Dynamical derivation of momentum diffusion coefficients at collisions of relativistic charged particles
- PDF / 233,819 Bytes
- 6 Pages / 612 x 792 pts (letter) Page_size
- 24 Downloads / 197 Views
TICAL, NONLINEAR, AND SOFT MATTER PHYSICS
Dynamical Derivation of Momentum Diffusion Coefficients at Collisions of Relativistic Charged Particles V. V. Ognivenko National Science Center Kharkov Institute of Physics and Technology, ul. Akademicheskaya 1, Kharkov, 61108 Ukraine e-mail: [email protected] Received July 22, 2015
Abstract—An expression has been obtained for the diffusion tensor of particles in the momentum space on the basis of the dynamics of particles motion. The general equations have been used to determine the rms momentum spread at collisions of relativistic charged particles at times shorter than the time of randomization of particles motion and at greater times when motion is completely random. DOI: 10.1134/S1063776116010064
1. INTRODUCTION As is known, diffusion processes in the momentum space in systems consisting of a large number of particles are studied using kinetic equations with collision integrals constructed for the description of physical phenomena under consideration (see, e.g., [1–6] and references therein). In particular, the collision integral for nonrelativistic charged particles interacting with each other through the Coulomb force was first derived in [1] from the Boltzmann collision integral. The collision integral for relativistic charged particles was derived in [2] by the relativistic transformation of the collision integral obtained in [1]. The kinetic equations with such collision integrals describe the diffusion of particles in the momentum space at the kinetic stage of evolution of the system, i.e., at times larger than a certain characteristic time of randomization of particles motion. In this work, the momentum diffusion coefficients are derived directly from the dynamics of motion of individual particles initiated by the total force generated by all other particles. Such an approach makes it possible not only to study the diffusion of particles in the momentum space at the kinetic stage of evolution of the system, when the motion of particles is completely random, but also to describe change in the rms momentum of the particles at the initial stage of evolution of the system in the case of pre-Brownian motion of the particles. This method is used to study the process of radiative relaxation of the beam of initially monoenergetic ultrarelativistic electrons moving in a static spatially periodic magnetic field of the undulator [7]. Using this method, the diffusion in the momentum space at collisions between relativistic charged particles in the absence of external fields has been considered in this work. Since expressions for the rms
momentum spread were previously obtained for the one-dimensional motion of particles of one type, this method is generalized in this work to the case of systems consisting of particles of different types and an expression for the three-dimensional diffusion tensor in the momentum space is obtained. 2. MOMENTUM DIFFUSION COEFFICIENT We consider a system consisting of N particles of different types that occupy a certain volume and sa
Data Loading...
