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Stochastic phenomena occurring within charged particle beams can be handled using the Vlasov-Fokker-Planck generalization of the Vlasov equation. In particular, this non-deterministic approach can deal with effects due to Coulomb scattering…
The aim of this contribution is to study the particle dynamics in a storage ring under the influence of noise. Some simplified stochastic beam dynamics problems are treated by solving the corresponding Fokker-Planck equations numerically.
Diffusion of particles in velocity space undergoing turbulent field was extensively studied in the problem of warm beam relaxation. Under low field intensities the diffusion is described by the Fokker-Planck equation with the diffusion…
The Vlasov equation embodies the smooth field approximation of the self-consistent equation of motion for charged particle beams. This framework is fundamentally altered if we include the fluctuating forces that originate from the actual…
This report provides a description of unbunched beam stochastic cooling in the framework of control theory. The main interest in the investigation is concentrated on the beam stability in an active cooling system. A stochastic cooling…
We study the dynamics of inertial particles in turbulence using datasets obtained from both direct numerical simulations and laboratory experiments of turbulent swirling flows. By analyzing time series of particle velocity increments at…
The dynamical evolution of a Brownian particle in an inhomogeneous medium with spatially varying friction and temperature field is important to understand conceptually. It requires to address the basic problem of relative stability of…
For a plasma in a stationary homogeneous turbulence, the Fokker-Planck equation is derived from the nonlinear Vlasov equation by introducing the entropy principle. The ensemble average in evaluating the kinetic diffusion tensor, whose…
Using the scheme of mesoscopic nonequilibrium thermodynamics, we construct the one- and two- particle Fokker-Planck equations for a system of interacting Brownian particles. By means of these equations we derive the corresponding balance…
A pointlike particle of finite mass m, moving in a one-dimensional viscous environment and biased by a spatially dependent force, is considered. We present a rigorous mapping of the Fokker-Planck equation, which determines evolution of the…
The Fokker--Planck Equation can be used in a partially-coherent imaging context to model the evolution of the intensity of a paraxial x-ray wave field with propagation. This forms a natural generalisation of the transport-of-intensity…
An analytic solution for a Fokker-Planck equation that describes propagation of energetic particles through a scattering medium is obtained. The solution is found in terms of an infinite series of mixed moments of particle distribution. The…
Missing cascades from TeV blazar beams indicate that collective plasma effects may play a significant role in their energy loss. It is possible to mimic the evolution of such highly energetic pair beams in laboratory experiments using…
We present a general framework in which we can accurately describe the non-equilibrium dynamics of trapped atomic gases. This is achieved by deriving a single Fokker-Planck equation for the gas. In this way we are able to discuss not only…
We analyze the diffusion of a Brownian particle in a fluid under stationary flow. By using the scheme of non-equilibrium thermodynamics in phase space, we obtain the Fokker-Planck equation which is compared with others derived from kinetic…
Many physical, biological or social systems are governed by history-dependent dynamics or are composed of strongly interacting units, showing an extreme diversity of microscopic behaviour. Macroscopically, however, they can be efficiently…
The new scheme of stochastic quantization is proposed. This quantization procedure is equivalent to the deformation of an algebra of observables in the manner of deformation quantization with an imaginary deformation parameter (the Planck…
Fokker-Planck equations are extensively employed in various scientific fields as they characterise the behaviour of stochastic systems at the level of probability density functions. Although broadly used, they allow for analytical treatment…
We describe a new approach for modeling the transport of high energy particles accelerated during flares from the acceleration region in the solar corona until their eventual thermalization in the flare footpoint. Our technique numerically…
A new Fokker-Planck equation is developed for treating resonance line scattering, especially relevant to the treatment of Lyman alpha in the early universe. It is a "corrected" form of the equation of Rybicki & Dell'Antonio that now obeys…