Related papers: Jacobi equations and particle accelerator beam dyn…
First order Fermi acceleration at astrophysical shocks is often invoked as a mechanism for the generation of non-thermal particles. This mechanism is especially simple in the approximation that the accelerated particles behave like test…
The Fermi acceleration model was introduced to describe how cosmic ray particles are accelerated to great speeds by interacting with moving magnetic fields. We identify a new variation of the model where light ions interact with a moving…
Continuum mechanics can be formulated in the Lagrangian frame (addressing motion of individual continuum particles) or in the Eulerian frame (addressing evolution of fields in an inertial frame). There is a canonical Hamiltonian structure…
By identifying Hamiltonian flows with geodesic flows of suitably chosen Riemannian manifolds, it is possible to explain the origin of chaos in classical Newtonian dynamics and to quantify its strength. There are several possibilities to…
We lay down the foundations of particle dynamics in mechanical theories that satisfy the relativity principle and whose kinematics can be formulated employing reference frames of the type usually adopted in special relativity. Such…
In this study we derive a single-particle equation of motion, from first-principles, starting out with a microscopic description of a tracer particle in a one-dimensional many-particle system with a general two-body interaction potential.…
While a growing body of research indicates that relativistic magnetic reconnection is a prodigious source of particle acceleration in high-energy astrophysical systems, the dominant acceleration mechanism remains controversial. Using a…
This paper is concerned with basic geometric properties of the phase space of a classical general relativistic particle, regarded as the 1st jet space of motions, i.e. as the 1st jet space of timelike 1--dimensional submanifolds of…
We present a formal derivation of the key equations governing gravitational lensing in arbitrary space-times, starting from the basic properties of Jacobi fields and their expressions in terms of the exponential map. A careful analysis of…
In this paper, we present a relation between Jacobi-Reeb dynamics and the dynamics associated with a mechanical Hamiltonian system with respect to a linear Poisson structure on a vector bundle. For this purpose, we will use the so-called…
We extend the equations of motion that describe non-relativistic elastic collision of two particles in one dimension to an arbitrary associative algebra. Relativistic elastic collision equations turn out to be a particular case of these…
The present article deals with general mechanics in an unconventional manner. At first, Newtonian mechanics for a point particle has been described in vectorial picture, considering Cartesian, polar and tangent-normal formulations in a…
One of the most severe limitations in particle accelerators and beam transport are non-linear effects. Techniques to study and possibly suppress some of these detrimental effects exist, the most popular are based on particle tracking and…
It has long been known that the ellipse normally used to model the phase space extension of a beam in linear dynamics may be represented by a complex number which can be interpreted similarly to a complex impedance in electrical circuits,…
The investigation of single-particle dynamics in circular particle accelerators can be traced back to pioneering works in the 1950s. Traditionally, the design of new circular accelerators has focused on optimising linear dynamics, striving…
We analyze the geometry of a rotating disk with a tangential acceleration in the framework of the Special Theory of Relativity, using the kinematic linear differential system that verifies the relative position vector of time-like curves in…
In the paper a solution for equilibrium configurations of an elastic beam subject to three points bending is given in terms of Jacobi elliptical functions. General equations are derived and the domain of solution is established. Several…
A wide range of physical problems can be described by randomly-oriented linear trajectories, including any system of objects, organisms, particles, or rays that follow a linear path. Dependent upon the particular random variables that…
A kinetic theory is developed to describe radiating electrons whose motion is governed by the Lorentz-Dirac equation. This gives rise to a generalized Vlasov equation coupled to an equation for the evolution of the physical submanifold of…
We consider the problem of approximating the Langevin dynamics of inertial particles being transported by a background flow. In particular, we study an acceleration corrected advection-diffusion approximation to the Langevin dynamics, a…