Related papers: Jacobi equations and particle accelerator beam dyn…
Aggregation of particles whose interaction potential depends on their mutual orientation is considered. The aggregation dynamics is derived using a version of Darcy's law and a variational principle depending on the geometric nature of the…
Understanding transverse coupling dynamics is crucial for beam physics, accelerator design, and operations. Currently, most accelerators are designed for uncoupled beams, and coupling is treated as an error or perturbation. Many transverse…
This manuscript introduces novel approaches to three phenomena. First, we extend the algebraic formulation of kinetic theory within the contact framework by making explicit the gauge freedom, thereby obtaining a formulation in which the…
The goal of this manuscript is to give an introduction into the design of the magnet lattice and as a consequence into the transverse dynamics of the particles in a synchrotron or storage ring. Starting from the basic principles of how to…
We consider the acceleration of particles due to a velocity shear in relativistic astrophysical flows. The basic physical picture and the formation of power law momentum spectra is discussed for a non-relativistic velocity field using a…
In accelerator and plasma physics it is accepted that there is no need to solve the dynamical equations for particles in covariant form, i.e. by using the coordinate-independent proper time to parameterize particle world-lines in…
Motivated by obtaining a consistent mathematical description for the radiation reaction of point charged particles in linear classical electrodynamics, a theory of generalized higher order tensors and differential forms is introduced. The…
Beginning with a relativistic action principle for the irrotational flow of collisionless matter, we compute higher order corrections to the Zel'dovich approximation by deriving a nonlinear Hamilton-Jacobi equation for the velocity…
The fate of the molecular geometric phase in an exact dynamical framework is investigated with the help of the exact factorization of the wavefunction and a recently proposed quantum hydrodynamical description of its dynamics. An…
A vacuum medium model is advanced. The motion of a relativistic particle in relation to its interaction with the medium is discussed. It is predicted that elementary excitations of the vacuum, called "inertons," should exist. The equations…
We give a justification for generalizing the notion of the energy momentum stress tensor in general relativity which results in the Jacobi curvature tensor being the embodiment of total energy momentum stress including gravity in general…
In this study, we use the concept of Bohmian trajectories to present a dynamical and deterministic interpretation for the gravity induced wave function reduction. We shall classify all possible regimes for the motion of a particle, based on…
A quantum mechanics representation based on position ($\vec{r}$), linear momentum($\vec{p}$) and energy($E$) eigenvalues is presented here. A set of equations, explicitly independent on wave function, was derived relating these observables.…
Linear accelerators containing the sequence of independently phased cavities with constant geometrical velocity along each structure are widely used in practice. The chain of cavities with identical cell lengths is utilized within a certain…
We discuss some Lagrangian and presymplectic models concerning test particles in electromagnetic and gravitational fields, with the aim of describing an upper bound to the acceleration. Some models are based on the relativistic phase space…
The probability that a particle, crossing the shock along a given direction, be reflected backwards along another direction, was shown to be the key element in determining the spectrum of non--thermal particles accelerated via Fermi…
We consider a relativistic extended object described by a reparametrization invariant local action that depends on the extrinsic curvature of the worldvolume swept out by the object as it evolves. We provide a Hamiltonian formulation of the…
The definitions and some basic properties of the linear transports along paths in vector bundles and the normal frames for them are recalled. The formalism is specified on line bundles and applied to a geometrical description of the…
The dynamical systems of identical particles admitting quadratic integrals of motion are classified. The relevant integrals are explicitly constructed and their relation to separation of variables in H-J equation is clarified.
Phase transitions with spontaneous symmetry breaking and vector order parameter are considered in multidimensional theory of general relativity. Covariant equations, describing the gravitational properties of topological defects, are…