The Motion of a Charged Particle in a Nearly Axisymmetric Magnetic Field PDF Download
Are you looking for read ebook online? Search for your book and save it on your Kindle device, PC, phones or tablets. Download The Motion of a Charged Particle in a Nearly Axisymmetric Magnetic Field PDF full book. Access full book title The Motion of a Charged Particle in a Nearly Axisymmetric Magnetic Field by H. Weitzner. Download full books in PDF and EPUB format.
Author: H. Weitzner
Publisher: Franklin Classics Trade Press
ISBN: 9780353305366
Category : History
Languages : en
Pages : 60
Get Book Here
Book Description
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author: H. Weitzner
Publisher: Franklin Classics Trade Press
ISBN: 9780353305366
Category : History
Languages : en
Pages : 60
Get Book Here
Book Description
This work has been selected by scholars as being culturally important and is part of the knowledge base of civilization as we know it. This work is in the public domain in the United States of America, and possibly other nations. Within the United States, you may freely copy and distribute this work, as no entity (individual or corporate) has a copyright on the body of the work. Scholars believe, and we concur, that this work is important enough to be preserved, reproduced, and made generally available to the public. To ensure a quality reading experience, this work has been proofread and republished using a format that seamlessly blends the original graphical elements with text in an easy-to-read typeface. We appreciate your support of the preservation process, and thank you for being an important part of keeping this knowledge alive and relevant.
Author: Harold Weitzner
Publisher: Forgotten Books
ISBN: 9780484468770
Category : Science
Languages : en
Pages : 68
Get Book Here
Book Description
Excerpt from The Motion of a Charged Particle in a Nearly Axisymmetric Magnetic Field The motion of a single charged particle in a given magnetic field, one of the first problems studied in plasma physics, (1) has recently become of interest again. Two topics of immediate significance in magnetic fusion energy research have sparked the current concernzlz) the confinement of high energy alpha particles and the drift motion of moderate energy particles induced by small magnetic fields that break axial symmetry. The large body of older theory has been used to provide a base for extensive numerical computations. Here, we examine the problemiwith analytic tools to discover what improved descriptions of single particle motion we are able to provide. The critical concept in the study of the single particle dynamics is the existence of adiabatic invariants of the motion which allows great simplifications in the study of the dynamics. The adiabatic invariants are associated with the presence of a physical parameter which is small, the ratio of the larmor radius to the characteristic distance over which magnetic fields vary; and we denote this parameter by 6. Unlike the earlier treatments we assume that parts of the axisymmetric magnetic field may be small in e and we also take the symmetry breaking field to be small in e. Not surprisingly, we find that these assumptions do allow considerably more analysis than is possible without them. About the Publisher Forgotten Books publishes hundreds of thousands of rare and classic books. Find more at www.forgottenbooks.com This book is a reproduction of an important historical work. Forgotten Books uses state-of-the-art technology to digitally reconstruct the work, preserving the original format whilst repairing imperfections present in the aged copy. In rare cases, an imperfection in the original, such as a blemish or missing page, may be replicated in our edition. We do, however, repair the vast majority of imperfections successfully; any imperfections that remain are intentionally left to preserve the state of such historical works.
Author:
Publisher:
ISBN:
Category :
Languages : en
Pages :
Get Book Here
Book Description
The motion of a charged particle in a static magnetic field is studied by means of repeated canonical transformations of a Hamiltonian system. Adiabatic invariants are generated based on the assumption that the particle larmor radius is small compared with the characteristic distance over which the magnetic field varies. Unlike many earlier treatments the transformations presented here preserve the axisymmetry of the dynamics when the magnetic field is axisymmetric. It is assumed that the magnetic field consists of a small nonaxisymmetric part plus the axisymmetric toroidal and poloidal parts. After the introduction of the magnetic moment adiabatic invariant the motion of the guiding center is studied. The results depend sensitively on the ratio of the poloidal magnetic field to the total magnetic field. In some cases a second adiabatic invariant exists and direct inferences concerning long time particle drifts are possible. In one case where a second adiabatic invariant fails to exist, long term drifts are studied by conventional perturbation expansions. At some points resonance or lack of resonance phenomena appear and determine the drift effects.
