scholarly journals Exact Solutions of the Heisenberg Equations and Zitterbewegung of the Electron in a Constant Uniform Magnetic Field

1982 ◽  
Vol 35 (4) ◽  
pp. 353 ◽  
Author(s):  
AO Barut ◽  
AJ Bracken
Keyword(s):  
Magnetic Field ◽  
Rest Frame ◽  
Relativistic Quantum ◽  
Three Dimensional ◽  
Internal Motion ◽  
Mass Motion ◽  
Internal Dynamics ◽  
Classical Motion ◽  
Dirac Electron ◽  
Heisenberg Equations

For a free Dirac electron, the Heisenberg equations define an internal dynamical system in the rest frame, isomorphic to a finite three-dimensional oscillator with a compact SO(5) phase space, such that the spin of the electron is the orbital angular momentum of the internal dynamics (Barut and Bracken 1980, 1981a). In the present work, the change in this internal dynamics due to an external magnetic field is studied. In order that the internal motion can be distinguished from the centre of mass motion, the solutions of the corresponding Hamilton and Heisenberg equations for the relativistic classical motion and the relativistic quantum mechanical spinless motion are also presented. The solutions for the electron exhibit the effect of the spin terms both in the internal motion and external motion, and we are able to identify the properties of the Zitterbewegung in the external field.

Dense plasma in Z-pinches and the plasma focus

1981 ◽  
Vol 300 (1456) ◽  
pp. 649-663 ◽  
Keyword(s):  
Magnetic Field ◽  
Plasma Focus ◽  
Axial Magnetic Field ◽  
Ohmic Heating ◽  
Scaling Law ◽  
Three Dimensional ◽  
Power Input ◽  
Larmor Radius ◽  
Mass Motion ◽  
Enhanced Stability

Many of the earliest experiments in controlled thermonuclear fusion research were Z -pinches. However these pinches were found to be highly unstable to the m = 0, the m — 1 (kink), and the Rayleigh-Taylor instability. The addition of an axial magnetic field and the removal of end losses by proceeding to a toroidal geometry has led to the class of discharges known as tokamaks and the reversed field pinch. But, at fusion temperatures and with practical values of applied magnetic field this restricts the plasma density to 10 20 to 10 21 m- 3 , thereby requiring a containment time of several seconds and a plasma radius of about 1 m. Meanwhile studies of the plasma focus, which after its three-dimensional compression closely resembles a Z -pinch, have shown that a plasma of density 10 25 m- 3 and temperature 1 keV can be achieved in a narrow filament of radius 1 mm. It has enhanced stability properties which might be attributable to the effects of finite ion Larmor radius. Its neutron yield in deuterium can be as high as 10 12 per discharge, with a favourable empirical scaling law, but the thermonuclear origin of the neutrons is doubtful because of the evidence of centre-of-mass motion and the formation of electron and ion beams. The development of high voltage, high current pulse technology has permitted the reconsideration of the Z -pinch to attain dense fusion plasmas which might be stabilized by scaling the ion Larmor radius to be comparable with the pinch radius. Experiments at Imperial College show that the plasma remains stationary for about twenty Alfven radial transit times, limited only by the period of the current waveform. Theory indicates that a dense compact Z -pinch can satisfy Lawson conditions with a power input dependent on the enhanced stability time, or, if stable, with ohmic heating balancing axial heat losses. Preliminary results on a laser-initiated Z -pinch are also presented.

scholarly journals Exact nonlinear solutions for three-dimensional Alfvén-wave packets in relativistic magnetohydrodynamics

2021 ◽  
Vol 87 (6) ◽  
Author(s):  
Alfred Mallet ◽  
Benjamin D.G. Chandran
Keyword(s):  
Magnetic Field ◽  
Large Amplitude ◽  
Rest Frame ◽  
Three Dimensional ◽  
Alfven Wave ◽  
Magnetohydrodynamic Equations ◽  
Astrophysical Objects ◽  
Analytic Expressions ◽  
Relativistic Magnetohydrodynamics ◽  
Nonlinear Solutions

We show that large-amplitude, non-planar, Alfvén-wave (AW) packets are exact nonlinear solutions of the relativistic magnetohydrodynamic equations when the total magnetic-field strength in the local fluid rest frame ( $b$ ) is a constant. We derive analytic expressions relating the components of the fluctuating velocity and magnetic field. We also show that these constant- $b$ AWs propagate without distortion at the relativistic Alfvén velocity and never steepen into shocks. These findings and the observed abundance of large-amplitude, constant- $b$ AWs in the solar wind suggest that such waves may be present in relativistic outflows around compact astrophysical objects.

Multiple characteristics of three‐dimensional radiative Cross fluid with velocity slip and inclined magnetic field over a stretching sheet

Heat Transfer ◽  
2021 ◽  
Author(s):  
Hafiz Abdul Wahab ◽  
Syed Zahir Hussain Shah ◽  
Assad Ayub ◽  
Zulqurnain Sabir ◽  
Muhammad Bilal ◽  
...  
Keyword(s):  
Magnetic Field ◽  
Stretching Sheet ◽  
Three Dimensional ◽  
Velocity Slip ◽  
Inclined Magnetic Field ◽  
Multiple Characteristics

scholarly journals Laser Assisted Dirac Electron in a Magnetized Annulus

Symmetry ◽  
2021 ◽  
Vol 13 (4) ◽  
pp. 642
Author(s):  
Emilio Fiordilino
Keyword(s):  
Magnetic Field ◽  
Analytical Form ◽  
Relative Energy ◽  
Radial Force ◽  
Rate Of Change ◽  
Orthogonal Direction ◽  
Linearly Polarized ◽  
Dirac Electron ◽  
A Charge ◽  
Stretching Effect

We study the behaviour of a charge bound on a graphene annulus under the assumption that the particle can be treated as a massless Dirac electron. The eigenstates and relative energy are found in closed analytical form. Subsequently, we consider a large annulus with radius ρ∈[5000,10,000]a0 in the presence of a static magnetic field orthogonal to its plane and again the eigenstates and eigenenergies of the Dirac electron are found in both analytical and numerical form. The possibility of designing filiform currents by controlling the orbital angular momentum and the magnetic field is shown. The currents can be of interest in optoelectronic devices that are controlled by electromagnetic radiation. Moreover, a small radial force acts upon the annulus with a stretching effect. A linearly polarized electromagnetic field propagating in the orthogonal direction is added; the time evolution of the operators show that the acceleration of the electron is proportional to the rate of change of the spin of the particle.

ON A RESULT CONCERNING THE BEHAVIOR OF A RELATIVISTIC QUANTUM SYSTEM IN THE COSMIC STRING SPACETIME

2009 ◽  
Vol 24 (08n09) ◽  
pp. 1549-1556 ◽  
Author(s):  
V. B. BEZERRA ◽  
GEUSA DE A. MARQUES
Keyword(s):  
Magnetic Field ◽  
Energy Spectrum ◽  
Dirac Equation ◽  
Quantum System ◽  
Relativistic Electron ◽  
Coulomb Potential ◽  
Cosmic String ◽  
Relativistic Quantum

We consider the problem of a relativistic electron in the presence of a Coulomb potential and a magnetic field in the background spacetime corresponding to a cosmic string. We find the solution of the corresponding Dirac equation and determine the energy spectrum of the particle.

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