Brownian motion in a magnetic field

Kursunoglu, Behram N.

doi:10.1016/0003-4916(62)90027-1

Cited by 53 publications

(25 citation statements)

References 4 publications

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“…We also assume that the particle is influenced by a linear friction force. Such formulation is a natural generalization of the classical problem for the Brownian particle [14]. It allows us to consider in a simplest way the peculiarities of the motion stipulated by non-Gaussian Levy statistics of a random electric field.…”

Section: Resultsmentioning

confidence: 99%

“…[18]. We consider a test charged particle with the mass m and the charge e, embedded in constant external magnetic field B and subjected to stochastic electric field E (t) .We also assume, as in the classical problem for the charged Brownian particle [14], that the particle is influenced by the linear friction force −νm v, ν is the friction coefficient. For this particle the Langevin equations of motion are…”

Section: Fractional Fokker-planck Equation For Charged Particle In Mamentioning

confidence: 99%

“…We consider the motion of a charged Levy particle in a constant external magnetic field and random electric field obeying non-Gaussian Levy statistics. Our problem is a natural generalization of the classical example of the motion of a charged Brownian particle [14]. We solve the fractional Fokker-Planck equation with fractional velocity derivative, study the relaxation processes in phase and real spaces as well, and estimate fractional moments of energy and coordinate.…”

Section: Introductionmentioning

confidence: 99%

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Fractional kinetics for relaxation and superdiffusion in a magnetic field

2002

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We propose fractional Fokker-Planck equation for the kinetic description of relaxation and superdiffusion processes in constant magnetic and random electric fields. We assume that the random electric field acting on a test charged particle is isotropic and possesses non-Gaussian Levy stable statistics. These assumptions provide us with a straightforward possibility to consider formation of anomalous stationary states and superdiffusion processes, both properties are inherent to strongly non-equilibrium plasmas of solar systems and thermonuclear devices. We solve fractional kinetic equations, study the properties of the solution, and compare analytical results with those of numerical simulation based on the solution of the Langevin equations with the noise source having Levy stable probability density. We found, in particular, that the stationary states are essentially non-Maxwellian ones and, at the diffusion stage of relaxation, the characteristic displacement of a particle grows superdiffusively with time and is inversely proportional to the magnetic field.

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Section: Resultsmentioning

confidence: 99%

Section: Fractional Fokker-planck Equation For Charged Particle In Mamentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Fractional kinetics for relaxation and superdiffusion in a magnetic field

2002

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“…To our knowledge, except for the paper [2] (mentioned in [5] as a footnote reference for the purpose of evaluation of the mean square velocity and its mean square displacement at equilibrium), for a Brownian particle in a constant magnetic field no attempt was made in the literature to give a complete characterization of the stochastic process itself, nor pass to the associated macrosopic (hydrodynamical formalism) balance equations. (Cf.…”

Section: Introductionmentioning

confidence: 99%

“…That issue has originated from studies of the diffusion of plasma across a magnetic field [1], [2] and nowadays, together with a free Brownian motion example, stands for a textbook illustration of how transport and auto-correlation functions should be computed in generic situations governed by the Langevin equation (to a suitable degree of approximation of a kinetic theory, when collisions are stochastically modeled in terms of a random force), cf. [3] but also [4], [5].…”

Section: Introductionmentioning

confidence: 99%