Author: Ronald J. Schertler
Publisher:
ISBN:
Category : High temperature plasmas
Languages : en
Pages : 36
Get Book Here
Book Description
Author: J. Reece Roth
Publisher:
ISBN:
Category : Dynamics of a particle
Languages : en
Pages : 84
Get Book Here
Book Description
Author: John Reece Roth
Publisher:
ISBN:
Category : Controlled fusion
Languages : en
Pages : 262
Get Book Here
Book Description
A study was made of the motion of a single charged particle in the magnetic induction generated by an axisymmetric current sheet, the current of which was sinusoidally modulated along the axis. Several adiabatically invariant quantities were investigated, and it was found that M varied least along a given trajectory. A particle was considered to be adiabatic if M varied by less than 5% during a single interaction with the magnetic barrier. An averaging process was found which made it possible to predict the relations between particle mass and energy, and the magnetic induction strength and geometry, which cause M to vary by more than 5% during a single interaction with the magnetic barrier. Experimental apparatus was constructed which made it possible to study a single interaction of a beam of charged particles with a magnetic barrier under steady-state conditions. An experimental procedure was developed which made it possible to detect the transition from adiabatic to nonadiabatic reflection of the ion beam, and the results were compared with the results of the numerical computation. (Author).
Author:
Publisher:
ISBN:
Category : Aeronautics
Languages : en
Pages : 280
Get Book Here
Book Description
Author: Sadrilla Abdullaev
Publisher: Springer Science & Business Media
ISBN: 3319018906
Category : Science
Languages : en
Pages : 422
Get Book Here
Book Description
This is the first book to systematically consider the modern aspects of chaotic dynamics of magnetic field lines and charged particles in magnetically confined fusion plasmas. The analytical models describing the generic features of equilibrium magnetic fields and magnetic perturbations in modern fusion devices are presented. It describes mathematical and physical aspects of onset of chaos, generic properties of the structure of stochastic magnetic fields, transport of charged particles in tokamaks induced by magnetic perturbations, new aspects of particle turbulent transport, etc. The presentation is based on the classical and new unique mathematical tools of Hamiltonian dynamics, like the action--angle formalism, classical perturbation theory, canonical transformations of variables, symplectic mappings, the Poincaré-Melnikov integrals. They are extensively used for analytical studies as well as for numerical simulations of magnetic field lines, particle dynamics, their spatial structures and statistical properties. The numerous references to articles on the latest development in the area are provided. The book is intended for graduate students and researchers who interested in the modern problems of magnetic stochasticity in magnetically confined fusion plasmas. It is also useful for physicists and mathematicians interested in new methods of Hamiltonian dynamics and their applications.
Author:
Publisher:
ISBN:
Category : Controlled fusion
Languages : en
Pages : 310
Get Book Here
Book Description
Author: Abdallah M. Al Zahrani
Publisher:
ISBN:
Category : Black holes (Astronomy)
Languages : en
Pages : 73
Get Book Here
Book Description
Magnetic fields have become an essential ingredient of black hole astrophysics. The study of simplified models of magnetized black holes can shed light on some of the complicated phenomena observed near astrophysical black holes. In this thesis we studied the three-dimensional motion of charged particles in the background of Schwarzschild and Kerr black holes immersed in a weak uniform axisymmetric magnetic field. We studied in particular the escape of charged particles after they are kicked out of circular orbits. We started with neutral particles and gave analytical conditions for their escape. Unlike with the Schwarzschild black hole, the escape conditions were non-trivial when the black hole is rotating where escape depends essentially on the particle initial position. It was not possible to give analytical conditions for charged particles escape. The magnetic field renders their equations of motion non-integrable in general. Numerical study of the problem revealed that the dynamics of charged particles near magnetized black holes is generally chaotic. With the help of the basin of attraction approach, we could give empirical formulae for guaranteed escape. We found that the final fate of a charge particle is nearly determined by its proximity to the black holes. No general relationship between the chaoticness in the dynamics and black hole rotation could be found.
