Fractional dynamics of charged particles in magnetic fields

2016 ◽  
Vol 27 (08) ◽  
pp. 1650084 ◽  
Author(s):  
A. Coronel-Escamilla ◽  
J. F. Gómez-Aguilar ◽  
E. Alvarado-Méndez ◽  
G. V. Guerrero-Ramírez ◽  
R. F. Escobar-Jiménez
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Numerical Solutions ◽  
Charged Particles ◽  
Classical Case ◽  
Transverse Motion ◽  
Fractional Dynamics ◽  
Dissipative Effects ◽  
Relevant Role ◽  
Fractional Differential

In many physical applications the electrons play a relevant role. For example, when a beam of electrons accelerated to relativistic velocities is used as an active medium to generate Free Electron Lasers (FEL), the electrons are bound to atoms, but move freely in a magnetic field. The relaxation time, longitudinal effects and transverse variations of the optical field are parameters that play an important role in the efficiency of this laser. The electron dynamics in a magnetic field is a means of radiation source for coupling to the electric field. The transverse motion of the electrons leads to either gain or loss energy from or to the field, depending on the position of the particle regarding the phase of the external radiation field. Due to the importance to know with great certainty the displacement of charged particles in a magnetic field, in this work we study the fractional dynamics of charged particles in magnetic fields. Newton’s second law is considered and the order of the fractional differential equation is [Formula: see text]. Based on the Grünwald–Letnikov (GL) definition, the discretization of fractional differential equations is reported to get numerical simulations. Comparison between the numerical solutions obtained on Euler’s numerical method for the classical case and the GL definition in the fractional approach proves the good performance of the numerical scheme applied. Three application examples are shown: constant magnetic field, ramp magnetic field and harmonic magnetic field. In the first example the results obtained show bistability. Dissipative effects are observed in the system and the standard dynamic is recovered when the order of the fractional derivative is 1.

scholarly journals Nonlinear force-free modeling of magnetic fields in flare-productive active regions

2015 ◽  
Vol 11 (S320) ◽  
pp. 167-174
Author(s):  
M. S. Wheatland ◽  
S. A. Gilchrist
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Boundary Data ◽  
Numerical Solutions ◽  
Free Field ◽  
Active Regions ◽  
Coronal Magnetic Field ◽  
Nonlinear Force ◽  
The Magnetic Field ◽  
Force Free Field

AbstractWe review nonlinear force-free field (NLFFF) modeling of magnetic fields in active regions. The NLFFF model (in which the electric current density is parallel to the magnetic field) is often adopted to describe the coronal magnetic field, and numerical solutions to the model are constructed based on photospheric vector magnetogram boundary data. Comparative tests of NLFFF codes on sets of boundary data have revealed significant problems, in particular associated with the inconsistency of the model and the data. Nevertheless NLFFF modeling is often applied, in particular to flare-productive active regions. We examine the results, and discuss their reliability.

scholarly journals The Magnetic Fields of Pulsars

1974 ◽  
Vol 64 ◽  
pp. 187-187
Author(s):  
D. M. Sedrakian
Keyword(s):  
Magnetic Field ◽  
Angular Velocity ◽  
Magnetic Fields ◽  
Relative Motion ◽  
Kinematic Viscosity ◽  
Charged Particles ◽  
Normal Fluid ◽  
Inertia Effects ◽  
Generation Mechanisms ◽  
Image Position

Two generation mechanisms of magnetic fields in pulsars are considered.If the temperature of a star is more than 108K, the star consists of a normal fluid of neutrons, protons and electrons. Because the angular velocity of pulsars is not constant dω/dt ≠0, inertia effects can occur, and generate magnetic fields through the relative motion of charged particles with different masses. The kinematic viscosity of electrons is 30 times larger than that of protons; hence electrons move with the crust, but the proton-neutron fluid will move relative to the electrons. The magnetic momentum can be calculated by the following formula where Meff = Mp + Mn(Nn/Np), R = radius of the star, σ = conductivity. For typical neutron stars we have dω/dt~ 10-8 s-2, R~106 cm, σ~1029 s-1 and we get a magnetic field of the order of 1010 G.

scholarly journals Guiding-centre transformation of the radiation–reaction force in a non-uniform magnetic field

2015 ◽  
Vol 81 (5) ◽  
Author(s):  
E. Hirvijoki ◽  
J. Decker ◽  
A. J. Brizard ◽  
O. Embréus
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Uniform Magnetic Field ◽  
Reaction Force ◽  
Charged Particles ◽  
Collision Operator ◽  
Radiation Reaction ◽  
Transform Method ◽  
Lie Transform ◽  
Radiation Reaction Force

