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Fermi acceleration can take place at ultra-relativistic shock waves if the upstream or downstream magnetic field has been remodeled so that most of the magnetic power lies on short spatial scales. The relevant conditions under which Fermi…

Astrophysics · Physics 2009-11-13 Guy Pelletier , Martin Lemoine , Alexandre Marcowith

We investigate the physics of particle acceleration at non-relativistic shocks exploiting two different and complementary approaches, namely a semi-analytic modeling of cosmic-ray modified shocks and large hybrid (kinetic protons/fluid…

High Energy Astrophysical Phenomena · Physics 2015-06-11 Damiano Caprioli

Theory of the first-order Fermi acceleration of cosmic ray particles at relativistic shock waves is reviewed. We consider shocks with parallel and oblique, sub- and super-luminal magnetic field configurations and with finite-amplitude…

Astrophysics · Physics 2007-05-23 M. Ostrowski

We describe the theory of Fermi-type acceleration, including first-order Fermi acceleration at a parallel shock front and second-order Fermi acceleration in a test particle limit. Including the theory of the turbulent acceleration and the…

High Energy Astrophysical Phenomena · Physics 2018-07-11 Y. G. Zheng , G. B. Long , C. Y. Yang , J. M. Bai

Charged particles scattering on moving inhomogenities of the magnetised interstellar medium can gain energy through the process of second-order Fermi acceleration. This energy gain depletes in turn the magnetic wave spectrum around the…

High Energy Astrophysical Phenomena · Physics 2020-10-14 M. Kachelriess , J. Tjemsland

The process of cosmic ray first-order Fermi acceleration at relativistic shock waves is studied with the method of Monte Carlo simulations. The simulations are based on numerical integration of particle equations of motion in a turbulent…

Astrophysics · Physics 2009-11-10 Jacek Niemiec , Michal Ostrowski

Fermi acceleration is the process of energy transfer from massive objects in slow motion to light objects that move fast. The model for such process is a time-dependent Hamiltonian system. As the parameters of the system change with time,…

Chaotic Dynamics · Physics 2015-03-17 Tiago Pereira , Dmitry Turaev

We include alignment interactions in a well-studied first-order attractive-repulsive macroscopic model for aggregation. The distinctive feature of the extended model is that the equation that specifies the velocity in terms of the…

Analysis of PDEs · Mathematics 2016-06-22 Razvan C. Fetecau , Weiran Sun , Changhui Tan

Theoretical studies of cosmic ray particle acceleration in the first-order Fermi process at relativistic shocks are reviewed. At the beginning we discuss the acceleration processes acting at mildly relativistic shock waves. An essential…

Astrophysics · Physics 2007-05-23 Michal Ostrowski

The influence of the gravity acceleration on the regularized energy-momentum tensor of the quantized electromagnetic field between two plane parallel conducting plates is derived. We use Fermi coordinates and work to first order in the…

High Energy Physics - Theory · Physics 2007-05-23 Giuseppe Bimonte , Enrico Calloni , Giampiero Esposito , Luigi Rosa

It has been proposed that particles bouncing between magnetized flows converging in a reconnection region can be accelerated by the first order Fermi mechanism. Analytical considerations of this mechanism have shown that the spectral index…

Space Physics · Physics 2016-07-06 Elena Provornikova , John Martin Laming , Vyacheslav S. Lukin

The physics of particle acceleration in turbulent plasmas is a topic of broad interest, which is making rapid progress thanks to dedicated, large-scale numerical experiments. The first part of this paper presents an effective theory of…

Plasma Physics · Physics 2025-07-08 M. Lemoine

Turbulence is ubiquitous in astrophysics. It radically changes many astrophysical phenomena, in particular, the propagation and acceleration of cosmic rays. We present the modern understanding of compressible magnetohydrodynamic (MHD)…

Solar and Stellar Astrophysics · Physics 2015-06-12 A. Lazarian , L. Vlahos , G. Kowal , H. Yan , A. Beresnyak , E. de Gouveia Dal Pino

The description of Fermi acceleration developing in the phase-randomized simplified Fermi-Ulam model (SFUM) can be achieved in terms of a random walk taking place in momentum space. Within this framework the evolution of the probability…

Chaotic Dynamics · Physics 2011-02-09 A. K. Karlis , F. K. Diakonos , V. Constantoudis , P. Schmelcher

This paper presents numerical simulations of test particle Fermi acceleration at relativistic shocks of Lorentz factor Gamma_sh = 2-60, using a realistic downstream magnetic structure obtained from the shock jump conditions. The upstream…

Astrophysics · Physics 2009-11-13 Martin Lemoine , Benoit Revenu

Particles are accelerated to very high, non-thermal energies during explosive energy-release phenomena in space, solar, and astrophysical plasma environments. While it has been established that magnetic reconnection plays an important role…

We consider the acceleration of energetic particles by Fermi processes (i.e., diffusive shock acceleration, second order Fermi acceleration, and gradual shear acceleration) in relativistic astrophysical jets, with particular attention given…

Astrophysics · Physics 2008-11-26 Frank M. Rieger , Valenti Bosch-Ramon , Peter Duffy

This proceedings paper reports on the theoretical modelling of particle acceleration in magnetised turbulent plasmas. It briefly reviews some recent findings obtained from fully kinetic numerical simulations of large-amplitude, semi to…

High Energy Astrophysical Phenomena · Physics 2025-12-18 M. Lemoine

The subject of this paper is stochastic acceleration by plasma turbulence, a process akin to the original model proposed by Fermi. We review the relative merits of different acceleration models, in particular the so called first order Fermi…

High Energy Astrophysical Phenomena · Physics 2015-06-05 Vahe Petrosian

A modification of the one-dimensional Fermi accelerator model is considered in this work. The dynamics of a classical particle of mass $m$, confined to bounce elastically between two rigid walls where one is described by a non-linear van…

Chaotic Dynamics · Physics 2015-06-05 Tiago Botari , Edson Denis Leonel