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Author(s):
A. Maluckov, N. Nakajima, M. Okamoto, S. Murakami and R. Kanno
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Title:
Statistical Properties of the Particle Radial Diffusion in a Radially Bounded Irregular Magnetic Field
Date of publication:
Oct. 2001
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Key words:
statistical properties, radial particle diffusion, radially bounded irregular magnetic field, Wiener process, uniform mixing process, strange diffusive process
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Abstract:
Statistical properties of the particle radial diffusion are clarified in the various types of the radially bounded irregular magnetic field inside a torus plasma, where the collisional (statistical) stochasticity due to the Coulomb collision and the magnetic (deterministic) stochasticity due to a radially bounded perturbed field coexist. The former is initialized in the velocity space, and the latter is in the configuration space. Extensive numerical analyses are performed in the two dimensional parameter space (s_b/s_bc,nu/nu_t), where s_b and nu are the strength of a magnetic field perturbation and the collision (deflection) frequency, respectively. The normalization parameter s_bc corresponds to the islands overlapping criterion, and nu_t is the characteristic frequency of the passing particle orbits in the corresponding regular magnetic field. In the absence of the Coulomb collision, as s_b/s_bc(geq 1) increases, the magnetic field stochasticity or the particle radial diffusion with only parallel drift motion comes to appear as a uniform mixing process reflecting the non-locality of orbits in a radially bounded stochastic region, which is a non-diffusive, uniform, statistically stationary, and Markov process after the exponentially fast relaxation of correlations. The Coulomb collisions interrupt the fast non-local radial displacement of particles along the stochastic magnetic field lines, however, the radial displacement is still non-local, so that the particle radial diffusion develops as a strange diffusive process in the long time limit: subdiffusive, neither uniform nor Gaussian, and statistically non-stationary process, in almost all
(s_b/s_bc,nu/nu_t)parameter space. When the collisions are fairly frequent (nu/nu_gg1) and uniformity of the magnetic field stochasticity is fairly lost (s_b/s_bc geq 1), the locality of the particle motion is recovered, leading to a Wiener process with normal diffusivity, Gaussianity, statistical non-stationarity, and Markovianity, as well as the neoclassical diffusion in the regular magnetic field. Non-locality of particle orbits due to magnetic stochasticity produces the various types of diffusion process under the influence of the Coulomb collisions.
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