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Transport of Particles in a Turbulent Field

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Part of the Springer Series on Atomic, Optical, and Plasma Physics book series (SSAOPP,volume 78)

Abstract

In this chapter we study a particle transport in Hamiltonian systems perturbed by a weak turbulent wave field. This problem is a very simplified version of an important but a complex problem of energy and particle transport in magnetically confined turbulent plasmas (Wesson 2004; see also Sect. 11.3 for some bibliographic comments). One expects that this study allows one to understand some features of the complex problem of transport in fusion plasmas. Specifically, we consider the dynamics of a one-degree of freedom Hamiltonian system perturbed by a weak turbulent wave field and closely related problem of a runaway electron transport via micro-turbulence in tokamaks.

Keywords

  • Turbulence Level
  • Magnetic Surface
  • Runaway Electron
  • Transport Barrier
  • Turbulent Field

These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Notes

  1. 1.

    The Kubo number \(K\) measures the particle’s capacity of exploring the space structure (see, e.g., Bakunin 2008). The definition of \(K\) (11.6) is, probably, more adequate in our problem of the test particle transport in a turbulent wave field, particularly, a runaway electron transport in a fluctuating magnetic field which will be studied in Sect. 11.2. Particularly, such a definition (11.6) \(K\) has been used by Vlad and Spineanu (2005) and Vlad et al. (2005) in the similar problems of the test particle transport in the turbulent field. There is also another definition of \(K\) used by Pommois et al. (2001) for the transport of the magnetic field lines in a turbulent magnetic field.

  2. 2.

    The existence of gaps in the density of rational tori has been pointed out already in a number works, for example, by Austin et al. (2006), Brakel et al. (2002), Eriksson et al. (2002), Garbet et al. (2003), Gohil et al. (2003), Hogeweij et al. (2004), Kasilov et al. (2002), Joffrin et al. (2003), Lopes Cardozo (2004), and Razumova et al. (2003, 2008). However, to my knowledge no quantitative estimations have been given.

  3. 3.

    This mechanism, particularly has been discussed by Austin et al. (2006), Brakel et al. (2002), Eriksson et al. (2002), Garbet et al. (2003), Gohil et al. (2003), Hogeweij et al. (2004), Kasilov et al. (2002), Joffrin et al. (2003), Lopes Cardozo (2004), and Razumova et al. (2003, 2008).

  4. 4.

    The fractal behavior of the diffusion coefficients has been also observed in dynamical systems described by one-dimensional, piecewise linear, chaotic mappings (Klages and Dorfman 1995; Knight and Klages 2011). In these systems the diffusion coefficients have a fractal structure as a function of the mapping parameter.

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Correspondence to Sadrilla Abdullaev .

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Abdullaev, S. (2014). Transport of Particles in a Turbulent Field. In: Magnetic Stochasticity in Magnetically Confined Fusion Plasmas. Springer Series on Atomic, Optical, and Plasma Physics, vol 78. Springer, Cham. https://doi.org/10.1007/978-3-319-01890-4_11

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