In this paper, we present the guiding-centre transformation of the radiation–reaction force of a classical point charge travelling in a non-uniform magnetic field. The transformation is valid as long as the gyroradius of the charged particles is much smaller than the magnetic field non-uniformity length scale, so that the guiding-centre Lie-transform method is applicable. Elimination of the gyromotion time scale from the radiation–reaction force is obtained with the Poisson-bracket formalism originally introduced by Brizard (Phys. Plasmas, vol. 11, 2004, 4429–4438), where it was used to eliminate the fast gyromotion from the Fokker–Planck collision operator. The formalism presented here is applicable to the motion of charged particles in planetary magnetic fields as well as in magnetic confinement fusion plasmas, where the corresponding so-called synchrotron radiation can be detected. Applications of the guiding-centre radiation–reaction force include tracing of charged particle orbits in complex magnetic fields as well as the kinetic description of plasma when the loss of energy and momentum due to radiation plays an important role, e.g. for runaway-electron dynamics in tokamaks.

scholarly journals The Effect of Small Scale Motion on an Essentially-Nonlinear Dynamo

2010 ◽  
Vol 6 (S271) ◽  
pp. 367-368
Author(s):  
Benjamin M. Byington ◽  
Nicholas H. Brummell ◽  
Steven M. Tobias
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Numerical Simulations ◽  
Small Scale ◽  
Local Velocity ◽  
Dissipative Effects ◽  
Dynamo Mechanism ◽  
New Type ◽  
Scale Motion

AbstractA dynamo is a process by which fluid motions sustain magnetic fields against dissipative effects. Dynamos occur naturally in many astrophysical systems. Theoretically, we have a much more robust understanding of the generation and maintenance of magnetic fields at the scale of the fluid motions or smaller, than that of magnetic fields at scales much larger than the local velocity. Here, via numerical simulations, we examine one example of an “essentially nonlinear” dynamo mechanism that successfully maintains magnetic field at the largest available scale (the system scale) without cascade to the resistive scale. In particular, we examine whether this new type of dynamo at the system scale is still effective in the presence of other smaller-scale dynamics (turbulence).

Analysis of Biological Effect of AC-DC Electromagnetic Fields using the Lorenz Model

2011 ◽  
pp. 31-53
Author(s):  
Malka N. Halgamuge ◽  
Chathurika D. Abeyrathne ◽  
Priyan Mendis
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Electric Field ◽  
Electromagnetic Fields ◽  
Biological Effect ◽  
Initial Velocity ◽  
Charged Particles ◽  
Initial Position ◽  
Dc Magnetic Field ◽  
Ac Electric Field

Electromagnetic fields (EMF) are essential to various applications directly involving humans. Fears about the biological effect of exposure to electromagnetic fields drive enormous research into this area. This research generates conflicting results, and consequently, uncertainty regarding possible health effects. This chapter studies a nonlinear Lorenz model describing interactions among charged particles and combined alternating (AC: alternating current) and static (DC: direct current) electromagnetic fields, for various combinations of frequencies, field strengths and relative angle (?) between the AC and DC magnetic fields. We investigate the effect on charged particles of three possible combinations of alternating and static electromagnetic fields: (i) AC electric field and DC magnetic field (ii) AC magnetic field and DC magnetic field (iii) AC electric field and AC and DC magnetic field. Then the behavior of the particle in these fields with different initial conditions and strong directional effects is observed when the angle between AC and DC magnetic fields is varied. The results show that the cyclotron resonance frequency is affected by charged particles’ initial position and initial velocity. Further, we observe strong effects of electric and magnetic fields on a charged particle in a biological cell with initial position and initial velocity.

scholarly journals An Efficient Approach for Solving Fractional Dynamics of a Predator-Prey System

2019 ◽  
Vol 13 (11) ◽  
pp. 116
Author(s):  
Hegagi Mohamed Ali ◽  
Ismail Gad Ameen
Keyword(s):  
Differential Equations ◽  
Numerical Solutions ◽  
Equilibrium Points ◽  
Nonlinear Partial Differential Equations ◽  
Fractional Dynamics ◽  
Predator Prey ◽  
Analytical Technique ◽  
Biological Population ◽  
Fractional Differential ◽  
The Stability

In this work, we execute a generally new analytical technique, the modified generalized Mittag-Leffler function method (MGMLFM) for solving nonlinear partial differential equations containing fractional derivative emerging in predator-prey biological population dynamics system. This dynamics system are given by a set of fractional differential equations in the Caputo sense. A new solution is constructed in a power series. The stability of equilibrium points is studied. Moreover, numerical solutions for different cases are given and the methodology is displayed. We conducted a comparing between the results obtained by our method with the results obtained by other methods to illustrate the reliability and effectiveness of our main results.

