Eur. Phys. J. D 48, 95-109 (2008)
https://doi.org/10.1140/epjd/e2008-00091-5

Modelling of Lévy walk kinetics of charged particles in edge electrostatic turbulence in tokamaks

¹ Institute of Plasma Physics, Academy of Sciences of the Czech Republic, v.v.i, Za Slovankou 3, 18200 Prague 8, Czech Republic
² Faculty of Mathematics and Physics, Charles University, Prague, Czech Republic
³ Faculty of Nuclear Engineering, Czech Technical University, Prague, Czech Republic

Corresponding author: ^a krlin@ipp.cas.cz

Received: 6 November 2007
Revised: 14 February 2008
Published online: 16 May 2008

Abstract

We model and discuss the possible types of motion that charged particles may undergo in a stationary and spatially periodic electrostatic potential and a homogeneous magnetic field. The model is considered to be the simplest approximation of more complex phenomena of plasma edge turbulence in tokamaks. Therein, low frequency turbulence appears in the plasma edge, resulting in a fluctuation of the electron density, and also in the generation of a turbulent electrostatic field. Typical parameters of this turbulent electrostatic field are an electrical potential amplitude of 10–100 V and wave numbers k≈10³ m^-1. In our model, we consider these regimes, together with a homogeneous magnetic field with a magnitude of 1 T. We investigate the dynamics of singly-ionized carbon ions – a typical plasma impurity – with kinetic energies on the order of 10 eV. Besides the obvious Larmor and drift motions, a motion of random-walk and of Lévy walk character appear therein. All of these types of motion can play an important role in the modelling of the anomalous diffusion of particles from the plasma edge turbulence region. The dynamics mentioned will cause an inevitable escape of energetic particles and thus of power loss from the thermonuclear reactor. Moreover, Lévy walk kinetics represents a very interesting kind of kinetics, currently of great interest, which was previously not so often discussed.