A stochastic model for the semiclassical collective dynamics of charged beams in particle accelerators

We obtain a limit when mass tends to zero of the relativistic diffusion of Schay and Dudley. The diffusion process has the log-normal distribution. We discuss Langevin stochastic differential equations leading to an equilibrium distribution.We show that for the Juttner equilibrium distribution the relativistic diffusion is a linear approximation to the Kompaneetz equation describing a photon diffusion in an electron gas.The stochastic equation corresponding to the Juttner dis...

Radiation reaction against a relativistic electron is of critical importance since the experiment to check this "quantumness" becomes possible soon with an extremely high-intensity laser beam. However, there is a fundamental mathematical quest to apply any laser profiles to laser focusing and superposition beyond the Furry picture of its usual method by a plane wave. To give the apparent meaning of $q(\chi)$ the quantumness factor with respect to a radiation process is absent...

This paper considers a main particle and an incident particle classical mechanics elastic collision preserving energy and momentum while ignoring the angular momentum, spin or other particle characteristics. The main result of the paper shows that the colliding two particle classical Hamiltonian energy can be represented in four weighted individual particle in symmetric and anti-symmetric (osmotic) terms similar to the quadratic Nelson measure used in the derivation of the Sc...

A kinetic equation for the joint probability distribution for fixed values of the classical action, momentum and density has been derived. Further, the hydrodynamic equations of continuity and balance of momentum density have been transformed into a Schroedinger-like equation, describing particle motion in an effective electro-magnetic field and an expression for the gauge potentials has been obtained.

Wallstrom's criticism of existing formulations of stochastic mechanics is that they fail to derive the empirical predictions of orthodox quantum mechanics because they require an ad hoc quantization condition on the postulated velocity potential, \emph{S}, in order to derive Schr\"odinger wave functions. We propose an answer to this criticism by modifying the Nelson-Yasue formulation of non-relativistic stochastic mechanics for a spinless particle with the following hypothesi...

Stochastic electrodynamics is the classical electrodynamic theory of interacting point charges which includes random classical radiation with a Lorentz-invariant spectrum whose scale is set by Planck's constant. Here we give a cursory overview of the basic ideas of stochastic electrodynamics, of the successes of the theory, and of its connections to quantum theory.

Tracking a real trajectory of a quantum particle still has been treated as the interpretation problem. It shall be expressed by a Brownian (stochastic) motion suggested by E. Nelson, however, the well-defined mechanism of field generation from a stochastic particle hasn't been proposed yet. For the improvement of this, I propose the extension of Nelson's quantum dynamics, for describing a relativistic scalar electron with its radiation equivalent to the Klein-Gordon particle ...

We present a novel technique for studying the evolution of a particle distribution using single particle dynamics such that the distribution can be accurately reconstructed using fewer particles than existing approaches. To demonstrate this, the Landau-Lifshiftz description of radiation reaction is adapted into a semi-classical model, for which the Vlasov equation is intractable. Collision between an energetic electron bunch and high-intensity laser pulses are then compared u...

I propose that quantum mechanics is a stochastic theory and quantum phenomena derive from the existence of real vacuum stochastic fields filling space. I revisit stochastic electrodynamics (SED), a theory that studies classical systems of electrically charged particles immersed in an electromagnetic (zeropoint) radiation field with spectral density proportional to the cube of the frequency, Planck's constant appearing as the parameter fixing the scale. Asides from briefly rev...

The connection is established between two theories that have developed independently with the aim to describe quantum mechanics as a stochastic process, namely stochastic quantum mechanics (sqm) and stochastic electrodynamics (sed). Important commonalities and complementarities between the two theories are identified, notwithstanding their dissimilar origins and approaches. Further, the dynamical equation of sqm is completed with the radiation terms that are an integral eleme...