The orbits of electrons and ions in the fields of the rotamak

1987 ◽  
Vol 37 (1) ◽  
pp. 1-13 ◽  
Author(s):  
W. N. Hugrass ◽  
M. Turley
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Charged Particles ◽  
The Self ◽  
Rotating Magnetic Field ◽  
Plasma Equilibrium ◽  
Rotating Magnetic Fields ◽  
Cylindrical Plasma ◽  
Electrons And Ions ◽  
Self Consistent

The motion of electrons and ions in the self-consistent fields of a compact toroidal equilibrium maintained by means of a rotating magnetic field is studied. It is found that the particles are confined although the lines of the instantaneous magnetic field are open. The results are compared with those obtained in an earlier study of the motion of charged particles in the self-consistent fields appropriate to cylindrical plasma equilibrium maintained by means of rotating magnetic fields.

scholarly journals Electronic Currents and Magnetic Fields in H2+ Induced by Coherent Resonant Bichromatic Circularly Polarized Laser Pulses: Effects of Orientation, Phase, and Helicity

2021 ◽  
Vol 9 ◽  
Author(s):  
André D. Bandrauk ◽  
Szczepan Chelkowski ◽  
Kai-Jun Yuan
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Numerical Solutions ◽  
Resonant Excitation ◽  
Electron Dynamics ◽  
Magnetic Field Generation ◽  
Phase Dependence ◽  
Circularly Polarized ◽  
Field Generation ◽  
Pulse Phase

We theoretically study pulse phase and helicity effects on ultrafast magnetic field generation in intense bichromatic circularly polarized laser fields. Simulations are performed on the aligned molecular ion H2+ from numerical solutions of corresponding time-dependent Schrödinger equations. We demonstrate how electron coherent resonant excitation influences the phase and helicity of the optically induced magnetic field generation. The dependence of the generated magnetic field on the pulse phase arises from the interference effect between multiple excitation and ionization pathways, and is shown to be sensitive to molecular alignment and laser polarization. Molecular resonant excitation induces coherent ring electron currents, giving enhancement or suppression of the phase dependence. Pulse helicity effects control laser-induced electron dynamics in bichromatic circular polarization excitation. These phenomena are demonstrated by a molecular attosecond photoionization model and coherent electron current theory. The results offer a guiding principle for generating ultrafast magnetic fields and for studying coherent electron dynamics in complex molecular systems.

scholarly journals A Velocity Profile of a Ferrofluid in the Presence of Rotating Magnetic Fields. Pseudo-Analytical and Numerical Solutions

2020 ◽  
pp. 1-6
Author(s):  
Rodrigo Correa ◽  
Cristian Jimenez ◽  
Hermann Vargas
Keyword(s):  
Magnetic Field ◽  
Magnetic Fields ◽  
Linear Model ◽  
Numerical Solutions ◽  
Velocity Profiles ◽  
Analytical Models ◽  
Parallel Plates ◽  
Rotating Magnetic Fields ◽  
Analytical Strategy ◽  
The Magnetic Field

From the beginning of ferro-hydrodynamics, several authors have proposed analytical models to describe the movement of ferrofluids in the presence of rotating external magnetic fields. To this effect they have made valid simplifications in certain and very restricted physical situations. In this work we analyze the effects of these approaches against numerical solutions that do not make use of them. A sample of ferrofluid immersed in containers with three types of geometries was considered: one of flat and parallel plates, one cylindrical and another coaxial cylindrical. Velocity ​​profiles were obtained by these two strategies. The analytical solution leads to a linear model with several simplifications, while the second, numerical in nature, generates a non-linear model, but without approximations. The simulation results showed that the simplifications made in the analytical strategy generate profiles that are valid only for magnetic field intensities lower than the respective ferrofluid saturation values. Additionally, and given the level of development of analytical modeling, it was found that the numerical solution is currently the most appropriate to evaluate the ferro-hydrodynamic model, since it does not have restrictions related to the intensity of the magnetic field. In the same way, it allows to evidence the phenomenon of saturation in the velocity profiles by increasing the intensity of the magnetic field, a situation observed experimentally, and unpredictable by means of these currently available pseudo-analytical solutions.

scholarly journals Propagators of charged particles in an external magnetic field, expanded over Landau levels

2015 ◽  
Vol 30 (24) ◽  
pp. 1550140 ◽  
Author(s):  
A. V. Kuznetsov ◽  
A. A. Okrugin ◽  
A. M. Shitova
Keyword(s):  
Magnetic Field ◽  
External Magnetic Field ◽  
Magnetic Fields ◽  
Standard Model ◽  
Constant Magnetic Field ◽  
Charged Particles ◽  
Landau Levels ◽  
The Standard Model ◽  
First Time

Various forms of expressions for the propagators of charged particles in a constant magnetic field that should be used for investigations of electroweak processes in an external uniform magnetic fields are discussed. Formulas for the propagators of the Standard Model charged [Formula: see text]- and scalar [Formula: see text]-bosons in an arbitrary [Formula: see text]-gauge, expanded over Landau levels, are derived for the first time.

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