On the classical approach to describing the diffusion of cosmic rays in a turbulent medium

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Abstract

The inhomogeneous structure of the interstellar medium (ISM) is characterized by largescale fluctuations that significantly affect the cosmic ray propagation process. Accounting for this influence can not only lead to adjustments in the diffusion process parameters but even to pass from differential operators to integral ones. The most crucial characteristics of a turbulent medium is its power spectrum. Including appropriate approximations of this spectrum allows us to consider this problem in the framework of the traditional diffusion approach [1, 2]. This article explores the analytical representations of this spectrum applied in the cosmic ray transfer theory, including the four-parameter Uchaikin—Zolotarev approximation, derived from the generalized Ornstein—Zernike equation. Testing of the latter revealed that, with carefully chosen parameters, it accurately replicates numerical modeling results both in the inertial interval and beyond. Therefore, it can be effectively employed in addressing cosmic ray transfer issues within a turbulent interstellar medium.

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About the authors

Vladimir V. Uchaikin

Ulyanovsk State University

Author for correspondence.
Email: vuchaikin@gmail.com

Department of Theoretical Physics

Russian Federation, Ulyanovsk

Ilya I. Kozhemyakin

Ulyanovsk State University

Email: kozhilya@gmail.com

Department of Theoretical Physics

Russian Federation, Ulyanovsk

Vladimir A. Litvinov

Barnaul Law Institute of the Ministry of Internal Affairs of Russia

Email: vuchaikin@gmail.com
Russian Federation, Barnaul

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2. Fig. 1. (a–z) Ultrasonic approximations of the power spectra of turbulent velocity fluctuations in four different regimes numerically modeled in [25–27]. Dashed curves represent the modeling results, solid curves represent their approximations using formula (4). Sloping lines correspond to purely power-law spectra.

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