Fractional dynamics of charged particles in magnetic fields

A. Coronel-Escamilla, J. F. Gómez-Aguilar (), E. Alvarado-Méndez, G. V. Guerrero-Ramírez and R. F. Escobar-Jiménez
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A. Coronel-Escamilla: Centro Nacional de Investigación, y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México
J. F. Gómez-Aguilar: #x2020;Catedrático CONACYT-Centro Nacional de Investigación, y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México
E. Alvarado-Méndez: #x2021;Departamento de Ingeniería Electrónica, DICIS, Universidad de Guanajuato, Carretera Salamanca-Valle de Santiago, km. 3.5+1.8 km, Comunidad de Palo Blanco, Salamanca, Guanajuato, México
G. V. Guerrero-Ramírez: Centro Nacional de Investigación, y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México
R. F. Escobar-Jiménez: Centro Nacional de Investigación, y Desarrollo Tecnológico, Tecnológico Nacional de México, Interior Internado Palmira S/N, Col. Palmira, C.P. 62490, Cuernavaca, Morelos, México

International Journal of Modern Physics C (IJMPC), 2016, vol. 27, issue 08, 1-15

Abstract: 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 (0;1]. 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.

Keywords: Fractional calculus; fractional dynamics; Grünwald–Letnikov derivative; classical electromagnetism; fractional differential equations (search for similar items in EconPapers)
Date: 2016
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Citations: View citations in EconPapers (1)

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DOI: 10.1142/S0129183116500844

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