Related papers: Acceleration Mechanisms
We derive a relativistically covariant (although not manifestly so) equation for the distribution function of particles accelerated at shocks, which applies also to extremely relativistic shocks, and arbitrarily anisotropic particle…
There are many problems that lead to analysis of dynamical systems in which one can distinguish motions of two types: slow one and fast one. An averaging over fast motion is used for approximate description of the slow motion. First…
This text is a slightly edited version of lecture notes for a course I gave at ETH, during the Winter term 2000-2001, to undergraduate Mathematics and Physics students. Contents: Chapter 1 - Examples of Dynamical Systems Chapter 2 -…
The scattering of electromagnetic waves by an obstacle is analyzed through a set of partial differential equations combining the Maxwell's model with the mechanics of fluids. Solitary type EM waves, having compact support, may easily be…
The acceleration of a light buoyant object in a fluid is analyzed. Misconceptions about the magnitude of that acceleration are briefly described and refuted. The notion of the added mass is explained and the added mass is computed for an…
Fractional diffusion equations are widely used to describe anomalous diffusion processes where the characteristic displacement scales as a power of time. For processes lacking such scaling the corresponding description may be given by…
We present some recent developments in the theory of particle acceleration at shock fronts in the presence of dynamical reaction of the accelerated particles and self-generation of magnetic field due to streaming instability. The spectra of…
Stationary solutions to the equations of non-linear diffusive shock acceleration play a fundamental role in the theory of cosmic-ray acceleration. Their existence usually requires that a fraction of the accelerated particles be allowed to…
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…
We investigate the impact of magnetic fields and diffusion mechanisms on the energy spectra of particles accelerated via diffusive shock acceleration. We analyse magnetised shock jump conditions and demonstrate how magnetisation and angular…
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 the Fermi…
We add to Galilean symmetries the transformations describing constant accelerations. The corresponding extended Galilean algebra allows, in any dimension $D=d+1$, the introduction of one central charge $c$ while in $D=2+1$ we can have three…
This article summarizes the various ways one may use to construct the Skew Brownian motion, and shows their connections. Recent applications of this process in modelling and numerical simulation motivates this survey. This article ends with…
Shock accelerated electrons are found in many astrophysical environments, and the mechanisms by which they are accelerated to high energies are still not completely clear. For relatively high Mach numbers, the shock is supercritical, and…
The analytical and numerical analysis of the dynamics of charged particles in the field of an intensive transverse electromagnetic wave in a vacuum presented in the article. Identifies the conditions for resonant acceleration of particles.…
The paper deals with systems of ordinary differential equations containing in the right-hand side controls which are discontinuous in phase variables. These controls cause the occurrence of sliding modes. If one uses one of the well-known…
We perform Monte Carlo simulations of diffusive shock acceleration at highly relativistic oblique shock waves. High upstream flow Lorentz gamma factors are used, which are relevant to models of ultra relativistic particle shock acceleration…
In addition to the ponderomotive acceleration of highly relativistic electrons at interaction of very short and very intense laser pulses, a further acceleration is derived from the interaction of these electron beams with the spontaneous…
This paper presents the latest trends in the powering of particle accelerators. A series of solutions is proposed for responding to the challenges of high performance machines. This paper covers the domains of magnetic field uncertainty,…
We model the diffusive shock acceleration of particles in a system of two colliding shock waves and present a method to solve the time-dependent problem analytically in the test-particle approximation and high energy limit. In particular,…