transfer Theory

Cited by 5 publications

References 46 publications

New Approach to Cross-Correlation Reflectometry Diagnostics of Nonlocality of Plasma Turbulence

New Approach to Cross-Correlation Reflectometry Diagnostics of Nonlocality of Plasma Turbulence

Lévy Walks as a Universal Mechanism of Turbulence Nonlocality

The $$\sqrt {\epsilon }$$ -law and the Nonlinear H-Equation

Contact Info

Product

Resources

About