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Effective radial Liapunov exponent for the radial diffusion of test electrons
Author(s) -
Maluckov A.,
Nakajima N.,
Okamoto M.,
Murakami S.,
Kanno R.
Publication year - 2003
Publication title -
contributions to plasma physics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.531
H-Index - 47
eISSN - 1521-3986
pISSN - 0863-1042
DOI - 10.1002/ctpp.200310015
Subject(s) - physics , exponent , electron , magnetic field , bounded function , lyapunov exponent , condensed matter physics , mathematical analysis , quantum mechanics , mathematics , nonlinear system , philosophy , linguistics
The radial diffusion of test electrons in the bounded magnetic field region with irregularities is a realization of the magnetic (deterministic) and collisional (statistical) stochasticities. To clarify the development of stochasticities the effective radial Liapunov exponent L er , the number of the electron trajectories (magnetic field lines) with positive radial Liapunov exponent N p , the distribution of the radial Liapunov exponent, Kolmogorov entropy and 3D Liapunov exponent are calculated numerically. In the absence of collisions the overlapping among magnetic islands (generation of the global stochasticity) is indicated by the qualitative change from negative to positive L er in the long time limit. The fact that N p < N , where N is the number of test electrons, is the sign of sticking to the magnetic field structures. From the viewpoint of the radial Liapunov exponents both stochasticities manifest similarly. It is shown that the distribution of the radial Liapunov exponents is not the elementary one, except in the region of the extremely frequent collisions and partially destroyed magnetic field. Transition of the radial diffusion from the strange to the standard diffusion [1] is related with neglecting sticking of the electrons to the magnetic field structures by enough frequent collisions.